We seek to describe the flight path of a spacecraft through interplanetary space or of a celestial body through the universe. In this effort, we simplify the mathematical model to get the most important features, while making the equations tractable. Thus, we will derive the two-body problem with its equation of motion as the mathematical model. We show that the solution to that equation travels through a conic section orbit, that is, a circle, ellipse, parabola, or a hyperbola. Then we discuss topics for use in the continuing development. Those topics include the velocity vector, Energy Equation, Vis-Viva Equation, geometric properties of conic sections, orbit classifications into conic section orbits, types of orbits, the flight path angle, Kepler’s Equation, astronomical constants, and geometric formulas for elliptic orbits. Later, we will add perturbations to the nominal trajectory.


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