This brief approaches General Relativity from a planetary navigation
perspective, delving into the unconventional mathematical methods
required to produce computer software for space missions. It provides a
derivation of the Einstein field equations and describes experiments
performed on the Near Earth Asteroid Rendezvous mission, spanning
General Relativity Theory from the fundamental assumptions to
experimental verification.
The software used for planetary missions is derived from mathematics
that use matrix notation. An alternative is to use Einstein summation
notation, which enables the mathematics to be presented in a compact
form but makes the geometry difficult to understand. In this book, the
relationship of matrix notation to summation notation is shown. The
purpose is to enable the reader to derive the mathematics used in the
software in either matrix notation or summation notation.
This brief is a useful tool for advanced students and young
professionals embarking on careers in planetary navigation.