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

by Richard H. Frick

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Abstract

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.

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