Moon’s Paradox: Why the Moon Is Not a Planet based on Desmos

1. Introduction

Gravitational systems frequently involve multiple competing influences rather than isolated two-body interactions. Desmos specifies a primitive scalar criterion that determines which interaction is causally dominant in multi-body systems. Structural classifications such as planet, satellite, binary companion, or Trojan object typically emerge only after detailed dynamical analysis.

The Earth–Moon–Sun system illustrates this limitation clearly: although the Sun exerts a larger Newtonian force on the Moon than the Earth does, the Moon remains an Earth satellite. Desmos theory addresses this conceptual gap by introducing a scalar binding-dominance functional that operates at the source level of causality.

2. Newtonian Gravity and Its Explanatory Domain

Newtonian gravity defines the pairwise force

$${\overrightarrow{F}}_{ij}^{\left(N\right)}=G{\displaystyle \frac{m_i{m}_j}{r_{ij}^2}} {\widehat{r}}_{ij},$$

and the equations of motion

$$m_i{\overrightarrow{a}}_i=\sum _{j\ne i}\mathrm{‍}{\overrightarrow{F}}_{ij}^{\left(N\right)}$$

This framework predicts trajectories and stability accurately. Desmos introduces a primitive scalar measure that ranks competing interactions in multi-body systems. Binding classifications therefore arise indirectly through post-dynamical reasoning.

3. Desmos Theory and the Interaction Functional

Desmos theory introduces a generalized interaction functional (Bond interaction)

$${\mathsf{\Delta }}_{ij}=k_B{\displaystyle \frac{E_i{E}_j}{r_{ij}^n}},$$

with the energy mapping

$$E_i=m_i{\varphi }_i, {\varphi }_i={\displaystyle \frac{G{M}_i}{r}}.$$

The quantity ${\mathsf{\Delta }}_{ij}$ is postulated as a primitive binding-dominance functional. It is not interpreted as a force or an energy, but as a scalar ordering measure that determines structural attachment independently of dynamical trajectories.

4. Newtonian Gravity as a Special Case of Desmos Theory

Newtonian gravity is recovered exactly as a special case of Desmos theory.

Imposing

$$n=2, k_B{\varphi }_i{\varphi }_j=G,$$

yields

$${\mathsf{\Delta }}_{ij}=G{\displaystyle \frac{m_i{m}_j}{r_{ij}^2}}=F_{ij}^{\left(N\right)}.$$

Thus, Newtonian gravity is embedded as a strict limiting case of Desmos theory.

5. The Moon Case

Although

$$F_{\mathrm{M}\mathrm{o}\mathrm{o}\mathrm{n}--\mathrm{S}\mathrm{u}\mathrm{n}}^{\left(N\right)}>F_{\mathrm{E}\mathrm{a}\mathrm{r}\mathrm{t}\mathrm{h}--\mathrm{M}\mathrm{o}\mathrm{o}\mathrm{n}}^{\left(N\right)},$$

Desmos theory yields

$${\mathsf{\Delta }}_{\mathrm{E}\mathrm{a}\mathrm{r}\mathrm{t}\mathrm{h}--\mathrm{M}\mathrm{o}\mathrm{o}\mathrm{n}}\gg {\mathsf{\Delta }}_{\mathrm{M}\mathrm{o}\mathrm{o}\mathrm{n}--\mathrm{S}\mathrm{u}\mathrm{n}}$$

classifying the Moon as Earth-bound at the interaction level. Newtonian mechanics remains correct but reaches this conclusion only indirectly.

6. Axiomatic Status of Binding Dominance

Axiom (Binding Dominance): In any gravitational system composed of more than two bodies, there exists a scalar interaction functional that orders pairwise bindings and determines structural attachment independently of dynamical trajectories.

Axiom (Desmos Functional):

$${\mathsf{\Delta }}_{ij}=k_B{\displaystyle \frac{E_i{E}_j}{r_{ij}^n}}, E_i=m_i{\varphi }_i.$$

Newtonian gravity emerges as a corollary under the inverse-square limit.

7. Desmos as a Connection Theory: A Holistic View of Causality

Desmos theory can be interpreted as a connection framework linking Newtonian gravity, General Relativity, and energetic (including quantum) descriptions within a unified causal structure.

7.1. Desmos to General Relativity

In the weak-field limit, the spacetime metric satisfies

$$g_{00}\approx -\left(1+{\displaystyle \frac{2\mathsf{\Phi }}{c^2}}\right),$$

where $\mathsf{\Phi }$ is the Newtonian gravitational potential. A relativistic potential proxy compatible with Desmos is defined as

$${\varphi }_{\mathrm{G}\mathrm{R}}=c^2\left({\displaystyle \frac{1}{\sqrt{-g_{00}}}}-1\right).$$

In the weak-field regime,

$${\varphi }_{\mathrm{G}\mathrm{R}}\approx -\mathsf{\Phi }={\displaystyle \frac{GM}{r}},$$

recovering the Desmos potential input. Substitution yields a GR-consistent Desmos interaction:

$${\mathsf{\Delta }}_{ij}^{\left(\mathrm{G}\mathrm{R}\right)}=k_B{\displaystyle \frac{\left(m_i{\varphi }_{\mathrm{G}\mathrm{R},i}\right)\left(m_j{\varphi }_{\mathrm{G}\mathrm{R},j}\right)}{r_{ij}^n}}.$$

7.2. Energetic and Quantum Correspondence

Since Desmos is explicitly formulated in terms of energy, a formal correspondence with quantized energy may be introduced:

$$E_i^{\left(\mathrm{D}\mathrm{e}\mathrm{s}\mathrm{m}\mathrm{o}\mathrm{s}\right)}=m_i{\varphi }_i ⟺ E_i^{\left(\mathrm{Q}\right)}=n_i\hslash {\omega }_i,$$

which implies

$$m_i{\varphi }_i=n_i\hslash {\omega }_i, n_i={\displaystyle \frac{m_i{\varphi }_i}{\hslash {\omega }_i}}$$

Substitution into the Desmos functional yields

$${\mathsf{\Delta }}_{ij}=k_B{\hslash }^2{\displaystyle \frac{n_i{n}_j{\omega }_i{\omega }_j}{r_{ij}^n}}.$$

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This correspondence does not imply quantum dynamics of macroscopic motion; it indicates that energetic discreteness may influence structural binding.

Desmos therefore acts as a causal and explanatory layer preceding dynamics, geometry, and quantization.

8. Conclusions

The Moon is not a planet orbiting the Sun because its dominant interaction, in the Desmos sense, is with the Earth. Desmos theory embeds Newtonian gravity, connects consistently with General Relativity, and admits a formal energetic correspondence, thereby functioning as a holistic causality and explanation framework. Detailed relativistic and cosmological implications are left for future work.