Constraints on the location of a putative distant massive body in the Solar System from recent planetary data

TL;DR

This paper derives constraints on the possible location of a distant massive object in the Solar System by analyzing its long-term gravitational effects on planetary orbits and comparing predictions with recent observational data.

Contribution

It provides analytical calculations of orbital variations caused by a distant massive body and sets lower bounds on its distance based on planetary perihelion precession data.

Findings

Lower bounds on the distance of the hypothetical body range from 150 to 4500 au depending on its mass.

The analysis constrains the presence of a distant massive object using planetary orbital data.

The method links orbital variations to the possible existence and location of unseen Solar System bodies.

Abstract

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).