Orbital Regression of Synchronous Satellites Due to the Combined Gravitational Effects of the Sun, the Moon, and the Oblate Earth

by Richard H. Frick


Download eBook for Free

FormatFile SizeNotes
PDF file 3.2 MB

Use Adobe Acrobat Reader version 10 or higher for the best experience.


Purchase Print Copy

 FormatList Price Price
Add to Cart Paperback186 pages $35.00 $28.00 20% Web Discount

Earth satellites in synchronous equatorial orbits are called "stationary," but over long periods their orbits do in fact vary. R-399-NASA analyzed the perturbations due to the gravitational effects of the sun and moon. This study extends the analysis to cover the effects of the sun, the moon, and the oblateness of the earth. The analysis applies to satellites in near-circular orbits at any inclination and with orbital radii less than 10 earth radii. The perturbed motion of satellites in various orbits is described as seen from inertial space and as seen from the rotating earth; by including higher-order terms, the analysis was extended to describe the regression of the moon. The ground trace of a synchronous altitude orbit at an angle to the reference plane is a figure eight that varies over time. For an orbit that is originally synchronous and equatorial, or "stationary," the ground trace starts as one point and gradually develops into a figure eight with crossing-point at the equator; its latitude excursion is 14 degrees 40 min after 26.6 years, after which the process is reversed. Fuel expenditure to prevent this regression is proportional to the sine of twice the inclination angle to the reference plane.

This report is part of the RAND Corporation Report series. The report was a product of the RAND Corporation from 1948 to 1993 that represented the principal publication documenting and transmitting RAND's major research findings and final research.

This document and trademark(s) contained herein are protected by law. This representation of RAND intellectual property is provided for noncommercial use only. Unauthorized posting of this publication online is prohibited; linking directly to this product page is encouraged. Permission is required from RAND to reproduce, or reuse in another form, any of its research documents for commercial purposes. For information on reprint and reuse permissions, please visit www.rand.org/pubs/permissions.

The RAND Corporation is a nonprofit institution that helps improve policy and decisionmaking through research and analysis. RAND's publications do not necessarily reflect the opinions of its research clients and sponsors.