SURF Report: High Accuracy Methods for Computing Gravitational Potential and Gravitational Force Fields Near the Surface of Irregularly Shaped 3-Dimensional Bodies

TL;DR

This paper introduces high-accuracy, fast computational methods for gravitational potential and force fields near irregularly shaped celestial bodies, crucial for future space missions and landing operations.

Contribution

It presents novel algorithms and a gravitational field calculus that improve accuracy and efficiency, especially near complex surface geometries, with implementation tools for space exploration.

Findings

Enhanced accuracy in gravity calculations near irregular surfaces

Effective use of GPU acceleration for computations

Compatibility with volumetric octree methods

Abstract

Accurate gravity field calculations are necessary for landing on planets, moons, asteroids, minimoons, or other irregularly shaped bodies, but current methods become increasingly inaccurate and slow near the surface. We present high accuracy, fast methods for computing gravitational potential and gravitational force fields, which are needed for future space missions. Notably, gravitational force and potential computations are simplified, with high accuracy enhanced by bringing the derivative inside the gravitational potential integral. In addition, we present a new gravitational field calculus, which lets us combine simpler potentials and force fields to create more complex ones without accuracy loss. Several examples are provided, for instance, where we subtract different shapes from a spherical body making a variety of craters. The calculus will also work well with volumetric octree methods. Additionally, we use new bounds in the gravitational potential integral, to avoid trying to fit smooth basis functions to non-smooth curves, and harness new computational tools where tasks can be migrated to GPUs. We also have found that cylindrical coordinates can have special advantages in tailoring shape models. We have created a series of algorithms and preliminary MATLAB and Mathematica toolboxes utilizing these methods and the gravitational calculus. These methods are newly customizable for necessary high-accuracy gravity computations in future missions planned by JPL and other space agencies to navigate near irregularly shaped bodies in the solar system.