The analysis delves into the equations governing the motion of the Earth and the Moon, emphasizing the necessity of constructing a locally inertial frame at their center of mass. The paper establishes that the center of mass of the Earth-Moon system is not subjected to acceleration in this setup, thus affirming the validity of Kepler's laws for their orbits. Furthermore, it addresses the challenges posed by singularities when deriving equations of motion in this context and discusses the implications of forces acting on test particles.
In constructing a freely falling center of mass frame for the Earth-Moon system, we find that the mutual orbit of both celestial bodies aligns with Kepler's laws.
The equation of motion for both the Earth and the Moon reveals the center of mass remains unaccelerated in this locally inertial frame, affirming the stability of the system.
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