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arXiv · 1705.11091

Analytically calculated post-Keplerian range and range-rate perturbations: the solar Lense-Thirring effect and BepiColombo

Lorenzo Iorio
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Abstract

We analytically calculate the time series for the perturbations $Δρ(t),~Δ\dotρ(t)$ induced by a general disturbing acceleration $\boldsymbol{A}$ on the mutual range $ρ$ and range-rate $\dotρ$ of two test particles $\textrm{A},~\textrm{B}$ orbiting the same spinning body. We apply it to the general relativistic Lense-Thirring effect, due to the primary's spin $\boldsymbol{S}$, and the classical perturbation arising from its quadrupole mass moment $J_2$ for arbitrary orbital geometries and orientation of the source's symmetry axis $\boldsymbol{\hat{S}}$. The Earth-Mercury range and range-rate are nominally affected by the Sun's gravitomagnetic field to the $10~\textrm{m},~10^{-3}~\textrm{cm s}^{-1}$ level, respectively, during the extended phase (2026-2028) of the forthcoming BepiColombo mission to Mercury whose expected tracking accuracy is of the order of $\simeq 0.1~\textrm{m},~2\times 10^{-4}~\textrm{cm s}^{-1}$. The competing signatures due to the solar quadrupole $J_2^\odot$, if modelled at the $σ_{J_2^\odot}\simeq 10^{-9}$ level of the latest planetary ephemerides INPOP17a, are nearly 10 times smaller than the relativistic gravitomagnetic effects. The position and velocity vectors $\mathbf{r},~\mathbf{v}$ of Mercury and Earth are changed by the solar Lense-Thirring effect by about $10~\textrm{m},~1.5~\textrm{m}$ and $10^{-3}~\textrm{cm s}^{-1},~10^{-5}~\textrm{cm s}^{-1}$, respectively, over 2 yr; neglecting such shifts may have an impact on long-term integrations of the inner solar system dynamics over $\sim\textrm{Gyr}$ timescales.

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Lorenzo Iorio. 2018-02-26. Analytically calculated post-Keplerian range and range-rate perturbations: the solar Lense-Thirring effect and BepiColombo. https://doi.org/10.1093/mnras%2Fsty351

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