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A numerical analysis of planar colliding binary companions
Authors: Caritá, G.A.; de Oliveira, V.M.; Mottola, S.; Silva, D.L.; Aljbaae, S.; Hussmann, H.; Willner, K.; Prado, AFBA
Ref.: Comm. Nonlinear Sci. 156, 109646 (2026)
Abstract: In the last few years, many interesting objects were discovered in the Solar System, such as the asteroid Arrokoth, a contact binary which was observed by NASA`s New Horizons mission. Understanding the dynamics of this type of objects is essential for unraveling the history of the Solar System, as collisions during the early stages of their formation may have significantly influenced their evolution. In this study, we propose that low-speed, non-elastic collisions could play a critical role in the formation of contact binaries. To investigate this, we model the dynamics of colliding binary systems using a numerical approach based on the full two-body problem (F2BP) in a planar configuration assuming rigid bodies. The equations of motion are solved numerically, with collisions handled by an ellipsoid overlap detection algorithm along with an impulse response model. Non-elastic collisions are considered by incorporating energy dissipation through a velocity-dependent model based on the relative velocity between the bodies and a constant coefficient of restitution (COR). The simulations yield three possible outcomes: merge, bound, and escape configurations. From random sampling simulation on the full phase space for different bodies` shapes, we observed an nearly constant percentage of escape cases (similar to 60%) going from an almost perfectly elastic (COR = 0.9) to an almost perfectly inelastic (COR = 0.1) collision scenario. The other cases have shown a dependent relation as we varied the coefficient of restitution, with the percentage of merge cases decreasing from similar to 34.6% to similar to 26% and the percentage of bounded cases increasing from similar to 8.4% up to similar to 20.2%. We apply our methodology to Antiope and Arrokoth, and we find that these systems present a higher likelihood of staying at their current state, namely, bounded for the former and merged for the latter. These results highlight that collisions are a significant energy dissipation mechanism and could play an important role in the formation of binary systems.
