The upcoming 2029 Earth close approach of the near-Earth asteroid (99942) Apophis provides an unprecedented opportunity to obtain in situ observations of a kilometer-scale asteroid experiencing a strong but non-disruptive tidal encounter with Earth. Multiple exploration mission concepts have been proposed and are being developed, some of which require that proximity operations be conducted safely and accurately within the rapidly varying dynamical environment about Apophis during this close approach. In this work, we perform uncertainty analyses for different cases of close proximity-operations orbits about Apophis during its Earth flyby.

The representative proximity-operations orbits are based on the study of Scheeres (2022), which identifies two proximity strategies: distant dynamics and hovering dynamics. We extend that work using the same dynamical framework, modeling the spacecraft motion with the Tschauner–Hempel equations in the Earth–Apophis rotating frame, with the angular rate determined by the relative hyperbolic flyby trajectory. Solar radiation pressure (SRP) and third-body perturbations are neglected, as they are expected to produce only secondary effects over the time interval considered. SRP typically has a long-term influence over several orbital periods about the asteroid, much longer than the short-term window of interest of roughly 16 hours. The 3rd body perturbations from Moon or Sun are not expected to play a significant role during the hours when Apophis is close to the Earth.

For the first strategy, the relative dynamics of the spacecraft with respect to Apophis are analyzed with an appropriate initial state error. We perform an uncertainty analysis for this configuration and characterize how errors in the initial conditions propagate during the Apophis flyby. For the second strategy, a hovering control maintains a nominally fixed position in the Earth–Apophis rotating frame. This approach requires active control to hold the hovering point, although the required control accelerations are small and can be implemented with occasional impulsive ΔV maneuvers. We first perform an uncertainty analysis for this hovering configuration to quantify the natural divergence of the orbit and then design a linear–quadratic regulator (LQR) control law to maintain the hovering position. These results provide a comparative assessment of distant and hovering proximity operations and their associated uncertainty growth, informing the design of robust Apophis observation strategies for spacecraft during its 2029 Earth close approach.

D.J. Scheeres. 2022. “Proximity Operations About Apophis Through Its 2029 Earth Flyby,” Journal of the Astronautical Sciences 69: 1514-1536.