Mass and orbit estimation of Planet X via a family of comets

The crucial assumption of this paper is, that the observed clustering of aphelion distances of intermediate-period comets in the 70–90 AU range is due to the influence of a tenth planet, called Planet X. We contribute to the search for Planet X a new and extended evaluation of a family of comets assumed to be Planet X's family of comets.By averaging the aphelion distances of comets that belong to a transplutonic family of comets, we get Planet X's semi-major axis a_x = (83.0 ± 5.3) AU. The comets' orbits also yield the upper limit of the planet's orbital eccentricity e_x - 0.019. If this planet played an important part in sending quasi-periodic comet showers to the inner solar system, we can calculate its orbital inclination i_x = 46 .1 ± 3 .6. By distributing all planets' masses into the heliocentric, torus-like zones, in which they were formed, we get the density distribution of the primordial solar nebula. Extrapolating this distribution we find the mass of the planet M_x = (5.1_–2.4^+3.6M_Earth. A few plausible assumptions (e.g. Uranus and Neptune perturbations being caused by Planet X) lead to Planet X's actual location with declination and eccliptic longitude being = 57 ± 17 and = 54 ± 34 , respectively (1989.5 position). In addition, we give Planet X's apparent brightness dependent on its unknown albedo. All those properties and predictions are more or less in agreement with earlier work on Planet X.