On the Particular Dynamics of Rubble-Pile Asteroid Rotation Following Projectile Impact on the Surface During Planetary Approach

The main motivation of this research is the semi-analytical exploration of the dynamics of an asteroid that is attacked while approaching a planet (with an inelastic collision of the projectile normally to the surface of the asteroid occurring just before approaching). Namely, the particular case of the spin dynamics of the asteroid that has been struck by a projectile almost perpendicularly to the maximal-inertia principal axis, with further perturbing the dynamics of rotation due to gravitational torques during close approach to the planet, is investigated. The initial surface of the asteroid is assumed to be a rubble pile, but preferably with a quasi-rigid internal structure, with circa constant distances between various parts of the asteroid as a first approximation. As a result of an inelastic collision with the surface of the asteroid, the rubble-pile material should be thrown off the surface into outer space in large amounts; thus, the mass of the asteroid and the moments of inertia along its principal axes should be changed (as well as the regime of angular rotation around its maximal-inertia principal axis). The updated Euler’s equations, stemming from the conservation of angular momentum, have been presented with gravitational torques acting during the approach of the asteroid to the planet (taking into account the impact on the asteroid that occurs just before it enters the zone of close approach). The evolution of the non-linear spin dynamical state is studied, along with kinematical findings for Euler angles via the governing equations, in accordance with two main rotational stages: first, immediately after the impact on the asteroid’s surface; and second, at the regime of asteroid rotation during its close approach to the planet, with perturbations caused by gravitational torques (just after being struck by the projectile).