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2019 | OriginalPaper | Chapter

6. Flight in Non-spherical Gravity Fields

Author : Ashish Tewari

Published in: Optimal Space Flight Navigation

Publisher: Springer International Publishing

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Abstract

Spaceflight involving orbital transfers around irregularly shaped bodies or in the gravity field of several large bodies is fundamentally different from the flight in the gravity field of a single spherical body, which was covered in the previous chapters. The primary reason for this difference is that the spacecraft is no longer in a time-invariant gravity field of the two-body problem, but instead encounters a time-dependent field due to the relative motion of the multiple large bodies with respect to one another, or due to the changing position of the spacecraft relative to a rotating, non-spherical body.

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previous chapter Optimal Maneuvers with Bounded Inputs
Footnotes
1
A different state-space representation is obtained by replacing the generalized momentum vector, p, with the velocity, \(\dot {\mathbf {q}}\):
$$\displaystyle \begin{aligned} \mathbf{f}(\mathbf{X})=\left\{\begin{array}{c}\dot{\mathbf{q}}\\\ddot{\mathbf{q}} \end{array}\right\}=\left\{\begin{array}{c}\dot{\mathbf{q}}\\{\mathbf{K}}^T\mathbf{K}\mathbf{q}-\nabla_q(U)+2\mathbf{K}\dot{\mathbf{q}} \end{array}\right\} \end{aligned}$$
whose Jacobian is given by
$$\displaystyle \begin{aligned} {\mathbf{f}}^{\prime}(\mathbf{X})=\left(\begin{array}{cccc}\mathbf{0} &&& \mathbf{I}\\\varOmega_{\mathbf{qq}} &&& 2\mathbf{K} \end{array}\right) \end{aligned}$$
 
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Metadata
Title
Flight in Non-spherical Gravity Fields
Author
Ashish Tewari
Copyright Year
2019
Book
Optimal Space Flight Navigation

Print ISBN: 978-3-030-03788-8

Electronic ISBN: 978-3-030-03789-5

Copyright Year: 2019

DOI
https://doi.org/10.1007/978-3-030-03789-5_6