The post-Newtonian motion around an oblate spheroid: the mixed orbital effects due to the Newtonian oblateness and the post-Newtonian mass monopole accelerations

Abstract

When a test particle moves about an oblate spheroid, it is acted upon, among other things, by two standard perturbing accelerations. One, of Newtonian origin, is due to the quadrupole mass moment $J_2$ of the orbited body. The other one, of the order of $\mathcal{O}\left(1/c^2\right)$, is caused by the static, post-Newtonian field arising solely from the mass of the central object. Both of them concur to induce \textrm{indirect}, \textrm{mixed} orbital effects of the order of $\mathcal{O}\left(J_2/c^2\right)$. They are of the same order of magnitude of the \textrm{direct} ones induced by the post-Newtonian acceleration arising in presence of an oblate source, not treated here. We calculate these less known features of motion in their full generality in terms of the osculating Keplerian orbital elements. Subtleties pertaining the correct calculation of their mixed net \textrm{precessions} per orbit to the full order of $\mathcal{O}\left(J_2/c^2\right)$ are elucidated. The obtained results hold for arbitrary orbital geometries and for any orientation of the body's spin axis $\hat{\mathbf{k}}$ in space. The method presented is completely general, and can be extended to any pair of post-Keplerian accelerations entering the equations of motion of the satellite, irrespectively of their physical nature.

arXiv commentLaTex2e, no Figures, no Tables, 20 pages. Version accepted for publication in General Relativity and Gravitation

References in corpus (9)

• General Relativity and Cosmology: Unsolved Questions and Future Directions
• On incorporating post-Newtonian effects in N-body dynamics
• Masses of the Main Asteroid Belt and the Kuiper Belt from the Motions of Planets and Spacecraft
• Fundamental Physics and General Relativity with the LARES and LAGEOS satellites
• Calculation of the Uncertainties in the Planetary Precessions with the Recent EPM2017 Ephemerides and their Use in Fundamental Physics and Beyond
• Post-Newtonian direct and mixed orbital effects due to the oblateness of the central body
• Post-Keplerian corrections to the orbital periods of a two-body system and their measurability
• On the mean anomaly and the mean longitude in tests of post-Newtonian gravity
• Analysis of the PPN Two-Body Problem Using Non-Osculating Orbital Elements

Cited by in corpus (1)

• Post-Newtonian orbital effects induced by the mass quadrupole and spin octupole moments of an axisymmetric body