Dynamical effect of the 9:16 resonance with Mars on some Datura asteroids, including the pair Balam and 312497

¹ Mathematical Institute, Slovak Academy of Science, Bratislava, Slovakia,
e-mail: plavalova@mat.savba.sk, plavalova@komplet.sk
² Research and Educational Center “Nonlinear Dynamics”, Yaroslavl State University, Yaroslavl, Russia
e-mail: hegem@mail.ru

Received: 24 June 2020
Accepted: 20 May 2021

Abstract

Context. We studied the effect of the mean motion 9:16 resonance with Mars (9:16M) on the dynamics of the very young asteroid family Datura and the young pair (3749) Balam and (312497) 2009 BR₆₀.

Aims. We aim to understand the mechanism of dynamical interaction of the members of a family that are subjected to mean motion resonance in order to precisely estimate the age of an asteroid family or pair and to reconstruct their breakup processes.

Methods. We calculated the expected (9:16M) resonance position, its boundaries, and multiplet fine structure and their time evolution under the effect of Mars orbit variations. We used the Lyapunov characteristic exponent and Euclid algorithm in our analytical calculations. We compared these results with backward numerical integrations of some Datura asteroids to check for consistency.

Results. We explain the strong variations in the semi-major axis of some Datura asteroids as caused by the variations in the orbit of Mars. Using the Datura family as an example, we show that the distance from resonance may be a better measure of chaos than the widely accepted Lyapunov exponent. Additionally, we find that asteroid (3749) Balam exhibits the conspicuous effects of dynamical perturbations that are likely induced by the 9:16M resonance.

Conclusions. Focusing on one of the most robust and well-established young asteroid families, the Datura family, we show that mean motion resonances play an important role as drivers of the dynamical evolution of asteroid families.