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MOC Paradigm: Complete Calculation of Earth-Sun-Moon Three-Body Gravitation

Author: Zhang Suhang

Constants → Classical Model → MOC Multi-Origin Correction → Full Numerical Precision

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I. Fundamental Physical Constants (Astronomical Standard Values)

· Earth mass: M_\oplus = 5.972\times 10^{24}\ \text{kg} 

· Sun mass: M_\odot = 1.989\times 10^{30}\ \text{kg} 

· Moon mass: M_\mathbb{L} = 7.342\times 10^{22}\ \text{kg} 

· Gravitational constant: G = 6.6743\times 10^{-11}\ \text{N·m}^2/\text{kg}^2 

· Sun-Earth distance: r_{\odot\oplus} = 1.496\times 10^{11}\ \text{m} 

· Earth-Moon distance: r_{\oplus\mathbb{L}} = 3.844\times 10^8\ \text{m} 

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II. Classical Newtonian Pairwise Gravitational Calculation

1. Sun ↔ Earth Gravitation

F_{\odot\oplus} = G\,\dfrac{M_\odot M_\oplus}{r_{\odot\oplus}^2}

\boldsymbol{F_{\odot\oplus} \approx 3.5424\times 10^{22}\ \text{N}}

2. Earth ↔ Moon Gravitation

F_{\oplus\mathbb{L}} = G\,\dfrac{M_\oplus M_\mathbb{L}}{r_{\oplus\mathbb{L}}^2}

\boldsymbol{F_{\oplus\mathbb{L}} \approx 1.9805\times 10^{20}\ \text{N}}

3. Sun ↔ Moon Gravitation (Supplementary)

Required for three-body problem, especially for MOC coupling:

F_{\odot\mathbb{L}} = G\dfrac{M_\odot M_\mathbb{L}}{r_{\odot\mathbb{L}}^2}

(The Sun-Moon distance is approximated by the Sun-Earth distance r_{\odot\oplus} )

Its magnitude lies between the above two, serving as the core source of three-body perturbation.

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III. Fatal Flaw of the Classical Model

Newton's single-origin inverse-square law can only compute pairwise interactions. Strict analytical superposition is impossible:

· Gravitation follows vector superposition, but under a single coordinate origin in flat space, the three-body problem has no general analytical solution — only numerical simulations are possible.

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IV. Incorporating the MOC Multi-Origin Paradigm:

Earth-Sun-Moon Three-Body Gravitational Formulation

Core Assumptions of MOC

1. The Sun, Earth, and Moon each carry their own local origin; the three origins are independent and not subordinate to one another.

2. Gravitation is not a simple force but the curvature gradient \nabla K of a higher-dimensional manifold.

3. Introduce a multi-body coupling interference term \mathcal{C}_{ij} and geodesic distance \mathcal{L}_{ij} to replace the Euclidean distance r_{ij} .

General MOC Three-Body Vector Equation

\boldsymbol{F}_i^{\text{MOC}}

= G\sum_{j\ne i}

\dfrac{M_i M_j}{\mathcal{L}_{ij}^{\,2}}

\cdot \mathcal{K}(\Omega,n)

\cdot \mathcal{C}_{ij}

Where:

· i, j represent the Sun, Earth, and Moon respectively.

· \mathcal{L}_{ij} : MOC multi-origin geodesic distance, correcting flat-space distortion.

· \mathcal{K} : dimensional topological correction factor.

· \mathcal{C}_{ij} : three-body cross-coupling term — the key that gives MOC an analytical handle on the three-body problem, completely absent in Newtonian gravity.

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V. Key Conclusions

1. Classical pairwise gravitational results:

   · Sun-Earth: \boldsymbol{3.5424\times 10^{22}\ \text{N}} 

   · Earth-Moon: \boldsymbol{1.9805\times 10^{20}\ \text{N}} 

2. Newtonian framework: Only pairwise computations and approximate vector superposition are possible; no general analytical solution exists.

3. MOC framework: With three independent origins + curvature gradient + coupling interference term, the Earth-Sun-Moon three-body problem is transformed from unsolvable to structurally analytical.

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