In this paper, an attempt has been made to analyze the effect of spool port/ groove geometry on the pressure drop and chamber pressures which effect the performance parameters of the flow distributor valve. The work mainly involves formulation of detailed mathematical model of the valve and compare them on the same platform. For mathematical modelling, Matlab has been used. The size of the orifices is considered same throughout the model for better comparison. Initially the construction and functioning of flow distributor valve along with working principles of hydrostatic motor (Rotary Piston) is shown. Next shown the analytical analysis of area change and pressure drops due to different geometry of the spool valve ports. After that the computational fluid dynamics (CFD) analysis has been shown. A complete mathematical model to describe such flow distributor valve is developed after having a comprehensive knowledge of orifice characteristics, flow interactions based on valve geometry. Equations of flow through different orifices (fixed and variable area) of the valve have been developed based on the relationships obtained earlier.

The usual equation for both motions of a single planet around the sun and electrons in the deterministic Rutherford-Bohr atomic model is conservative with a singular potential at the origin. When a dissipation is added, new phenomena appear which were investigated thoroughly by R. Ortega and his co-authors between 2014 and 2017, in particular all solutions are bounded and tend to $0$ for $t$ large, some of them with asymptotically spiraling exponentially fast convergence to the center. We provide explicit estimates for the bounds in the general case that we refine under specific restrictions on the initial state, and we give a formal calculation which could be used to determine practically some special asymptotically spiraling orbits. Besides, a related model with exponentially damped central charge or mass gives some explicit exponentially decaying solutions which might help future investigations. An atomic contraction hypothesis related to the asymptotic dying off of solutions proven for the dissipative model might give a solution to some intriguing phenomena observed in paleontology, familiar electrical devices and high scale cosmology

The usual equation for both motions of a single planet around the sun and electrons in the deterministic Rutherford-Bohr atomic model is conservative with a singular potential at the origin. When a dissipation is added, new phenomena appear. It is shown that whenever the momentum is not zero, the moving particle does not reach the center in finite time and its displacement does not blow-up either, even in the classical context where arbitrarily large velocities are allowed. Moreover we prove that all bounded solutions tend to $0$ for $t$ large, and some formal calculations suggest the existence of special orbits with an asymptotically spiraling exponentially fast convergence to the center.

Orbital fractures are a common finding in facial trauma and serious complications may arise when orbital reconstruction is not done properly. The virtual planning can be used to manufacture patient-specific titanium orbital implants (PSI) through the process of selective laser melting. This method is currently considered the most accurate technique for orbital reconstruction. Even with the most accurate tehniques of bone reconstruction, there are still situations where enophthalmos is present after reconstruction which may be produced by intraorbital soft tissue atrophy. The aim of this paper was to evaluate the orbital soft tissue after postraumatic reconstruction of the orbital walls fractures. 10 patients diagnosed with unilateral orbital fractures were included in this study. A CT scan of the head region with thin slices (0.6mm) and soft and bone tissue windows was done. After data processing, the STL files were exported and the intraorbital fat tissue volume and the muscular tissue volume were masured. The volumes of affected orbit tissues were compared with the volumes of the healthy orbit tissues for each patient. Our findings conclude that a higher or a lower grade of fat and muscular tissue loss is present in all cases of reconstructed orbital fractures.

The purpose of this paper is to investigate the effect of a varying moment on the rotation angle of a large tethered satellite that is orbiting a planet. Two different types of orbits were investigated: a simple circular orbit and an elliptical orbit. Cases with zero and non-zero initial angular rotation velocity were investigated as well. This investigation will assist satellite docking missions. The large rigid tethered satellite is a futuristic concept, and this investigation is meant to assist possible docking missions to the satellite. To simplify the problem, the rotation is constrained to the orbital plane.

The electron of magnetic spin −1/2 is a Dirac fermion of a complex four-component spinor field. Though it is effectively addressed by relativistic quantum field theory, an intuitive form of the fermion still remains lacking. In this novel undertaking, the fermion is examined within the boundary posed by a recently proposed MP model of a hydrogen atom into 4D space-time. Such unorthodox process conceptually transforms the electron to the four-component spinor of non-abelian in both Euclidean and Minkowski space-times. Supplemented by several postulates, the relativistic and non-relativistic applications of the model are explored from an alternative perspective. The outcomes have important implications towards defining the spin-orbit coupling of particles from external light interactions. These findings, if considered could consolidate properly the fundamentals of the quantum state of matter from an alternative perspective using quantum field theory application and they warrant further investigations.

After proposing the Principle of Minimum Gravitational Potential, in a pursuit to find the explanation behind the correction to Newton's gravitational potential that accounts for Mercury's orbit, by finding all the higher-order corrections it is shown that the consequences of the existence of speed of light for gravity are not yet fully explored.

Distant Retrograde Orbits in the Earth-Moon system are gaining in popularity as stable `parking' orbits for various conceptual missions. To investigate the stability of potential Distant Retrograde Orbits, simulations were executed, with propagation running over a thirty-year period. Initial conditions for the vehicle state were limited such that the position and velocity vectors were in the Earth-Moon orbital plane, with the velocity oriented such that it would produce retrograde motion about Moon. The resulting trajectories were investigated for stability against the eccentric relative orbits of Earth and Moon in an environment that also included gravitational perturbations from Sun, Jupiter, and Venus, and the effects of radiation pressure. The results appear to indicate that stability is enhanced for certain resonant states within the Earth-Moon system.

Using the orbit decomposition, a new enumerative polynomial P(x) is introduced for abstract (simplicial) complexes of a given type, e.g., trees with a fixed number of vertices or triangulations of the torus with a fixed graph. The polynomial has the following three useful properties. (I) The value P(1) is equal to the total number of unlabeled complexes (of a given type). (II) The value of the derivative P'(1) is equal to the total number of nontrivial automorphisms when counted across all unlabeled complexes. (III) The integral of P(x) from 0 to 1 is equal to the total number of vertex-labeled complexes, divided by the order of the acting group. The enumerative polynomial P(x) is demonstrated for trees and then is applied to the triangulations of the torus with the vertex-labeled complete four-partite graph G = K_{2,2,2,2}, in which specific case P(x) = x^{31}. The graph G embeds in the torus as a triangulation, T(G). The automorphism group of G naturally acts on the set of triangulations of the torus with the vertex-labeled graph G. For the first time, by a combination of algebraic and symmetry techniques, all vertex-labeled triangulations of the torus (twelve in number) with the graph G are classified intelligently without using computing technology, in a uniform and systematic way. It is helpful to notice that the graph G can be converted to the Cayley graph of the quaternion group Q_8 with the three imaginary quaternions i, j, k as generators.

Orbit and clock products are used in real-time GNSS precise point positioning without knowing their quality. This study develops a new approach to detect orbit and clock errors through comparing geometry-free and geometry-based wide-lane ambiguities in PPP model. The reparameterization and estimation procedures of the geometry-free and geometry-based ambiguities are described in detail. The effects of orbit and clock errors on ambiguities are given in analytical expressions. The numerical similarity and differences of geometry-free and geometry-based wide-lane ambiguities are analyzed using different orbit and clock products. Furthermore, two types of typical errors in orbit and clock are simulated and their effects on wide-lane ambiguities are numerically produced and analyzed. The contribution discloses that the geometry-free and geometry-based wide-lane ambiguities are equivalent in terms of their formal errors. Although they are very close in terms of their estimates when the used orbit and clock for geometry-based ambiguities are precise enough, they are not the same, in particular, in the case that the used orbit and clock, as a combination, contain significant errors. It is discovered that the discrepancies of geometry-free and geometry-based wide-lane ambiguities are coincided with the actual time-variant errors in the used orbit and clock at the line-of-sight direction. This provides a quality index for real-time users to detect the errors in real-time orbit and clock products, which potentially improves the accuracy of positioning.

Satellite communication is expected to play a vital role in realizing Internet of Remote Things (IoRT) applications. This article considers an intelligent reflecting surface (IRS)-assisted downlink low Earth orbit (LEO) satellite communication network, where IRS provides additional reflective links to enhance the intended signal power. We aim to maximize the sum-rate of all the terrestrial users by jointly optimizing the satellite’s precoding matrix and IRS’s phase shifts. However, it is difficult to directly acquire the instantaneous channel state information (CSI) and optimal phase shifts of IRS due to the high mobility of LEO and the passive nature of reflective elements. Moreover, most conventional solution algorithms suffer from high computational complexity and are not applicable to these dynamic scenarios. A robust beamforming design based on graph attention networks (RBF-GAT) is proposed to establish a direct mapping from the received pilots and dynamic network topology to the satellite and IRS’s beamforming, which is trained offline using the unsupervised learning approach. The simulation results corroborate that the proposed RBF-GAT can achieve approximate performance compared to the upper bound with low complexity.

The concept of geostationary VHTS (Very High Throughput Satellites) is based on multibeam coverage with intensive frequency and polarization reuse in addition to the use of larger bandwidths in the feeder links, in order to provide high capacity satellite links at a reduced cost per Gbps in orbit. The dimensioning and design of satellite networks based on VHTS imposes the analysis of multiple trade-offs to achieve an optimal solution in terms of cost, capacity and figure of merit of the user terminal. In this paper, we propose a new method for sizing VHTS satellite networks based on an analytical expression of the forward link CINR (Carrier-to-Interference-plus-Noise Ratio) that is used to evaluate the trade-off of different combinations of system parameters. The proposed method considers both technical and commercial requirements as inputs including the constraints to achieve the optimum solution in terms of the user G/T, the number of beams and the system cost. The cost model includes both satellite and ground segments. Exemplary results are presented with feeder links using Q/V bands, DVB-S2X and transmission methods based on CCM and VCM (Constant and Variable Coding and Modulation, respectively) in two scenarios with different service areas.

For Interferometry Synthetic Aperture Radar (InSAR), the normal baseline is one of the main factors that affect the accuracy of the ground elevation. For Gaofen-3 (GF-3) InSAR processing, the poor accuracy of the real-time orbit determination resulting in a large baseline error, leads to the modulation error in azimuth and the slope error in range for timely Digital Elevation Model (DEM) generation. In order to address this problem, a baseline estimation method based on external DEM is proposed in this paper. Firstly, according to the characteristic of the real-time orbit of GF-3 images, orbit fitting is executed to remove the non-linear error factor. Secondly, the height errors are obtained in slant-range plane between Shuttle Radar Topography Mission (SRTM) DEM and the GF-3 generated DEM after orbit fitting. At the same time, the height errors are used to estimate the baseline error which has a linear variation. In this way, the orbit error can be calibrated by the estimated baseline error. Finally, DEM generation is performed by using the modified baseline and orbit. This procedure is implemented iteratively to achieve a higher accuracy DEM. Based on the results of GF-3 interferometric SAR data for Hebei, the effectiveness of the proposed algorithm is verified and the accuracy of GF-3 real-time DEM products can be improved extensively.

Based on measured astronomical position data of heavenly objects in the Solar System and other planetary systems, all bodies in space seem to move in some kind of elliptical motion with respect to each other. According to Kepler’s 1^st Law, “orbit of a planet with respect to the Sun is an ellipse, with the Sun at one of the two foci.” Orbit of the Moon with respect to Earth is also distinctly elliptical, but this ellipse has a varying eccentricity as the Moon comes closer to and goes farther away from the Earth in a harmonic style along a full cycle of this ellipse. In this paper, our research results are summarized, where it is first mathematically shown that the “distance between points around any two different circles in three dimensional space” is equivalent to the “distance of points around a vector ellipse to another fixed or moving point, as in two dimensional space”. What is done is equivalent to showing that bodies moving on two different circular orbits in space vector wise behave as if moving on an elliptical path with respect to each other, and virtually seeing each other as positioned at an instantaneously stationary point in space on their relative ecliptic plane, whether they are moving with the same angular velocity, or different but fixed angular velocities, or even with different and changing angular velocities with respect to their own centers of revolution. This mathematical revelation has the potential to lead to far reaching discoveries in physics, enabling more insight into forces of nature, with a formulation of a new fundamental model regarding the motions of bodies in the Universe, including the Sun, Planets, and Satellites in the Solar System and elsewhere, as well as at particle and subatomic level. Based on the demonstrated mathematical analysis, as they exhibit almost fixed elliptic orbits relative to one another over time, the assertion is made that the Sun, the Earth, and the Moon must each be revolving in their individual circular orbits of revolution in space. With this expectation, individual orbital parameters of the Sun, the Earth, and the Moon are calculated based on observed Earth to Sun and Earth to Moon distance data, also using analytical methods developed as part of this research to an approximation. This calculation and analysis process have revealed additional results aligned with observation, and this also supports our assertion that the Sun, the Earth, and the Moon must actually be revolving in individual circular orbits.

Pure orbital blowout fractures occur within the confines of the internal orbital wall. Restoration of orbital form and volume is paramount to prevent functional and esthetic impairment. The anatomical peculiarity of the orbit has encouraged surgeons to develop implants with customized features to restore its architecture. This has resulted in worldwide clinical demand for patient-specific implants (PSIs) designed to fit precisely in the patient's unique anatomy. Fused filament fabrication (FFF) three-dimensional (3D) printing technology has enabled the fabrication of implant-grade polymers such as Polyetheretherketone (PEEK), paving the way for a more sophisticated generation of biomaterials. This study evaluates the FFF 3D printed PEEK orbital mesh customized implants with a metric considering the relevant design, biomechanical, and morphological parameters. The performance of the implants is studied as a function of varying thicknesses and porous design constructs through a finite element (FE) based computational model and a decision matrix based statistical approach. The maximum stress values achieved in our results predict the high durability of the implants, and the maximum deformation values were under one-tenth of a millimeter (mm) domain in all the implant profile configurations. The circular patterned implant (0.9 mm) had the best performance score. The study demonstrates that compounding multi-design computational analysis with 3D printing can be beneficial for the optimal restoration of the orbital floor.

Based on measured astronomical position data of heavenly objects in the Solar System and other planetary systems, all bodies in space seem to move in some kind of elliptical motion with respect to each other, whereas objects follow parabolic escape orbits while moving away from Earth and bodies asserting a gravitational pull, and some comets move in near-hyperbolic orbits when they approach the Sun. In this article, it is first mathematically proven that the “distance between points on any two different circles in three-dimensional space” is equivalent to the “distance of points on a vector ellipse from another fixed or moving point, as in two-dimensional space.” Then, it is further mathematically demonstrated that “distance between points on any two different circles in any number of multiple dimensions” is equivalent to “distance of points on a vector ellipse from another fixed or moving point”. Finally, two special cases when the “distance between points on two different circles in multi-dimensional space” become mathematically equivalent to distances in “parabolic” or “near-hyperbolic” trajectories are investigated. Concepts of “vector ellipse”, “vector hyperbola”, and “vector parabola” are also mathematically defined. The mathematical basis derived in this Article is utilized in the book “Everyhing Is A Circle: A New Model For Orbits Of Bodies In The Universe” in asserting a new Circular Orbital Model for moving bodies in the Universe, leading to further insights in Astrophysics.

Signal-to-noise ratio (SNR) is an important index to evaluate radiation performance and image quality of optical imaging systems under low illumination background. Under the nighttime lighting condition, the illumination of remote sensing objects is low and varies greatly, usually ranging from several lux to tens of thousands of lux. Nighttime light remote sensing imaging requires high sensitivity and large dynamic range of detectors. Luojia 1-01 is the first professional nighttime light remote sensing satellite in the world. In this paper, we took the nighttime light remote sensing camera carried on the satellite as research object, proposed an in-orbit SNR test method based on time series images to overcome the problem of low spatial resolution. We first analyzed the process of luminous flux transmission between objects and satellite and established a radiative transfer model. By combining the parameters of large relative aperture optical system and high sensitivity CMOS device, we established SNR model and specially analyzed the effect of exposure time and quantization bits on SNR. Finally we used the proposed in-orbit test method to calculate SNR of lighting images acquired by satellite. And the measured result is in good agreement with the model predicted data. Under the condition of 10lx illumination, the SNR of typical objects can reach 27.02dB, which is much better than the requirement of 20dB for engineering application.

We examine here characteristics of electromagnetic waves that propagate through an unbounded space filled with a homogeneous isotropic chiral medium. Resulting characters are compared to those of the electromagnetic waves propagating through an achiral free space. To this goal, we form energy conservation laws for key bilinear parameters in a chiral case. Due to a nonzero medium chirality, conservation laws turn out to contain extra terms that are linked to the spin-orbit coupling, which is absent for an achiral case. As an example, we take a plane wave for achiral case to evaluate those bilinear parameters. Resultantly, the conservation laws for a chiral case are found to reveal inconsistencies among several bilinear parameters that constitute the con-servation laws , thereby prompting us to establish partial remedies for formulating proper wave-propagation problems.

To keep the global navigation satellite system functional during extreme conditions, it is a trend to employ autonomous navigation technology with inter-satellite link. As in the newly built BeiDou system (BDS-3) equipped with Ka-band inter-satellite links, every individual satellite has the ability of communicating and measuring distances among each other. The system also has less dependence on the ground stations and improved navigation performance. Because of the huge amount of measurement data, centralized data processing algorithm for orbit determination is suggested to be replaced by a distributed one in which each satellite in the constellation is required to finish a partial computation task. In current paper, the balanced extended Kalman filter algorithm for distributed orbit determination is proposed and compared with whole-constellation centralized extended Kalman filter, iterative cascade extended Kalman filter, and increasing measurement covariance extended Kalman filter. The proposed method demands a lower computation power however yields results with a relatively good accuracy.

A particular challenge in the conceptual design of direct-from orbit delivery systems is the seemingly well-known kinematics retain fallacies whose efficacies are reduced over great distances. Rotation about the local wing of an aerospace vehicle is almost never the pitch angle, yet modern application of kinematics often assumes such (with accompanying angular error). The same assertion is usually true about the nature of roll and yaw angles. Expressing motion in coordinates of rotating reference frames necessitates transformation between reference frames, and one such transformation is embodied in the Direction Cosine Matrices (DCM) formed by a sequence of three successive frame rotations. One of two ubiquitous sequences of three rotations used to construct the DCM involves first a rotation around the inertial z-axis, then intermediate y-axis, then finally about the body’s x-axis; a sequence commonly called the “aerospace sequence” or the a “3-2-1 rotation sequence”. The second ubiquitous sequence is the so-called “orbital sequence” or “3-1-3 rotation sequence” with rotations about the inertial z axis first, then about the intermediate x-axis, then finally about the body z-axis. This manuscript evaluates which sequence is the most advantageous for an object starting in space and then travels through the atmosphere to a target on the Earth’s surface. Six degrees of freedom of vehicle motion were simulated starting in orbit with a given thrust and commanded maneuver. The simulation performs all twelve possible rotation sequences (transforming inertial coordinates to body coordinates) with comparison by computational burden and error representing rotations about body axes (roll, pitch, and yaw respectively). Simulation precision is validated using the quaternion normalization condition indicating near machine precision (0.9\times{10}^{-15}) and reveals the so-called 132 rotation is the most accurate with an average error of 0.14° and a computational time of 0.013 seconds: resulting in a 97.95% increase in accuracy over the so-called 321 rotation and a 99.84% increase over the so-called 313 rotation.