Author： Henderson Troy Junkins John Radice Gianmarco
Publisher： Springer Publishing Company
ISSN： 0923-2958
Source： Celestial Mechanics and Dynamical Astronomy, Vol.104, Iss.4, 2009-08, pp. : 355-368
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Abstract
A complex exponential solution has been derived which unifies the elliptic and hyperbolic trajectories into a single set of equations and provides an exact, analytical solution to the unperturbed, Keplerian two-body problem. The formulation eliminates singularities associated with the elliptic and hyperbolic trajectories that arise from these orbits. Using this complex exponential solution formulation, a variation of parameters formulation for the perturbed two-body problem has been derived. In this paper, we present the analytical formulation of the complex exponential solution, numerical simulations, a comparison with classical solution methods, and highlight the benefits of this approach compared with the classical developments.
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