Analytical theory of the spin-orbit state of a binary asteroid deflected by a kinetic impactor

TL;DR

This paper develops analytical models to predict the post-impact librational state of a binary asteroid system after a kinetic impact, aiding in the analysis of impact data for planetary defense.

Contribution

It introduces both linear and nonlinear analytical formulas for the asteroid's librational evolution post-impact, considering the impactor's momentum transfer parameter.

Findings

Derived formulas for post-impact librational states

Analytical models incorporating impact momentum transfer

Framework for analyzing impact effects on binary asteroids

Abstract

We study the perturbed-from-synchronous librational state of a double asteroid, modeled by the Full Two Rigid Body Problem (F2RBP), with primary emphasis on deriving analytical formulas which describe the system's evolution after deflection by a kinetic impactor. To this end, both a linear and nonlinear (canonical) theory are developed. We make the simplifying approximations (to be relaxed in a forthcoming paper) of planar binary orbit and axisymmetric shape of the primary body. To study the effect of a DART-like hit on the secondary body, the momentum transfer enhancement parameter $\beta$ is introduced and retained as a symbolic variable throughout all formulas derived, either by linear or nonlinear theory. Our approach can be of use in the context of the analysis of the post impact data from kinetic impactor missions, by providing a precise modeling of the impactor's effect on the seconadry's librational state as a function of $\beta$.