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The change in satellite orbital inclination due to 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 inclination of the orbital plane i during one anomalistic period of the satellite are integrated, with H, the density scale height, assumed to be constant. The resulting expressions for ∆iw, due to zonal winds, and ∆iϕ, due to meridional winds, are given. Compact expressions for ∆i and the ratio ∆i/∆TD, where ∆TD is the corresponding change in orbital period, are given when H varies linearly with height. An equivalence between the variable-H equation and the constant-H equation is demonstrated for ∆iw, when the value of H used in the latter is appropriately chosen. It is shown that there is no such equivalence for ∆iϕ and ∆i/∆TD.