Direct N-body Simulations of Satellite Formation around Small Asteroids: Insights from DART’s Encounter with the Didymos System

Abstract

We explore binary asteroid formation by spin-up and rotational disruption considering the NASA DART mission's encounter with the Didymos–Dimorphos binary, which was the first small binary visited by a spacecraft. Using a suite of N-body simulations, we follow the gravitational accumulation of a satellite from meter-sized particles following a mass-shedding event from a rapidly rotating primary. The satellite’s formation is chaotic, as it undergoes a series of collisions, mergers, and close gravitational encounters with other moonlets, leading to a wide range of outcomes in terms of the satellite's mass, shape, orbit, and rotation state. We find that a Dimorphos-like satellite can form rapidly, in a matter of days, following a realistic mass-shedding event in which only ∼2%–3% of the primary's mass is shed. Satellites can form in synchronous rotation due to their formation near the Roche limit. There is a strong preference for forming prolate (elongated) satellites, although some simulations result in oblate spheroids like Dimorphos. The distribution of simulated secondary shapes is broadly consistent with other binary systems measured through radar or lightcurves. Unless Dimorphos's shape is an outlier, and considering the observational bias against lightcurve-based determination of secondary elongations for oblate bodies, we suggest there could be a significant population of oblate secondaries. If these satellites initially form with elongated shapes, a yet-unidentified pathway is needed to explain how they become oblate. Finally, we show that this chaotic formation pathway occasionally forms asteroid pairs and stable triples, including coorbital satellites and satellites in mean-motion resonances.

The Yarkovsky Effect on the Long-term Evolution of Binary Asteroids

“…In fact, binary systems that have been discovered tend to exhibit a preferred inclination of approximately 0°or 180° (Pravec et al 2012). Since the YORP effect drives the primary's obliquity to 0°or 180° (Rubincam 2000), the optimum condition i < r p /a is usually easily satisfied for small binaries if they form via YORP-driven spin-up and mass shedding followed by reaccumulation in the equatorial plane of the primary (Walsh et al 2008;Pravec et al 2012;Agrusa et al 2024) For simplicity, in the following, we take i = 0°. We first develop a simple analytical YS effect model, and later in this section, we justify it by comparison with the results of a numerical simulation.…”

“…The majority of the binary asteroid systems are observed to have a synchronized secondary. Simulation of rotational disruption of asteroids shows that the secondary could be born either asynchronous or synchronous due to the frequent reshaping near the Roche limit (Agrusa et al 2024). Currently, there are two known mechanisms for the synchronization of the secondary asteroid: the tidal effect and the YORP effect.…”

“…Assume the parent body of the binary is disrupted either by rotational fission or a catastrophic collision. The resulting fragments that are bound to the parent body accumulate to form a satellite, which can be either in synchronous or asynchronous rotation (Agrusa et al 2024). The synchronous secondary evolves under the tidal and BYORP effects, resulting in a final state at the tide-BYORP equilibrium location (given that the BYORP torque is negative) or in a migration outward until it leaves the system or becomes chaotic (if the BYORP torque is positive) (Ćuk 2007;Ćuk & Nesvorný 2010;Jacobson & Scheeres 2011;Jacobson et al 2014).…”

BYORP and Dissipation in Binary Asteroids: Lessons from DART

“…Therefore, the total kinetic energy of the impact may be less important for starting landslides than the velocities involved. Collisional velocities generally tend to be lower around less massive primaries, so small binaries may harbor more soft-merger satellites than larger systems (see Agrusa et al 2024) If the idea that most of the dissipation in binary asteroids happens during relatively short periods of instability is true, long-term tidal dissipation rates cannot be derived from the age of the system. Pou & Nimmo (2024) consider binary asteroids that are members of heliocentric asteroid pairs and try to estimate a spin-synchronization and eccentricity-damping timescale for those binaries on the basis of the age of the heliocentric pair.…”