# DDA 2015 – Contact Binary Asteroids

This is one of a series of notes taken during the 2015 meeting of the AAS Division on Dynamical Astronomy, 3-7 May, at CalTech. An index to this series (all the papers presented at the meeting) is here.

Samantha Rieger (UC Boulder)

#### Abstract

Recent observations have found that some contact binaries are oriented such that the secondary impacts with the primary at a high inclination. This research investigates the evolution of how such contact binaries came to exist. This process begins with an asteroid pair, where the secondary lies on the Laplace plane. The Laplace plane is a plane normal to the axis about which the pole of a satellite’s orbit precesses, causing a near constant inclination for such an orbit. For the study of the classical Laplace plane, the secondary asteroid is in circular orbit around an oblate primary with axial tilt. This system is also orbiting the Sun. Thus, there are two perturbations on the secondary’s orbit: J2 and third body Sun perturbations. The Laplace surface is defined as the group of orbits that lie on the Laplace plane at varying distances from the primary. If the secondary is very close to the primary, the inclination of the Laplace plane will be near the equator of the asteroid, while further from the primary the inclination will be similar to the asteroid-Sun plane. The secondary will lie on the Laplace plane because near the asteroid the Laplace plane is stable to large deviations in motion, causing the asteroid to come to rest in this orbit. Assuming the secondary is asymmetrical in shape and the body’s rotation is synchronous with its orbit, the secondary will experience the BYORP effect. BYORP can cause secular motion such as the semi-major axis of the secondary expanding or contracting. Assuming the secondary expands due to BYORP, the secondary will eventually reach the unstable region of the Laplace plane. The unstable region exists if the primary has an obliquity of 68.875 degrees or greater. The unstable region exists at 0.9 Laplace radius to 1.25 Laplace radius, where the Laplace radius is defined as the distance from the central body where the inclination of the Laplace plane orbit is half the obliquity. In the unstable region, the eccentricity of the orbit increases. Once the eccentricity becomes very large or approaching 1, the orbit of the secondary intersects with the primary and will eventually collide and becomes a contact binary.

#### Notes

• Motivation
• contact binaries exist with high obliquity, ~90 deg
• Does Laplace plane have a role?
• Resonances between binary orbit and solar perturbations?
• Laplace plane
• $\omega_2 \sin 2 \phi + \omega_s \sin 2(\phi – \epsilon) = 0$
• $\phi$ = incl. orbit relative to equator
• Near asteroid, orbit lies close to equator. Further, orbit lies near orbit plane.
• LP unstable in $e$ for obliquity above 68.875 deg and $a$ between 0.9 and 1.25 Laplace radii (Tremaine et al. 2009)
• Evolution of contact binary
• Fission occurs. Jacobson & Scheeres 2011
• Dissipation $\rightarrow$ stable circ. orbit in LP
• Model: simple model — secular expansion of $a$ from BYORP and tides
• Const. accel. perp. to radial vector
• Use first Fourier coefficient for BYORP accel.
• Results
• Verify instability region
• Unstable region: eccentric instability causes deviation from LP, collision
• New (eccentricity) instability mode
• cf Cuk & Nesvorny 2010
• $\rightarrow$ contact binary