Shallow Encounters' Impact on Asteroid Deflection Prediction and Implications on Trajectory Design

TL;DR

The paper tackles the reliability of analytical deflection predictions in asteroid defense by comparing two semi-analytical methods against full n-body CRNBP simulations that include all Solar System planets. It demonstrates that shallow planetary encounters, even far outside a planet’s sphere of influence, can significantly distort deflection outcomes, challenging the validity of purely analytical estimates in preliminary design. A two-stage optimization using CRNBP-driven virtual asteroids illustrates how to obtain impact scenarios and quantify deflection metrics, while the authors propose a provisional threshold (15 SOIs) beyond which analytical models become unreliable. The findings have practical implications for trajectory design, suggesting when to rely on numerics versus simplified analytics, and highlight opportunities to leverage shallow encounters or to treat them with more robust numerical planning in mission studies.

Abstract

Analytical approximations are commonly employed in the initial trajectory design phase of a mission to rapidly explore a broad design space. In the context of an asteroid deflection mission, accurately predicting deflection is crucial to determining the spacecraft's trajectory that will produce the desired outcome. However, the dynamics involved are intricate, and simplistic models may not fully capture the system's complexity. This study assesses the precision and limitations of analytical models in predicting deflection, comparing them to more accurate numerical simulations. The findings reveal that encounters with perturbing bodies, even at significant distances (a dozen times the radii of the sphere of influence of the perturbing planet), can markedly disturb the deflected asteroid's trajectory, resulting in notable disparities between analytical and numerical predictions. The underlying reasons for this phenomenon are explained, and provisional general guidelines are provided to assist mission analysts in addressing such occurrences. By comprehending the impact of shallow encounters on deflection, this study equips designers with the knowledge to make informed decisions throughout the trajectory planning process, enhancing the efficiency and effectiveness of asteroid deflection missions.

Figures (18)

• Figure 1: Representation of the approach between the asteroid and Earth.
• Figure 2: Representation of the b-plane.
• Figure 3: Representation of the CRNBP in the synodic frame.
• Figure 4: Trajectory of the virtual asteroid 2005 ED224.
• Figure 5: Deflection obtained with $\Delta V =1$ cm/s or $A_t = 4\times 10^{-11}$ m/s$^2$ for asteroid 2005 ED224.