Abstract
The projection of an axially symmetric satellite's orbit on a plane perpendicular to the rotation axis (z=const.) is given by the second-order differential equation.
where the prime denotes the derivative with respect tox and\(\bar \Psi (x,y)\) is a known function. Two integrability cases have been investigated and it has been shown that for these two cases the integration can be carried out either by quadratures or reduced to a first-order differential equation. Analytical and physical properties are expressed, and it is shown that the equation can be derived from the calssical plane eikonal equation of geometric optics.
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Reference
Knothe, H.: 1969, ‘Satellites and Riemmannian Geometry’,Celes. Mech. 1, 36–45.
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Ghaffari, A. On the integrability cases of the equation of motion for a satellite in an axially symmetric gravitational field. Celestial Mechanics 4, 49–53 (1971). https://doi.org/10.1007/BF01230320
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DOI: https://doi.org/10.1007/BF01230320