Introduction

Gravitational models play a crucial role in engineering applications related to space missions, satellite operations, and celestial mechanics. These models provide a mathematical representation of the gravitational field of celestial bodies, enabling engineers to accurately predict orbits, plan trajectories, and design spacecraft missions with precision.

Various gravitational models are employed to meet specific requirements and account for different levels of complexity. One commonly used model is the Two-Body Problem, which assumes that the gravitational interaction between two celestial bodies, such as a satellite and a planet, is the dominant force affecting their motion. This simplified model is often leveraged for preliminary orbit design.

For more accurate calculations, more sophisticated models are required, such as the n-Body Problem: it considers the gravitational interactions among multiple celestial bodies, accounting for the gravitational influences of planets, moons, and other significant objects within a celestial system.

The gravity field of most of the bodies, however, is not usually well represented by one of a spherically symmetric body, when in vicinity of the body. For this reason, more accurate gravitational field representations are required, as the Spherical Harmonics Expansion or the Constant Density Polyhedron. The former is a gravity field expansion using spherical harmonics coefficients, the latter exploit a meshed representation of the body shape and compute the gravity field analytically, exploiting surface and line integrals.

The aim of this part of the documentation is to provide a concise, clear and mathematically accurate representation of gravitational models available within the JSMD ecosystem.