Preliminary constraints on the location of the recently hypothesized new planet of the Solar System from planetary orbital dynamics

Abstract

(Abridged) The trajectory of Saturn is nowadays known at essentially the same accuracy level of the inner planets due to the telemetry of the Cassini spacecraft. Thus, the expected perturbations $\dot\varpi,~\dot\Omega$ due to PX, for which we suggest the name Telisto in view of its remarkable distance, on the Kronian apsidal and draconitic orbital motions are theoretically investigated to tentatively constrain the configuration space of Telisto/Planet Nine itself. To this aim, we compare our predictions $\dot\varpi_\textrm{theo},~\dot\Omega_\textrm{theo}$ to the currently available experimental intervals of values $\Delta\dot\Omega_\textrm{obs},~\Delta\dot\varpi_\textrm{obs}$ determined by astronomers in the recent past without explicitly modeling and solving for PX itself. As such, our results, despite being plausible and in agreement to a large extent with other constraints released in the literature, should be regarded as proof-of-principle investigations aimed to encourage more accurate analyses in future. It turns out that the admissible region in its configuration space is moderately narrow as far as its position along its orbit, reckoned by the true anomaly $f_\textrm{X}$, is concerned, being concentrated around approximately $130~\textrm{deg}\lesssim f_\textrm{X}\lesssim 240~\textrm{deg}$. Telisto/Planet Nine is certainly far from its perihelion ($f_\textrm{X}=0~\textrm{deg}$), in agreement with other recent studies. The future analysis of the data from the ongoing New Horizons mission might be helpful in further constraining the scenario considered here for Telisto/Planet Nine. Its impact on the spaceraft's range over a multi-year span is investigated with a preliminary sensitivity analysis.