Conical Orbital Mechanics: A Rework of Classic Orbit Transfer Mechanics

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