Orbital Period Calculator

Estimate the orbital period of a satellite or planet using Kepler's third law. Provide the semi-major axis in meters and the central body's mass in kilograms to see how long one full revolution takes.

Average orbital radius measured from the center of the central body.
Mass of the planet or star being orbited.

Idealized calculation; ignores perturbations and relativistic effects.

Examples

  • 1.496e11 m around 1.989e30 kg (Earth around Sun) ⇒ 31,558,149 s
  • 6.78e6 m around 5.972e24 kg (ISS orbit) ⇒ 5,550 s
  • 3.84e8 m around 5.972e24 kg (Moon) ⇒ 2,360,592 s

FAQ

Can I input kilometers?

Convert kilometers to meters before entering values.

Does it account for orbital eccentricity?

No, it assumes a circular orbit for simplicity.

What is the central mass?

It is the mass of the body being orbited, such as a planet or star.

How accurate is the gravitational constant used?

The calculator uses the CODATA 2018 value of G (6.67430×10⁻¹¹ m³/kg·s²). Minor updates to G have little effect on most orbital estimates.

Additional Information

  • The formula is T = 2π × √(a³ / μ) where μ = G × M and G = 6.67430×10⁻¹¹ m³/kg·s².
  • Results are in seconds. Divide by 3,600 for hours or by 86,400 for days.
  • Assumes an ideal two-body system with negligible eccentricity.
  • Perturbations from other bodies, drag, or relativity can slightly alter real orbital periods.

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