Orbital Velocity Calculator

Written by Great Medico

Updated September 25, 2026 •2 min read

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Small changes can matter a lot in orbital velocity. Orbital and stellar quantities can change by orders of magnitude, which makes a transparent equation and careful units especially useful. Use the calculator as a transparent first model, then decide whether your real system needs a more detailed treatment.

What this calculator does

Use this page to evaluate orbital velocity from Semi-major axis, Semi-minor axis, Eccentricity. The result is most useful when the entered quantities describe one consistent physical setup and the displayed units stay attached to the number.

How to use it

Use measured, specified, or deliberately hypothetical values for Semi-major axis, Semi-minor axis, Eccentricity, Star mass, Satellite mass. Keep the quantity definitions and unit prefixes exactly as labeled; a correct number in the wrong physical quantity or prefix will still produce a misleading result.

How the calculation works

The calculator uses the vis-viva equation v = √[μ(2/r − 1/a)]. If μ is not entered, it forms μ = G(M+m). It also reports orbital period T = 2π√(a³/μ); eccentricity can be inferred from a and b but does not directly change the vis-viva result at fixed a and r.

Example

With the default setup (Semi-major axis = 1 AU; Star mass = 1 Solar masses; Satellite mass = 0 kg; Current orbital radius = 1 AU), the page reports orbital velocity of 29,785.142169 m/s. Treat the example as a consistency check, not a universal design target; its meaning depends on the inputs and assumptions above.

How to interpret the result

Read the orbital velocity inside the stated orbital, stellar, radiation, or cosmology model. Large differences can be physically meaningful at astronomical scales, but the number is only comparable with another case when the same assumptions and units are used.

Limitations and notes

These are idealized astrophysics or orbital relationships. Real missions and observations can require perturbations, noncircular geometry, uncertainty analysis, relativistic corrections, instrument response, and numerical propagation beyond a compact calculator. Pay particular attention to Semi-major axis, Semi-minor axis and their units. A mathematically correct result can still be incomplete when the real system includes effects not represented on the form.