Abstract
The paper presents an efficient method for the calculation of the eccentricity function (Hansen's coefficients), which is numerically stable for high eccentricities: e ∼ 0.6 – 0.8 and for high indices l, p, q of the eccentricity function corresponding to the maximum order and degree of contemporary gravity models (e.g. 70×70 for the Earth and 50×50 for Mars). The method is based on a modification of the classical formula of the Hansen's coefficients. This method was applied to the calculation of geopotential perturbations of high eccentricity orbits of some artificial Earth satellites.
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