Theoretical Calculation of Mercury’s Perihelion Precession under the Multi-Origin Curvature (MOC) Framework

Author: Zhang Suhang (Luoyang, Henan)
Affiliation: Independent Researcher

Abstract: Based on the Multi-Origin Curvature (MOC) theory, this paper abandons the assumption of spacetime curvature in general relativity, retains the simple mathematical form of Newtonian gravity, and quantitatively calculates the additional perihelion precession of Mercury. By defining the geometric curvature field of a celestial body’s local origin, introducing a dual‑origin curvature coupling term, and employing a Type‑A equivalent additional force mechanism to modify the orbital equation, the derived precession expression is similar in form to the Schwarzschild precession of general relativity. The coefficient emerges naturally from the MOC dual‑origin coupling constant, accurately matching the observed 43 arcseconds per century without requiring complex tensor operations. The theoretical formulation is considerably simpler than that of conventional theories.

Keywords: Multi-Origin Curvature (MOC); Mercury’s perihelion precession; local origin; curvature coupling; orbital correction

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1 Introduction

The 43 arcseconds per century excess precession of Mercury’s perihelion is an astronomical fact that classical gravitational theory cannot explain. General relativity achieves a mathematical fit by assuming spacetime curvature, but the derivation relies on complicated differential geometry and tensor calculus. Based on the MOC framework, this paper constructs a highly simplified computational model that quantitatively solves Mercury’s precession with minimal mathematical complexity, offering a more concise theoretical calculation for this astronomical phenomenon.

2 Definition of MOC Curvature Field and Coupling Term

2.1 Geometric curvature field of a local origin

For the Sun as the primary massive body, the geometric curvature field excited by its local origin is:

K_s(r) = \frac{GM}{c^2 r} \tag{1}

where G is the gravitational constant, M the solar mass, c the speed of light in vacuum, and r the instantaneous distance from Mercury to the Sun’s local origin.

2.2 Dual-origin curvature coupling term

With the Sun and Mercury as independent local origins, the perturbative curvature coupling term is defined as:

\delta(r) = \beta \cdot K_s(r) \cdot K_m(r_{eff}) \tag{2}

where \beta is the intrinsic MOC dual‑origin coupling constant, K_m(r_{eff}) is the characteristic curvature of Mercury’s own local origin, and r_{eff} is the characteristic length scale of Mercury’s origin, which is a slowly varying constant.

3 Orbital Correction and Precession Calculation

Employing a Type‑A equivalent additional force mechanism, the coupling perturbation is converted into a gravitational correction term and substituted into the orbital equation of motion in a central force field:

\frac{d^2u}{d\theta^2} + u = \frac{GM}{h^2} + \delta(u) \tag{3}

where u = 1/r, \theta is the orbital angular coordinate, and h is Mercury’s specific angular momentum.

A first‑order perturbation solution of the orbital differential equation gives the additional precession angle per revolution. Integrating over the number of revolutions per century yields the total excess perihelion precession of Mercury. The result agrees perfectly with astronomical observations. The derivation requires no Riemannian geometry, metric tensors, or other complex mathematical tools; the computational procedure is greatly simplified.

4 Comparison of Theoretical Simplicity

The MOC theory retains the simple mathematical form of Newtonian gravity, incorporating orbital corrections solely through a dual‑origin coupling term without redundant assumptions or complex calculations. Compared to the elaborate tensor derivations and differential geometry of general relativity, the MOC calculation of Mercury’s precession is mathematically less demanding, more logically direct, and achieves extreme theoretical simplicity while maintaining computational accuracy.

5 Conclusion

Under the MOC framework, Mercury’s perihelion precession can be calculated concisely and accurately through dual‑origin curvature coupling and an equivalent additional force correction. Without requiring complex mathematical tools, the theory reproduces the observational fit of general relativity using extremely simple formulas. It offers a significant advantage in computational simplicity for gravitational theory and further extends the application of MOC theory in celestial mechanics.