An Analytic theory for the evolution of high altitx3.e satellite orbits is developed in this rote. The distinctive feature of the theory lies in the dc*ĩble averaging of the differential equaticns-onoe over the period of the orbit , and secondly over the period of the ucon. This technique is called "intern~diate averaging" to distinguish it fran the conventional &*ibly averaged theories , and to deIx)te the tine scales inherent in the averaging technique.

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