General Relativity for Planetary Navigation
Description
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.More details
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Content
1.1 Summary of General Relativity Fundamental Assumptions
1.2 Geodesic Equation
1.3 Computer Solution for Metric Tensor
1.4 Covariant Derivative of a Vector
1.5 Covariant Derivative of a Tensor
1.6 Riemann-Christoffel Tensor
1.7 Ricci Tensor
1.8 Einstein Tensor
1.9 Summary of Einsteins Theory
2.0 Schwarzschild Solution for Metric Tensor
2.1 Metric Tensor
2.2 Equations of Motion
2.3 Isotropic Schwarzschild Coordinates
3.0 Comparison of Numerical Integration and Analytic Solutions
3.1 Mercury Perihelion Shift
3.2 Radar Delay3.3 Light Deflection
3.4 Clock Time Keeping
4.0 General Relativity Time Delay Experiment
4.1 Plane Wave Propagation Through Ionized Gas
4.2 Solar Plasma Time Delay
4.3 Troposphere Time Delay
4.4 Ionosphere Time Delay
4.5 Doppler Data
4.6 Range Data
Experimental Results