Distance in the space of energetically bounded Keplerian orbits |
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| Authors: | Jared M Maruskin |
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| Institution: | 1.Department of Mathematics,San José State University,San Jose,USA |
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| Abstract: | In this paper we derive an explicit, analytic formula for the geodesic distance between two points in the space of bounded
Keplerian orbits in a particular topology. The specific topology we use is that of a cone passing through the direct product
of two spheres. The two spheres constitute the configuration manifold for the space of bounded orbits of constant energy.
We scale these spheres by a factor equal to the semi-major axis of the orbit, forming a linear cone. This five-dimensional
manifold inherits a Riemannian metric, which is induced from the Euclidean metric on
\mathbbR6{\mathbb{R}^6}, the space in which it is embedded. We derive an explicit formula for the geodesic distance between any two points in this
space, each point representing a physical, gravitationally bound Keplerian orbit. Finally we derive an expression for the
Riemannian metric that we used in terms of classical orbital elements, which may be thought of as local coordinates on our
configuration manifold. |
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