A universal time of flight equation for any orbit is developed as a function of the initial and final radius, the change in true anomaly and the initial flight path angle. Lambert's theorem, a new corollary to this theorem, a trigonometric variable substitution and a continuing fraction expression are used in this development. The resulting equation is not explicitly dependent upon eccentricity and is determinate for -2n < (change in true anomaly) < 2n. A method to make the continuing fraction converge rapidly is evaluated using a top down algorithm. Finally, the accuracy of the universal time of flight equation is examined for a representative set of orbits including near parabolic and near rectilinear orbits. / Master of Science
| Identifer | oai:union.ndltd.org:VTETD/oai:vtechworks.lib.vt.edu:10919/43406 |
| Date | 22 June 2010 |
| Creators | Halter, Ronald Vaughn |
| Contributors | Aerospace Engineering, Lutze, Frederick H. Jr., Cliff, Eugene M., Stalford, Harold L. |
| Publisher | Virginia Tech |
| Source Sets | Virginia Tech Theses and Dissertation |
| Detected Language | English |
| Type | Thesis, Text |
| Format | x, 69 leaves, BTD, application/pdf, application/pdf |
| Rights | In Copyright, http://rightsstatements.org/vocab/InC/1.0/ |
| Relation | OCLC# 18585327, LD5655.V855_1988.H347.pdf |
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