Mission-Level Feasibility Assessment of Three CA21-Anchored Rapid Earth–Mars–Earth Architectures for 2031

1. Introduction

(Obs: This work benefited from the use of artificial intelligence tools (ChatGPT, OpenAI, 2026) exclusively for language refinement, structural editing, and limited code assistance. All theoretical developments, numerical implementations, validation procedures, and interpretations were performed and verified by the author. The author assumes full responsibility for all results presented.)

The possibility of substantially reducing the duration of crewed round-trip missions to Mars remains one of the most important challenges in interplanetary mission design. Conventional Earth–Mars transfer opportunities are typically associated with long cruise durations and extended mission timelines, which increase exposure to radiation, microgravity, operational risks, and life-support demands. For this reason, trajectories capable of reducing the outbound and total mission duration are of strong scientific, technological, and public interest [1,2,3].

In a previous work, the author proposed a method for identifying rapid Earth–Mars trajectories using early orbital data of asteroid 2001 CA21 as a geometric reference [1]. In that study, the orbital plane associated with the 2015 JPL Horizons Solution #11 for 2001 CA21 was used as a guiding constraint to search for Lambert transfer solutions between Earth and Mars. The original analysis used short-way Lambert-based trajectory construction constrained to remain within ($5^{\circ }$) of the CA21 orbital plane and high-fidelity JPL Horizons ephemerides [1,4,5]. Among the solutions found, a 2031 Earth–Mars–Earth architecture was selected, involving a 56-day outbound transfer, an approximately 35-day stay at Mars, and a 135-day return leg, with a total mission duration of approximately 226 days. This trajectory was classified in the original study as the feasible high-energy case of the CA21-anchored 2031 solution family [1].

After the publication of that work, the result received an unexpectedly broad dissemination in news reports, interviews, videos, and social media posts. This public response was not anticipated by the author. In Brazil, the author’s home country, the work led to numerous interviews and discussions. Outside Brazil, much of the international dissemination became known to the author only after the publication of articles, videos, and posts in several countries. The author is deeply grateful for the attention and generosity of all those who reported, discussed, translated, commented on, or shared the work.

Initially, the author considered that his contribution to this specific topic might have been completed with the publication of the original paper and its subsequent public impact. However, the selected trajectories were never intended to represent unique solutions. They were examples chosen among several promising possibilities found under the assumptions and constraints adopted in the original analysis. Other paths are possible, and new proposals will certainly emerge. The broader significance of the work may lie not only in the specific trajectories presented, but also in encouraging a change of perspective regarding the time required for future round-trip missions to Mars.

One particularly meaningful aspect of the public response was the interest shown by children and young people. If the dissemination of the original work contributed, even modestly, to inspiring scientific curiosity or awakening a vocation in a single child or young student, the author considers this the most important outcome. At the same time, the number of questions received about how such a rapid Mars mission could actually be implemented made clear the need for a more complete technical discussion. The original work was primarily a trajectory-level study. A mission-level analysis, including launch architecture, spacecraft mass, Earth departure, Mars arrival, pre-deployed infrastructure, and return capability, is therefore necessary.

The present paper addresses that need. It extends the previous CA21-anchored trajectory concept into a preliminary mission-level feasibility assessment. Three rapid Earth–Mars–Earth mission profiles are considered. The first is the original 56-day outbound architecture discussed in the previous paper. The other two are additional CA21-anchored solutions obtained with the same general method, involving outbound transfer times of 72 and 86 days. These additional profiles preserve the geometric relationship with the CA21 orbital plane while reducing the Mars-arrival excess velocity. Relative to the original 56-day case, the 72- and 86-day solutions reduce the Mars-arrival excess velocity by approximately 18% and 41%, respectively.

The three mission profiles therefore form a structured family of rapid Mars mission architectures. The 56-day case is treated here as the original feasible high-energy architecture, consistent with the terminology and classification adopted in the previous work [1]. The 72- and 86-day cases are treated as reduced-energy rapid architectures, with lower departure and arrival energy requirements while preserving short total mission durations. Profiles A and B each total 226 days, whereas Profile C totals 231 days. Profiles A and C share the 135-day Mars–Earth return; Profile B uses a distinct 140-day return. All three rely on return infrastructure sent to Mars in advance.

The objective of this paper is not to present a final engineering design, but to evaluate whether the three CA21-anchored trajectories can be embedded within physically plausible mission architectures using known or emerging mission concepts. The analysis considers a Starship-class Earth-departure system, orbital refueling, auxiliary propulsion stages, a compact two-person transfer spacecraft, propulsive pre-braking at Mars, deployable thermal protection, pre-deployed surface and orbital Mars assets, and trajectory-specific return propulsion. By combining trajectory analysis with first-order mass and velocity estimates, this work aims to clarify the technical requirements, limitations, and relative feasibility of the three proposed rapid Mars mission profiles.

2. Earth Departure

Translating a trajectory-level result into a mission architecture begins with Earth departure. A Lambert solution specifies the heliocentric boundary velocity that the spacecraft must attain, but it does not by itself define the launch sequence, the mass assembled in Earth orbit, or the propulsion arrangement needed to reach that state. The central question is therefore whether each CA21-anchored profile can inject the adopted 10 t crew vehicle onto its Mars transfer without also carrying the independently predeployed return system.

This chapter converts the three trajectory profiles into Earth-departure energy and first-order mass requirements. The supplied JPL Horizons ephemerides are used to determine the hyperbolic excess velocity and characteristic energy; these quantities are then translated into the local speed required at the perigee of a 200 km parking orbit. The resulting architectures are trajectory-specific: the 56-day transfer requires a large detachable residual stage, whereas the 72-day and 86-day transfers can avoid that stage in the direct-injection screening case. The resulting mass difference is a gross departure opportunity, not an automatic increase in Mars-delivered mass; any reassignment is constrained by the Chapter 3 arrival calculation. The robustness of all three solutions is tested using the same controlled boundary-state uncertainty envelope adopted in the original paper. Sensitivities are evaluated at $I_{sp}$= 450 s and 500 s.

2.1. Scope and Architectural Separation

This chapter evaluates the Earth-departure requirements of three CA21-anchored rapid Mars mission profiles. The first is the original 56 + 35 + 135 day architecture identified in the previous study; the second redistributes the same 226-day total as 72 + 14 + 140 days; and the third uses an 86-day outbound transfer, a 10-day Mars stay, and the original 135-day return, giving a total duration of 231 days [1]. The aim is to determine whether each outbound trajectory can be reached by a compact crew vehicle through a physically consistent high-energy departure sequence.

The architecture is deliberately divided into independently delivered systems. The 2031 outbound vehicle is a 10 t Mars-arrival crew module for two astronauts. It carries 120 days of first-phase consumables and 3 t of propellant reserved for the trajectory-specific Mars-arrival sequence. For the demanding 56-day profile, this module is attached to a detachable residual Earth-departure stage. Its working stack is 27 t before that stage is fired: the 10 t Mars-arrival module, 16 t of auxiliary propellant, and 1 t of auxiliary-stage dry mass. Profiles B and C do not carry this large stage in the direct-injection screening case. The Earth-return architecture is separate: cargo missions during the 2029 opportunity predeploy the chemical return stages, the spacecraft that retains 14 t after Mars injection, its 4 t Earth-entry capsule and 200-day consumables reserve, the Mars descent equipment, and the primary and reserve surface-to-orbit taxis. None of those predeployed masses is included in the 2031 outbound stack. This functional separation follows the general logic of predeployment used in earlier rapid-Mars and NASA reference architectures [2,3].

The selection of two astronauts is a deliberate mass-constrained reference-design assumption rather than a claim that two persons constitute the operationally optimal crew for Mars exploration. The architecture is intended to evaluate the minimum crewed system capable of using the rapid trajectories while retaining independent surface and return redundancy. It therefore relies on predeployed and remotely verified surface equipment, automated checkout, extensive robotic assistance, continuous Earth-based operational support, cross-trained crew members, and primary and reserve Mars Ascent Taxis. The two-person assumption directly supports the 10 t outbound module, the compact ascent vehicles, and the 4 t Earth-entry capsule, but it also increases individual workload and reduces medical and operational redundancy. These human-factors limitations require dedicated assessment before mission implementation. A four-person architecture would require the capsule, habitation volume, life-support hardware, ascent taxis, consumables, and propulsion stages to be resized together and is therefore outside the present two-person reference architecture; it cannot be represented by simply doubling the consumables mass.

Trajectory-dependent mass definitions For Profile A, 27 t is the stack immediately before the auxiliary Earth-departure burn: the 10 t Mars-arrival module plus a 17 t detachable stage. After that stage is expended and discarded, only the 10 t module continues to Mars. For Profiles B and C, 10 t remains the analyzed outbound mass because the large auxiliary stage is not required in the direct-injection screening case. The difference relative to 27 t is not added to the nominal vehicle: it is an unassigned gross headroom that can be used only after both departure performance and the heavier Mars-arrival state have been recalculated.

2.2. Ephemerides, Lambert Solution, and CA21-Plane Constraint

The heliocentric states of Earth and Mars were taken from the JPL Horizons system using DE441, a Sun-centered origin, geometric Cartesian states, the ecliptic of J2000.0, TDB epochs, and kilometers and kilometers-per-second units [4,5]. For each departure and arrival date, the boundary-value problem was solved as a zero-revolution, short-way Lambert transfer. The numerical formulation follows the standard Lambert and universal-variable framework described by Izzo and by established astrodynamics references [6,7,8,9].

If $r_E$ and $r_M$ are the heliocentric planetary position vectors and $v_1$ and $v_2$ are the corresponding Lambert velocities, the Earth-departure and Mars-arrival hyperbolic excess vectors are obtained by subtracting the appropriate planetary velocities. Their magnitudes are

$$v_{\infty ,E}=\Vert {\mathbf{v}}_1-{\mathbf{v}}_E\Vert ,\hspace{1em}\hspace{1em}{v}_{\infty ,M}=\Vert {\mathbf{v}}_2-{\mathbf{v}}_M\Vert .$$

(2.1)

As in the original paper, asteroid 2001 CA21 is not a waypoint, gravity-assist body, or propulsion resource. Its early orbital plane is used only as a geometric filter. The reference plane is taken from the 2015 JPL Horizons orbital Solution #11, with $i={4.966784995}^{\circ }$ and $\mathsf{\Omega }={46.435461372}^{\circ }$. The transfer-plane angular-momentum vector and its unit normal are

$$\mathbf{h}={\mathbf{r}}_E\times {\mathbf{v}}_1,\hspace{1em}\hspace{1em}\stackrel{\mathbf{ˆ}}{\mathbf{h}}={\displaystyle \frac{\mathbf{h}}{\Vert \mathbf{h}\Vert }}.$$

In the adopted J2000 heliocentric ecliptic frame, the unit normal to the CA21 orbital plane is

$${\stackrel{\mathbf{ˆ}}{\mathbf{n}}}_{\mathrm{C}\mathrm{A}21}=\left(\begin{array}{c}\sin i\sin \mathsf{\Omega }\\ -\sin i\cos \mathsf{\Omega }\\ \cos i\end{array}\right)$$

The acute angular separation between the two planes is therefore

$${\delta }_{\mathrm{p}\mathrm{l}\mathrm{a}\mathrm{n}\mathrm{e}}{=\cos }^{-1}\left(\left|\stackrel{\mathbf{ˆ}}{\mathbf{h}}\cdot {\stackrel{\mathbf{ˆ}}{\mathbf{n}}}_{\mathrm{C}\mathrm{A}21}\right|\right).$$

(2.2)

All three outbound solutions satisfy ${\delta }_{\mathrm{p}\mathrm{l}\mathrm{a}\mathrm{n}\mathrm{e}}\le 5^{\circ }$, preserving the criterion adopted in the original trajectory study [1].

The use of Solution #11 is methodological: it preserves the early orbital information that originally motivated the geometric search. Later CA21 solutions may alter the fitted asteroid-plane orientation and therefore determine whether a candidate remains inside the original $5^{\circ }$ filtering corridor. They do not alter the already selected Earth–Mars Lambert trajectories, because those trajectories are determined by the Earth and Mars DE441 boundary states, the specified dates, the time of flight, and the selected Lambert branch. Repeating the search with later CA21 solutions would therefore constitute a sensitivity study of the geometric search filter rather than a correction to the reported $C_3$, $v_{\infty }$, or flight times.

The present work does not claim that the CA21 plane is the only geometric corridor capable of identifying rapid Earth–Mars transfers. A systematic survey of other asteroid planes, cometary planes, and unconstrained transfer-plane families is an appropriate subject for future work.

2.3. Mission Profiles and Outbound Boundary Conditions

Table 2.1 defines the three mission timelines. Profiles A and B last exactly 226 days. Profile C lasts 231 days because 86 + 10 + 135 = 231; it is retained because its lower Mars-arrival velocity provides an important alternative to the two exact 226-day profiles. The 120-day first-phase consumables allocation used below is a resource duration and does not change Profile C’s 10-day surface interval.

Table 2.1. Mission timelines adopted in the present paper. 

Profile	Earth-Mars	Mars stay	Mars-Earth	Total
A	20 Apr-15 Jun 2031 56 days	15 Jun-20 Jul 35 days	20 Jul-2 Dec 135 days	226 days
B	6 Apr-17 Jun 2031 72 days	17 Jun-1 Jul 14 days	1 Jul-18 Nov 140 days	226 days
C	15 Apr-10 Jul 2031 86 days	10 Jul-20 Jul 10 days	20 Jul-2 Dec 135 days	231 days

Table 2.1. Mission timelines adopted in the present paper. 

Profile	Earth-Mars	Mars stay	Mars-Earth	Total
A	20 Apr-15 Jun 2031 56 days	15 Jun-20 Jul 35 days	20 Jul-2 Dec 135 days	226 days
B	6 Apr-17 Jun 2031 72 days	17 Jun-1 Jul 14 days	1 Jul-18 Nov 140 days	226 days
C	15 Apr-10 Jul 2031 86 days	10 Jul-20 Jul 10 days	20 Jul-2 Dec 135 days	231 days

The exact outbound Lambert results are summarized in Table 2.2. Profile A preserves the original high-energy solution. Profiles B and C have almost identical Earth-departure excess velocity, but Profile C reduces the Mars-arrival excess velocity from 13.671 to 9.866 km/s. The price of that reduction is five additional mission days and four fewer surface days relative to Profile B.

Table 2.2. Outbound Lambert results from the supplied JPL Horizons ephemerides. 

Profile	TOF	Earth ${\mathit{v}}_{\mathit{\infty }}$ (km/s)	C3 (km2/s2)	Mars ${\mathit{v}}_{\mathit{\infty }}$ (km/s)	CA21 offset (deg)
A	56 d	16.879	284.890	16.638	4.174
B	72 d	11.843	140.258	13.671	4.403
C	86 d	11.844	140.286	9.866	3.969

Table 2.2. Outbound Lambert results from the supplied JPL Horizons ephemerides. 

Profile	TOF	Earth ${\mathit{v}}_{\mathit{\infty }}$ (km/s)	C3 (km2/s2)	Mars ${\mathit{v}}_{\mathit{\infty }}$ (km/s)	CA21 offset (deg)
A	56 d	16.879	284.890	16.638	4.174
B	72 d	11.843	140.258	13.671	4.403
C	86 d	11.844	140.286	9.866	3.969

2.4. Uncertainty, Robustness, and Reporting Precision

The nominal values in Table 2.2 are deterministic outputs of the DE441 boundary states and the selected Lambert branch. Their numerical repeatability must not be confused with physical certainty. To retain direct comparability with the original paper, the present analysis adopts its controlled geometric uncertainty envelope rather than attempting a formal covariance reconstruction [1]. The reference perturbation scales are ±2 × 10⁻⁴ AU in position and ±1 × 10⁻⁶ AU/day in velocity, the latter corresponding to approximately ±1.731 × 10⁻³ km/s. In the original study these scales produced transfer-plane variations of order 0.08 degrees; 0.08 km/s was therefore retained as a common conservative uncertainty in the reported hyperbolic excess velocities.

The Monte Carlo test follows the published procedure. For each trajectory, 100 independent trials were generated by perturbing every Cartesian component of the Earth-departure and Mars-arrival position vectors with a uniform random variable over ±2 × 10⁻⁴ AU. The planetary velocity states, dates, transfer direction, and time of flight were held fixed, and the zero-revolution short-way Lambert problem was re-solved in every trial. A fixed seed of 20260820 was used so that the numerical experiment is exactly reproducible. For trial $k$ and boundary $i$ = 1, 2, the sampled positions are

$${\mathbf{r}}_i^{\left(k\right)}={\mathbf{r}}_i+\mathsf{\Delta }{\mathbf{r}}_i^{\left(k\right)},\hspace{1em}\hspace{1em}\mathsf{\Delta }{r}_{i,x}^{\left(k\right)},\mathsf{\Delta }{r}_{i,y}^{\left(k\right)},\mathsf{\Delta }{r}_{i,z}^{\left(k\right)}\sim \mathcal{U} \left(-2\times {10}^{-4},+2\times {10}^{-4}\right)\mathrm{A}\mathrm{U}.$$

(2.3)

A second, deliberately more conservative propagation uses the common $\Delta v_{\infty }=0.08$ km/s bound from the original paper. Since characteristic energy is the square of Earth-departure hyperbolic excess speed, its first-order uncertainty is

$$C_3=v_{\infty ,E}^{,2},\hspace{1em}\hspace{1em}\mathsf{\Delta }{C}_3\simeq 2v_{\infty ,E}\mathsf{\Delta }{v}_{\infty }.$$

(2.4)

Table 2.3. Conservative propagation of the common Δv_∞ = 0.08 km/s uncertainty. 

Profile	$\mathit{\Delta }\mathit{C}₃$(km2/s2)	Relative $\mathit{\Delta }\mathit{C}₃$	Nominal CA21 offset	Offset with +0.08° bound
A	2.70	0.95%	4.174°	4.254°
B	1.89	1.35%	4.403°	4.483°
C	1.90	1.35%	3.969°	4.049°

Table 2.3. Conservative propagation of the common Δv_∞ = 0.08 km/s uncertainty. 

Profile	$\mathit{\Delta }\mathit{C}₃$(km2/s2)	Relative $\mathit{\Delta }\mathit{C}₃$	Nominal CA21 offset	Offset with +0.08° bound
A	2.70	0.95%	4.174°	4.254°
B	1.89	1.35%	4.403°	4.483°
C	1.90	1.35%	3.969°	4.049°

Even under this conservative plane-variation bound, every trajectory remains within the adopted 5-degree CA21-plane corridor. Profile B is closest to the boundary, but its worst-case offset is 4.483 degrees, leaving 0.517 degrees of margin. The C₃ uncertainty is approximately 1% for Profile A and 1.35% for Profiles B and C; it does not erase the large energy separation between the 56-day trajectory and the two longer outbound transfers.

For direct comparison with the original paper, velocity-vector and transfer-plane deviations were evaluated relative to the nominal Lambert solution. The velocity deviations are

$$\Vert \mathsf{\Delta }{\mathbf{v}}_1^{\left(k\right)}\Vert =\Vert {\mathbf{v}}_1^{\left(k\right)}-{\mathbf{v}}_1\Vert ,\hspace{1em}\hspace{1em}\Vert \mathsf{\Delta }{\mathbf{v}}_2^{\left(k\right)}\Vert =\Vert {\mathbf{v}}_2^{\left(k\right)}-{\mathbf{v}}_2\Vert .$$

(2.5)

The perturbed transfer-plane normal and its angular displacement from the nominal plane are

$${\stackrel{\mathbf{ˆ}}{\mathbf{n}}}_{\mathrm{t}\mathrm{r}}^{\left(k\right)}={\displaystyle \frac{{\mathbf{r}}_1^{\left(k\right)}\times {\mathbf{v}}_1^{\left(k\right)}}{\Vert {\mathbf{r}}_1^{\left(k\right)}\times {\mathbf{v}}_1^{\left(k\right)}\Vert }},\hspace{1em}\hspace{1em}\mathsf{\Delta }{\psi }^{\left(k\right)}={\cos }^{-1} \left({\stackrel{\mathbf{ˆ}}{\mathbf{n}}}_{\mathrm{t}\mathrm{r}}^{\left(k\right)}\cdot {\stackrel{\mathbf{ˆ}}{\mathbf{n}}}_{\mathrm{t}\mathrm{r}}\right).$$

(2.6)

Table 2.4. Monte Carlo robustness results using the original-paper position envelope. 

Profile	Converged	Mean ||Δv1|| (km/s)	Mean ||Δv2|| (km/s)	Mean $\mathit{\Delta }\mathit{\psi }$ (deg)	Maximum $\mathit{\Delta }\mathit{\psi }$ (deg)
A	100/100	0.0084	0.0085	0.0127	0.0292
B	100/100	0.0067	0.0067	0.0098	0.0211
C	100/100	0.0058	0.0057	0.0094	0.0199

Table 2.4. Monte Carlo robustness results using the original-paper position envelope. 

Profile	Converged	Mean ||Δv1|| (km/s)	Mean ||Δv2|| (km/s)	Mean $\mathit{\Delta }\mathit{\psi }$ (deg)	Maximum $\mathit{\Delta }\mathit{\psi }$ (deg)
A	100/100	0.0084	0.0085	0.0127	0.0292
B	100/100	0.0067	0.0067	0.0098	0.0211
C	100/100	0.0058	0.0057	0.0094	0.0199

All 300 perturbed Lambert problems converged. The 56-day result closely reproduces the sensitivity reported in the original paper, which provides an internal check on the implementation. The newly evaluated 72-day and 86-day trajectories are less sensitive than the 56-day case under the same perturbation model. The standard deviations of Earth-departure $v_{\infty }$ are 0.0059, 0.0051, and 0.0046 km/s for Profiles A, B, and C, respectively; the corresponding Mars-arrival values are 0.0052, 0.0042, and 0.0036 km/s. All are well below the adopted conservative 0.08 km/s bound.

Accordingly, three decimal places are retained in the trajectory tables to identify and reproduce the nominal numerical solutions, not to claim physical knowledge at the meter-per-second level. Mission design and mass sizing should use the ±0.08 km/s envelope until a full covariance-based, n-body navigation and targeting analysis is performed. Within that stated precision, the conclusion is robust: Profiles B and C require substantially less Earth-departure energy than Profile A, and Profile C also provides the lowest Mars-arrival excess velocity.

2.5. Characteristic Energy, Local Perigee speed, and the Oberth Maneuver

The characteristic departure energy is $C₃=v_{\infty ,E}^{²}$. It is a property of the required Earth-relative hyperbola; it is not itself a propulsive velocity increment. To translate C₃ into a local burn requirement, the present screening calculation assumes an initially circular 200 km Earth parking orbit. Using the Horizons Earth gravitational parameter ${\mu }_E$ = 398600.435436 km³/s² and equatorial radius $R_E$ = 6378.137 km, the circular and escape speeds at the reference perigee are 7.784 and 11.009 km/s, respectively [4].

For an impulsive prograde burn at perigee, the required hyperbolic perigee speed and ideal departure increment are [7,8,9]

$$v_p=\sqrt{v_{\infty ,E}^{\hspace{0.17em}2}+{\displaystyle \frac{2{\mu }_E}{r_p}}},\hspace{1em}\hspace{1em}\mathsf{\Delta }{v}_{\mathrm{L}\mathrm{E}\mathrm{O}}=v_p-\sqrt{{\displaystyle \frac{{\mu }_E}{r_p}}}.$$

(2.7)

Table 2.5 gives the total ideal increments measured from a 200 km circular parking orbit. They are energy indicators, not the velocity increment that must be supplied by the auxiliary spacecraft stage alone. In the selected architecture, the refueled Starship-class stage supplies the principal acceleration and performs the high-energy perigee passage; the attached Mars-bound stack supplies only any residual increment. The burn is concentrated near perigee because the Oberth effect maximizes the change in orbital energy produced by a given impulsive velocity increment at the point of highest local speed. The Oberth maneuver reduces the propellant required relative to applying the same energy increase far from Earth, but it does not remove the $C_3$ requirement.

Table 2.5. Ideal Earth-departure quantities from a 200 km circular parking orbit. 

Profile	${\mathit{v}}_{\mathit{\infty },\mathit{E}}$(km/s)	C3 (km2/s2)	Perigee speed (km/s)	Ideal $\mathit{\Delta }\mathit{v}$ (km/s)
A	16.879	284.890	20.152	12.367
B	11.843	140.258	16.169	8.385
C	11.844	140.286	16.170	8.386

Table 2.5. Ideal Earth-departure quantities from a 200 km circular parking orbit. 

Profile	${\mathit{v}}_{\mathit{\infty },\mathit{E}}$(km/s)	C3 (km2/s2)	Perigee speed (km/s)	Ideal $\mathit{\Delta }\mathit{v}$ (km/s)
A	16.879	284.890	20.152	12.367
B	11.843	140.258	16.169	8.385
C	11.844	140.286	16.170	8.386

2.6. Outbound Payload and First-Phase Consumables Allocation

The baseline crew-vehicle mass used in the Earth-departure calculation is 10 t after any auxiliary departure stage has been discarded. A common first-phase consumables allocation of 120 days for two astronauts is adopted for all three trajectories. This allocation covers the complete interval from Earth departure through the end of Mars surface operations; it does not represent 120 days of consumables for the surface stay alone. The corresponding outbound-plus-surface durations are 91 days for Profile A, 86 days for Profile B, and 96 days for Profile C. The common allocation therefore provides contingency reserves of 29, 34, and 24 days, respectively.

At the adopted planning rate of 13.0 $\mathrm{k}\mathrm{g}\mathrm{d}\mathrm{a}{\mathrm{y}}^{-1}$ for the two-person crew, the 120-day allocation is 1.56 t. This aggregate is not presented as a universal physiological consumption rate. It combines representative oxygen, food, and potable and food-preparation water requirements with architecture-level allowances for packaging, leakage, hygiene, medical supplies, and contingency logistics. The component rates are anchored to NASA beyond-low-Earth-orbit logistics and deep-space life-support studies [10,11]. Water-recovery and oxygen-regeneration hardware are included within the spacecraft systems mass rather than credited as negative consumables.

Table 2.6. First-phase consumables carried within the 10 t outbound vehicle. 

Profile	Outbound + stay	Nominal use at 13.0 kg/day	Allocated duration	Carried mass	Time reserve
A	91 days	1.183 t	120 days	1.560 t	29 days
B	86 days	1.118 t	120 days	1.560 t	34 days
C	96 days	1.248 t	120 days	1.560 t	24 days

Table 2.6. First-phase consumables carried within the 10 t outbound vehicle. 

Profile	Outbound + stay	Nominal use at 13.0 kg/day	Allocated duration	Carried mass	Time reserve
A	91 days	1.183 t	120 days	1.560 t	29 days
B	86 days	1.118 t	120 days	1.560 t	34 days
C	96 days	1.248 t	120 days	1.560 t	24 days

The common 120-day allocation fits within the adopted 10 t baseline module in all three cases. With 1.56 t assigned to consumables, the preliminary remaining systems and margin allocation is 1.14 t and the onboard propellant allocation remains 3.00 t. Table 2.7 makes this internal mass balance explicit.

Table 2.7. First-order mass allocation within the 10 t outbound module. 

Mass element	All three profiles
Mars-arrival structure, aeroshell, systems, and jettison package	4.00 t
First-phase consumables for 120 days	1.56 t
Crew, suits, and personal equipment	0.30 t
Remaining systems and preliminary margin	1.14 t
Onboard Mars-arrival propellant	3.00 t
Baseline outbound module	10.00 t

Table 2.7. First-order mass allocation within the 10 t outbound module. 

Mass element	All three profiles
Mars-arrival structure, aeroshell, systems, and jettison package	4.00 t
First-phase consumables for 120 days	1.56 t
Crew, suits, and personal equipment	0.30 t
Remaining systems and preliminary margin	1.14 t
Onboard Mars-arrival propellant	3.00 t
Baseline outbound module	10.00 t

The 4.00 t systems line includes the 0.5 t braking-package and cruise-hardware assembly separated in Chapter 3; it is not added to the 10 t module at Mars. The return consumables are likewise not double-counted. A separate 200-day allocation is aboard the return spacecraft delivered to Mars in 2029. At the end of surface operations the astronauts transfer, through the Mars Ascent Taxi, to that predeployed spacecraft. Its 14 t retained mass and the larger disposable Mars-departure stages analyzed in Chapter 4 therefore do not increase the Earth-departure payload calculated here.

2.7. Starship-Class Pre-Energization and Residual Departure Stage

The three trajectories require different departure architectures. A refueled Starship-class vehicle acts as the principal Earth-departure stage in every case, using orbital refueling, orbit raising, and a final low-perigee passage to exploit the Earth Oberth effect. Profile A then requires a large detachable auxiliary stage to reach its much higher Lambert energy. Profiles B and C require almost identical Earth-departure states and should instead use direct Starship-class injection or, if detailed performance falls slightly short, a much smaller detachable trim stage. The calculation must be performed in local perigee speed: hyperbolic excess velocities cannot be added directly.

If the Starship-class stage leaves the Mars-bound stack with an Earth-relative excess velocity $v_{\infty ,0}$, the corresponding local perigee speed and the residual increment needed by the attached auxiliary stage are

$$v_{p,0}=\sqrt{v_{\infty ,0}^{\hspace{0.17em}2}+{\displaystyle \frac{2{\mu }_E}{r_p}}},\hspace{1em}\hspace{1em}\mathsf{\Delta }{v}_{\mathrm{a}\mathrm{u}\mathrm{x}}=v_{p,\mathrm{t}\mathrm{a}\mathrm{r}\mathrm{g}\mathrm{e}\mathrm{t}}-v_{p,0}.$$

(2.8)

Table 2.8 separates the three cases. For a common gross departure-mass comparison of 27 t, Profile A spends 17 t on the detachable auxiliary stage. Profiles B and C do not require that large stage in the direct-injection screening case. The resulting difference remains unassigned in the reference architecture: it is an Earth-departure mass opportunity rather than a claim that 17 t can be added to the Mars-arrival vehicle or landed on Mars.

At the adopted two-person planning rate, each additional 30-day consumables block would add 0.390 t. Such an increment can be considered for Profiles B and C, but it must either remain inside a rebalanced 10 t module or be included in a new departure-and-arrival mass closure. The nominal Chapter 3 atmospheric calculations retain entry masses of 6.6 t for Profile A and 9.0 t for Profiles B and C.

Table 2.8. Trajectory-specific use of the 27 t gross departure-mass comparison. 

Profile	Earth ${\mathit{v}}_{\mathit{\infty }}$	Mars-arrival ${\mathit{v}}_{\mathit{\infty }}$	Earth-departure configuration	Gross mass opportunity
A 56 + 35 + 135	16.879 km/s	16.638 km/s	10 t module + 16 t auxiliary propellant + 1 t auxiliary dry mass	No payload headroom within 27 t; 17 t is departure stage
B 72 + 14 + 140	11.843 km/s	13.671 km/s	10 t baseline module; direct injection or small trim stage if required	Gross headroom unassigned; 9 t entry case analyzed in Chapter 3
C 86 + 10 + 135	11.844 km/s	9.866 km/s	10 t baseline module; direct injection or small trim stage if required	Gross headroom unassigned; greatest prospective arrival margin

Table 2.8. Trajectory-specific use of the 27 t gross departure-mass comparison. 

Profile	Earth ${\mathit{v}}_{\mathit{\infty }}$	Mars-arrival ${\mathit{v}}_{\mathit{\infty }}$	Earth-departure configuration	Gross mass opportunity
A 56 + 35 + 135	16.879 km/s	16.638 km/s	10 t module + 16 t auxiliary propellant + 1 t auxiliary dry mass	No payload headroom within 27 t; 17 t is departure stage
B 72 + 14 + 140	11.843 km/s	13.671 km/s	10 t baseline module; direct injection or small trim stage if required	Gross headroom unassigned; 9 t entry case analyzed in Chapter 3
C 86 + 10 + 135	11.844 km/s	9.866 km/s	10 t baseline module; direct injection or small trim stage if required	Gross headroom unassigned; greatest prospective arrival margin

For Profile A, the required final perigee speed is 20.152 km/s. The working comparison adopts a common Starship-class pre-energization state of $v_{\infty ,0}=11.870$ km/s, corresponding to a local perigee speed of 16.189 km/s. The auxiliary stage must therefore provide 3.963 km/s. Its ideal increment follows the Tsiolkovsky equation [12].

$$\mathsf{\Delta }{v}_{\mathrm{a}\mathrm{u}\mathrm{x}}=g_0{I}_{\mathrm{s}\mathrm{p}}\ln \left({\displaystyle \frac{m_0}{m_f}}\right).$$

(2.9)

For a 10 t module and a 1 t auxiliary-stage dry mass, the required propellant is obtained directly from

$$m_{\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{p},\mathrm{a}\mathrm{u}\mathrm{x}}=\left(m_{\mathrm{m}\mathrm{o}\mathrm{d}\mathrm{u}\mathrm{l}\mathrm{e}}+m_{\mathrm{d}\mathrm{r}\mathrm{y},\mathrm{a}\mathrm{u}\mathrm{x}}\right)\left[\exp \left({\displaystyle \frac{\mathsf{\Delta }{v}_{\mathrm{a}\mathrm{u}\mathrm{x}}}{g_0{I}_{\mathrm{s}\mathrm{p}}}}\right)-1\right].$$

(2.10)

Table 2.9. Profile A closure at a common pre-energization state. 

${\mathit{I}}_{\mathit{s}\mathit{p}}$	Pre-burn ${\mathit{v}}_{\mathit{\infty }}$	Required auxiliary $\mathit{\Delta }\mathit{v}$	Required auxiliary propellant	Auxiliary dry mass	Initial stack	Headroom within 27 t
450 s	11.870 km/s	3.963 km/s	16.000 t	1.000 t	27.000 t	0.000 t
500 s	11.870 km/s	3.963 km/s	13.681 t	1.000 t	24.681 t	2.319 t

Table 2.9. Profile A closure at a common pre-energization state. 

${\mathit{I}}_{\mathit{s}\mathit{p}}$	Pre-burn ${\mathit{v}}_{\mathit{\infty }}$	Required auxiliary $\mathit{\Delta }\mathit{v}$	Required auxiliary propellant	Auxiliary dry mass	Initial stack	Headroom within 27 t
450 s	11.870 km/s	3.963 km/s	16.000 t	1.000 t	27.000 t	0.000 t
500 s	11.870 km/s	3.963 km/s	13.681 t	1.000 t	24.681 t	2.319 t

At $I_{sp}=450$s, the nominal Profile A architecture uses the full 27 t comparison: 16 t of auxiliary propellant, 1 t of auxiliary dry mass, and the 10 t module. At $I_{sp}=500$s, the same pre-energization state and target require only 13.681 t of auxiliary propellant, reducing the initial stack to 24.681 t and releasing 2.319 t for structural margin, equipment, or reserve propellant. These are ideal impulsive results and remain conditional on the Starship-class stage reaching the stated pre-energization state with the attached mass.

Profiles B and C target $v_{\infty ,E}=$ 11.843 and 11.844 km/s, slightly below the 11.870 km/s pre-energization state used in the Profile A calculation. Consequently, under the same ideal screening assumption, the 10 t reference module can be injected without the 17 t auxiliary stage. No additional mass is inserted into the baseline calculation. A trajectory-specific Starship payload-performance model and a repeated Chapter 3 entry analysis are required before any part of the gross difference can be assigned to equipment or consumables.

After any auxiliary or trim-stage operation, the baseline 10 t module retains its 3 t onboard propellant. Chapter 3 uses this inventory differently for the three trajectories; Table 2.10 adopts that same profile-specific ledger rather than imposing one generic cruise-and-landing split.

Table 2.10. Profile-specific use of the 3 t onboard propellant retained in the 10 t module. 

Case	Arrival use	Propellant	Mass interval	$\mathit{\Delta }\mathit{v}$ (450 s)	$\mathit{\Delta }\mathit{v}$ (500 s)	Post-burn state
A	Pre-entry braking	2.9 t	10.0 to 7.1 t	1.511 km/s	1.679 km/s	6.6 t after 0.5 t jettison; 0.1 t orbital reserve
B/C	Pre-entry trim	1.0 t	10.0 to 9.0 t	0.465 km/s	0.517 km/s	9.0 t; 2.0 t retained for orbit, contingency, or terminal descent

Table 2.10. Profile-specific use of the 3 t onboard propellant retained in the 10 t module. 

Case	Arrival use	Propellant	Mass interval	$\mathit{\Delta }\mathit{v}$ (450 s)	$\mathit{\Delta }\mathit{v}$ (500 s)	Post-burn state
A	Pre-entry braking	2.9 t	10.0 to 7.1 t	1.511 km/s	1.679 km/s	6.6 t after 0.5 t jettison; 0.1 t orbital reserve
B/C	Pre-entry trim	1.0 t	10.0 to 9.0 t	0.465 km/s	0.517 km/s	9.0 t; 2.0 t retained for orbit, contingency, or terminal descent

For Profile A, the remaining 0.1 t closes the small post-aerocapture periapsis-raise maneuver, while terminal landing is performed by a descent stage predeployed in 2029. Profiles B and C expend less propellant before entry and retain 2 t, but the common baseline also uses aerocapture followed by the independently delivered descent system. The retained propellant is therefore margin or an alternate terminal resource, not part of the 14 t Earth-return spacecraft. If additional equipment increases the post-departure mass above 10 t, every increment in Table 2.10 must be recalculated.

2.8. High-C₃ Context and Operational Implementation

The departure energies should be compared through C₃, not by confusing local post-burn speed with hyperbolic excess speed. New Horizons established a flight precedent near C₃ = 157 km²/s² for a sub-ton spacecraft, and dedicated high-C₃ launch studies examine additional-stage architectures for still higher energies [13,14]. Profiles B and C, at C₃ approximately 140 km²/s², lie slightly below that historical energy level but carry a baseline 10 t module and may use part of the released departure-stage mass for additional payload. Profile A, at C₃ approximately 285 km²/s², is about 1.8 times the New Horizons C₃ and has no direct flown analogue.

For this reason, the Starship-class system is used as a refueled in-space departure stage rather than merely as the vehicle that delivers an independent multistage stack to low Earth orbit. Large-scale cryogenic propellant management and transfer remain active development areas [15]. Manufacturer-stated payload capability is used only as architectural context and is not treated as validation of a specific payload-to-$C_3$ combination [16]. For Profile A, the mass attached during the final pre-energization operation is the explicitly defined 27 t stack in Table 2.9. Profiles B and C exchange most or all of that detachable-stage mass for useful payload only if the pre-energization and Mars-arrival calculations close at the resulting delivered mass.

A practical implementation raises the combined vehicle into a suitably phased elliptical orbit and performs the final Starship-class burn near low perigee. When required, an auxiliary or trim stage then supplies only the residual increment required by the selected Lambert solution. This division preserves the Oberth benefit but cannot reduce the heliocentric $C_3$ fixed by the trajectory. The final design must account for finite burns and the associated loss of ideal Oberth efficiency.

2.9. Limitations of the Departure Model

The results are mission-screening values rather than launch-vehicle performance guarantees. The Lambert legs are heliocentric two-body solutions based on the supplied DE441 boundary states. A final design must include n-body propagation, finite-burn targeting, launch and parking-orbit geometry, Earth oblateness, lunar perturbations, correction maneuvers, navigation dispersion, and arrival targeting.

The uncertainty calculation is a controlled robustness test, not a statistical confidence interval derived from a full covariance matrix. It deliberately reproduces the reference envelope of the original paper so that the three trajectories can be compared on the same basis. It does not represent launch-date uncertainty, ephemeris-model error, maneuver-execution error, or correlated navigation uncertainties. Those effects require covariance propagation and a navigation simulation around the final n-body reference trajectories.

The pre-energization calculation is idealized. A trajectory-specific Starship model must verify that the attached mass can reach the states used in Table 2.8 and 2.9. The auxiliary-stage estimates exclude finite-burn losses, residuals, boiloff, insulation, interstage and docking structures, pressurization, restart systems, attitude control, abort hardware, and integration margins. These effects can change both the residual increment and the preferred stage mass. In particular, a 1 t dry mass for a 16 t propellant stage is an aggressive screening assumption and must be replaced by a hardware-level stage design. Similarly, the 17 t headroom identified for Profiles B and C is a gross departure-mass opportunity, not a demonstrated landed-payload capability.

Most importantly, “feasible” is used at the preliminary mission-design level. The calculation shows that a refueled Starship-class stage and a compact residual stage can represent the required departure energy without carrying the Mars return system from Earth in 2031. It does not establish that the combined vehicle is already designed or human-rated. Mars-arrival velocity, propellant consumption, and landing mass are examined in Chapter 3.

3. Mars Arrival, Aerocapture, and Landing

Earth departure establishes whether the required heliocentric trajectory can be reached; Mars arrival determines whether the crew can survive the energy that the trajectory delivers. The three CA21-anchored profiles are therefore not interchangeable at Mars. Their nominal arrival excess velocities are 16.638, 13.671, and 9.866 km/s, producing materially different atmospheric-interface speeds, heating environments, guidance corridors, and demands on terminal propulsion.

The arrival architecture adopted here is deliberately layered. Atmospheric deceleration removes the dominant fraction of the kinetic energy, while chemical propulsion is reserved for trajectory-specific pre-entry braking and post-capture maneuvering. Aerocapture into a temporary Mars orbit is preferred over immediate landing because it separates the most severe thermal pulse from terminal descent and permits vehicle checkout before the crew commits to the surface. The 10 t Mars-arrival module is distinct from the predeployed descent stage, the primary and reserve Mars Ascent Taxis, and the Earth-return assembly. The latter retains 14 t after Mars injection, contains the 4 t Earth-entry capsule and 200-day consumables reserve analyzed in Chapters 4 and 5, and never descends to the Martian surface.

3.1. Mars-Arrival Boundary Conditions

The Mars-arrival excess velocities are taken from the same zero-revolution, short-way Lambert solutions and DE441 boundary states used in Chapter 2 [1,4,5]. A representative atmospheric interface altitude of 125 km is used for comparison. With the Mars gravitational parameter ${\mu }_M$= 42828.375 km³/s² and equatorial reference radius $R_M$ = 3396.19 km, the local escape speed at the interface is 4.932 km/s. Neglecting atmospheric rotation and winds at this stage, the inertial entry speed is [7,8,9]

$$v_{\mathrm{E}\mathrm{I}}=\sqrt{v_{\infty ,M}^2+{\displaystyle \frac{2{\mu }_M}{R_M+h_{\mathrm{E}\mathrm{I}}}}}.$$

(3.1)

The associated kinetic energy per unit entry mass is a useful first-order discriminator. It is not a heat-load calculation, because heat transfer also depends on density history, trajectory, vehicle shape, nose radius, catalytic behavior, and radiative and nonequilibrium chemistry.

$${\epsilon }_k={\displaystyle \frac{E_k}{m}}={\displaystyle \frac{1}{2}}{v}_{\mathrm{E}\mathrm{I}}^2.$$

(3.2)

Table 3.1. Nominal Mars atmospheric-interface conditions at 125 km altitude. 

Profile	Mars ${\mathit{v}}_{\mathit{\infty }}$ (km/s)	Entry speed (km/s)	Specific energy (MJ/kg)	10 t energy indicator (TJ)
A 56 + 35 + 135	16.638	17.354	150.575	1.506
B 72 + 14 + 140	13.671	14.533	105.611	1.056
C 86 + 10 + 135	9.866	11.030	60.832	0.608

Table 3.1. Nominal Mars atmospheric-interface conditions at 125 km altitude. 

Profile	Mars ${\mathit{v}}_{\mathit{\infty }}$ (km/s)	Entry speed (km/s)	Specific energy (MJ/kg)	10 t energy indicator (TJ)
A 56 + 35 + 135	16.638	17.354	150.575	1.506
B 72 + 14 + 140	13.671	14.533	105.611	1.056
C 86 + 10 + 135	9.866	11.030	60.832	0.608

Profile B carries approximately 70% of the Profile A specific entry energy, whereas Profile C carries only about 40%. Profile C is consequently the most favorable landing case. Profile B remains a high-energy human-entry problem rather than a near-copy of Profile C, and Profile A defines the upper-bound arrival architecture.

3.2. Propagation of Trajectory Uncertainty to Mars Entry

Chapter 2 adopts the conservative $\Delta v_{\infty }=$0.08 km/s uncertainty used in the original paper. Holding the interface altitude fixed, first-order propagation through the energy relation gives

$$\mathsf{\Delta }{v}_{\mathrm{E}\mathrm{I}}\simeq {\displaystyle \frac{v_{\infty ,M}}{v_{\mathrm{E}\mathrm{I}}}}\mathsf{\Delta }{v}_{\infty },\hspace{1em}\hspace{1em}\mathsf{\Delta }{\epsilon }_k\simeq v_{\infty ,M}\mathsf{\Delta }{v}_{\infty }.$$

(3.3)

Table 3.2. Conservative trajectory-uncertainty propagation at Mars arrival. 

Profile	Adopted $\mathit{\Delta }{\mathit{v}}_{\mathit{\infty }}$	$\mathit{\Delta }{\mathit{v}}_{\mathit{E}\mathit{I}}$(km/s)	$\mathit{\Delta }{\mathit{\epsilon }}_{\mathit{k}}$(MJ/kg)	Relative energy uncertainty
A	±0.080 km/s	±0.0767	±1.331	±0.88%
B	±0.080 km/s	±0.0753	±1.094	±1.04%
C	±0.080 km/s	±0.0716	±0.789	±1.30%

Table 3.2. Conservative trajectory-uncertainty propagation at Mars arrival. 

Profile	Adopted $\mathit{\Delta }{\mathit{v}}_{\mathit{\infty }}$	$\mathit{\Delta }{\mathit{v}}_{\mathit{E}\mathit{I}}$(km/s)	$\mathit{\Delta }{\mathit{\epsilon }}_{\mathit{k}}$(MJ/kg)	Relative energy uncertainty
A	±0.080 km/s	±0.0767	±1.331	±0.88%
B	±0.080 km/s	±0.0753	±1.094	±1.04%
C	±0.080 km/s	±0.0716	±0.789	±1.30%

These dispersions are small enough that they do not change the ranking of the trajectories. They are not, however, the dominant uncertainty in an entry design. Mars atmospheric density variability, winds, dust loading, aerodynamic coefficients, navigation delivery error, and flight-path-angle error control the usable entry corridor and must be propagated in a high-fidelity simulation [17,18,19,20,21].

3.3. Profile A Mass Staging and Propulsive Pre-Braking

The conservative calculation begins with the complete 10.0 t Mars-approach module, including the 120-day consumables allocation. No mass credit is assigned to consumed food, recovered water, or discarded waste. The module expends 2.9 t of its 3.0 t chemical-propellant inventory in a retrograde burn near Mars atmospheric interface and retains 0.1 t in an independent orbital-maneuver subsystem. A 0.5 t empty braking-package and cruise-hardware assembly is jettisoned only after the burn, leaving 6.6 t for atmospheric capture. This 0.5 t package is already contained in the 4.0 t systems allocation of Table 2.7 and is not additional arrival mass. The velocity change comes from the rocket burn; passive jettison changes neither velocity nor specific energy, but it lowers total kinetic energy and ballistic coefficient.

$$\mathsf{\Delta }{v}_b=g_0{I}_{\mathrm{s}\mathrm{p}}\ln \left({\displaystyle \frac{m_0}{m_f}}\right),\hspace{1em}\hspace{1em}{v}_{\mathrm{E}\mathrm{I},b}\simeq v_{\mathrm{E}\mathrm{I},0}-\mathsf{\Delta }{v}_b.$$

(3.4)

$$m_{\mathrm{E}\mathrm{I}}=m_f-m_j,\hspace{1em}\hspace{1em}{E}_{k,\mathrm{E}\mathrm{I}}={\displaystyle \frac{1}{2}}{m}_{\mathrm{E}\mathrm{I}}{v}_{\mathrm{E}\mathrm{I},b}^2.$$

(3.5)

Table 3.3. Conservative Profile A pre-entry mass and velocity state. 

${\mathit{I}}_{\mathit{s}\mathit{p}}$	Burn sequence	Burn $\mathit{\Delta }\mathit{v}$ (km/s)	Entry mass after 0.5 t jettison	Entry speed (km/s)	Entry-energy indicator (TJ)
450 s	10.0 → 7.1 t	1.511	6.6 t	15.842	0.828
500 s	10.0 → 7.1 t	1.679	6.6 t	15.674	0.811

Table 3.3. Conservative Profile A pre-entry mass and velocity state. 

${\mathit{I}}_{\mathit{s}\mathit{p}}$	Burn sequence	Burn $\mathit{\Delta }\mathit{v}$ (km/s)	Entry mass after 0.5 t jettison	Entry speed (km/s)	Entry-energy indicator (TJ)
450 s	10.0 → 7.1 t	1.511	6.6 t	15.842	0.828
500 s	10.0 → 7.1 t	1.679	6.6 t	15.674	0.811

The unmodified 10 t module at 17.354 km/s carries a 1.506 TJ kinetic-energy indicator. Propulsive braking plus post-burn hardware jettison reduces the atmospheric-entry indicator by 45.0% at 450 s and 46.2% at 500 s. A mass-managed variant can approach Mars near 9 t after certified disposal of expended outbound items; burning all 3 t and jettisoning the same 0.5 t package then produces a 5.5 t entry vehicle at 15.564 or 15.366 km/s. This variant supplies additional margin but is not used in the conservative reference case.

Bookkeeping rule No velocity reduction is assigned to passive mass jettison. The 0.5 t item is assumed to contain no usable propellant after the braking event and to separate without hazardous recontact. The independent 0.1 t orbital reserve remains with the crew vehicle. If the empty hardware cannot be safely jettisoned, it remains attached and the atmospheric model must be rerun at 7.1 t.

3.4. Compact Lifting-Aerocapture Model

The reference atmospheric configuration is a compact 6.0 m equivalent-drag-diameter lifting vehicle with $C_D$= 1.5, an effective nose radius of 3.0 m, and a controllable hypersonic aerodynamic lift-to-drag capability up to 1.7. The physical aerodynamic ratio L/D is a nonnegative vehicle property. A 4.5 m sensitivity case quantifies the diameter trade. For the conservative 6.6 t entry mass, the ballistic coefficient is

$$\beta ={\displaystyle \frac{m}{C_{D}A}},\hspace{1em}\hspace{1em}A={\displaystyle \frac{\pi D_{\mathrm{e}\mathrm{q}}^2}{4}},\hspace{1em}\hspace{1em}{\beta }_{6\hspace{0.17em}\mathrm{m}}=155.6\mathrm{k}\mathrm{g}\hspace{0.17em}{\mathrm{m}}^{-2}.$$

(3.6)

The atmosphere is represented by an exponential density profile with ρ₀ = 0.020 kg/m3 and H = 10.8 km. Let α denote the commanded angle of attack and σ the commanded bank angle measured from the lift-up plane. The signed in-plane lift-to-drag command is denoted by λ∥,c. The aerodynamic definitions and command bound are

$$\begin{array}{c}\rho \left(h\right)={\rho }_0\exp \left(-{\displaystyle \frac{h}{H}}\right),\hspace{1em}\hspace{1em}D={\displaystyle \frac{1}{2}}\rho v^2{C}_{D}A,\\ \left({\displaystyle \frac{L}{D}}\right)\left({\alpha }_c\right)={\displaystyle \frac{C_L\left({\alpha }_c\right)}{C_D\left({\alpha }_c\right)}},\hspace{1em}\hspace{1em}0\le \left({\displaystyle \frac{L}{D}}\right)\left({\alpha }_c\right)\le 1.7,\\ {\lambda }_{\parallel ,c}\equiv {\displaystyle \frac{L_{\parallel ,c}}{D}}=\left({\displaystyle \frac{L}{D}}\right)\left({\alpha }_c\right){\cos \sigma }_c,\hspace{1em}\hspace{1em}\left|{\lambda }_{\parallel ,c}\right|\le 1.7.\end{array}$$

(3.7)

$$\begin{array}{c}\dot{r}=v\sin \gamma ,\hspace{1em}\hspace{1em}\dot{v}=-{\displaystyle \frac{D}{m}}-{\displaystyle \frac{{\mu }_M}{r^2}}\sin \gamma ,\\ \dot{\gamma }={\displaystyle \frac{D}{mv}}{\lambda }_{\parallel ,c}+\left({\displaystyle \frac{v}{r}}-{\displaystyle \frac{{\mu }_M}{v{r}^2}}\right)\cos \gamma .\end{array}$$

(3.8)

The planar integration does not propagate angle of attack and bank as independent states. Instead, guidance commands λ∥,c directly. The numerical control allocation uses angle-of-attack modulation to set its magnitude and a lift-up or lift-down bank orientation to set its sign; consequently, the modeled lift is entirely in the trajectory plane and L∥,c = Dλ∥,c. Guidance tracks a density-versus-speed schedule derived from an equilibrium-glide force balance and then commands atmospheric exit after the specific orbital energy becomes negative. Within this planar model, the aerodynamic acceleration delivered to the crew is constrained at every integration point by

$$n_a={\displaystyle \frac{1}{g_0}}\sqrt{{\left({\displaystyle \frac{D}{m}}\right)}^2+{\left({\displaystyle \frac{L_{\parallel ,c}}{m}}\right)}^2}={\displaystyle \frac{D}{m{g}_0}}\sqrt{1+{\lambda }_{\parallel ,c}^2}\le 8.0.$$

(3.9)

An 8 g aerodynamic-load ceiling is adopted. The early NASA high-energy Mars study planned a constant 8 g deceleration at supercircular speeds [22], whereas Apollo 11 reached approximately 6.5 g during Earth return [23] and modern crewed-Mars studies commonly use a 5 g design constraint at lower entry speeds [18,20]. At the Profile A entry speed and the modeled 38 km minimum altitude, the net curvature-following acceleration, v²/r minus local gravity, is approximately 7.0 g before additional guidance demand is included. A 6 g ceiling would therefore not close this constructive high-energy aerocapture path. This Mars-specific 8 g cap is distinct from the 6 g structural target and 4.27 g calculated maximum adopted for Earth arrival in Chapter 5. It assumes a properly oriented crew in contoured couches; medical qualification after 56 days of microgravity remains a mission requirement.

3.5. Numerical Atmospheric-Capture Result

The initial atmospheric flight-path angle was searched in 0.25-degree increments. The signed command λ∥,c was continuously limited by Eq. (3.7), and the modeled aerodynamic load was limited by Eq. (3.9). Guidance begins the exit maneuver near 6.25 km/s so that the vehicle becomes bound during the atmospheric climb rather than remaining at high load until a deep ellipse is produced. Table 3.4 gives representative solutions for the conservative 6.6 t, 6 m vehicle. Both propulsion assumptions exit the 125 km interface with negative specific orbital energy; therefore the atmosphere has captured the vehicle rather than merely slowed an escaping hyperbola.

$${\epsilon }_{\mathrm{e}\mathrm{x}\mathrm{i}\mathrm{t}}={\displaystyle \frac{v_{\mathrm{e}\mathrm{x}\mathrm{i}\mathrm{t}}^2}{2}}-{\displaystyle \frac{{\mu }_M}{r_{\mathrm{e}\mathrm{x}\mathrm{i}\mathrm{t}}}}<0.$$

(3.10)

Table 3.4. Three-degree-of-freedom Profile A aerocapture solutions; 6.6 t and 6.0 m equivalent diameter. 

${\mathit{I}}_{\mathit{s}\mathit{p}}$	Entry state	Initial γ	Minimum altitude	Peak load	Exit state at 125 km	Specific orbital energy
450 s	15.842 km/s	-11.0°	38.1 km	8.00 g	4.864 km/s, +17.09°	-0.332 MJ/kg
500 s	15.674 km/s	-10.75°	38.1 km	8.00 g	4.865 km/s, +17.09°	-0.328 MJ/kg

Table 3.4. Three-degree-of-freedom Profile A aerocapture solutions; 6.6 t and 6.0 m equivalent diameter. 

${\mathit{I}}_{\mathit{s}\mathit{p}}$	Entry state	Initial γ	Minimum altitude	Peak load	Exit state at 125 km	Specific orbital energy
450 s	15.842 km/s	-11.0°	38.1 km	8.00 g	4.864 km/s, +17.09°	-0.332 MJ/kg
500 s	15.674 km/s	-10.75°	38.1 km	8.00 g	4.865 km/s, +17.09°	-0.328 MJ/kg

The integrated atmospheric-pass durations are 257 and 254 s. The corresponding times above 7 g are approximately 156 and 151 s. Both trajectories satisfy the equations of motion, the bound on the signed in-plane command, the modeled load bound, the atmospheric-exit condition, and the negative-energy capture condition. Crew tolerance to the extended high-load interval is therefore a principal Profile A qualification requirement.

Table 3.5. Compact-vehicle sensitivity for Profile A. 

Equivalent diameter	Entry mass	Ballistic coefficient	Maximum aerodynamic L/D	Peak dynamic pressure	Result
6.0 m	6.6 t	155.6 kg/m2	≤ 1.7	11.4 kPa	Captured; lower thermal demand
4.5 m	5.5 t mass-managed case	230.6 kg/m2	≤ 1.7	16.3 kPa	Captured; higher thermal demand

Table 3.5. Compact-vehicle sensitivity for Profile A. 

Equivalent diameter	Entry mass	Ballistic coefficient	Maximum aerodynamic L/D	Peak dynamic pressure	Result
6.0 m	6.6 t	155.6 kg/m2	≤ 1.7	11.4 kPa	Captured; lower thermal demand
4.5 m	5.5 t mass-managed case	230.6 kg/m2	≤ 1.7	16.3 kPa	Captured; higher thermal demand

The modeled vehicle is a compact mid-to-high-lift hypersonic configuration whose effective 6 m drag footprint is comparable in diameter to the LOFTID flight article. LOFTID itself was a low-L/D inflatable decelerator and is not the proposed crew vehicle [24,25]. The aerodynamic moldline, control authority, stability, and TPS attachment require dedicated integration and qualification.

3.6. Thermal Screening and Margin

Convective heating is screened with a Sutton-Graves-type stagnation relation [26]. For the Mars CO2 screening calculation, k = 1.90 x 10^-4 in SI units and the effective nose radius is 3.0 m.

$${\dot{q}}_c=k\sqrt{{\displaystyle \frac{\rho }{R_n}}}{v}^3,\hspace{1em}\hspace{1em}{Q}_c={\int }_{t_0}^{t_f}{\dot{q}}_c\hspace{0.17em}dt.$$

(3.11)

A factor of three is applied to both the convective proxy peak and integrated load before comparison with the HEEET capability envelope. This factor is a screening allowance for omitted radiative and nonequilibrium contributions; it is not a substitute for coupled radiation, ablation, and CFD analysis. HEEET development literature reports capability above 1500 W/cm2 and an extreme integrated-load range of approximately 75-250 kJ/cm2, while NASA ground testing has reached substantially higher local fluxes [27,28].

Table 3.6. Profile A thermal screening for the compact 6 m conservative solution. 

${\mathit{I}}_{\mathit{s}\mathit{p}}$	Peak q	Convective proxy peak	3× design peak	Convective proxy load	3× design load
450 s	11.4 kPa	368 W/cm2	1,105 W/cm2	33.8 kJ/cm2	101.5 kJ/cm2
500 s	11.4 kPa	358 W/cm2	1,074 W/cm2	32.7 kJ/cm2	98.1 kJ/cm2

Table 3.6. Profile A thermal screening for the compact 6 m conservative solution. 

${\mathit{I}}_{\mathit{s}\mathit{p}}$	Peak q	Convective proxy peak	3× design peak	Convective proxy load	3× design load
450 s	11.4 kPa	368 W/cm2	1,105 W/cm2	33.8 kJ/cm2	101.5 kJ/cm2
500 s	11.4 kPa	358 W/cm2	1,074 W/cm2	32.7 kJ/cm2	98.1 kJ/cm2

Both three-times-margin cases remain below the cited HEEET peak-flux threshold and inside its extreme integrated-load range. The 4.5 m mass-managed sensitivity case also produces captured trajectories, but its three-times values approach 1.25-1.47 kW/cm² and 131-143 kJ/cm². The 6 m configuration is used as the reference case because of its larger thermal margin.

3.7. Layered Arrival and Landing Architecture

The 56-day arrival uses a sequence of operations rather than a direct descent to the surface. First, the complete 10 t module burns 2.9 t in the retrograde maneuver while preserving a 0.1 t orbital reserve. Second, the empty 0.5 t braking package is separated, and the 6.6 t lifting vehicle executes the guided 8 g-capped atmospheric pass. The nominal exit ellipses have apoapses of approximately 122,500 and 124,200 km above Mars. Their osculating periapses remain inside Mars, as expected after a single drag pass, so a small prograde maneuver is required at apoapsis before the next encounter with the planet.

$$\mathsf{\Delta }{v}_{p\uparrow }=\sqrt{{\mu }_M \left({\displaystyle \frac{2}{r_a}}-{\displaystyle \frac{1}{a_t}}\right)}-{\displaystyle \frac{h_o}{r_a}},\hspace{1em}\hspace{1em}{a}_t={\displaystyle \frac{r_a+r_{p,t}}{2}}.$$

(3.12)

Taking a 250 km target periapsis, Eq. (3.12) gives 8.3 and 8.2 m/s at apoapsis. Even a conservative 230 s orbital-maneuver system obtains 34.4 m/s from the retained 0.1 t reserve on a 6.6-to-6.5 t burn, leaving margin for dispersions and rendezvous. The time from atmospheric exit to apoapsis is about 69 h, allowing navigation and systems checkout before the burn. After the orbit is stabilized, a descent stage delivered by the slow 2029 infrastructure mission rendezvous with the crew vehicle or is already integrated with the orbital arrival complex. The crew then performs a separate orbital-speed entry and terminal landing.

Table 3.7. Physical function of each Profile A arrival layer. 

Layer	State or resource	Function	Analysis basis
Propulsive pre-brake	10.0 → 7.1 t; 2.9 t propellant	Remove 1.511-1.679 km/s	Rocket equation
Post-burn separation	0.5 t inert hardware	Reduce entry mass and β	Mass and energy bookkeeping
Compact lifting pass	6.6 t; 6 m; L/D ≤ 1.7; |λ∥,c| ≤ 1.7	Remove hyperbolic energy	Integrated 3-DOF capture
Periapsis raise	0.1 t retained reserve	8.2-8.3 m/s at apoapsis	Vis-viva; 34.4 m/s available
Predeployed descent	Delivered before crew departure	Orbital entry and touchdown	Independent terminal stage

Table 3.7. Physical function of each Profile A arrival layer. 

Layer	State or resource	Function	Analysis basis
Propulsive pre-brake	10.0 → 7.1 t; 2.9 t propellant	Remove 1.511-1.679 km/s	Rocket equation
Post-burn separation	0.5 t inert hardware	Reduce entry mass and β	Mass and energy bookkeeping
Compact lifting pass	6.6 t; 6 m; L/D ≤ 1.7; |λ∥,c| ≤ 1.7	Remove hyperbolic energy	Integrated 3-DOF capture
Periapsis raise	0.1 t retained reserve	8.2-8.3 m/s at apoapsis	Vis-viva; 34.4 m/s available
Predeployed descent	Delivered before crew departure	Orbital entry and touchdown	Independent terminal stage

Profiles B and C expend only 1.0 t in the pre-entry trim, giving 0.465 km/s at 450 s or 0.517 km/s at 500 s and leaving a 9.0 t entry vehicle with 2.0 t of propellant retained. Their resulting entry speeds are 14.017-14.069 km/s and 10.514-10.565 km/s, respectively. The same three-degree-of-freedom equations were integrated for these heavier entry states with the 6.0 m aerodynamic system, C_D = 1.5, an available aerodynamic L/D up to 1.7, the signed command λ∥,c of Eq. (3.7), and an initial flight-path angle of -10.5 degrees. The commanded in-plane lift was modulated to reach an exit specific energy near -0.330 MJ/kg, comparable to the Profile A reference orbit. Table 3.8 shows that both lower-energy profiles also reach bound exits without requiring the Profile A propellant expenditure.

Table 3.8. Three-degree-of-freedom capture solutions for the 9 t Profile B and C entry vehicles. 

Profile	${\mathit{I}}_{\mathit{s}\mathit{p}}$	Entry state	Initial γ	Minimum altitude	Peak load	Peak q̇c / Qc	Exit state
B	450 s	9.0 t; 14.069 km/s	-10.5°	36.14 km	8.00 g	308 W/cm2 / 29.94 kJ/cm2	4.865 km/s; -0.330 MJ/kg
B	500 s	9.0 t; 14.017 km/s	-10.5°	36.14 km	8.00 g	306 W/cm2 / 29.54 kJ/cm2	4.865 km/s; -0.330 MJ/kg
C	450 s	9.0 t; 10.565 km/s	-10.5°	39.45 km	7.66 g	146 W/cm2 / 14.68 kJ/cm2	4.865 km/s; -0.330 MJ/kg
C	500 s	9.0 t; 10.514 km/s	-10.5°	39.45 km	7.66 g	145 W/cm2 / 14.44 kJ/cm2	4.865 km/s; -0.330 MJ/kg

Table 3.8. Three-degree-of-freedom capture solutions for the 9 t Profile B and C entry vehicles. 

Profile	${\mathit{I}}_{\mathit{s}\mathit{p}}$	Entry state	Initial γ	Minimum altitude	Peak load	Peak q̇c / Qc	Exit state
B	450 s	9.0 t; 14.069 km/s	-10.5°	36.14 km	8.00 g	308 W/cm2 / 29.94 kJ/cm2	4.865 km/s; -0.330 MJ/kg
B	500 s	9.0 t; 14.017 km/s	-10.5°	36.14 km	8.00 g	306 W/cm2 / 29.54 kJ/cm2	4.865 km/s; -0.330 MJ/kg
C	450 s	9.0 t; 10.565 km/s	-10.5°	39.45 km	7.66 g	146 W/cm2 / 14.68 kJ/cm2	4.865 km/s; -0.330 MJ/kg
C	500 s	9.0 t; 10.514 km/s	-10.5°	39.45 km	7.66 g	145 W/cm2 / 14.44 kJ/cm2	4.865 km/s; -0.330 MJ/kg

With the same factor-of-three thermal allowance used for Profile A, the Profile B design values are 0.92 kW/cm² and approximately 89 kJ/cm²; the Profile C values are 0.44 kW/cm² and approximately 44 kJ/cm². Thus Profile B remains a demanding guided-aerocapture case, while Profile C retains the largest thermal margin. Direct entry remains a secondary trade for Profile C, but the common reference architecture uses aerocapture followed by a separately delivered descent stage for all three profiles.

After crew touchdown, the surface module transmits its measured position and relative-navigation beacon. The primary Mars Ascent Taxi then leaves the orbital cooling platform and lands within rover range; the reserve taxi remains in orbit until the primary vehicle is verified. Following the 35-, 14-, or 10-day surface stay for Profiles A, B, and C, respectively, the crew uses the taxi to reach Mars orbit and transfers to the predeployed Earth-return spacecraft. The Mars-arrival module, descent equipment, and ascent taxi are left at Mars and do not enter either the Chapter 4 departure mass retained after injection or the Chapter 5 Earth-entry mass.

3.8. Uncertainty, Limitations, and Verification Path

The conservative trajectory uncertainty changes the Profile A interface speed by approximately ±0.0767 km/s. The point-mass search was repeated at both velocity limits and at density scale factors of 0.70, 1.00, and 1.30. Density-aware guidance shifts the commanded altitude schedule by H ln(frho), equal to -3.85 km for the low-density case and +2.83 km for the high-density case. Captured solutions satisfying the 8 g ceiling and requiring less than 9.3 m/s for the 250 km periapsis raise were found for all twelve combinations of propulsion assumption, velocity bound, and density factor.

$$\mathsf{\Delta }{h}_{\rho }=H{\ln f}_{\rho }.$$

(3.13)

Table 3.9. Dispersed Profile A compact-capture envelope; 6.6 t and 6 m. 

Quantity	450 s cases	500 s cases	Interpretation
Captured entry-angle corridors	-11.75° to -9.25° overall	-11.25° to -9.25° overall	Corridor retargets with measured density
Minimum altitude	34.2-41.0 km	34.3-41.0 km	Density-scaled geometric shift
Peak dynamic pressure	11.0-12.1 kPa	11.0-12.2 kPa	Below 12.2 kPa in sampled set
Convective proxy peak	252-384 W/cm2	304-368 W/cm2	Three-times peak remains < 1.16 kW/cm2
Convective proxy load	33.2-37.2 kJ/cm2	32.0-34.8 kJ/cm2	Three-times load remains < 112 kJ/cm2
Exit energy; apoapsis raise	-0.367 to -0.318 MJ/kg; 7.9-9.3 m/s	-0.358 to -0.309 MJ/kg; 7.7-9.1 m/s	All exits bound; reserve closes orbit

Table 3.9. Dispersed Profile A compact-capture envelope; 6.6 t and 6 m. 

Quantity	450 s cases	500 s cases	Interpretation
Captured entry-angle corridors	-11.75° to -9.25° overall	-11.25° to -9.25° overall	Corridor retargets with measured density
Minimum altitude	34.2-41.0 km	34.3-41.0 km	Density-scaled geometric shift
Peak dynamic pressure	11.0-12.1 kPa	11.0-12.2 kPa	Below 12.2 kPa in sampled set
Convective proxy peak	252-384 W/cm2	304-368 W/cm2	Three-times peak remains < 1.16 kW/cm2
Convective proxy load	33.2-37.2 kJ/cm2	32.0-34.8 kJ/cm2	Three-times load remains < 112 kJ/cm2
Exit energy; apoapsis raise	-0.367 to -0.318 MJ/kg; 7.9-9.3 m/s	-0.358 to -0.309 MJ/kg; 7.7-9.1 m/s	All exits bound; reserve closes orbit

The dispersed Profile A solutions define a nonzero controlled corridor across the sampled velocity and density ranges, while Table 3.8 provides independent nominal captures for Profiles B and C. Subsequent analyses should apply the same velocity-density grid to the two lower-energy profiles, replace the exponential atmosphere with MarsGRAM ensembles, propagate full navigation covariance and flight-path-angle error, model Mars rotation and winds, replace the effective λ∥,c command with explicit angle-of-attack and bank dynamics, use Mach- and angle-dependent aerodynamic databases, include six-degree-of-freedom stability, crossrange motion, and control saturation, and couple convective plus radiative nonequilibrium heating to recession and structural response. The atmospheric-trajectory results assume successful separation of the empty 0.5 t braking package and nominal operation of the predeployed descent system. These operations use conventional mission-staging principles and do not alter the calculated aerocapture trajectory.

4. Mars Departure and Pre-Deployed Return Architecture

Mars departure is treated as a sequence of independent functions rather than as the launch of a single vehicle from the Martian surface. The astronauts first reach Mars orbit in a compact ascent taxi. They then transfer to a pre-deployed Earth-return spacecraft already connected to disposable chemical propulsion stages. The ascent taxi, landing equipment, cooling platforms, and other masses not required for the interplanetary leg are left at Mars before the high-energy departure maneuver.

The architecture preserves the return durations obtained from the CA21-anchored trajectory search. Profiles A and C share the same 135-day Mars-Earth return and therefore use one propulsion solution. Profile B uses the distinct 140-day return and has a smaller Mars-departure requirement. The chemical calculations are presented for two cases, $I_{sp}$= 450 s and $I_{sp}$= 500 s.

All return components are delivered before the crew mission by slower uncrewed transfers. Separate launch and delivery of the modules removes the requirement for the complete Mars-departure stack to fit within one Starship payload. Assembly, checkout, thermal conditioning, and propellant verification are completed in Mars orbit before the astronauts begin the return sequence.

4.1. Return Profiles and Adopted Departure Requirements

The three mission chronologies are summarized in Table 4.1. Profiles A and C are grouped in all propulsion tables because their common 135-day return has the same departure boundary condition. Profile B remains separate because its 140-day return reduces the required chemical velocity increment.

Table 4.1. Mars-departure conditions for the three CA21-anchored mission profiles. 

Profile	Mission chronology	Return duration	${\mathit{v}}_{\mathit{\infty },\mathit{M}}$	Adopted $\mathit{\Delta }\mathit{V}$	Design $\mathit{\Delta }\mathit{V}$
A	56 + 35 + 135 days	135 days	13.60 km/s	9.586 km/s	10.065 km/s
B	72 + 14 + 140 days	140 days	12.34 km/s	8.358 km/s	8.776 km/s
C	86 + 10 + 135 days	135 days	13.60 km/s	9.586 km/s	10.065 km/s

Table 4.1. Mars-departure conditions for the three CA21-anchored mission profiles. 

Profile	Mission chronology	Return duration	${\mathit{v}}_{\mathit{\infty },\mathit{M}}$	Adopted $\mathit{\Delta }\mathit{V}$	Design $\mathit{\Delta }\mathit{V}$
A	56 + 35 + 135 days	135 days	13.60 km/s	9.586 km/s	10.065 km/s
B	72 + 14 + 140 days	140 days	12.34 km/s	8.358 km/s	8.776 km/s
C	86 + 10 + 135 days	135 days	13.60 km/s	9.586 km/s	10.065 km/s

The design velocity increments in the last column contain a 5% allowance for finite-burn effects, targeting corrections, residual propellant, and operational dispersion. The nominal trajectory values are retained separately so that the propulsion margin is explicit rather than incorporated invisibly into the Lambert solution.

4.2. Mars Ascent Taxi and Post-Landing Deployment

The main Earth-return spacecraft remains in Mars orbit throughout the mission and never descends to the surface. Surface-to-orbit transport is provided by a smaller Mars Ascent Taxi whose only crewed function is to carry two astronauts from Mars to the rendezvous orbit. The 500 km Mars-ascent architecture evaluated by Polsgrove et al. requires a 3.901 $\mathrm{k}\mathrm{m}{\mathrm{s}}^{-1}$ powered ascent followed by approximately 0.275 $\mathrm{k}\mathrm{m}{\mathrm{s}}^{-1}$ of remaining maneuvers, giving approximately 4.18 $\mathrm{k}\mathrm{m}{\mathrm{s}}^{-1}$ before mission-specific rendezvous and operational reserves [30, Table 2, p. 3]. The present architecture therefore adopts a design interval of 4.5–5.0 $\mathrm{k}\mathrm{m}{\mathrm{s}}^{-1}$ and a surface-vehicle mass of approximately 8-12 t.

The ascent taxi waits in Mars orbit together with a reserve taxi and the orbital thermal-control platform. After the astronauts land, their surface module determines its position and activates a coded radio-ranging beacon. The primary taxi then performs autonomous entry, descent, hazard avoidance, and powered terminal guidance relative to the measured crew location. A preliminary operational requirement is a landing distance of 1-3 km, while the surface rover is sized for a range of at least 10 km. The reserve taxi remains in orbit until the primary taxi has landed and passed its propulsion, power, communications, and propellant checks. Terrain-relative navigation and local hazard mapping provide the basis for this relative-landing mode [31].

LOX/methane propulsion is preferred for the ascent taxi because methane is denser and substantially easier to store than liquid hydrogen. The taxi lands with a detachable surface power and cooling pallet containing solar arrays, batteries, sunshades, radiators, and cryocoolers. The pallet remains on Mars when the taxi launches. Consequently, the cryogenic surface-storage interval is reduced from approximately two years to 14, 35, or 10 days for Profiles B, A, and C, respectively.

Table 4.2. Architecture-level parameters for the Mars Ascent Taxi. 

Quantity	Adopted value	Mission role
Crew	2 astronauts	Surface-to-orbit transport only
Design ascent ΔV	4.5-5.0 km/s	Includes gravity, steering, targeting, and rendezvous margins
Surface mass	8-12 t	Taxi, EDL hardware, ascent propellant, and surface support
Mass reaching orbit	1.5-2.5 t	Crew capsule and docking element
Primary landing requirement	1-3 km from crew	Relative navigation to the crew-lander beacon
Surface mobility requirement	At least 10 km	Provides tolerance to landing dispersion
Reserve system	Second taxi in Mars orbit	Independent landing opportunity if the primary fails

Table 4.2. Architecture-level parameters for the Mars Ascent Taxi. 

Quantity	Adopted value	Mission role
Crew	2 astronauts	Surface-to-orbit transport only
Design ascent ΔV	4.5-5.0 km/s	Includes gravity, steering, targeting, and rendezvous margins
Surface mass	8-12 t	Taxi, EDL hardware, ascent propellant, and surface support
Mass reaching orbit	1.5-2.5 t	Crew capsule and docking element
Primary landing requirement	1-3 km from crew	Relative navigation to the crew-lander beacon
Surface mobility requirement	At least 10 km	Provides tolerance to landing dispersion
Reserve system	Second taxi in Mars orbit	Independent landing opportunity if the primary fails

4.3. Periapsis-Centred Chemical Departure and the Oberth Benefit

After rendezvous and crew transfer, the ascent taxi is discarded. The pre-deployed return stack is placed in a highly elliptical Mars orbit with a representative periapsis altitude of 125 km. With Mars gravitational parameter ${\mu }_M$ and periapsis radius $r_p=R_M+h_p$, the parabolic periapsis speed is

$$v_{\mathrm{e}\mathrm{s}\mathrm{c},p}=\sqrt{{\displaystyle \frac{2{\mu }_M}{r_p}}}.$$

(4.1)

For ${\mu }_M=4.28284\times {10}^4$ km³ s⁻², $R_M$= 3396.2 km, and $h_p$= 125 km, this gives $v_{esc,p}$ ≃ 4.93 km s⁻¹. The periapsis speed on the required departure hyperbola is

$$v_{p,+}=\sqrt{v_{\infty ,M}^{,2}+{\displaystyle \frac{2{\mu }_M}{r_p}}}.$$

(4.2)

The impulsive lower bound for departure from a nearly parabolic staging orbit is therefore

$$\mathsf{\Delta }{V}_{\mathrm{O}\mathrm{b}\mathrm{e}\mathrm{r}\mathrm{t}\mathrm{h}}=v_{p,+}-v_{\mathrm{e}\mathrm{s}\mathrm{c},p}.$$

(4.3)

The adopted trajectory values, 9.586 km/s for Profiles A/C and 8.358 km/s for Profile B, include the small difference between the idealized periapsis estimate and the operational departure state. The propulsion design requirement is

$$\mathsf{\Delta }{V}_{\mathrm{d}\mathrm{e}\mathrm{s}\mathrm{i}\mathrm{g}\mathrm{n}}=1.05\hspace{0.17em}\mathsf{\Delta }{V}_{\mathrm{a}\mathrm{d}\mathrm{o}\mathrm{p}\mathrm{t}\mathrm{e}\mathrm{d}}.$$

(4.4)

The burns are centered as closely as practical on periapsis. This maximizes the energy gained per unit propellant and avoids the approximately 11 km/s impulse that would be required if the same departure began directly from a low circular Mars orbit.

4.4. Retained Earth-Return Spacecraft Mass

The mass accelerated onto the Earth-return trajectory must include the complete two-person spacecraft rather than only its pressure vessel and consumables. The retained mass adopted here is 14 t. It includes the Earth-entry capsule, 200-day consumables, environmental control, radiation and micrometeoroid protection, communications, power, reaction control, the empty internal propulsion tanks, the main engine, insulation, and integration margin.

Burke et al. adopted a consumables planning rate of 2.45 kg crewmember−1 day−1 for the crewed payload element of a short-stay Mars mission [11, PDF p. 11]. For two astronauts and 200 days, the corresponding mass is 0.98 t; applying the adopted 20% reserve gives approximately 1.2 t, as included in Table 4.3.

Table 4.3. Retained Earth-return spacecraft mass budget. 

Component	Mass	Included function
Earth-entry capsule	4.0 t	Pressure shell, seats, thermal protection, parachutes, and recovery equipment
Transit structure and interfaces	1.5 t	Pressure vessel, docking, MMOD protection, and structural attachments
ECLSS hardware and spares	1.0 t	Two-person environmental control and life support
200-day consumables	1.2 t	Food, oxygen, water allowance, packaging, and contingency
Power, avionics, and communications	0.9 t	Electrical system, navigation, command, and communications
Thermal and radiation protection	1.0 t	Cabin thermal control and storm-shelter allowance
RCS and correction capability	0.7 t	Attitude control, navigation correction, and residual propellant
Main engine and feed system	0.6 t	Internal return-stage propulsion hardware
Empty main tanks and insulation	1.6 t	LOX/LH2 tanks, supports, insulation, and retained cold-side hardware
Integration and growth margin	1.5 t	Cryogenic interfaces, redundancy, cabling, and mass growth
Total retained spacecraft	14.0 t	Mass after depletion of the internal return propellant

Table 4.3. Retained Earth-return spacecraft mass budget. 

Component	Mass	Included function
Earth-entry capsule	4.0 t	Pressure shell, seats, thermal protection, parachutes, and recovery equipment
Transit structure and interfaces	1.5 t	Pressure vessel, docking, MMOD protection, and structural attachments
ECLSS hardware and spares	1.0 t	Two-person environmental control and life support
200-day consumables	1.2 t	Food, oxygen, water allowance, packaging, and contingency
Power, avionics, and communications	0.9 t	Electrical system, navigation, command, and communications
Thermal and radiation protection	1.0 t	Cabin thermal control and storm-shelter allowance
RCS and correction capability	0.7 t	Attitude control, navigation correction, and residual propellant
Main engine and feed system	0.6 t	Internal return-stage propulsion hardware
Empty main tanks and insulation	1.6 t	LOX/LH2 tanks, supports, insulation, and retained cold-side hardware
Integration and growth margin	1.5 t	Cryogenic interfaces, redundancy, cabling, and mass growth
Total retained spacecraft	14.0 t	Mass after depletion of the internal return propellant

The internal propulsion stage begins its burn at 42 t and retains the 14 t spacecraft after consuming 28 t of propellant. Its ideal velocity increment is calculated from the Tsiolkovsky equation [12],

$$\mathsf{\Delta }V=I_{sp}{g}_0\ln \left({\displaystyle \frac{m_0}{m_f}}\right).$$

(4.5)

Thus, for the fixed internal mass ratio $m_0/m_f$= 3,

$$\mathsf{\Delta }{V}_{\mathrm{i}\mathrm{n}\mathrm{t}}=I_{sp}{g}_0\ln \left(3\right).$$

(4.6)

This gives 4.848 km/s at 450 s and 5.387 km/s at 500 s. The tanks, feed system, engine, and insulation associated with this burn are already included in the 14 t retained mass; they are not treated as zero-mass propulsion hardware.

4.5. Three-Stage Chemical Return Stack

The 450 s case represents the high-performance LOX/LH2 chemical baseline. The 500 s case is retained as an optimistic effective-performance bound for the same staged architecture and quantifies the mass leverage of a 50 s increase in specific impulse. No nuclear-propulsion performance is used in either calculation.

Two disposable external stages provide the velocity increment not supplied by the internal stage. The remaining requirement is divided equally between them in the present screening design. For each external stage, the dry fraction is

$$ϵ={\displaystyle \frac{m_d}{m_d+m_p}}=0.12.$$

(4.7)

If P is the payload accelerated by one external stage and R is the stage burn mass ratio,

$$R=\exp \left({\displaystyle \frac{\mathsf{\Delta }{V}_s}{I_{sp}{g}_0}}\right),\hspace{1em}\hspace{1em}\mathsf{\Delta }{V}_s={\displaystyle \frac{\mathsf{\Delta }{V}_{\mathrm{d}\mathrm{e}\mathrm{s}\mathrm{i}\mathrm{g}\mathrm{n}}-\mathsf{\Delta }{V}_{\mathrm{i}\mathrm{n}\mathrm{t}}}{2}}.$$

(4.8)

The required wet mass of that stage follows directly from the burn mass balance:

$$m_s=P\hspace{0.17em}{\displaystyle \frac{R-1}{1-ϵR}}.$$

(4.9)

Equation (4.9) is applied recursively, first to the inner external stage carrying the 42 t main vehicle and then to the outer stage carrying the complete inner stack. The resulting masses are shown in Table 4.4.

Table 4.4. Three-stage Mars-departure mass for the two propulsion cases. 

Return family	${\mathit{I}}_{\mathit{s}\mathit{p}}$	Main vehicle	Inner stage	Outer stage	Total stack	Propellant
A/C: 135 days	450 s	42.0 t	43.2 t	87.7 t	172.9 t	143.2 t
A/C: 135 days	500 s	42.0 t	31.8 t	56.0 t	129.8 t	105.3 t
B: 140 days	450 s	42.0 t	29.0 t	48.9 t	119.9 t	96.6 t
B: 140 days	500 s	42.0 t	20.9 t	31.3 t	94.1 t	73.9 t

Table 4.4. Three-stage Mars-departure mass for the two propulsion cases. 

Return family	${\mathit{I}}_{\mathit{s}\mathit{p}}$	Main vehicle	Inner stage	Outer stage	Total stack	Propellant
A/C: 135 days	450 s	42.0 t	43.2 t	87.7 t	172.9 t	143.2 t
A/C: 135 days	500 s	42.0 t	31.8 t	56.0 t	129.8 t	105.3 t
B: 140 days	450 s	42.0 t	29.0 t	48.9 t	119.9 t	96.6 t
B: 140 days	500 s	42.0 t	20.9 t	31.3 t	94.1 t	73.9 t

At 450 s, the 135-day family requires 172.9 t in Mars orbit, while the 140-day Profile B requires 119.9 t. At 500 s, these values fall to 129.8 and 94.1 t, respectively. The difference between Profiles A/C and B is therefore preserved throughout the mass analysis; the three returns are not represented by one common propellant value.

The corresponding non-propellant masses, including the complete 14 t retained spacecraft and both empty external stages, are 29.7 t for A/C at 450 s, 24.5 t for A/C at 500 s, 23.3 t for B at 450 s, and 20.3 t for B at 500 s. Propellant and dry hardware therefore close independently in every tabulated case.

The 12% external-stage dry fraction includes tanks, engines, feed systems, structural attachments, insulation, and residual hardware. Increasing it to 15% raises the total mass, whereas a 10% stage would reduce it. The adopted 12% value is used consistently in the launch and volume calculations below.

4.6. Separate Starship Delivery and Mars-Orbit Assembly

The assembled Mars-departure mass is not a single Earth-launch payload. Each stage has an independent docking interface and is delivered during the pre-deployment campaign. SpaceX publishes a Starship design payload capacity of more than 100 t to orbit [16]. The return stack can therefore be divided at its natural stage interfaces, as shown in Table 4.5. A provisional allowance of 8-12 t per cargo flight is included for the deployment adapter, interplanetary power and communications, navigation, and Mars capture or delivery equipment.

Table 4.5. Two-flight delivery manifest for the return propulsion stack. 

Return family	${\mathit{I}}_{\mathit{s}\mathit{p}}$	Cargo flight 1	With delivery system	Cargo flight 2	With delivery system
A/C	450 s	Outer stage: 87.7 t	95.7-99.7 t	Inner + main: 85.2 t	93.2-97.2 t
A/C	500 s	Outer stage: 56.0 t	64.0-68.0 t	Inner + main: 73.8 t	81.8-85.8 t
B	450 s	External stages: 77.9 t	85.9-89.9 t	Main vehicle: 42.0 t	50.0-54.0 t
B	500 s	External stages: 52.1 t	60.1-64.1 t	Main vehicle: 42.0 t	50.0-54.0 t

Table 4.5. Two-flight delivery manifest for the return propulsion stack. 

Return family	${\mathit{I}}_{\mathit{s}\mathit{p}}$	Cargo flight 1	With delivery system	Cargo flight 2	With delivery system
A/C	450 s	Outer stage: 87.7 t	95.7-99.7 t	Inner + main: 85.2 t	93.2-97.2 t
A/C	500 s	Outer stage: 56.0 t	64.0-68.0 t	Inner + main: 73.8 t	81.8-85.8 t
B	450 s	External stages: 77.9 t	85.9-89.9 t	Main vehicle: 42.0 t	50.0-54.0 t
B	500 s	External stages: 52.1 t	60.1-64.1 t	Main vehicle: 42.0 t	50.0-54.0 t

All four return-stack manifests remain below 100 t per cargo flight. The 450 s Profiles A/C case is the closest to the payload boundary and therefore provides the controlling launch condition. The primary and reserve Mars Ascent Taxis are not included in Table 4.5; they may use remaining manifest capacity where available or be assigned to an additional cargo mission. Each cargo Starship requires orbital refilling before trans-Mars injection. The return propellant remains reserved if Starship or a dedicated delivery bus performs the Mars capture and placement maneuver.

The modules rendezvous at low relative velocity in Mars orbit. Autonomous assembly is completed before the crew departs Earth, permitting repeated docking attempts, leak tests, electrical checks, propulsion-health assessment, and full-duration thermal verification.

4.6.1. Representative 2029 Predeployment Transfer

The predeployment architecture does not require the cargo vehicles to use the rapid 2031 crew trajectories. A conventional Earth–Mars cargo opportunity was therefore screened using the same DE441 planetary boundary states and zero-revolution, short-way Lambert formulation adopted in Chapter 2. A representative transfer departing on 1 January 2029 and arriving on 23 August 2029 has a time of flight of 234 days.

Table 4.6. Representative conventional transfer for the 2029 predeployment campaign. 

Quantity	Screening value
Earth departure	1 January 2029
Mars arrival	23 August 2029
Time of flight	234 days
Earth hyperbolic excess velocity	3.88 $\mathrm{k}\mathrm{m}{\mathrm{s}}^{-1}$
Characteristic energy $C_3$	15.08 $\mathrm{k}{\mathrm{m}}^2{\mathrm{s}}^{-2}$
Ideal departure increment from a 200 km circular orbit	3.89 $\mathrm{k}\mathrm{m},{\mathrm{s}}^{-1}$
Mars-arrival hyperbolic excess velocity	3.76 $\mathrm{k}\mathrm{m},{\mathrm{s}}^{-1}$

Table 4.6. Representative conventional transfer for the 2029 predeployment campaign. 

Quantity	Screening value
Earth departure	1 January 2029
Mars arrival	23 August 2029
Time of flight	234 days
Earth hyperbolic excess velocity	3.88 $\mathrm{k}\mathrm{m}{\mathrm{s}}^{-1}$
Characteristic energy $C_3$	15.08 $\mathrm{k}{\mathrm{m}}^2{\mathrm{s}}^{-2}$
Ideal departure increment from a 200 km circular orbit	3.89 $\mathrm{k}\mathrm{m},{\mathrm{s}}^{-1}$
Mars-arrival hyperbolic excess velocity	3.76 $\mathrm{k}\mathrm{m},{\mathrm{s}}^{-1}$

The cargo-launch energy is substantially lower than the $C_3$=140.3–284.9 $\mathrm{k}{\mathrm{m}}^2{\mathrm{s}}^{-2}$ values of the 2031 crewed departures. This confirms that the predeployment campaign can use a conventional transfer-energy regime. It does not, by itself, establish the payload delivered to the final Mars parking orbit, because Mars capture and orbital placement remain separate operations.

At a 125 km Mars periapsis, the minimum impulsive velocity change required only to convert the representative arrival hyperbola into a zero-energy captured orbit is approximately

$$\mathsf{\Delta }{v}_{\mathrm{c}\mathrm{a}\mathrm{p},\mathrm{m}\mathrm{i}\mathrm{n}}\sqrt{v_{\infty ,M}^{,2}+{\displaystyle \frac{2{\mu }_M}{r_p}}}\sqrt{{\displaystyle \frac{2{\mu }_M}{r_p}}}\approx 1.27\mathrm{k}\mathrm{m}{\mathrm{s}}^{-1}.$$

(4.10)

Additional velocity change would be required for circularization and transfer to the selected assembly orbit. The cargo carrier must therefore retain its own capture propellant, employ cargo aerocapture, or use a separately sized low-thrust delivery bus. The propellant reserved for the crewed Mars-departure stack is not consumed during cargo delivery. The values in this subsection are mission-screening Lambert results; finite-burn launch-vehicle performance, atmospheric capture, navigation, and Mars-orbit insertion require a dedicated cargo-delivery analysis.

4.7. Propellant Volume and Long-Duration Thermal Control

For a representative LOX/$\mathrm{L}{\mathrm{H}}_2$ oxidizer-to-fuel mass ratio of 6, the required liquid volume is

$$V_p={\displaystyle \frac{m_p/7}{{\rho }_{\mathrm{L}{\mathrm{H}}_2}}}+{\displaystyle \frac{6m_p/7}{{\rho }_{\mathrm{L}\mathrm{O}\mathrm{X}}}}$$

(4.11)

Using ${\rho }_{LH2}$= 70.8 kg m⁻³ and ${\rho }_{LOX}$ = 1141 kg m⁻³ [32], 100 t of LOX/$\mathrm{L}{\mathrm{H}}_2$ occupies approximately 277 m³ before ullage and tank-geometry allowances. Table 4.7 applies a 15% installed volume allowance.

Table 4.7. Propellant masses and installed tank-volume estimates. 

Return family	${\mathit{I}}_{\mathit{s}\mathit{p}}$	Propellant mass	Net liquid volume	Installed volume (+15%)
A/C	450 s	143.2 t	396.5 m3	456.0 m3
A/C	500 s	105.3 t	291.4 m3	335.2 m3
B	450 s	96.6 t	267.4 m3	307.5 m3
B	500 s	73.9 t	204.6 m3	235.3 m3

Table 4.7. Propellant masses and installed tank-volume estimates. 

Return family	${\mathit{I}}_{\mathit{s}\mathit{p}}$	Propellant mass	Net liquid volume	Installed volume (+15%)
A/C	450 s	143.2 t	396.5 m3	456.0 m3
A/C	500 s	105.3 t	291.4 m3	335.2 m3
B	450 s	96.6 t	267.4 m3	307.5 m3
B	500 s	73.9 t	204.6 m3	235.3 m3

The volume is compatible with wide-body cargo integration, particularly because the stages are launched separately. The dominant thermal challenge is liquid hydrogen storage from the 2029 delivery opportunity until Mars departure in 2031. The thermal system therefore combines solar shielding, multilayer insulation, radiative heat rejection, a broad-area 90 K shield, and a 20 K hydrogen cryocooler. NASA experiments have demonstrated the physical basis of zero-boil-off pressure control and high-capacity 20 K reverse-Brayton cooling [15,33,34].

Heat rejection to deep space is governed by

$${\dot{Q}}_{\mathrm{r}\mathrm{a}\mathrm{d}}=\epsilon \sigma A\left(T_{\mathrm{r}\mathrm{a}\mathrm{d}}^4-T_{\mathrm{s}\mathrm{p}\mathrm{a}\mathrm{c}\mathrm{e}}^4\right).$$

(4.12)

Radiative rejection is highly effective on the warm side of the refrigerator, where a 250-300 K radiator can reject hundreds of watts per square metre. Direct radiation becomes weak near 20 K, so passive cooling reduces but does not eliminate the active refrigeration requirement. An optimized design interval of 2-5 kW is adopted for the cryogenic system. At the mean Mars solar flux, this corresponds to approximately 30-60 m² of tracking photovoltaic array after efficiency and operational derating.

The solar arrays, cryocooler compressors, warm radiators, batteries, and power electronics are placed on a 0.9-1.9 t Mars Orbital Cryogenic Service Module. Cold-side tubing, insulation, and tank sensors remain with the propulsion stages. Before departure, the tanks are subcooled, the thermal and electrical umbilicals are disconnected, and the service module moves to a safe orbit. It is not accelerated onto the Earth-return trajectory. The same principle is applied to the ascent taxi: its surface solar-cooling pallet remains on Mars when the astronauts launch.

The 0.9–1.9 t interval is a system-level allowance rather than the mass of the cryocooler alone. It includes the cold-head and compressor assembly, warm-side radiators, photovoltaic arrays, batteries, power-conditioning electronics, structural support, thermal and electrical umbilicals, attitude control, communications, and integration margin. As a component-level reference, the 20 W/20 K reverse-Brayton system reported in [34] had an experimental assembly mass of approximately 336.9 kg while a projected flight-like implementation was estimated at approximately 106.3kg. The larger allowance adopted here accounts for the complete orbital thermal-control installation and its supporting spacecraft systems rather than linearly scaling the cryocooler mass alone.

The cryogenic service module is separately delivered during the predeployment campaign and is included in the cargo logistics rather than in the 14t Earth-return spacecraft. It remains connected while the return stages wait in Mars orbit, is disconnected only after final propellant conditioning, and remains at Mars when the crewed departure stack performs the Oberth maneuver. Consequently, its mass is not accelerated onto the 135- or 140-day return trajectory.

4.8. Trajectory Uncertainty and Propulsion Margin

The original CA21-anchored trajectory analysis obtained a representative hyperbolic-excess-velocity dispersion of approximately ${\sigma }_{v_{\infty }}$= 0.08 km s⁻¹ [1]. Differentiating Equation (4.2) gives the corresponding first-order periapsis-speed uncertainty:

$${\sigma }_{\mathsf{\Delta }V}\simeq {\displaystyle \frac{v_{\infty ,M}}{\sqrt{v_{\infty ,M}^{,2}+2{\mu }_M/r_p}}}\hspace{0.17em}{\sigma }_{v_{\infty }}.$$

(4.13)

Table 4.8. Propagation of return-trajectory uncertainty into the departure burn. 

Return family	${\mathit{v}}_{\mathit{\infty },\mathit{M}}$	${\mathit{\sigma }}_{{\mathit{v}}_{\mathit{\infty }}}$	${\mathit{\sigma }}_{\mathit{\Delta }\mathit{V}}$	Adopted 5% allowance
A/C: 135 days	13.60 km/s	0.08 km/s	0.075 km/s	0.479 km/s
B: 140 days	12.34 km/s	0.08 km/s	0.074 km/s	0.418 km/s

Table 4.8. Propagation of return-trajectory uncertainty into the departure burn. 

Return family	${\mathit{v}}_{\mathit{\infty },\mathit{M}}$	${\mathit{\sigma }}_{{\mathit{v}}_{\mathit{\infty }}}$	${\mathit{\sigma }}_{\mathit{\Delta }\mathit{V}}$	Adopted 5% allowance
A/C: 135 days	13.60 km/s	0.08 km/s	0.075 km/s	0.479 km/s
B: 140 days	12.34 km/s	0.08 km/s	0.074 km/s	0.418 km/s

The 5% propulsion allowance is more than five times the one-sigma trajectory contribution in both return families. Stage dry mass and cryogenic integration consequently dominate the mass uncertainty rather than the propagated ephemeris dispersion. These uncertainties are retained explicitly through the 12% external-stage dry fraction, the complete 14 t retained spacecraft, the separate delivery-system allowance, and the cryogenic-service-module allocation.

4.9. Mars-Departure Operational Sequence

-

During the 2029 opportunity, separate uncrewed cargo missions deliver the return spacecraft, external chemical stages, primary Mars Ascent Taxi, reserve taxi, and cryogenic service equipment.

-

The propulsion modules rendezvous and are assembled in Mars orbit. Docking, leak, electrical, engine, propellant, guidance, and thermal tests are completed before the 2031 crew departure.

-

The return stack and both taxis remain connected to solar-powered thermal-control systems while waiting for the astronauts.

-

After the crew lands, the surface module transmits its measured coordinates and relative-navigation beacon.

-

The primary taxi disconnects from the orbital cooling platform and lands within the prescribed rover range. The reserve taxi remains in orbit until the primary vehicle is verified.

-

During the 14-, 35-, or 10-day surface interval, the taxi propellant is maintained by the detachable surface solar-cooling pallet.

-

At the end of the surface stay, the astronauts enter the taxi, ascend to Mars orbit, rendezvous with the return spacecraft, and transfer with the 200-day consumables reserve already aboard.

-

The taxi is discarded. The return stack is conditioned for the low-periapsis Oberth maneuver, and the orbital cryogenic service module is disconnected and left at Mars.

-

The outer stage burns near periapsis and is discarded. The inner stage then burns and is discarded. The main vehicle completes the injection burn and retains the 14 t Earth-return spacecraft.

-

Profiles A and C enter their common 135-day Mars-Earth trajectory; Profile B enters the lower-energy 140-day trajectory.

The resulting chemical architecture closes the Mars-departure sequence by dividing the complete stack among independently delivered modules. At $I_{sp}=$450 s, the assembled masses are 172.9 t for Profiles A/C and 119.9 t for Profile B. At $I_{sp}$= 500 s, they are reduced to 129.8 and 94.1 t. Separate delivery keeps every return-stack cargo manifest below the 100 t planning boundary, while the propulsion stages, ascent taxis, and thermal-control systems are verified at Mars before crew use.

5. Earth Arrival and Two-Pass Guided Entry

Earth arrival is treated as the final independent element of the pre-deployed return architecture. Profiles A and C share the 135-day return boundary and therefore have the same Earth-arrival condition. Profile B follows the distinct 140-day return and reaches Earth with a smaller hyperbolic excess velocity. In every case, the interplanetary habitation and propulsion hardware is discarded before atmospheric entry, and only a compact two-person capsule is recovered.

The atmospheric phase uses the physical sequence demonstrated by Orion skip-entry guidance: a first lifting pass removes most of the energy, the vehicle exits the sensible atmosphere on a bound trajectory, and a second entry completes deceleration before parachute deployment and ocean recovery. The CA21 return is more energetic than a lunar return, so the entry boundary is first reduced to 16.0 km/s by a small disposable braking stage carried within the 14 t spacecraft retained in Chapter 4. The resulting two-pass trajectory is then evaluated with a point-mass lifting-entry model and convective-plus-radiative thermal screening.

The analysis below keeps the trajectory uncertainty, the propulsion reserve, the capsule mass, and the atmospheric calculation in one ledger. The 500 s case is an effective-stage sensitivity only; no nuclear-thermal propulsion is introduced in this chapter.

5.1. Earth-Approach Boundary Conditions

At an atmospheric interface altitude of 125 km, the geocentric entry speed follows from the Earth-arrival hyperbolic excess velocity and the local gravitational potential [1,7,8,9,35]:

$$v_{EI}=\sqrt{v_{\infty ,E}^{,2}+{\displaystyle \frac{2{\mu }_E}{r_{EI}}}},\hspace{1em}\hspace{1em}{r}_{EI}=R_E+h_{EI}.$$

(5.1)

Using ${\mu }_E$= 398600.435436 km³/s², $R_E$= 6378.137 km, and $h_{EI}$ = 125 km gives a local escape speed of 11.0719 km/s. The specific kinetic-energy indicator and its first-order uncertainty are

$${\epsilon }_k={\displaystyle \frac{v_{EI}^{,2}}{2}},\hspace{1em}\hspace{1em}{\sigma }_{v_{EI}}={\displaystyle \frac{v_{\infty ,E}}{v_{EI}}}\hspace{0.17em}{\sigma }_{v_{\infty }},\hspace{1em}\hspace{1em}{\sigma }_{v_{\infty }}=0.08\mathrm{k}\mathrm{m}\hspace{0.17em}{\mathrm{s}}^{-1}.$$

(5.2)

Table 5.1. Earth-arrival conditions for the CA21-anchored return profiles. 

Profile	Mission chronology	${\mathit{v}}_{\mathit{\infty },\mathit{E}}$	${\mathit{v}}_{\mathit{E}\mathit{I}}$ at 125 km	${\mathit{\sigma }}_{{\mathit{v}}_{\mathit{E}\mathit{I}}}$	Specific energy	Relative to 11.2 km/s
A/C	56 + 35 + 135 / 86 + 10 + 135	15.1226 km/s	18.74245 km/s	±0.0645 km/s	175.64 MJ/kg	2.80
B	72 + 14 + 140	13.659 km/s	17.58282 km/s	±0.0621 km/s	154.58 MJ/kg	2.46

Table 5.1. Earth-arrival conditions for the CA21-anchored return profiles. 

Profile	Mission chronology	${\mathit{v}}_{\mathit{\infty },\mathit{E}}$	${\mathit{v}}_{\mathit{E}\mathit{I}}$ at 125 km	${\mathit{\sigma }}_{{\mathit{v}}_{\mathit{E}\mathit{I}}}$	Specific energy	Relative to 11.2 km/s
A/C	56 + 35 + 135 / 86 + 10 + 135	15.1226 km/s	18.74245 km/s	±0.0645 km/s	175.64 MJ/kg	2.80
B	72 + 14 + 140	13.659 km/s	17.58282 km/s	±0.0621 km/s	154.58 MJ/kg	2.46

An Orion-class lunar-return speed of approximately 11.2 km/s corresponds to 62.72 MJ/kg. The unmodified CA21 interface energies are therefore 2.80 times the lunar-return value for Profiles A/C and 2.46 times for Profile B. This comparison establishes the required energy class; it does not by itself determine the heat-shield mass because heating also depends on trajectory, atmospheric density, nose radius, ballistic coefficient, and lift control [26,35,36].

5.2. Recoverable Capsule and Deployable Aerodynamic Area

The recoverable element is limited to 4.0 t for two astronauts. This is an upper-bound design mass rather than the mass of the complete 135- or 140-day return spacecraft. The crew uses the larger transit volume during interplanetary cruise and occupies the capsule for the final approach, braking, entry, descent, and recovery sequence. The Apollo command module provides a useful mass-scale comparison: NASA documentation gives a diameter near 13 ft and a mass near 11,000 lb, approximately 5.0 t, for a three-person capsule [37].

Table 5.2. Screening mass budget for the two-person Earth-entry capsule. 

Capsule element	Mass	Function
Pressure shell and primary structure	1.10 t	Two-person pressure vessel, load path, and hatch
Deployable aeroshell and ablative TPS	1.20 t	High-area forebody, backshell protection, and deployment hardware
Parachutes, flotation, and recovery equipment	0.45 t	Drogue and main parachutes, flotation, beacons, and recovery fittings
Seats, restraints, pressure suits, and crew provisions	0.35 t	Human-load attenuation and final-entry provisions
Avionics, guidance, communications, and entry RCS	0.35 t	Closed-loop bank guidance, navigation, and attitude control
Batteries, short-duration ECLSS, and supplies	0.30 t	Independent operation through both atmospheric passages
Capsule-level growth allowance	0.25 t	Integration and mass-development reserve
Total recoverable capsule	4.00 t	Maximum mass delivered to ocean recovery

Table 5.2. Screening mass budget for the two-person Earth-entry capsule. 

Capsule element	Mass	Function
Pressure shell and primary structure	1.10 t	Two-person pressure vessel, load path, and hatch
Deployable aeroshell and ablative TPS	1.20 t	High-area forebody, backshell protection, and deployment hardware
Parachutes, flotation, and recovery equipment	0.45 t	Drogue and main parachutes, flotation, beacons, and recovery fittings
Seats, restraints, pressure suits, and crew provisions	0.35 t	Human-load attenuation and final-entry provisions
Avionics, guidance, communications, and entry RCS	0.35 t	Closed-loop bank guidance, navigation, and attitude control
Batteries, short-duration ECLSS, and supplies	0.30 t	Independent operation through both atmospheric passages
Capsule-level growth allowance	0.25 t	Integration and mass-development reserve
Total recoverable capsule	4.00 t	Maximum mass delivered to ocean recovery

The decisive atmospheric calculation previously used a 2.0 t vehicle behind a 5.0 m effective aerodynamic diameter. The 4.0 t capsule preserves the same ballistic coefficient by scaling the deployable diameter with the square root of mass:

$$\beta ={\displaystyle \frac{m}{C_{D}S}},\hspace{1em}\hspace{1em}S={\displaystyle \frac{\pi D^2}{4}},\hspace{1em}\hspace{1em}{D}_{4t}=D_{2t}\sqrt{{\displaystyle \frac{m_{4t}}{m_{2t}}}}=5.0\sqrt{2}=7.07\mathrm{m}.$$

(5.3)

For CD = 1.35, both configurations have β = 75.5 kg/m2. The 7.1 m outer diameter belongs to the deployable aerodynamic and thermal-protection system, not to the pressure capsule. It is far smaller than the 12-20 m concepts rejected during the architecture trade and represents an 18% diameter increase relative to the 6 m LOFTID flight article. LOFTID demonstrated deployable-area technology at a different entry condition and lift class; the present mid-lift crew system combines that packaging principle with an independently designed lifting moldline and extreme-entry TPS [24,25].

5.3. Earth-Braking Stage and Staged-Mass Sequence Within the Retained 14t Spacecraft

The atmospheric solution developed in the following sections begins at an Earth atmospheric-interface speed of $16.000\mathrm{k}\mathrm{m}{\mathrm{s}}^{-1}$. The local retrograde velocity increment required to establish this condition is

$$\mathsf{\Delta }{v}_b=v_{\mathrm{E}\mathrm{I}}-16.000\mathrm{k}\mathrm{m}{\mathrm{s}}^{-1}..$$

(5.4)

A design increment is obtained by adding 5% for burn execution and the propagated one-sigma trajectory contribution:

$$\mathsf{\Delta }{v}_{b,d}=1.05\mathsf{\Delta }{v}_b+{\sigma }_{v_{\mathrm{E}\mathrm{I}}}.$$

(5.5)

The 5% allowance also exceeds the increase obtained if the impulse is completed above the 125 km atmospheric interface. Moving the ideal burn point to an altitude of 1000 km adds approximately $0.069\mathrm{k}\mathrm{m}{\mathrm{s}}^{-1}$ for Profiles A/C and $0.043\mathrm{k}\mathrm{m}{\mathrm{s}}^{-1}$ for Profile B.

The retained $14.0\mathrm{t}$ mass introduced in Chapter 4 is the complete spacecraft leaving Mars and supporting the astronauts during the interplanetary return. It is not the mass subjected to the final Earth-braking maneuver. Before that maneuver, the astronauts enter and seal the $4.0\mathrm{t}$ recovery capsule. The disposable cruise/service section is then separated onto a controlled Earth-avoidance trajectory. This section contains the hardware required only during the Mars–Earth cruise, including the transit habitation interfaces, long-duration power and thermal-control equipment, cruise communications and navigation systems, correction and attitude-control hardware, expended Mars-departure propulsion equipment, empty tanks, structural and docking interfaces, and other equipment no longer required for Earth entry. The $4.0\mathrm{t}$ capsule retains the two astronauts and all equipment and supplies required for braking, atmospheric entry, parachute descent, ocean recovery, and post-landing survival.

For the controlling A/C case at $I_{sp}=450\mathrm{s}$, the disposable cruise/service allocation is $5.23\mathrm{t}$. This allocation includes the integration and growth allowance introduced in Table 4.3; that allowance is part of the fixed $14.0\mathrm{t}$ design envelope and is not an additional mass added to the spacecraft. In the reference architecture, hardware represented by this allowance is assigned to the disposable cruise/service section and is therefore separated before the Earth-braking burn. If subsequent hardware-level design assigns additional mass to the capsule or braking package, the propellant requirement must be recalculated. The separation itself produces no significant reduction in inertial velocity or orbital energy. Its purpose is to ensure that the braking propulsion system decelerates only the equipment required for atmospheric entry.

Table 5.3. Mass sequence from Mars departure to Earth atmospheric entry for the controlling A/C case at$I_{sp}=450s$

Mission event	Mass before event	Mass removed or consumed	Mass after event	Physical interpretation
Mars departure and interplanetary return	$14.00\mathrm{t}$	----	$14.00\mathrm{t}$	Complete return spacecraft
Cruise/service-section separation	$14.00\mathrm{t}$	$5.23\mathrm{t}$	$8.77\mathrm{t}$	Transit-only equipment placed on an Earth-avoidance trajectory
Retrograde braking maneuver	$8.77\mathrm{t}$	$4.27\mathrm{t}$	$4.50\mathrm{t}$	Propellant supplies the Earth-braking impulse
Empty braking-package separation	$4.50\mathrm{t}$	$0.50\mathrm{t}$	$4.00\mathrm{t}$	Engine, empty tanks and associated structure are discarded
Atmospheric entry and recovery	$4.00\mathrm{t}$	----	$4.00\mathrm{t}$	Two-person capsule entering the atmosphere and landing in the ocean

Table 5.3. Mass sequence from Mars departure to Earth atmospheric entry for the controlling A/C case at$I_{sp}=450s$

Mission event	Mass before event	Mass removed or consumed	Mass after event	Physical interpretation
Mars departure and interplanetary return	$14.00\mathrm{t}$	----	$14.00\mathrm{t}$	Complete return spacecraft
Cruise/service-section separation	$14.00\mathrm{t}$	$5.23\mathrm{t}$	$8.77\mathrm{t}$	Transit-only equipment placed on an Earth-avoidance trajectory
Retrograde braking maneuver	$8.77\mathrm{t}$	$4.27\mathrm{t}$	$4.50\mathrm{t}$	Propellant supplies the Earth-braking impulse
Empty braking-package separation	$4.50\mathrm{t}$	$0.50\mathrm{t}$	$4.00\mathrm{t}$	Engine, empty tanks and associated structure are discarded
Atmospheric entry and recovery	$4.00\mathrm{t}$	----	$4.00\mathrm{t}$	Two-person capsule entering the atmosphere and landing in the ocean

The mass identity for this controlling case is therefore

$14.00 t={5.23 t}_{\mathrm{c}\mathrm{r}\mathrm{u}\mathrm{i}\mathrm{s}\mathrm{e}/\mathrm{s}\mathrm{e}\mathrm{r}\mathrm{v}\mathrm{i}\mathrm{c}\mathrm{e}}+{4.27 t}_{\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{p}\mathrm{e}\mathrm{l}\mathrm{l}\mathrm{a}\mathrm{n}\mathrm{t}}+{0.50 t}_{\mathrm{b}\mathrm{r}\mathrm{a}\mathrm{k}\mathrm{i}\mathrm{n}\mathrm{g}\mathrm{d}\mathrm{r}\mathrm{y}}+{4.00 t}_{\mathrm{c}\mathrm{a}\mathrm{p}\mathrm{s}\mathrm{u}\mathrm{l}\mathrm{e}}$.

After separation of the $5.23\mathrm{t}$ cruise/service section, the entry capsule and a $0.5\mathrm{t}$ disposable engine-and-tank package form the final mass remaining after the braking burn. In the controlling A/C case at $I_{sp}=450\mathrm{s}$, the $0.5\mathrm{t}$ package corresponds to a 10.5% dry fraction relative to its loaded stage mass, close to the 12% external-stage screening value used in Chapter 4. The fixed $0.5\mathrm{t}$ allowance becomes progressively more conservative for cases requiring less braking propellant.

The reserved propellant follows from the rocket equation [12]:

$$m_{p,b}=\left(m_{\mathrm{c}\mathrm{a}\mathrm{p}}+m_{\mathrm{d}\mathrm{r}\mathrm{y},b}\right)\left[\exp \left({\displaystyle \frac{\mathsf{\Delta }{v}_{b,d}}{g_0{I}_{sp}}}\right)-1\right],\hspace{1em}\hspace{1em}{m}_{\mathrm{c}\mathrm{a}\mathrm{p}}=4.0\mathrm{t},\hspace{1em}\hspace{1em}{m}_{\mathrm{d}\mathrm{r}\mathrm{y},b}=0.5\mathrm{t}.$$

(5.6)

Table 5.4. Earth-braking mass closure for the 4 t capsule. 

Profile	${\mathit{I}}_{\mathit{s}\mathit{p}}$	Nominal $\mathsf{\Delta }{\mathit{v}}_{\mathit{b}}$	Design $\mathsf{\Delta }{\mathit{v}}_{\mathit{b},\mathit{d}}$	Braking propellant	Mass at beginning of burn	Cruise/service mass separated before burn
A/C	450s	2.742 $km{s}^{-1}$	$2.944$ $\mathrm{k}\mathrm{m}{\mathrm{s}}^{-1}$	4.27 t	8.77 t	5.23 t
A/C	500s	2.742 $km{s}^{-1}$	$2.944$ $\mathrm{k}\mathrm{m}{\mathrm{s}}^{-1}$	3.70 t	8.20 t	5.80 t
B	450s	1.583 $km{s}^{-1}$	$1.724$ $\mathrm{k}\mathrm{m}{\mathrm{s}}^{-1}$	2.15 t	6.65 t	7.35 t
B	500s	1.583 $km{s}^{-1}$	$1.724$ $\mathrm{k}\mathrm{m}{\mathrm{s}}^{-1}$	1.90 t	6.40 t	7.60 t

Table 5.4. Earth-braking mass closure for the 4 t capsule. 

Profile	${\mathit{I}}_{\mathit{s}\mathit{p}}$	Nominal $\mathsf{\Delta }{\mathit{v}}_{\mathit{b}}$	Design $\mathsf{\Delta }{\mathit{v}}_{\mathit{b},\mathit{d}}$	Braking propellant	Mass at beginning of burn	Cruise/service mass separated before burn
A/C	450s	2.742 $km{s}^{-1}$	$2.944$ $\mathrm{k}\mathrm{m}{\mathrm{s}}^{-1}$	4.27 t	8.77 t	5.23 t
A/C	500s	2.742 $km{s}^{-1}$	$2.944$ $\mathrm{k}\mathrm{m}{\mathrm{s}}^{-1}$	3.70 t	8.20 t	5.80 t
B	450s	1.583 $km{s}^{-1}$	$1.724$ $\mathrm{k}\mathrm{m}{\mathrm{s}}^{-1}$	2.15 t	6.65 t	7.35 t
B	500s	1.583 $km{s}^{-1}$	$1.724$ $\mathrm{k}\mathrm{m}{\mathrm{s}}^{-1}$	1.90 t	6.40 t	7.60 t

The controlling A/C case requires $4.27\mathrm{t}$ of braking propellant at $I_{sp}=450\mathrm{s}$ or $3.70\mathrm{t}$ at $I_{sp}=500\mathrm{s}$. Profile B requires only 2.15 or 1.90 t, respectively. In every case, the complete spacecraft leaves Mars with the same retained mass of 14.0 t. The difference is the division of that mass between the disposable cruise/service section and the Earth-braking system.

For Profiles A/C at $I_{sp}=450\mathrm{s}$, separation reduces the mass subjected to the braking maneuver from 14.0 to 8.77 t. Consuming the 4.27 t propellant then provides the design impulse of 2.944 $\mathrm{k}\mathrm{m}{\mathrm{s}}^{-1}$), reducing the atmospheric-interface speed from (18.742) to 16.000 $\mathrm{k}\mathrm{m}{\mathrm{s}}^{-1}$. The empty 0.5 t braking package is subsequently jettisoned, leaving only the 4.0 t capsule for the two-pass atmospheric-entry sequence. Thus, the propellant does not perform a fully propulsive Earth landing; it establishes the entry condition from which atmospheric drag, lift guidance, parachutes, and the recovery system complete the deceleration.

For a representative LOX/$\mathrm{L}{\mathrm{H}}_2$ oxidizer-to-fuel mass ratio of 6:1, the corresponding net liquid volumes are approximately 11.8, 10.2, 6.0, and 5.3 ${\mathrm{m}}^3$ for A/C at 450 s, A/C at 500 s, B at 450 s, and B at 500 s, respectively. A 15% ullage and installation allowance raises these values to approximately 13.6, 11.8, 6.9, and 6.1 ${\mathrm{m}}^3$. These volumes are small relative to the Mars-departure tanks analyzed in Chapter 4 and use the same insulation, sunshade, and active zero-boil-off thermal-control architecture during the interplanetary coast.

Immediately before braking, the crew completes capsule activation and verifies independent power, communications, environmental control, guidance, attitude control, thermal protection, and atmospheric-entry configuration. The cruise/service section is then separated and targeted away from the Earth-entry corridor. The high-thrust braking stage remains attached to the capsule through the retrograde impulse, is released afterward onto a safe destructive-entry or Earth-avoidance trajectory, and the 7.1 m aerodynamic system is placed in its entry configuration. The 4.0 t capsule then begins the first guided atmospheric pass at the 16.000 $\mathrm{k}\mathrm{m}{\mathrm{s}}^{-1}$ design boundary.

5.4. Point-Mass Lifting-Entry and Heating Model

The atmospheric calculation uses a planar, non-rotating point-mass model with bank-angle control. Drag and lift are written in terms of the ballistic coefficient and the commanded lift direction [17,19,35]:

$${\displaystyle \frac{D}{m}}={\displaystyle \frac{\rho v^2}{2\beta }},\hspace{1em}\hspace{1em}{\displaystyle \frac{L}{m}}=\left({\displaystyle \frac{L}{D}}\right){\displaystyle \frac{D}{m}},\hspace{1em}\hspace{1em}{\displaystyle \frac{L}{D}}=0.70.$$

(5.7)

$$\dot{r}=v\sin \gamma ,\hspace{1em}\hspace{1em}\dot{v}=-{\displaystyle \frac{D}{m}}-{\displaystyle \frac{{\mu }_E}{r^2}}\sin \gamma .$$

(5.8)

$$\dot{\gamma }={\displaystyle \frac{L\cos \sigma }{mv}}+\left({\displaystyle \frac{v}{r}}-{\displaystyle \frac{{\mu }_E}{v{r}^2}}\right)\cos \gamma ,$$

(5.9)

Here $\gamma$ is the flight-path angle and $\sigma$ is the bank angle. Both angles are expressed in radians in the differential equations and numerical integration; degree values are used only when reporting initial conditions or commanded orientations.

Density is represented by an exponential fit to the 75-125 km region of the U.S. Standard Atmosphere, with ${\rho }_0$= 1.225 kg/m³ and H = 7.2 km [38]:

$$\rho \left(h\right)={\rho }_0\exp \left(-{\displaystyle \frac{h}{H}}\right).$$

(5.10)

Convective stagnation heating is screened with the Sutton-Graves relation, using $k=1.83\mathrm{x}{10}^{-4}$ in SI units. Radiative heating is added by interpolation of the Sutton-Hartung equilibrium Earth-entry tables [26,39].

$${\dot{q}}_c=k\sqrt{{\displaystyle \frac{\rho }{R_n}}}{v}^3,\hspace{1em}\hspace{1em}\dot{q}={\dot{q}}_c+{\dot{q}}_r,\hspace{1em}\hspace{1em}Q={\int }_{t_0}^{t_f}\dot{q}\hspace{0.17em}dt.$$

(5.11)

Closed-loop bank guidance commands lift down during the initial penetration, modulates bank to control the energy-removal rate, and then commands lift up to exit the first pass on a bound ellipse. The second entry uses the same energy and range feedback to reach the parachute-deployment corridor. The numerical integration begins at $h_{EI}$ = 125 km, $v_{EI}$ = 16.000 km/s, and ${\gamma }_{EI}$ = -5.75 degrees.

5.5. Decisive Two-Pass Solution

The first pass reaches a minimum altitude of 78.21 km and removes enough energy to produce a bound Earth orbit. The exit speed is 10.239 km/s at the 125 km interface, and the recovered osculating orbit has an apogee approximately 32,100 km above Earth. The energy, angular momentum, eccentricity, and apogee are obtained from

$$\mathcal{E}={\displaystyle \frac{v^2}{2}}-{\displaystyle \frac{{\mu }_E}{r}},\hspace{1em}\hspace{1em}{h}_r=rv\cos \gamma ,\hspace{1em}\hspace{1em}e=\sqrt{1+{\displaystyle \frac{2\mathcal{E}{h}_r^2}{{\mu }_E^2}}},\hspace{1em}\hspace{1em}{r}_a=-{\displaystyle \frac{{\mu }_E}{2\mathcal{E}}}\left(1+e\right).$$

(5.12)

The reported acceleration is the magnitude of the aerodynamic load calculated by the planar point-mass model; it does not independently resolve the acceleration components in the capsule body axes. The crew couches are assumed to be reclined and oriented so that the dominant entry acceleration acts approximately in the $+G_x$, chest-to-back direction, for which short-duration human tolerance is greater than for acceleration directed along the spine. This convention is consistent with NASA’s Artemis human-tolerance assessment, which places the large majority of reentry acceleration in the $+G_x$ direction [46]. A six-degree-of-freedom vehicle and occupant analysis is required to determine the transient $G_x$, $G_y$, and $G_z$ components, couch angles, restraint loads, vibration environment, and the effects of off-nominal attitude motion.

The time from the first atmospheric exit to the intermediate apogee is approximately 4.7 h; the second atmospheric passage follows roughly 9.3 h after the first exit. This interval is short enough for independent capsule power and environmental control and long enough for navigation updates, thermal-state assessment, and recovery-area retargeting.

The trajectory in Table 5.5 was calculated for the 2 t, 5 m reference vehicle. Equation (5.3) gives the 4 t capsule the same β and L/D, so the point-mass acceleration and flight path are unchanged. The larger effective nose radius would reduce the Sutton-Graves convective term; no thermal credit is taken for that reduction, and the original 367 W/cm² peak and 60.73 kJ/cm² integrated load are retained for the 4 t design. With the 1.5 thermal allowance, the installed values remain below the cited HEEET peak-flux capability above 1500 W/cm2 and within its reported extreme integrated-load range of approximately 75-250 kJ/cm² [27,28].

Table 5.5. Two-pass guided-entry result at the common 16.000 km/s atmospheric boundary. 

Atmospheric phase	Entry / exit condition	Minimum altitude	Maximum load	Peak combined heating	Integrated heat
First lifting pass	16.000 → 10.239 km/s; bound exit	78.21 km	3.98 g	367 W/cm2	49.40 kJ/cm2
Second entry	Bound-orbit return → parachute corridor	Guidance controlled	4.27 g	62.8 W/cm2	11.33 kJ/cm2
Combined trajectory	Two atmospheric passages	—	4.27 g	367 W/cm2	60.73 kJ/cm2
Installed design value	1.5 x thermal allowance	—	6 g structural target	550 W/cm2	91 kJ/cm2

Table 5.5. Two-pass guided-entry result at the common 16.000 km/s atmospheric boundary. 

Atmospheric phase	Entry / exit condition	Minimum altitude	Maximum load	Peak combined heating	Integrated heat
First lifting pass	16.000 → 10.239 km/s; bound exit	78.21 km	3.98 g	367 W/cm2	49.40 kJ/cm2
Second entry	Bound-orbit return → parachute corridor	Guidance controlled	4.27 g	62.8 W/cm2	11.33 kJ/cm2
Combined trajectory	Two atmospheric passages	—	4.27 g	367 W/cm2	60.73 kJ/cm2
Installed design value	1.5 x thermal allowance	—	6 g structural target	550 W/cm2	91 kJ/cm2

A 3 m Orion-scale geometry with L/D near 0.3 produced approximately 9-19 g in the same screening model and was rejected. The acceptable result follows from the combination of mass reduction, a 7.1 m deployable area, L/D = 0.70, propulsive establishment of the 16 km/s boundary, and closed-loop lift modulation; no single element produces the result by itself.

5.6. Relation to the Orion/Artemis Skip Entry

Orion demonstrated closed-loop skip-entry guidance during Artemis I, and the same guidance topology forms part of the Artemis crew-return architecture [36,40]. Orion separates its service module, uses bank-controlled capsule lift to climb back toward space after the initial atmospheric penetration, and subsequently completes entry, parachute descent, and ocean recovery. The CA21 architecture adopts this operational sequence but does not adopt the Orion aerodynamic configuration or heat shield. Its atmospheric-interface speed of 16.000 $\mathrm{k}\mathrm{m}{\mathrm{s}}^{-1}$ remains substantially greater than the approximately $11.2\mathrm{k}\mathrm{m}{\mathrm{s}}^{-1}$ lunar-return condition. The CA21 vehicle therefore uses a smaller recoverable mass, a larger effective aerodynamic area, a greater (L/D), an independently sized extreme-entry thermal-protection system, and chemical pre-braking before the first atmospheric contact.

Table 5.6. Orion heritage and the CA21 Earth-arrival implementation. 

Characteristic	Orion/Artemis reference	CA21 return design
Atmospheric sequence	Guided skip followed by second entry and splashdown	Same two-pass physical sequence
Entry speed	Approximately 11.2 km/s lunar return	16.000 km/s after dedicated braking
Recoverable mass	Artemis II landing mass about 20,500 lb (9.3 t)	Maximum 4.0 t for two astronauts
Aerodynamic system	Low-lift 5.0 m-class rigid capsule	7.1 m effective deployable mid-lift aeroshell; L/D = 0.70
Primary first-pass purpose	Range control and landing-site targeting	Energy removal, Earth capture, and load management
Thermal system	Avcoat lunar-return heat shield	HEEET-class woven/ablative extreme-entry allocation

Table 5.6. Orion heritage and the CA21 Earth-arrival implementation. 

Characteristic	Orion/Artemis reference	CA21 return design
Atmospheric sequence	Guided skip followed by second entry and splashdown	Same two-pass physical sequence
Entry speed	Approximately 11.2 km/s lunar return	16.000 km/s after dedicated braking
Recoverable mass	Artemis II landing mass about 20,500 lb (9.3 t)	Maximum 4.0 t for two astronauts
Aerodynamic system	Low-lift 5.0 m-class rigid capsule	7.1 m effective deployable mid-lift aeroshell; L/D = 0.70
Primary first-pass purpose	Range control and landing-site targeting	Energy removal, Earth capture, and load management
Thermal system	Avcoat lunar-return heat shield	HEEET-class woven/ablative extreme-entry allocation

The difference between the two energy regimes can be quantified independently of the detailed heat-shield designs. For equal atmospheric density and nose radius, specific kinetic energy varies as $v^2$, while the Sutton–Graves convective-heating correlation varies as $v^3$. Consequently,

$${\displaystyle \frac{{\epsilon }_{k,\mathrm{C}\mathrm{A}21}}{{\epsilon }_{k,\mathrm{O}\mathrm{r}\mathrm{i}\mathrm{o}\mathrm{n}}}}{\left({\displaystyle \frac{16.0}{11.2}}\right)}^2=2.04 \mathrm{a}\mathrm{n}\mathrm{d} {\displaystyle \frac{{\dot{q}}_{c,\mathrm{C}\mathrm{A}21}}{{\dot{q}}_{c,\mathrm{O}\mathrm{r}\mathrm{i}\mathrm{o}\mathrm{n}}}}{\left({\displaystyle \frac{16.0}{11.2}}\right)}^3=2.92.$$

Table 5.7. Controlled same-density and same-nose-radius comparison of the lunar-return and CA21 entry boundaries. 

Quantity	Lunar-return reference	CA21 design boundary	CA21/reference ratio
Atmospheric-interface speed	11.2 $\mathrm{k}\mathrm{m}{\mathrm{s}}^{-1}$	16.0 $\mathrm{k}\mathrm{m},{\mathrm{s}}^{-1}$	1.43
Specific kinetic energy	62.72 $\mathrm{M}\mathrm{J}\mathrm{k}{\mathrm{g}}^{-1}$	128.00 $\mathrm{M}\mathrm{J}\mathrm{k}{\mathrm{g}}^{-1}$	2.04
Sutton–Graves convective-heating factor at equal $\rho$ and $R_n$	1.00	2.92	2.92
Entry system	Rigid low-lift Orion capsule	Deployable 7.1 m, (L/D=0.70) system	Not directly scalable
Thermal protection	Avcoat lunar-return TPS	Independently sized HEEET-class allocation	No heritage equivalence assumed

Table 5.7. Controlled same-density and same-nose-radius comparison of the lunar-return and CA21 entry boundaries. 

Quantity	Lunar-return reference	CA21 design boundary	CA21/reference ratio
Atmospheric-interface speed	11.2 $\mathrm{k}\mathrm{m}{\mathrm{s}}^{-1}$	16.0 $\mathrm{k}\mathrm{m},{\mathrm{s}}^{-1}$	1.43
Specific kinetic energy	62.72 $\mathrm{M}\mathrm{J}\mathrm{k}{\mathrm{g}}^{-1}$	128.00 $\mathrm{M}\mathrm{J}\mathrm{k}{\mathrm{g}}^{-1}$	2.04
Sutton–Graves convective-heating factor at equal $\rho$ and $R_n$	1.00	2.92	2.92
Entry system	Rigid low-lift Orion capsule	Deployable 7.1 m, (L/D=0.70) system	Not directly scalable
Thermal protection	Avcoat lunar-return TPS	Independently sized HEEET-class allocation	No heritage equivalence assumed

Radiative heating is not assigned a universal velocity-only scaling factor because it depends strongly on density, shock-layer temperature, gas chemistry, nose radius, and nonequilibrium effects. It is therefore evaluated separately in the CA21 calculation through interpolation of the Sutton–Hartung equilibrium radiative-heating tables [39]. The calculated CA21 peak of 367 $\mathrm{W}\mathrm{c}{\mathrm{m}}^{-2}$ is a combined convective-plus-radiative screening result for the selected trajectory, not an extrapolation of Orion flight performance.

The Orion comparison therefore supplies heritage only for service-module separation, bank-controlled skip guidance, the multi-pass operational sequence, navigation updates between atmospheric passages, parachute deployment, and ocean recovery. It does not provide direct thermal-protection or aerodynamic qualification for the CA21 capsule. Qualification of the CA21 system requires its own high-enthalpy ground testing, aerothermal analysis, material-response modeling, deployment demonstration, and flight validation at progressively increasing entry energies.

5.7. Entry Uncertainty and Installed Margins

The original ±0.08 km/s excess-velocity envelope becomes ±0.0645 km/s at the A/C interface and ±0.0621 km/s for B through Eq. (5.2). These contributions are included explicitly in the design braking increments of Table 5.3. Onboard radiometric and optical navigation controls the engine cutoff to the 16.000 km/s atmospheric target, so the atmospheric solution is not required to absorb the complete uncorrected Lambert dispersion.

Atmospheric density dispersion is treated as a shift of the guidance altitude schedule. For a density scale factor fρ, the equivalent shift in an exponential atmosphere is

$$\mathsf{\Delta }{h}_{\rho }=H{\ln f}_{\rho }.$$

(5.13)

For fρ = 0.70-1.30 and H = 7.2 km, the commanded schedule moves by -2.57 to +1.89 km. This preserves approximately the same density, dynamic-pressure, and heating history while bank guidance corrects the remaining energy and range error. The installed 6 g structural target exceeds the computed 4.27 g maximum by 40%, and the 1.5 thermal allowance raises the required peak-flux and integrated-load capabilities to 550 W/cm² and 91 kJ/cm², respectively.

5.8. Earth-Arrival Operational Sequence

-

Earth-based tracking and onboard navigation refine the incoming hyperbola and select the atmospheric corridor.

-

The two astronauts transfer from the interplanetary habitation section into the 4 t entry capsule and verify independent power, life support, guidance, communications, parachutes, and flotation systems.

-

The spent cruise/service section is separated onto a controlled Earth-miss or designated destructive-disposal trajectory.

-

The capsule and disposable braking stage perform the retrograde burn, using the profile- and Isp-specific propellant allocation in Table 5.3 and targeting 16.000 km/s at 125 km altitude.

-

The empty 0.5 t braking stage separates; the deployable 7.1 m aerodynamic system is confirmed in its entry configuration.

-

The first guided atmospheric pass begins at ${\gamma }_{EI}$ = -5.75 degrees, remains below 3.98 g, and exits at 10.239 km/s on a bound orbit with an apogee near 32,100 km.

-

During the approximately 9.3 h interval between atmospheric passages, the capsule updates navigation, evaluates TPS and cabin state, and retargets the recovery footprint.

-

The second guided entry completes atmospheric deceleration with a calculated maximum load of 4.27 g.

-

Drogue and main parachutes deploy after the hypersonic and supersonic phases, followed by ocean splashdown, flotation, beacon activation, and crew recovery.

6. Advanced Propulsion and Mission-Growth Options

The chemical architectures developed in Chapters 2-5 establish the reference mission without requiring nuclear propulsion. Advanced propulsion is introduced here as a mass-reduction and robustness option, not as a correction to the Lambert trajectories and not as an unstated assumption in the preceding chapters. The analysis concentrates on nuclear thermal propulsion (NTP) at Isp = 800 s and 900 s because it combines substantially higher exhaust velocity than chemical propulsion with the high thrust required for a short periapsis-centered Oberth maneuver [41,42,43].

The benefit is strongly mission-phase dependent. NTP can reduce the residual Earth-departure stage of the demanding 56-day outbound case and can reduce the much larger predeployed Mars-departure stack for all three profiles. It is not assigned to Mars terminal descent or Earth atmospheric arrival, where the reactor, shielding, engine, and hydrogen-tank dry mass would be carried into phases already closed by aerodynamic braking and compact chemical systems. Nuclear-electric and solar-electric propulsion are evaluated separately as slow cargo and infrastructure technologies; their low thrust makes them unsuitable substitutes for the impulsive crew-departure burns considered here [42,44].

6.1. Architectural Boundary and Profile-Specific Use

Table 6.1 preserves the distinct chronology and energy of each profile. Profiles A and C are grouped only for Mars departure because they share the same 135-day Mars-Earth return. Profile B retains its separate 140-day return. On the outbound leg, Profiles B and C do not need the large residual stage used by Profile A in the Chapter 2 screening architecture; adding an NTP stage to those two cases would therefore introduce nuclear hardware without solving a demonstrated mass problem.

Table 6.1. Assignment of advanced propulsion within the three mission profiles. 

Profile	Chronology	Earth-departure role	Mars-departure role	Unchanged systems
A	56 + 35 + 135 days	Optional 3.963 km/s NTP residual stage	135-day NTP return stage	Mars EDL and Earth entry
B	72 + 14 + 140 days	No NTP stage in reference case	140-day NTP return stage	Mars EDL and Earth entry
C	86 + 10 + 135 days	No NTP stage in reference case	Same 135-day stage as A	Mars EDL and Earth entry

Table 6.1. Assignment of advanced propulsion within the three mission profiles. 

Profile	Chronology	Earth-departure role	Mars-departure role	Unchanged systems
A	56 + 35 + 135 days	Optional 3.963 km/s NTP residual stage	135-day NTP return stage	Mars EDL and Earth entry
B	72 + 14 + 140 days	No NTP stage in reference case	140-day NTP return stage	Mars EDL and Earth entry
C	86 + 10 + 135 days	No NTP stage in reference case	Same 135-day stage as A	Mars EDL and Earth entry

The predeployed return spacecraft still retains 14 t after Mars injection, including the 4 t Earth-entry capsule and the 200-day return consumables allocation. The NTP stage is external and disposable. It is delivered on the uncrewed 2029 cargo opportunity, checked out in Mars orbit, and discarded after the departure burn. The chemical Earth-braking stage of Chapter 5 therefore remains attached to the 14 t return spacecraft, while the NTP reactor does not approach Earth.

6.2. Nuclear-Thermal Stage Model

For an NTP engine, hydrogen is heated by the reactor and expelled through a nozzle. The effective exhaust velocity is related to specific impulse by

$$v_e=g_0{I}_{\mathrm{s}\mathrm{p}}.$$

(6.1)

The ideal mass ratio required for an assigned impulsive increment is

$$R={\displaystyle \frac{m_0}{m_f}}=\exp \left({\displaystyle \frac{\mathsf{\Delta }v}{g_0{I}_{\mathrm{s}\mathrm{p}}}}\right).$$

(6.2)

A fixed dry mass cannot be assumed before an engine, tank, shield, and support system have been selected. The stage is therefore represented by a structural coefficient ε, defined as dry stage mass divided by dry-plus-propellant stage mass. If P is the payload remaining after the disposable stage is discarded, the complete stage mass follows directly from the rocket equation:

$$m_s={\displaystyle \frac{P\left(R-1\right)}{1-\epsilon R}}.$$

(6.3)

$$m_{\mathrm{d}\mathrm{r}\mathrm{y}}=\epsilon m_s,\hspace{1em}\hspace{1em}{m}_{\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{p}}=\left(1-\epsilon \right)m_s,\hspace{1em}\hspace{1em}{m}_0=P+m_s.$$

(6.4)

A finite positive solution exists only when

$$\epsilon R<1\hspace{1em}\hspace{1em}⟺\hspace{1em}\hspace{1em}\epsilon <\exp \left(-{\displaystyle \frac{\mathsf{\Delta }v}{g_0{I}_{\mathrm{s}\mathrm{p}}}}\right).$$

(6.5)

Two structural coefficients are carried through the calculation. The 15% case is the nominal mission-screening value for a large expendable NTP stage; the 20% case tests the penalty of heavier tanks, reactor shielding, engine hardware, insulation, interfaces, residuals, and auxiliary systems. These values are design variables rather than claims about a completed engine. The resulting dry-mass allowances are reported explicitly so that any future hardware concept can be accepted or rejected by comparison with the available dry-mass budget.

6.3. Optional NTP Residual Stage for Profile A Earth Departure

Chapter 2 assigns the refueled Starship-class departure stage the principal Earth-escape work and leaves a residual 3.963 km/s for the detachable stage attached to Profile A. The chemical screening stacks are 27.000 t at $I_{sp}$ = 450 s and 24.681 t at $I_{sp}$= 500 s, including the 10 t Mars-arrival module. Applying Equations (6.2)-(6.4) to the same residual increment gives Table 6.2.

Table 6.2. Profile A residual Earth-departure stage at NTP specific impulse. 

${\mathit{I}}_{\mathit{s}\mathit{p}}$	Stage dry fraction	NTP dry mass	LH2 propellant	Initial stack	Installed LH2 volume
800 s	15%	1.312 t	7.434 t	18.746 t	121 m3
900 s	15%	1.111 t	6.298 t	17.409 t	102 m3
800 s	20%	1.966 t	7.864 t	19.830 t	128 m3
900 s	20%	1.651 t	6.603 t	18.254 t	107 m3

Table 6.2. Profile A residual Earth-departure stage at NTP specific impulse. 

${\mathit{I}}_{\mathit{s}\mathit{p}}$	Stage dry fraction	NTP dry mass	LH2 propellant	Initial stack	Installed LH2 volume
800 s	15%	1.312 t	7.434 t	18.746 t	121 m3
900 s	15%	1.111 t	6.298 t	17.409 t	102 m3
800 s	20%	1.966 t	7.864 t	19.830 t	128 m3
900 s	20%	1.651 t	6.603 t	18.254 t	107 m3

At the nominal 15% coefficient, the NTP residual stage reduces the Profile A stack to 18.746 t at 800 s and 17.409 t at 900 s. The corresponding reductions relative to the 27.000 t chemical 450 s case are 30.6% and 35.5%. The comparison does not by itself select NTP for Earth departure: the 1.11-1.97 t dry-mass allowances are small for a reactor-powered stage, and nuclear launch approval, shielding, abort disposition, ground safety, and crew integration would have to be resolved. The calculation therefore identifies a possible growth path while retaining the chemical Chapter 2 architecture as the reference.

6.4. NTP Closure of the Mars-Departure Mass Driver

Mars departure is the stronger application because the propulsion system is predeployed, the burn occurs far from Earth, and the chemical stacks of Chapter 4 are the largest mission masses. The design increments, already including the Chapter 4 five-percent allowance, are 10.065 km/s for the common 135-day return of Profiles A/C and 8.776 km/s for the 140-day return of Profile B.

Simply replacing the propellant in the Chapter 4 internal 42-to-14 t vehicle does not close every case. A fixed mass ratio of three provides only 8.619 km/s at 800 s and 9.696 km/s at 900 s. Thus, 900 s closes Profile B but remains 0.369 km/s below the A/C design requirement, while 800 s is below both design values. The NTP stage must consequently be sized from the trajectory requirement rather than forced into the former 42 t boundary.

Table 6.3. Nominal single-stage NTP Mars-departure solution (ε = 15%, payload after staging = 14 t). 

Profile	Design $\mathit{\Delta }\mathit{v}$	${\mathit{I}}_{\mathit{s}\mathit{p}}$	NTP dry mass	LH2 propellant	Assembled mass
A/C	10.065 km/s	800 s	11.93 t	67.61 t	93.54 t
A/C	10.065 km/s	900 s	8.42 t	47.71 t	70.13 t
B	8.776 km/s	800 s	8.00 t	45.33 t	67.34 t
B	8.776 km/s	900 s	6.01 t	34.08 t	54.10 t

Table 6.3. Nominal single-stage NTP Mars-departure solution (ε = 15%, payload after staging = 14 t). 

Profile	Design $\mathit{\Delta }\mathit{v}$	${\mathit{I}}_{\mathit{s}\mathit{p}}$	NTP dry mass	LH2 propellant	Assembled mass
A/C	10.065 km/s	800 s	11.93 t	67.61 t	93.54 t
A/C	10.065 km/s	900 s	8.42 t	47.71 t	70.13 t
B	8.776 km/s	800 s	8.00 t	45.33 t	67.34 t
B	8.776 km/s	900 s	6.01 t	34.08 t	54.10 t

All four nominal NTP cases remain below 100 t in assembled Mars-orbit mass: 93.54 and 70.13 t for Profiles A/C at 800 and 900 s, and 67.34 and 54.10 t for Profile B. Relative to the 450 s chemical stacks, the reductions are 45.9%, 59.4%, 43.8%, and 54.9%, respectively. Relative to the optimistic 500 s chemical cases, the reductions are 27.9%, 46.0%, 28.4%, and 42.5%. The comparison includes the same 14 t retained spacecraft in every case and therefore does not obtain the reduction by removing crew systems or return consumables.

6.5. Dry-Mass, Hydrogen-Volume, and Trajectory-Uncertainty Sensitivity

The stage result is nonlinear in dry fraction because the propulsion system must accelerate its own dry mass. Table 6.4 repeats the calculation at ε = 20% and also gives the mathematical upper dry-fraction boundary from Equation (6.5). The upper boundary is not a recommended design point: stage mass tends to infinity as ε approaches that value.

Table 6.4. Mars-departure sensitivity to a 20% NTP stage dry fraction. 

Profile	${\mathit{I}}_{\mathit{s}\mathit{p}}$	Closure limit on ε	NTP dry mass	LH2 propellant	Assembled mass
A/C	800 s	27.7%	26.21 t	104.83 t	145.03 t
A/C	900 s	32.0%	15.91 t	63.66 t	93.57 t
B	800 s	32.7%	14.88 t	59.50 t	88.38 t
B	900 s	37.0%	10.38 t	41.52 t	65.89 t

Table 6.4. Mars-departure sensitivity to a 20% NTP stage dry fraction. 

Profile	${\mathit{I}}_{\mathit{s}\mathit{p}}$	Closure limit on ε	NTP dry mass	LH2 propellant	Assembled mass
A/C	800 s	27.7%	26.21 t	104.83 t	145.03 t
A/C	900 s	32.0%	15.91 t	63.66 t	93.57 t
B	800 s	32.7%	14.88 t	59.50 t	88.38 t
B	900 s	37.0%	10.38 t	41.52 t	65.89 t

The heavier 20% stage still closes all four cases. The most demanding A/C, 800 s combination increases to 145.03 t; it must therefore be assembled or refuelled from more than one cargo delivery. The other three cases remain below 100 t. More importantly, Table 6.4 converts the unknown engine-and-tank mass into a testable requirement: a hardware design must remain below 27.7% dry fraction for A/C at 800 s, 32.0% for A/C at 900 s, 32.7% for B at 800 s, or 37.0% for B at 900 s to admit a one-stage ideal solution.

NTP reduces mass but replaces mixed LOX/LH2 propellant with a large volume of very-low-density hydrogen. Using ρ_LH2 = 70.8 kg/m3 and a 15% installed-volume allowance for ullage and tank accommodation, the required volume is

$$V_{\mathrm{L}\mathrm{H}2,\mathrm{i}\mathrm{n}\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{l}\mathrm{l}\mathrm{e}\mathrm{d}}=1.15\hspace{0.17em}{\displaystyle \frac{m_{\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{p}}}{{\rho }_{\mathrm{L}\mathrm{H}2}}}.$$

(6.6)

Table 6.5. Hardware mass and liquid-hydrogen volume for the nominal 15% NTP stage. 

Profile	${\mathit{I}}_{\mathit{s}\mathit{p}}$	Dry stage + 14 t spacecraft	LH2 mass	Installed LH2 volume
A/C	800 s	25.93 t	67.61 t	1098 m3
A/C	900 s	22.42 t	47.71 t	775 m3
B	800 s	22.00 t	45.33 t	736 m3
B	900 s	20.01 t	34.08 t	554 m3

Table 6.5. Hardware mass and liquid-hydrogen volume for the nominal 15% NTP stage. 

Profile	${\mathit{I}}_{\mathit{s}\mathit{p}}$	Dry stage + 14 t spacecraft	LH2 mass	Installed LH2 volume
A/C	800 s	25.93 t	67.61 t	1098 m3
A/C	900 s	22.42 t	47.71 t	775 m3
B	800 s	22.00 t	45.33 t	736 m3
B	900 s	20.01 t	34.08 t	554 m3

The 554-1098 m³ installed hydrogen volumes are the dominant integration constraint and should not be interpreted as a single-launch payload volume. A practical predeployment sequence separates dry hardware delivery from propellant delivery and refuels the NTP stage in Mars orbit. Solar arrays and radiators remain stowed during launch and deploy after orbital insertion. Multilayer insulation, sunshields, vapor-cooled shields, active cryocoolers, and continuous health monitoring are required for storage from the 2029 cargo opportunity to the 2031 crew departure [15,33,34]. Radiation to space provides the final heat-rejection path, but space is not an automatic zero-temperature sink; absorbed sunlight, Mars infrared radiation, engine conduction, and equipment heat must all be included in the thermal balance.

The Chapter 4 trajectory uncertainties are ${\sigma }_{\Delta v}$ = 0.075 km/s for Profiles A/C and 0.074 km/s for Profile B. Linearizing Equation (6.3) gives the corresponding assembled-mass sensitivity

$${\sigma }_{m_0}\simeq {\displaystyle \frac{P\left(1-\epsilon \right)R}{g_0{I}_{\mathrm{s}\mathrm{p}}{\left(1-\epsilon R\right)}^2}}\hspace{0.17em}{\sigma }_{\mathsf{\Delta }v}.$$

(6.7)

Equation (6.7) uses consistent velocity units; the numerical evaluation below converts the reported kilometre-per-second uncertainty to metres per second.

Table 6.6. Propagation of the Chapter 4 trajectory uncertainty into nominal NTP assembled mass. 

Profile	${\mathit{I}}_{\mathit{s}\mathit{p}}$	${\mathit{\sigma }}_{\mathit{\Delta }\mathit{v}}$	Nominal mass	${\mathit{\sigma }}_{\mathit{m}\mathit{a}\mathit{s}\mathit{s}}$
A/C	800 s	0.075 km/s	93.54 t	1.95 t
A/C	900 s	0.075 km/s	70.13 t	1.12 t
B	800 s	0.074 km/s	67.34 t	1.17 t
B	900 s	0.074 km/s	54.10 t	0.76 t

Table 6.6. Propagation of the Chapter 4 trajectory uncertainty into nominal NTP assembled mass. 

Profile	${\mathit{I}}_{\mathit{s}\mathit{p}}$	${\mathit{\sigma }}_{\mathit{\Delta }\mathit{v}}$	Nominal mass	${\mathit{\sigma }}_{\mathit{m}\mathit{a}\mathit{s}\mathit{s}}$
A/C	800 s	0.075 km/s	93.54 t	1.95 t
A/C	900 s	0.075 km/s	70.13 t	1.12 t
B	800 s	0.074 km/s	67.34 t	1.17 t
B	900 s	0.074 km/s	54.10 t	0.76 t

The one-standard-deviation mass responses are 1.95 and 1.12 t for Profiles A/C and 1.17 and 0.76 t for Profile B at 800 and 900 s. The five-percent design increments inherited from Chapter 4 are approximately 5.6-6.4 times the quoted one-standard-deviation velocity dispersions, so the uncertainty is not added a second time to Table 6.3-6.5. The final design must nevertheless replace the impulsive model with a finite-burn, n-body, guidance, navigation, and targeting simulation using the selected engine thrust and stage inertia.

6.6. Nuclear-Electric and Solar-Electric Roles

Nuclear-electric propulsion (NEP) and solar-electric propulsion can reach specific impulse values far above 900 s, but high specific impulse alone does not establish suitability for this mission. If electrical input power is $P_e$, thruster efficiency is η, and exhaust velocity is $v_e$, the ideal thrust is

$$F\simeq {\displaystyle \frac{2\eta P_e}{v_e}}={\displaystyle \frac{2\eta P_e}{g_0{I}_{\mathrm{s}\mathrm{p}}}},\hspace{1em}\hspace{1em}{t}_{\mathrm{b}\mathrm{u}\mathrm{r}\mathrm{n}}\simeq {\displaystyle \frac{m\hspace{0.17em}\mathsf{\Delta }v}{F}}.$$

(6.8)

For fixed power, increasing specific impulse reduces thrust and lengthens the acceleration interval. A low-thrust spiral would spread the maneuver over many orbital periods, weaken the periapsis Oberth benefit, complicate passage through Mars radiation environments, and alter the departure geometry used to obtain the 135- and 140-day return arcs. NEP is therefore not substituted for the crewed impulsive Mars-departure burn in the present profiles.

Electric propulsion remains valuable for the slower uncrewed system that makes the rapid crew mission possible. Candidate uses include delivery of the return spacecraft and empty propulsion hardware during the 2029 opportunity, transport of hydrogen tankers, relocation and phasing of cargo among Mars orbits, long-duration stationkeeping, and disposal of expended modules. A fission-electric power module can also support cryogenic refrigeration and spacecraft checkout while the return system waits for the crew. These roles exploit long available time and do not require a single high-thrust encounter or a momentum-exchange tether.

Table 6.7. Technology allocation by mission function. 

Mission function	Preferred propulsion or system	Reason
Profile A residual Earth departure	Chemical baseline; NTP growth option	High thrust; NTP mass benefit must exceed reactor-integration cost
Profiles B/C Earth departure	Chemical / refueled launch stage	No large residual stage in the reference screening case
Mars arrival and landing	Aerodynamic capture + chemical terminal systems	Avoid carrying reactor and hydrogen tanks into EDL
Mars departure	Chemical baseline; predeployed NTP growth option	Largest mass saving and compatible with periapsis Oberth burn
Earth arrival	Two-pass capsule entry + compact chemical braking	Reactor remains at Mars; Chapter 5 mass ledger is preserved
2029 cargo and orbital logistics	SEP or NEP tug	Long transfer time makes low thrust acceptable

Table 6.7. Technology allocation by mission function. 

Mission function	Preferred propulsion or system	Reason
Profile A residual Earth departure	Chemical baseline; NTP growth option	High thrust; NTP mass benefit must exceed reactor-integration cost
Profiles B/C Earth departure	Chemical / refueled launch stage	No large residual stage in the reference screening case
Mars arrival and landing	Aerodynamic capture + chemical terminal systems	Avoid carrying reactor and hydrogen tanks into EDL
Mars departure	Chemical baseline; predeployed NTP growth option	Largest mass saving and compatible with periapsis Oberth burn
Earth arrival	Two-pass capsule entry + compact chemical braking	Reactor remains at Mars; Chapter 5 mass ledger is preserved
2029 cargo and orbital logistics	SEP or NEP tug	Long transfer time makes low thrust acceptable

6.7. Integration and Verification Path

The advanced architecture preserves conventional rendezvous and docking. The crew reaches Mars orbit in the ascent taxi, transfers to the already checked return spacecraft, and performs standard leak, propulsion, navigation, and abort checks before committing to the departure sequence. There is no rotating tether, tip capture, or single-opportunity momentum-exchange event. The NTP system is an ordinary docked propulsion stage whose interfaces can be tested repeatedly before the crew arrives.

The Mars-departure NTP option also differs operationally from the optional Earth-departure application. The reactor is launched in a cold, nonoperating and subcritical configuration and is not activated in the terrestrial environment. Depending on the selected cargo-delivery architecture, initial operation would occur only after achievement of an approved safe orbit or after departure from the Earth vicinity. At Mars, the uncrewed stage is placed in its assembly orbit and undergoes reactor-control, propulsion, thermal, communications, and fault-response verification before the astronauts arrive. During crewed operations, separation distance, vehicle orientation, a structural boom, and shadow shielding place the habitat within the protected region behind the reactor and propellant tanks.

After the Mars-departure maneuver, the NTP stage is separated onto a stable Mars orbit or another approved disposal trajectory. Neither the reactor nor its hydrogen tanks enter the Earth-return corridor. The optional use of NTP for Profile A Earth departure is more demanding because it introduces reactor launch, Earth-orbit assembly, abort disposition, and crew-proximity requirements near Earth. For this reason, chemical propulsion remains the Earth-departure reference architecture, while NTP is treated as a more favorable mass-reduction option for the predeployed Mars-departure stage.

Before incorporation into the mission baseline, an NTP option must demonstrate four independent closure conditions. First, the measured dry hardware mass must fit within the budgets in Table 6.3 and 6.4. Second, full-duration hydrogen storage and orbital refuelling must be demonstrated at the required scale. Third, finite-burn trajectory propagation must show that the selected thrust level preserves the Oberth advantage and the Lambert departure state within the adopted margin. Fourth, reactor safety, launch approval, Mars-orbit operations, crew shielding, engine restart, stage disposal, and fault tolerance must be defined. Current ground-development and testing programs support continued evaluation of NTP, but they do not yet constitute a flight-qualified crew stage at 800-900 s [41,42,43,45].

The chemical system of Chapter 4 remains the reference that establishes mission closure with Isp = 450 s and 500 s. If a large expendable NTP stage achieves a 15% dry fraction, the Mars-departure stack falls to 93.54-70.13 t for Profiles A/C and 67.34-54.10 t for Profile B at 800-900 s.

At a 20% dry fraction every case still closes mathematically, although the A/C 800 s stack rises to 145.03 t. NTP therefore provides a quantitatively defined mass-reduction path, while hydrogen volume, long-duration cryogenic storage, and verified dry hardware mass become the controlling technology requirements.

7. Conclusions

This study has extended the CA21-anchored trajectory concept from a heliocentric boundary-value result to a preliminary end-to-end mission architecture. The three trajectories are not treated as interchangeable: Profile A preserves the original 56 + 35 + 135-day, 226-day round trip; Profile B redistributes the same total duration as 72 + 14 + 140 days; and Profile C uses 86 + 10 + 135 days for a 231-day mission. In every case, the early orbit of 2001 CA21 serves only as a geometric plane reference. It is neither a waypoint nor a gravity-assist or propulsion resource. The nominal Lambert solutions remain inside the adopted 5-degree plane corridor, and the controlled perturbation analysis preserves both their ranking and their architectural roles.

The Earth-departure analysis shows why the three profiles require different implementations. Profile A has an Earth hyperbolic excess velocity of 16.879 km/s and a characteristic energy of 284.890 km²/s². Under the adopted Starship-class pre-energization model, its remaining 3.963 km/s is supplied by a detachable stage, giving an initial Mars-bound stack of 27.000 t at 450 s or 24.681 t at 500 s. Profiles B and C require nearly identical Earth excess velocities of 11.843 and 11.844 km/s and therefore avoid this large residual stage in the reference screening case. All three profiles use the same 10 t two-person Mars-arrival module with 120 days of first-phase consumables; the independently predeployed return system is not carried in the 2031 crew launch.

The principal feasibility question for the original 56-day trajectory is Mars arrival. Its 16.638 km/s Mars excess velocity produces a 17.354 km/s atmospheric-interface speed before braking. The constructive reference sequence expends 2.9 t of the module’s 3.0 t propellant, separates 0.5 t of inert cruise and braking hardware, and enters with 6.6 t at 15.842 or 15.674 km/s for specific impulses of 450 or 500 s. A 6.0 m equivalent-drag-diameter lifting configuration with aerodynamic L/D not exceeding 1.7 produces captured trajectories at an 8 g modeled ceiling, approximately 11.4 kPa peak dynamic pressure, and three-times thermal screening values below 1.11 kW/cm² and 102 kJ/cm². The sampled velocity-density dispersion grid also remains captured, with less than 9.3 m/s required to raise periapsis. Profiles B and C close with only a 1.0 t pre-entry trim and 9.0 t entry mass; Profile C retains the largest thermal margin.

Mars departure is the dominant chemical mass driver, but it closes through predeployment and orbital assembly rather than by carrying the return spacecraft on the rapid outbound leg. The three-stage chemical stacks are 172.9 and 129.8 t for the common 135-day return of Profiles A and C at 450 and 500 s, and 119.9 and 94.1 t for the 140-day Profile B return. Each stack can be divided between two cargo manifests that remain below the adopted 100 t per-flight planning boundary, including the delivery-system allowance. The retained 14 t Earth-return spacecraft contains the 4 t recovery capsule and the independent 200-day consumables reserve. Primary and reserve Mars Ascent Taxis, the descent stage, and the return hardware are delivered and checked before the crew depends on them.

Earth arrival is closed by separating the recoverable capsule from the interplanetary cruise hardware and using trajectory-specific chemical pre-braking before atmospheric entry. The controlling 135-day return family requires 4.27 t of braking propellant at 450 s or 3.70 t at 500 s; Profile B requires 2.15 or 1.90 t. The 4 t capsule then enters at the common 16.000 km/s design boundary and performs two guided atmospheric passages. The point-mass solution reaches a 4.27 g maximum load, 367 W/cm² peak combined heating, and 60.73 kJ/cm² integrated heat, remaining within the installed 1.5-times thermal allowance. The sequence uses the same physical skip-entry principle as Orion while assigning the first pass primarily to energy removal and Earth capture.

The chemical architecture at specific impulses of 450 and 500 s is therefore the reference mission-closure result. Nuclear-thermal propulsion is not required to make the trajectories mathematically close, but it offers a defined growth path for the largest Mars-departure masses. At 800-900 s and a 15% stage dry fraction, the assembled NTP stacks fall to 93.54-70.13 t for Profiles A/C and 67.34-54.10 t for Profile B. Electric propulsion is better assigned to the slow uncrewed 2029 logistics, cargo relocation, stationkeeping, and cryogenic-service roles, where low thrust does not compromise the crewed periapsis Oberth maneuver.

The resulting conclusion is that the rapid trajectories identified in the original work are not excluded by first-order mission physics or mass bookkeeping. In particular, the original 56-day outbound result can be embedded in a coherent architecture by separating mission functions, predeploying the return and surface systems, concentrating high-thrust maneuvers near periapsis, and using the atmospheres of Mars and Earth as controlled energy-removal systems. This is a preliminary mission-level feasibility result rather than a flight-certified design. The next stage must replace the patched-conic and point-mass models with coupled n-body finite-burn optimization, covariance-based navigation, six-degree-of-freedom entry simulations, CFD and radiative-heating analysis, human-tolerance assessment, hardware-level stage design, and full cryogenic-storage demonstrations. Subject to those verification steps, the CA21-anchored family provides a physically structured basis for future crewed round trips to Mars lasting approximately 226-231 days.