Abstract
The planetary bodies are more of a spheroid than they are a sphere thereby making it necessary to describe motions in a spheroidal coordinate system. Using the oblate spheroidal coordinate system, a more approximate and realistic description of motion in these bodies can be realized. In this paper, we derive the Riemannian acceleration for motion in oblate spheroidal coordinate system using the golden metric tensor in oblate spheroidal coordinates. The Riemannian acceleration in the oblate spheroidal coordinate system reduces to the pure Newtonian acceleration in the limit of c0 and contains post-Newtonian correction terms of all orders of c-2. The result obtained thereby opens the way for further studies and applications of the motion of particles in oblate spheroidal coordinate system.
Highlights
Most planetary bodies have been assumed to be spherical and many treatments of motion involving these bodies have been taken into consideration the spherical approximation of the bodies [1]-[3]
Despite the spherical assumption of planetary bodies, studies have shown that the oblate spheroid is a more approximate description of these bodies [4]-[7], the need for a description of the planetary bodies in terms of the oblate spheroidal coordinate system
In this paper, we employ the Metric Tensors in oblate spheroidal coordinate system [9] to derive the Riemannian acceleration for the oblate spheroidal coordinate system
Summary
Most planetary bodies have been assumed to be spherical and many treatments of motion involving these bodies have been taken into consideration the spherical approximation of the bodies [1]-[3]. Despite the spherical assumption of planetary bodies, studies have shown that the oblate spheroid is a more approximate description of these bodies [4]-[7], the need for a description of the planetary bodies in terms of the oblate spheroidal coordinate system. How to cite this paper: Omaghali, N.E.J. and Howusu, S.X.K. Howusu had been considerable interest in the Riemannian Geometry. In this paper, we employ the Metric Tensors in oblate spheroidal coordinate system [9] to derive the Riemannian acceleration for the oblate spheroidal coordinate system
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