Calibration of the angular momenta of the minor planets in the solar system

¹ School of Astronomy and Space Science & Key Laboratory of Modern Astronomy and Astrophysics in Ministry of Education, Nanjing University, 163 Xianlin Road, Nanjing 210023, PR China
e-mail: ljian@nju.edu.cn
² Department of Mathematics, Northwestern University, 2033 Sheridan Road, Evanston, IL 60208, USA
e-mail: xia@math.northwestern.edu

Received: 5 September 2018
Accepted: 15 July 2019

Abstract

Aims. We aim to determine the relative angle between the total angular momentum of the minor planets and that of the Sun-planets system, and to improve the orientation of the invariable plane of the solar system.

Methods. By utilizing physical parameters available in public domain archives, we assigned reasonable masses to 718 041 minor planets throughout the solar system, including near-Earth objects, main belt asteroids, Jupiter trojans, trans-Neptunian objects, scattered-disk objects, and centaurs. Then we combined the orbital data to calibrate the angular momenta of these small bodies, and evaluated the specific contribution of the massive dwarf planets. The effects of uncertainties on the mass determination and the observational incompleteness were also estimated.

Results. We determine the total angular momentum of the known minor planets to be 1.7817 × 10⁴⁶ g cm² s⁻¹. The relative angle α between this vector and the total angular momentum of the Sun-planets system is calculated to be about 14.74°. By excluding the dwarf planets Eris, Pluto, and Haumea, which have peculiar angular momentum directions, the angle α drops sharply to 1.76°; a similar result applies to each individual minor planet group (e.g., trans-Neptunian objects). This suggests that, without these three most massive bodies, the plane perpendicular to the total angular momentum of the minor planets would be close to the invariable plane of the solar system. On the other hand, the inclusion of Eris, Haumea, and Makemake can produce a difference of 1254 mas in the inclination of the invariable plane, which is much larger than the difference of 9 mas induced by Ceres, Vesta, and Pallas as found previously. By taking into account the angular momentum contributions from all minor planets, including the unseen ones, the orientation improvement of the invariable plane is larger than 1000 mas in inclination with a 1σ error of ∼50−140 mas.