Constraints on the location of a putative distant massive body in the Solar System from recent planetary data
Abstract
We analytically work out the longterm variations caused on the motion of a planet orbiting a star by a very distant, pointlike massive object X. Apart from the semimajor axis a, all the other Keplerian osculating orbital elements experience longterm 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 longterm variation of the longitude of the perihelion {\varpi} to the latest empirical determinations of the corrections {∆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 d _{X} for the assumed masses of X quoted in brackets: 150200 au (Mars), 250450 au ({0.7 m_{oplus}}), 35004500 au (4 m _{Jup}).
 Publication:

Celestial Mechanics and Dynamical Astronomy
 Pub Date:
 February 2012
 DOI:
 10.1007/s1056901193867
 arXiv:
 arXiv:1101.2634
 Bibcode:
 2012CeMDA.112..117I
 Keywords:

 Planets;
 Planet X;
 Solar System perturbations;
 General Relativity and Quantum Cosmology;
 Astrophysics  Earth and Planetary Astrophysics;
 Physics  Space Physics
 EPrint:
 LaTex2e, 21 pages. 1 figure, 1 table. Uncited references deleted. Expired link removed and replaced with published references. At press in Celestial Mechanics and Dynamical Astronomy