Simultaneous Mass Determination for Gravitationally Coupled Asteroids

Abstract

Abstract The conventional least-squares asteroid mass determination algorithm allows us to solve for the mass of a large subject asteroid that is perturbing the trajectory of a smaller test asteroid. However, this algorithm is necessarily a first approximation, ignoring the possibility that the subject asteroid may itself be perturbed by the test asteroid, or that the encounter’s precise geometry may be entangled with encounters involving other asteroids. After reviewing the conventional algorithm, we use it to calculate the masses of 30 main-belt asteroids. Compared to our previous results, we find new mass estimates for eight asteroids (11 Parthenope, 27 Euterpe, 51 Neimausa, 76 Freia, 121 Hermione, 324 Bamberga, 476 Hedwig, and 532 Herculina) and significantly more precise estimates for six others (2 Pallas, 3 Juno, 4 Vesta, 9 Metis, 16 Psyche, and 88 Thisbe). However, we also find that the conventional algorithm yields questionable results in several gravitationally coupled cases. To address such cases, we describe a new algorithm that allows the epoch state vectors of the subject asteroids to be included as solve-for parameters, allowing for the simultaneous solution of the masses and epoch state vectors of multiple subject and test asteroids. We then apply this algorithm to the same 30 main-belt asteroids and conclude that mass determinations resulting from current and future high-precision astrometric sources (such as Gaia) should conduct a thorough search for possible gravitational couplings and account for their effects.