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.
Keplerian Motion
Orbital Mechanics and Astrodynamics ; Chapter : 2 ; 23-59
2023-01-12
37 pages
Article/Chapter (Book)
Electronic Resource
English
Conic sections , Elliptical orbit , Energy Equation , Flight path angle , Kepler’s Equation , Semimajor axis , True anomaly , Two-body problem , Vis-Viva Equation Engineering , Aerospace Technology and Astronautics , Space Sciences (including Extraterrestrial Physics, Space Exploration and Astronautics) , Classical Mechanics , Physics and Astronomy
Wiley | 2021
|Wiley | 2015
|Springer Verlag | 2015
|Springer Verlag | 2023
|Springer Verlag | 2015
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