ZONAL HARMONIC PERTURBATIONS OF AN ARTIFICIAL SATELLITE.
BALLISTIC RESEARCH LABS ABERDEEN PROVING GROUND MD
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This paper extends the known solution of the main problem of the artificial satellite theory to include the effects of all the higher zonal harmonics of the geopotential. The method of von Zeipel is used to calculate the secular and the longperiodic variations of orders J sub m and J sub mJ sub 2 respectively. The results are exhibited in a compact form, in terms of the associated Legendre polynomials in 1 - e to the 2nd power to the minus 12 power and in cos i. Author