The change in satellite mean anomaly due to a rotating oblate atmosphere with a diurnal variation in density

Abstract

The effect of atmospheric drag on satellite orbits of small eccentricity e ≲ 0.2, is considered. The atmospheric model allows for oblateness, and has a density profile that approximates to the observed day-to-night variation. The equation governing the changes due to drag in the mean anomaly M , during one revolution of the satellite is integrated, assuming that H , the density scale height is constant. Two particular cases are detailed. In the first, the change ∆ M in M over one anomalistic period is given for eccentricity e in the range 0.01 ≲ e ≲ 0.2, and in the second the change in ( M + ω) over one draconic period, ∆( M + ω) is given for eccentricity e in the range 0 ≼ e ≲ 0.01, where ω is the argument of perigee. Finally a compact expression for e ∆ M is derived for an atmosphere with a linear variation of H with altitude, if 0.01 ≲ e ≲ 0.2. This is the final paper in a series describing the secular and long-periodic effects of drag on the six Keplerian elements that determine the orbit of a satellite.