Improved Pork-Chop Plot for Asteroid Kinetic Impact Deflection Test Mission Trajectory Optimization

Abstract

For the mission requirements of the preliminary design phase for kinetic impact deflection of asteroids, an improved pork-chop plot design method is proposed which comprehensively considers both engineering constraints and deflection effectiveness. This method enables the visualization of engineering constraints, such as launch site, launch vehicle, and impact visibility, as well as the deflection distance after impact, all within a single plot. It provides a set of initial values that meet the requirements within the designated window for subsequent trajectory correction, based on different mission needs. Based on the patched conic technique, this paper first establishes a dynamical model for the spacecraft’s trajectory to the asteroid and then determines the parameters for both Earth departure and asteroid impact by solving the Lambert problem. Then, based on the departure parameters, the expression for Earth parking orbit escape is derived, and the constraints of rocket coasting time and launch site latitude, respectively, are transformed into parameter constraints on the argument of perigee and launch declination. Based on the impact parameters, an asteroid deflection dynamics model is established to compute the asteroid’s apparent magnitude and deflection distance. Finally, the improved pork-chop plot is generated using the aforementioned models. The plot comprehensively displays the optimized target parameters and engineering constraint parameters throughout the entire process, from launch vehicle departure to the post-impact deflection distance, within the given launch window. This provides initial values that satisfy both engineering constraints and mission requirements for the trajectory design of an in-orbit kinetic impactor asteroid deflection test mission. Compared to other trajectory design methods that provide only a single trajectory, the improved pork-chop plot enables a rapid, intuitive, and comprehensive visualization of a cluster of launch trajectories within the feasible window that satisfy engineering constraints. This approach reduces the number of iterations required for matching the deep-space transfer trajectory with the launch vehicle injection phase from more than five to one. The proposed method can serve as a valuable reference for target selection and trajectory optimization in in-orbit validation missions for kinetic impact deflection of asteroids.