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

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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 d X for the assumed masses of X quoted in brackets: 150–200 au (Mars), 250–450 au \(({0.7 m_{\oplus}})\), 3500–4500 au (4 m Jup).

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  1. Ministero dell’Istruzione, dell’Università e della Ricerca (M.I.U.R.)-Istruzione, Viale Unità di Italia 68, 70125, Bari, BA, Italy

    Lorenzo Iorio

  2. Fellow of the Royal Astronomical Society (F.R.A.S.), International Institute for Theoretical Physics and Advanced Mathematics, Einstein-Galilei, Via Santa Gonda 14, 59100, Prato, Italy

    Lorenzo Iorio

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Iorio, L. Constraints on the location of a putative distant massive body in the Solar System from recent planetary data. Celest Mech Dyn Astr 112, 117–130 (2012). https://doi.org/10.1007/s10569-011-9386-7

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