Asteroid deflection: Do multiple impacts from a split-impactor increase total momentum transfer?

Asteroid impacts pose a significant threat to Earth, making planetary defense strategies vital. Among these, kinetic impact has emerged as a promising method for asteroid deflection. This study investigates how to maximize momentum transfer to an asteroid within a fixed payload budget of mass $m$. Two impact configurations were examined: (i) three to four repeated impacts at the same location using varied targets and velocities, and (ii) simultaneous impacts with two impactors, each with half the total mass ($m/2$), delivered at different proximities on rock targets. The goal was to determine if the total momentum enhancement factor, $\beta$, in these configurations exceeds that of a single, unsplit impactor. In configuration (i), $\beta$ generally decreased with each successive impact. Interestingly, $\beta$ did not always scale with cratering efficiency; although larger ejecta mass was produced, its lower velocity sometimes reduced the overall momentum transfer. CTH shock physics simulations revealed that pre-existing crater geometry contributed to the decrease in $\beta$. In configuration (ii), the simultaneous impacts yielded a $\beta$ value lower than that of the single unsplit impactor. Surprisingly, $\beta$ from two simultaneous impacts was similar to that of a single half-mass ($m/2$) impactor, even with higher cratering efficiency at certain proximities. These results indicate that splitting the impactor does not increase momentum enhancement for the investigated conditions. Overall, the relationship between cratering efficiency and $\beta$ appears nonlinear and highly dependent on the specific impact configuration.