Numerical Modeling and Analysis of Spatial Monotonic Approach Conditions of Two Satellites in Mars Orbit

This study investigates the problem of the spatial monotonic rendezvous of two spacecraft, initially orbiting Mars in distinct circular paths. The maneuvering spacecraft is tasked to rendezvous with a passive spacecraft, which strictly adheres to its orbit without executing any maneuvers. The aim of this study is to numerically model and analyze the conditions that facilitate the spatial monotonic approach of these spacecraft. The mathematical modeling of their relative motion employs the linearized Hill-Clohessy-Wiltshire equations, which have a known analytical solution when the passive spacecraft sustains a constant orbital motion. The analysis involves using expressions for the first and second derivatives of the distance between the spacecraft, calculated through differential calculus of functions of several variables. The boundary problem of achieving a rendezvous between the maneuvering and passive satellites in Mars orbit is addressed by utilizing solutions to the linearized Hill-Clohessy-Wiltshire equations. This study also explores the use of a control strategy based on a PD (Proportional-Derivative) regulator integrated with a genetic algorithm to ensure precise and optimal monotonic rendezvous. From a practical standpoint, this rendezvous could facilitate the remote recharging of the passive satellite’s battery, where the maneuvering satellite employs an onboard LED lamp to beam light to the solar panels of the passive satellite. The light transmission device consists of a parabolic emitter with a powerful LED lamp positioned at its focal point, enhancing the efficiency of the energy transfer.