A Novel Approach to Gravitation: Variational Interaction Theory

This work explores solutions to the Two-Body Problem in Celestial Mechanics through the lens of Variational Interaction Theory, a novel approach to gravitation. We begin by examining the fundamental physical entities in the universe and the structure of scalar fields and manipulator entities within this physical framework. We investigate three theories of gravity: Newton's Universal Law of Gravitation, Einstein's General Theory of Relativity, and Variational Interaction Theory, which introduces gravity as a variation in the density of scalar fields around bodies, particularly imperfect ones, providing a solid physical foundation for this work. We establish the equivalence in the uniform regions of imperfect bodies and hypothesize a Fundamental Dynamics Law, supported by mathematical proofs. Newton's Law is re-evaluated under conditions of low mass, large distances, and uniform variation in scalar field density using Variational Interaction Theory. We derive two critical parameters of the scalar field density function through continuity and differentiability analysis. By applying the variational interaction method, we solve the Two-Body Problem within the normal solar system, obtaining conic section solutions in the Newtonian region. We also derive solutions for the Two-Body Problem in two distinctly different regions around central bodies (the inner radius region and the outer radius region of imperfect bodies). The study further compares solutions obtained using Variational Interaction Theory with Einstein's General Relativistic solution for Mercury's Schwarzschild orbit. Finally, we address the Two-Body Problem in the inner radius regions of massive bodies, approximately demonstrating the stability of cores in stars and other celestial bodies.