Dynamics of Asteroid Binary Systems through the Use of Surface Integrals

A new technique that utilizes surface integrals to find the force, torque and potential energy between two non-spherical, rigid bodies is presented. The method has been used to study the 1999 KW4 system, and gives a relative error in the total energy that is smaller than 10^-15 and relative errors in the total angular momentum are smaller than 10^-11. We have also used this method to study the dynamics of an asteroid binary system the moment after a rotational fission process. Two models are studied, one where the bodies have equal densities and one where the densities are different. We find that collisions between the two bodies are more common when the bodies have equal densities. Vast majority of the collisions occur when the initial angle of the secondary is between 20 to 80 degrees, even when the density of the secondary is varied. The collision region changes when we instead vary the shape of the density, where collisions now take place when the initial angle of the secondary is between 10 to 90 degrees.