Test of the Hypothesis for an Unknown Distant Massive Planet in the Solar System Applying Tisserand’s Criterion to a System of Long-Period Comets

This article presents the results of an analysis of Tisserand’s constant for 1389 long-period comets in relation to a hypothetical planet. A mechanism is proposed to apply Tisserand’s criterion for a relatively trans-Neptunian planet with a notable inclination and orbit eccentricity. In particular, the algorithm considers the planet’s heliocentric distance in the era of a clearly-defined transformational change in the cometary orbit. Thus, we carried out the corresponding calculations by simulating the planet motion plane. This study allows a comparative analysis of Tisserand constant values for proposed hypothetical planet parameters. The most notable result is for a planet at a proposed distance of 340 AU.