The contraction of satellite orbits under the influence of air drag V. With day-to-night variation in air density

Abstract

The effect of air drag on satellite orbits of small eccentricity (< 0-2) was studied in part I on the assumption that the atmosphere was spherically symmetrical. In reality the density of the upper atmosphere depends on the elevation of the Sun above the horizon and has a maximum when the Sun is almost overhead. In the present paper the theory is extended to an atmosphere in which the air density at a given height varies sinusoidally with the geocentric angular distance from the maximum-density direction. Equations are derived which show how perigee distance and orbital period vary with eccentricity throughout the satellite’s life, and how eccentricity varies with time. Expressions are also obtained for lifetime and air density at perigee in terms of the rate of change of orbital period. The main geometrical parameter determining the long-term effect of this day-to-night variation is the angular distance <f>p of perigee from the maximum-density direction. Results are obtained for <})pconstant and <j)pvarying linearly with time.