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

Abstract

We analytically calculate the time series for the perturbations ∆ρ (t) , ∆ρ (t) induced by a general disturbing acceleration A on the mutual range ρ and range-rateρ of two test particles A, B orbiting the same spinning body. We apply it to the general relativistic Lense-Thirring 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 axisŜ. The Earth-Mercury range and range-rate are nominally affected by the Sun's gravitomagnetic field to the 10 m, 10 −3 cm s −1 level, respectively, during the extended phase (2026-2028) of the forthcoming Bepi-Colombo 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 , if modelled at the σ J ⊙ 2 ≃ 10 −9 level of the latest planetary ephemerides INPOP17a, are nearly 10 times smaller than the relativistic gravitomagnetic effects. The position and velocity vectors r, v of Mercury and Earth are changed by the solar Lense-Thirring 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 long-term integrations of the inner solar system dynamics over ∼ Gyr timescales.

Gravitoelectromagnetism, Solar System Tests, and Weak-Field Solutions in f (T,B) Gravity with Observational Constraints

“…Gravitomagnetic tests offer offer an ideal vehicle to probe the rotational behaviour of theories of gravity in their weak field limits [34][35][36][37][38][39]. In fact, gravitomagnetic effects are the result of mass currents appearing in the weak field limit of GR where the Einstein field equations take on a form reminiscent of Maxwell's equations [40] (and do not involve actual electromagnetic effects).…”

Monitoring Jovian Orbital Resonances of a Spacecraft: Classical and Relativistic Effects

“…Anyway, it is surprising, in a certain sense, that even in the local environment of the Solar System there are tests that have not been completed to the precision required. Particularly, the problem of the relativistic contributions to the precision of the longitude of the ascending node and the argument of the pericenter of bodies orbiting around a rotating planet, also known as Lense-Thirring effect, is still a controversial subject [47][48][49][50][51][52][53][54].…”

A Test of Gravitational Theories Including Torsion with the BepiColombo Radio Science Experiment

“…• the "relativity" parameters, which are the PPN parameters γ, β, α 1 , α 2 and the Nordtvedt parameter η, which characterize the expansion of the spacetime metric in the limit of slow motion and weak field (see, e.g., [8,18]) 1 , together with some related parameters, such as the oblateness of the Sun J 2 , the solar gravitational mass µ = GM (where G is the gravitational constant and M the mass of the Sun), possibly its time derivative ζ = 1/µ dµ /dt, and the solar angular momentum GS which appears in the Lense-Thirring effect on the orbit of Mercury (see, e.g., [19][20][21] for a general discussion; moreover, the topic has been addressed by the authors in the case of MORE in [22]).…”