Celestial Mechanics and Dynamical Astronomy

, Volume 112, Issue 2, pp 117–130

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

Original Article


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 dX 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 (Mars), 250–450 au \(({0.7 m_{\oplus}})\), 3500–4500 au (4 mJup).


Planets Planet X Solar System perturbations 


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Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.Ministero dell’Istruzionedell’Università e della Ricerca (M.I.U.R.)-IstruzioneBariItaly
  2. 2.Fellow of the Royal Astronomical Society (F.R.A.S.)International Institute for Theoretical Physics and Advanced Mathematics, Einstein-GalileiPratoItaly

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