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

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.

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 ∆ Ω ω , due to zonal winds, and ∆ Ω Φ , due to meridional winds, are given. It is shown that there can be appreciable changes in ∆ Ω /∆ T D , where ∆ T D 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 /∆ T D 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.

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 ∆ i w , due to zonal winds, and ∆ i ϕ , due to meridional winds, are given. Compact expressions for ∆ i and the ratio ∆ i /∆ T D , where ∆ T D 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 ∆ i w , when the value of H used in the latter is appropriately chosen. It is shown that there is no such equivalence for ∆ i ϕ and ∆ i /∆ T D .