Abstract
The equations of motion may be numerically integrated to obtain the trajectory of a spacecraft or the path of a photon or radio wave. These equations may also be solved for certain parameters that can be verified by experiment or used to verify the results of numerical integration. The parameters of most interest are the precession of Mercury’s orbit, the bending of light by the sun’s gravity field, the delay in a signal transmitted from a spacecraft to Earth, clock time keeping, solar pressure, and planetary and stellar aberration. Formulas for these parameters are compared with the results of numerical integration.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
A. Einstein, The foundation of the general theory of relativity. Ann. Phys. 49, 769–822 (1916)
I.S. Sokolnikoff, Tensor Analysis Theory and Applications to Geometry and Mechanics of Continua (Wiley, New York, 1964)
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2021 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this chapter
Cite this chapter
Miller, J., Weeks, C.J. (2021). Comparison of Numerical Integration and Analytic Solutions. In: General Relativity for Planetary Navigation. SpringerBriefs in Space Development. Springer, Cham. https://doi.org/10.1007/978-3-030-77546-9_3
Download citation
DOI: https://doi.org/10.1007/978-3-030-77546-9_3
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-77545-2
Online ISBN: 978-3-030-77546-9
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)