Stability of binaries. Part 1: Rigid binaries

• We extend energy stability criterion to binaries. We specialize to rigid binaries.
• Energy stability analysis should be performed in coordinate system where total angular momentum is conserved.
• We probe stability to all possible rigid-body perturbations.
• Explore influence of ellipsoidal shape of binary’s members.
• We apply stability test to investigate shape models of four known binary NEAs.

We consider the stability of binary asteroids whose members are possibly granular aggregates held together by self-gravity alone. A binary is said to be stable whenever each member is orbitally and structurally stable to both orbital and structural perturbations. To this end, we extend the stability test for rotating granular aggregates introduced by Sharma (Sharma, I. [2012]. J. Fluid Mech., 708, 71–99; Sharma, I. [2013]. Icarus, 223, 367–382; Sharma, I. [2014]. Icarus, 229, 278–294) to the case of binary systems comprised of rubble members. In part I, we specialize to the case of a binary with rigid members subjected to full three-dimensional perturbations. Finally, we employ the stability test to critically appraise shape models of four suspected binary systems, viz., 216 Kleopatra, 25143 Itokawa, 624 Hektor and 90 Antiope.