Capture Trajectory Using Multiple Gravity Assists of Galilean Moons with Coplanar Circular Assumption

Abstract

To determine the existence of gravity assist capture trajectories in the vicinity of Jupiter's equator, the paper assumes that the Galilean moons orbit in coplanar circles. Capture trajectories obtained by repeatedly using gravity assists are examined on the orbital plane. Due to the symmetry of coplanar circular orbits and applying phase differences between the moons, the gravity assist time windows can be calculated. Then, orbital geometry rotation is applied to match the spacecraft's position and the time windows. Through analyzing various gravity assist sequences and employing a breadth-first search strategy for each incoming velocity that intersects with the spacecraft's orbit post gravity assist, the rotation angles of relative velocity in each gravity assist are determined. This process helps estimate the maximum number of continuous gravity assists and their capture effects. The examples set two kinds of gravity assist sequences to study the distribution of capture orbits with periods ranging from 0 to 200 days, after 1 to 4 gravity assists, when the incoming velocity ranges from 11.5 to 12 km/s. The search results show that the minimum period of the capture orbits corresponding to each incoming velocity is less than 50 days, enhancing the design efficiency of gravity assist capture orbits.

Keywords

• gravity assist(ga)
• galilean moons
• coplanar circular orbits
• breadth-first search