Investigation of the incremental benefits of eccentric collisions in kinetic deflection of potentially hazardous asteroids

Abstract

In asteroid momentum deflection missions, the presence of ejecta leads to a phenomenon where the system’s momentum appears “amplified” after the impact. This paper makes use of this phenomenon and demonstrates through computational simulations that targeting a point off the geometric center of an asteroid can further enhance the collisional benefit after impact. Due to uncertainties in the attitude of the asteroid and the momentum transfer coefficient $(\beta ,\gamma )$, this study employs a Monte Carlo approach to address these uncertainties. The results indicate that the strategy proposed in this paper can increase the post-collision deflection distance of the asteroid relative to Earth by an average of 81.05%, while also reducing the standard deviation by an order of magnitude, significantly lowering the uncertainty of the deflection mission. Furthermore, the results show that for certain asteroids particularly sensitive to changes in velocity $\Delta v$, blindly targeting their geometric center could result in a 48% probability of reducing the minimum distance to Earth. However, the striking strategy developed in this study can avoid this negative outcome. Finally, based on the computational results, a statistical formula is derived to predict the relative gain of the two strategies, concluding that for asteroids with smaller semi-major axes $a$, and the interception angle $\alpha$ at impact is greater, the benefits of employing the approach discussed in this paper are greater.