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Vis-Viva Elliptical Orbit Velocity Calculator

Speed at radius r in an elliptical orbit of semi-major axis a.

Compute the orbital speed at distance r from the central body for an elliptical orbit of semi-major axis a, using the vis-viva equation v² = GM (2/r − 1/a).

Dr. Helena Ortiz By Dr. Helena Ortiz
Published Last reviewed 1 min read

Inputs

km
km

Results

Enter values and click Calculate to see results.
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How to use this calculator

  1. Fill in the inputs above using the units you already have.
  2. Values update automatically as you type — no submit button needed.
  3. Hover any result row for the underlying formula and intermediate values.

Formula

v = √(GM · (2/r − 1/a))

In depth

Compute the orbital speed at distance r from the central body for an elliptical orbit of semi-major axis a, using the vis-viva equation v² = GM (2/r − 1/a).