How this calculator works
The vis-viva relation gives speed at a chosen separation on a bound two-body ellipse. Eccentricity fixes the periapsis and apoapsis, so the supplied separation must lie between them. Gravity can be supplied as a parameter or calculated from both masses. Reported energy uses the entered satellite mass times the relative specific energy, which is the usual test-particle energy when the satellite is much lighter than the primary.
Formula
v² = mu(2/r-1/a); rp = a(1-e); ra = a(1+e); b = a sqrt(1-e²); T = 2 pi sqrt(a³/mu); specific energy = -mu/(2a).
Worked example
With mu = 1, a = 2 m and e = 0.5, the separation ranges from 1 m to 3 m. Speed is 1.224745 m/s at periapsis and 0.408248 m/s at apoapsis.
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Frequently asked questions
Why must radius fit the eccentricity?
Semi-major axis and eccentricity define a particular ellipse. A position outside its apsidal limits cannot be on that orbit.
Is speed constant?
Only for a circular orbit. An elliptical orbit is faster near periapsis.
Does this model hyperbolic escape?
No. This page restricts the geometry to bound ellipses with eccentricity below one.