## Abstract

The orbits of Earth satellites with perigee heights less than 600 km are liable to be appreciably perturbed by the aerodynamic forces resulting from winds in the upper atmosphere, and analysis of the changes in the orbits provides a method of determining zonal (west-to-east) and meridional (north-to-south) winds. The theory hitherto used has been developed for orbits of eccentricity $e<0.2$. Here we develop the theory for the effect of zonal and meridional winds on the inclination i and right ascension of the node $\Omega $ for satellites in orbits with $e>0.2$ moving in an oblate atmosphere. The results are expressed in terms of the change in orbital period, which is accurately known for actual satellites, so that the equations are independent of variations in air density and satellite cross-sectional area. The results, summarized in equations (58) and (59), show that the changes depend on e through the function $(1-e)^{\frac{5}{2}}$ $(1+e)^{-\frac{3}{2}}$. For zonal winds, the change in i is nearly proportional to sin i cos$^{2}\omega $ and the change in $\Omega $ to sin $2\omega $,, where $\omega $ is the argument of perigee. For meridional winds, the change in i is nearly proportional to (sec$^{2}\omega $ + tan$^{2}i$)$^{-\frac{1}{2}}$, and the change in $\Omega $ to cot i sin $\omega $(1-sin$^{2}i$sin$^{2}\omega $)$^{-\frac{1}{2}}$.

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