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Astronomy · L4 · Choosing an orbital-energy regime from vis-viva

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How the sign of specific orbital energy (set by semi-major axis a) determines whether a trajectory is bound, marginally escaping, or hyperbolic.

by @openstemUpdated Astronomy
Vis-viva: v² = GM(2/r − 1/a)Compute specific energyε = v²/2 − GM/r = −GM/(2a)ε < 0?Bound orbitEllipse (or circle if e = 0)Parabolic trajectoryMarginal escape, v → 0 at r → ∞Hyperbolic trajectoryEscapes with excess speedUse case: satellites,planets, moonsUse case: theoreticalescape-velocity limitUse case: interplanetaryflyby / escape trajectoriesYes, a > 0ε = 0, a → ∞ε > 0, a < 0

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