An Exploration of the Complex Orbital Motion of the Moon Using a Fully General-Relativistic, Post-Newtonian N-body Framework

We model the lunar orbit with a fully general-relativistic, post-Newtonian (PN) N-body framework to quantify the richness of the Moon’s dynamical spectrum. Beyond the canonical Sun–Earth–Moon three-body interactions, our integrations include Newtonian perturbations from the major planets—dominated by Jupiter—and figure effects by treating Earth and Moon as extended bodies. The PN equations of motion are solved with a seventh-order Runge–Kutta–Nyström integrator to produce high-precision Earth–Moon range time series. Fourier/power-spectrum analysis of the simulated range reveals a dense set of fundamental frequencies and forced sidebands arising from planetary perturbations, extended-body gravitation, and relativistic corrections. The results highlight how even modest non-Keplerian effects imprint measurable structure in the range spectrum, underscoring the need for PN dynamics and extended-body physics when interpreting precision lunar ranging and planning next-generation tests of gravity

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