Numerical solution to Vinti's Problem
Document Type
Article
Publication Date
9-2015
Abstract
A practical, calculable solution to Vinti’s problem is offered. Vinti’s problem describes the motion of a satellite orbiting an oblate planet, including the point mass and oblateness J2 terms and differing from the actual geopotential only at the higher harmonics. Vinti’s original solution is extended to cover motion over a rotating Earth. An eccentric-anomaly-like transform removes the singularities in the elliptic integrals, rendering them accessible to numerical calculation. The prediction problem requires the simultaneous solution of two “Kepler’s equations.” Reduction to canonical action angle variables can also be accomplished via numerical techniques. This new realization of Vinti’s solution is free of series expansions that limit accuracy and uses only simple well-understood numerical techniques. Possible use of Vinti’s solution for further efforts is discussed.
Source Publication
Journal of Guidance, Control, and Dynamics (ISSN 0731-5090 | eISSN 1533-3884)
Recommended Citation
Wiesel, W. E. (2015). Numerical solution to Vinti’s Problem. Journal of Guidance, Control, and Dynamics, 38(9), 1757–1764. https://doi.org/10.2514/1.G000661
Comments
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