The contraction of satellite orbits under the influence of air drag. II. With oblate atmosphere

Abstract

The effect of air drag on satellite orbits of small eccentricity e (< 0.2) was studied in part I on the assumption that the atmosphere was spherically symmetrical. Here the theory is extended to an atmosphere in which the surfaces of constant density are spheroids of arbitrary small ellipticity. Equations are derived which show how perigee distance and orbital period vary with eccentricity, and how eccentricity is related to time. Expressions are also obtained which give lifetime and air density at perigee in terms of the rate of change of period. In most of the equations, terms of order e 4 and higher are neglected. The results take different forms according as the eccentricity is greater or less than about 0.025, while circular orbits are dealt with in a separate section. The influence of atmospheric oblateness is difficult to summarize fairly, because it depends on four independent parameters. If these simultaneously assume their ‘worst’ values, some of the spherical-atmosphere results can be altered by up to 30% as a result of oblateness. But usually the influence of atmospheric oblateness is much smaller, and 5 to 10% would be a more representative figure.