Has Kronos devoured Planet Nine and its epigones?

Abstract

The Planet Nine hypothesis encompasses a body of about 5-8 Earth's masses whose orbital plane would be inclined to the ecliptic by one or two tens of degrees and whose perihelion distance would be as large as about 240-385 astronomical units. Recently, a couple of his epigones have appeared: Planet X and Planet Y. The former is a sort of minor version of Planet Nine in that all its physical and orbital parameters would be smaller. Instead, the latter would have a mass ranging from that of Mercury to the Earth's one and semimajor axis within 100-200 astronomical units. By using realistic upper bounds for the orbital precessions of Saturn, one can get insights on their position which, for Planet Nine, appears approximately confined around its aphelion. Planet Y can be just a Mercury-sized object at no less than about 125 astronomical units, while Planet X appears to be ruled out. Dedicated data reductions by modeling such perturber(s) are required to check the present conclusions, to be intended as hints of what might be detectable should planetary ephemerides include them. A probe on the same route of Voyager 1 would be perturbed by Planet Nine by about 20-40 km after some decades.