https://doi.org/10.1140/epjc/s10052-018-6011-x
Regular Article - Theoretical Physics
Is it possible to measure new general relativistic third-body effects on the orbit of Mercury with BepiColombo?
Ministero dell’Istruzione, dell’Università e della Ricerca (M.I.U.R.)-Istruzione, Viale Unità di Italia 68, 70125, Bari, BA, Italy
Received:
31
May
2018
Accepted:
18
June
2018
Published online:
5
July
2018
Recently, Will calculated an additional contribution to the Mercury’s precession of the longitude of perihelion 
of the order of 
(
). It is partly a direct consequence of certain 1pN third-body accelerations entering the planetary equations of motion, and partly an indirect, mixed effect due to the simultaneous interplay of the standard 1pN pointlike acceleration of the primary with the Newtonian N-body acceleration, to the quadrupole order, in the analytical calculation of the secular perihelion precession with the Gauss equations. We critically discuss the actual measurability of the mixed effects with respect to direct ones. The current uncertainties in either the magnitude of the Sun’s angular momentum 
and the orientation of its spin axis 
impact the precessions 
induced by the Sun’s quadrupole mass moment and angular momentum via the Lense–Thirring effect to a level which makes almost impossible to measure 
, even in the hypothesis that it comes entirely from the aforementioned 1pN third-body accelerations. On the other hand, from the point of view of the Lense–Thirring effect itself, the mismodeled quadrupolar precession 
due to the uncertainties in corresponds to a bias of 
of the relativistic one. The resulting simulated mismodeled range and range-rate times series of BepiColombo are at about the per cent level of the nominal gravitomagnetic ones.
An Erratum to this article is available online at https://doi.org/10.1140/epjc/s10052-022-11146-7.
© The Author(s) 2018
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
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