Gravity assist in 3D like in Ulysses mission

TL;DR

This paper presents a simplified model of gravity assist maneuvers in three dimensions, demonstrating how spacecraft can be diverted out of their original plane of motion, with application to the Ulysses mission.

Contribution

It introduces a basic, physics-based derivation of 3D gravity assist, extending traditional coplanar models to more general scenarios.

Findings

Gravity assist can effectively change a spacecraft's out-of-plane trajectory.

The model successfully replicates the Ulysses mission's trajectory deviations.

Simple physics principles suffice for understanding complex gravity assist maneuvers.

Abstract

We study the gravity assist in the general case, i.e. when the spacecraft is not in a coplanar motion with respect to the planet's orbit. Our derivation is based on Kepler's planetary motion and Galilean addition of velocities, subjects covered in introductory physics courses. The main purpose of this paper is to illustrate how the gravity assist can be used to deviate a spacecraft outside its original plane of motion. As an example, we use the NASA-ESA's Ulysses mission to "test" our simple model.