A Dynamical Solution of the Triple Asteroid System (45) Eugenia

TL;DR

This paper provides the first detailed dynamical analysis of the triple asteroid system (45) Eugenia, revealing the orbital characteristics of its moons, their stability, and the primary's gravitational field, with implications for asteroid interior structure.

Contribution

It offers the first dynamical solution for (45) Eugenia's triple system, including orbital parameters, stability analysis, and insights into the primary's gravitational harmonics, advancing understanding of such systems.

Findings

Moons orbit at 1165 km and 610 km with nearly circular, inclined orbits.

No resonances or Lidov-Kozai mechanisms detected in the system.

Primary's J2 value is lower than theoretical, indicating complex interior structure.

Abstract

We present the first dynamical solution of the triple asteroid system (45) Eugenia and its two moons Petit-Prince (Diameter~7 km) and S/2004 (45) 1 (Diameter~5 km). The two moons orbit at 1165 and 610 km from the primary, describing an almost-circular orbit (e~6x10-3 and e~7x10-2 respectively). The system is quite different from the other known triple systems in the main belt since the inclinations of the moon orbits are sizeable (9 deg and 18 deg with respect to the equator of the primary respectively). No resonances, neither secular nor due to Lidov-Kozai mechanism, were detected in our dynamical solution, suggesting that these inclinations are not due to excitation modes between the primary and the moons. A 10-year evolution study shows that the orbits are slightly affected by perturbations from the Sun, and to a lesser extent by mutual interactions between the moons. The estimated J2 of the primary is three times lower than the theoretical one, calculated assuming the shape of the primary and an homogeneous interior, possibly suggesting the importance of other gravitational harmonics.