Equations of Motion

  • James Miller
Part of the Space Technology Library book series (SPTL, volume 37)


The equations of motion describe the path that a spacecraft, planet, satellite, molecule, electromagnetic wave or any body will follow. In space, the path that a spacecraft follows is called a trajectory and for a planet it is called an ephemeris. For the purpose of navigation, a planet is defined as any object that orbits the sun and thus, includes comets and asteroids. A satellite is any body that orbits a planet. Flight operations are generally conducted using solutions of Newton’s equation of motion obtained by numerical integration. Analytic solutions of Newton’s equation of motion provide some insight into trajectory design and navigation analysis, but these solutions are seldom used in the conduct of flight operations. For spacecraft near the Sun and Jupiter, and for the planet ephemerides, Newton’s equations of motion are augmented with terms from the n-body solution of General Relativity.


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© Springer International Publishing AG, part of Springer Nature 2019

Authors and Affiliations

  • James Miller
    • 1
  1. 1.Porter RanchUSA

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