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2022 Paper for January.pdf
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Final Accepted Manuscript
Author
May, Douglas H.Affiliation
University of ArizonaIssue Date
2022-12-29
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May, D. H. (2022). Modeling Orbital Motion in a Circular Conic Reference Frame. AIAA Science and Technology Forum and Exposition, AIAA SciTech Forum 2022.Rights
Copyright © 2022 by Douglas H. May. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.Collection Information
This item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at repository@u.library.arizona.edu.Abstract
Two-body orbital trajectories conform to conic sections. However, typically in the literature their motion is analyzed in a plane. Kepler modeled elliptic orbital motion in a plane, stated his second law, and derived the geometric position-time relationship as the uniform change in area with respect to time. Kepler’s equation has been applied extensively and proven to give time as a function of position for exact solutions to orbital problems. An identical equation has been derived without reliance on geometry alone by applying basic principle of classical mechanics and the calculus. When the elliptic orbit is analyzed as a section of a circular cone and represented in three dimensions, additional variables relate position and time. In a conical reference frame, the planar and conic representations merge. This paper combines the conic section knowledge and characteristics of the cone to introduce a third dimension to modeling orbital motion. Force and potential energy have indeterminate limits because potential energy approaches zero as the radius approaches infinity and the gravitational force approaches infinity as the radius vector approaches zero, a singularity. The conic frame includes the apex where the singularity of a radius of zero is an established point in the reference system.Note
Immediate accessVersion
Final accepted manuscriptae974a485f413a2113503eed53cd6c53
10.2514/6.2022-1431