The objective of this chapter is to model the effects of small perturbations on a two‐body orbit. It shows how the concept of an osculating orbit can be applied to approximate the perturbed equations of motion if the magnitude of the perturbing acceleration is much smaller than that of the primary acceleration. An approach based upon the concept of the osculating orbit is the classical Lagrange method of variation of parameters. In this chapter, the Lagrange brackets are computed for an elliptic orbit. The Gauss variational model is such a method where the small perturbing acceleration is expressed in spherical polar coordinates, and the resulting variations in the two‐body orbit are resolved into a set of first‐order differential equations in time for the classical orbital elements. The concept of the mean perturbation (or variation) provides a rough approximation for determining the osculating orbital parameters at any instant.
Orbital Perturbations
Foundations of Space Dynamics ; 191-254
2021-02-01
64 pages
Article/Chapter (Book)
Electronic Resource
English
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