Journal Article

Analytical solution of a satellite orbit disturbed by atmospheric drag

Guochang Xu, Xu Tianhe, Wu Chen and Ta-Kang Yeh

in Monthly Notices of the Royal Astronomical Society

Published on behalf of The Royal Astronomical Society

Volume 410, issue 1, pages 654-662
Published in print January 2011 | ISSN: 0035-8711
Published online December 2010 | e-ISSN: 1365-2966 | DOI:
Analytical solution of a satellite orbit disturbed by atmospheric drag

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In this paper, we derive the analytical solution of a satellite orbit disturbed by atmospheric drag. The disturbance force vector is first transformed and rotated to the orbital frame so that it can be used in the simplified Gaussian equations of satellite motion. Then, the force vector is expanded to triangular functions of the Keplerian angular elements and the disturbances are separated into three parts: short-periodic terms with triangular functions of M, long-periodic terms with triangular functions of (ω, i) and secular terms [non-periodic functions of (a, e)] with a program using mathematical symbolic operation software. The integrations are then carried out with respect to M, (ω, i) and t, respectively, to obtain the analytical solutions of satellite orbits disturbed by atmospheric drag. Some interesting conclusions are obtained theoretically. The atmospheric disturbance force is not a function of Ω. The semimajor axis a of the orbital ellipse is reduced in a constant and strong manner by the air disturbance; the shape of the ellipse (eccentricity e) changes towards a more circular orbit in a linear and weak manner. The right ascension of the ascending node Ω and the mean anomaly M are influenced by the disturbance only short periodically.

Keywords: atmospheric effects; methods: analytical; celestial mechanics; Earth; planets and satellites: atmospheres

Journal Article.  2513 words.  Illustrated.

Subjects: Astronomy and Astrophysics

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