Abstract
Summary The equations for the variation of the osculating elements of a satellite are integrated to yield the complete perturbations of the first order due to the second harmonic, together with the secular perturbations of the second order due to the second harmonic and of the first order due to the third to sixth harmonics. A set of smoothed elements is then derived, in which the perturbations of the even harmonics have no singularities, the semi-major axis and eccentricity have no variation due to the second harmonic and the other elements have the smallest possible amplitudes of oscillation. The formulae presented will be extremely useful in the reduction of earth-satellite observations and geopotential studies based on these.
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