Date of Award

Fall 12-2020

Document Type

Thesis

Degree Name

Master of Science (MS)

Department

Mechanical & Aerospace Engineering

Program/Concentration

Aerospace Engineering

Committee Director

Brett Newman

Committee Member

Robert Ash

Committee Member

Sharan Asundi

Committee Member

Dimitrie Popescu

Abstract

Simple orbital maneuvers obeying Kepler’s Laws, when taken with respect to Newton’s framework, require considerable time and effort to interpret and understand. Instead of a purely mathematical approach relying on the governing relations, a graphical geometric conceptual representation provides a useful alternative to the physical realities of orbits. Conic sections utilized within the full scope of a modified cone (frustum) were employed to demonstrate and develop a geometric approach to elliptical orbit transformations. The geometric model in-question utilizes the rotation of a plane intersecting the orbital frustum at some angle β (and the change in this angle) in a novel approach to analyze and develop two-body elliptical orbital transformations. Beginning with simple algebraic concepts such as Newton’s Second Law and the total specific orbital energy equation, equations combining two-body concepts with more general, Newtonian physics are explored; several equations relating eccentricity directly to a change in orbital energy are developed and applied; and conclusions regarding their importance and usefulness are drawn. Orbital energy exchange, eccentricity, and orbital shape from both inertial and non-inertial perspectives have been developed. Visualizations of transformations are presented throughout to aid in comprehension and clarity. Finally, efficacy of the model, extensions to non-stable orbits, and accuracy and precision with example calculations have been outlined in the Appendices.

DOI

10.25777/vnvw-af67

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