Analytically calculated postKeplerian range and rangerate perturbations: the solar LenseThirring effect and BepiColombo
Abstract
We analytically calculate the time series for the perturbations Δ ρ \left(t\right), Δ \dot{ρ }\left(t\right) induced by a general disturbing acceleration A on the mutual range ρ and rangerate \dot{ρ } of two test particles A, B orbiting the same spinning body. We apply it to the general relativistic LenseThirring effect, due to the primary's spin S, and the classical perturbation arising from its quadrupole mass moment J_{2} for arbitrary orbital geometries and orientation of the source's symmetry axis {\hat{S}}. The EarthMercury range and rangerate are nominally affected by the Sun's gravitomagnetic field to the 10 m, 10^{3} cm s^{1} level, respectively, during the extended phase (20262028) of the forthcoming BepiColombo mission to Mercury whose expected tracking accuracy is of the order of ≃0.1 m, 2 × 10^{4} cm s^{1}. The competing signatures due to the solar quadrupole J_2^{\odot }, if modelled at the σ _{J_2^{\odot }}∼eq 10^{9} level of the latest planetary ephemerides INPOP17a, are nearly 10 times smaller than the relativistic gravitomagnetic effects. The position and velocity vectors \boldsymbol {r}, \boldsymbol {v} of Mercury and Earth are changed by the solar LenseThirring effect by about 10 m, 1.5 m and 10^{3} cm s^{1}, 10^{5} cm s^{1}, respectively, over 2 yr; neglecting such shifts may have an impact on longterm integrations of the inner Solar system dynamics over ∼Gyr timescales.
 Publication:

Monthly Notices of the Royal Astronomical Society
 Pub Date:
 May 2018
 DOI:
 10.1093/mnras/sty351
 arXiv:
 arXiv:1705.11091
 Bibcode:
 2018MNRAS.476.1811I
 Keywords:

 gravitation;
 space vehicles;
 celestial mechanics;
 Sun: rotation;
 General Relativity and Quantum Cosmology;
 Physics  Space Physics
 EPrint:
 LaTex2e, 29 pages, 8 figures, no tables. Matching the version at press in Monthly Notices of the Royal Astronomical Society (MNRAS)