Abstract
The present work aims at constructing an atlas of the balanced Earth satellite orbits with respect to the secular and long periodic effects of Earth oblateness with the harmonics of the geopotential retained up to the 4th zonal harmonic. The variations of the elements are averaged over the fast and medium angles, thus retaining only the secular and long periodic terms. The models obtained cover the values of the semi-major axis from 1.1 to 2 Earth’s radii, although this is applicable only for 1.1 to 1.3 Earth’s radii due to the radiation belts. The atlas obtained is useful for different purposes, with those having the semi-major axis in this range particularly for remote sensing and meteorology.
Highlights
Earth oblateness. en, the Lagrange planetary equations for perturbations of the elements are investigated to get sets of orbital values at which the variations of the elements can be cancelled simultaneously
Earth Potential e actual shape of the Earth is that of an eggplant. e center of mass does not lie on the spin axis, and neither the meridian nor the latitudinal contours are circles. e net result of this irregular shape is to produce a variation in the gravitational acceleration to that predicted using a point mass distribution
The motion along a latitudinal contour can be visualized as consisting of different periodic motions called “tesseral harmonics.” e zonal harmonics describe the deviations of a meridian from a great circle, while the tesseral harmonics describe the deviations of a latitudinal contour from a circle
Summary
Earth oblateness. en, the Lagrange planetary equations for perturbations of the elements are investigated to get sets of orbital values at which the variations of the elements can be cancelled simultaneously. It is a purely geometrical transformation to express the potential function V(r, δ), given by the above equations, as a function of the Keplerian orbital elements a, e, i, Ω, ω, and I in their usual meanings (Figure 2, [12]), where a and e are the semi-major axis and the eccentricity of the orbit, respectively, i is the inclination of the orbit to the Earth’s equatorial plane, Ω and ω describes the position of the orbit in space where Ω is the longitude of the ascending node and ω is the argument of perigee, and l is the mean anomaly to describe the position of the satellite with respect to the orbit. Substituting for the averaged disturbing function 〈R〉 due to Earth oblateness, the Lagrange equations become a_ 0, (16)
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