The Perturbed Full Two-Body Problem: Application to Post-DART Didymos

TL;DR

This paper analyzes the post-impact dynamics of the Didymos-Dimorphos binary asteroid system after NASA's DART impact, introducing observable elements and numerical methods to estimate changes in the system's orbit and physical properties.

Contribution

It presents a novel analysis of post-impact asteroid dynamics using physical separation-based observable elements and fully spin-orbit-coupled numerical simulations.

Findings

Changes in mutual orbit depend on impact separation distance.

Post-impact tumbling state may be observable through orbit changes.

Reshaping of Dimorphos reduces the needed impact velocity change.

Abstract

With the successful impact of the NASA DART spacecraft in the Didymos-Dimorphos binary asteroid system, we provide an initial analysis of the post-impact perturbed binary asteroid dynamics. To compare our simulation results with observations, we introduce a set of "observable elements" calculated using only the physical separation of the binary asteroid, rather than traditional Keplerian elements. Using numerical methods that treat the fully spin-orbit-coupled dynamics, we estimate the system's mass and the impact-induced changes in orbital velocity, semimajor axis, and eccentricity. We find that the changes to the mutual orbit depend strongly on the separation distance between Didymos and Dimorphos at the time of impact. If Dimorphos enters a tumbling state after the impact, this may be observable through changes in the system's eccentricity and orbit period. We also find that any DART-induced reshaping of Dimorphos would generally reduce the required change in orbital velocity to achieve the measured post-impact orbit period and will be assessed by the ESA Hera mission in 2027.