Spin-Spin Coupling in the Solar System

TL;DR

This paper investigates how gravitational interactions between elongated, closely orbiting binary objects in the solar system can lead to spin-spin resonances, affecting their rotational evolution and stability.

Contribution

It introduces a detailed analysis of spin-spin coupling in binary systems, deriving capture probabilities and applying them to specific asteroid examples.

Findings

Spin-spin resonances can occur in closely orbiting, deformed binary objects.

Capture probabilities for spin-spin resonances are derived.

Spin-spin coupling significantly influences the rotational dynamics of certain asteroid systems.

Abstract

The richness of dynamical behavior exhibited by the rotational states of various solar system objects has driven significant advances in the theoretical understanding of their evolutionary histories. An important factor that determines whether a given object is prone to exhibiting non-trivial rotational evolution is the extent to which such an object can maintain a permanent aspheroidal shape, meaning that exotic behavior is far more common among the small body populations of the solar system. Gravitationally bound binary objects constitute a substantial fraction of asteroidal and TNO populations, comprising systems of triaxial satellites that orbit permanently deformed central bodies. In this work, we explore the rotational evolution of such systems with specific emphasis on quadrupole-quadrupole interactions, and show that for closely orbiting, highly deformed objects, both prograde and retrograde spin-spin resonances naturally arise. Subsequently, we derive capture probabilities for leading order commensurabilities and apply our results to the illustrative examples of (87) Sylvia and (216) Kleopatra asteroid systems. Cumulatively, our results suggest that spin-spin coupling may be consequential for highly elongated, tightly orbiting binary objects.