Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2011-01-13
Celest.Mech.Dyn.Astron.112:117-130,2012
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
LaTex2e, 21 pages. 1 figure, 1 table. Uncited references deleted. Expired link removed and replaced with published references.
Scientific paper
10.1007/s10569-011-9386-7
We analytically work out the long-term variations caused on the motion of a planet orbiting a star by a very distant, pointlike massive object X. Apart from the semi-major axis a, all the other Keplerian osculating orbital elements experience long-term variations which are complicated functions of the orbital configurations of both the planet itself and of X. We infer constraints on the minimum distance d_X at which X may exist by comparing our prediction of the long-term variation of the longitude of the perihelion \varpi to the latest empirical determinations of the corrections \Delta\dot\varpi to the standard Newtonian/Einsteinian secular precessions of several solar system planets recently estimated by independent teams of astronomers. We obtain the following approximate lower bounds on dX for the assumed masses of X quoted in brackets: 150 - 200 au (m_Mars), 250 - 450 au (0.7 m_Earth), 3500 - 4500 au (4 m_Jup).
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