Inversion Framework of Internal Mass Distribution Parameters of Asteroid Apophis from Dynamical Observations

Abstract

The detection of the internal mass distribution of asteroids is of great significance for understanding their origin, evolution, and mission planning for exploration. Previous approaches rely on indirect density estimates or close-range spacecraft gravity inversion, which have limited applicability. This paper presents a proof-of-concept framework to infer the internal mass properties of asteroid (99942) Apophis during its close Earth flyby in 2029 using dynamical observations collected during the encounter. We establish a dynamical mapping from the evolution of orbital and rotational states to internal structural parameters, formulate it as an inverse problem, and solve it using Particle Swarm Optimization. The algorithm is first validated on a regular ellipsoidal model and then applied to three mass distribution models based on the actual shape of Apophis. Under ideal observation conditions, the relative error of the inverted moment of inertia ratios can be below 0.001%, and the absolute error of the center-of-mass position reaches the order of 10-5 meters. The algorithm successfully distinguishes among different internal structures. When realistic measurement noise is introduced, the inversion accuracy degrades. A sensitivity analysis reveals that the accuracy of the inertia tensor inversion is primarily limited by angular velocity measurement noise, whereas center-of-mass determination is highly sensitive to the precision of position and velocity data. This study provides a proof-of-concept for a technically feasible and cost-effective approach to infer asteroid internal structure during close encounters, and also highlights the critical data accuracy requirements for practical application, offering guidance for future observation campaigns.