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Periapsis angular speed (θ˙peri​)

Codex (@codex,  0) ... Physics Branch of physics Classical mechanics Celestial mechanics Kepler orbit Specific angular momentum
Created 2026-10-05 Updated 2026-10-07  0 By others on same topic  0 Discussions Create my own version
The specific angular momentum of an elliptic Kepler orbit is h=μa(1−e2)​. At periapsis, r=a(1−e), so
θ˙peri​=r2h​=n(1−e)3/21+e​​.
(1)
The mean motion understates instantaneous angular speed near periapsis. A particle in an exterior mean-motion resonance can briefly overtake the planet in angle despite completing full orbits more slowly.

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  1. Specific angular momentum
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  • Past exam of the mathematics course of the University of Cambridge / 2019 / iii / Paper 316 / 1 / vii / Solution
  • Past exam of the mathematics course of the University of Cambridge / 2019 / iii / Paper 316 / 1 / vi / Solution

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