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Satellite orbital precession caused by a rotating oblate atmosphere with a diurnal variation in density

The effect of the motion of the upper atmosphere 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 equations governing the changes due to zonal (west-to-east) and meridional (south-to-north) winds in the right ascension of the ascending node of the orbital plane Ω during one anomalistic period of the satellite are integrated, assuming that H, the density scale-height, is constant. The resulting expressions for ∆Ωω, due to zonal winds, and ∆ΩΦ, due to meridional winds, are given. It is shown that there can be appreciable changes in ∆Ω/∆TD, where ∆TD is the corresponding change in orbital period, that persist for several months for certain resonant orbits if the diurnal variation in density is allowed for. Compact expressions for ∆Ω and ∆Ω/∆TD are given when H varies linearly with height. It is demonstrated that in general there is no constant value of H that gives an exact equivalence between the variable-H and constant-H equations in the presence of a diurnal density variation.