Orbital Period Calculator

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Kepler's Third Law

Kepler's third law of planetary motion relates the orbital period of a body to the semi-major axis of its orbit and the mass of the central body it orbits. The general form, derived from Newtonian gravity, is:

Where:

• T — Orbital period (seconds)
• a — Semi-major axis of the orbit (meters)
• G — Gravitational constant (6.674 × 10^-11 m³ kg^-1 s^-2)
• M — Mass of the central body (kg)

Assumptions

• The orbiting body's mass is negligible compared to the central body (valid for planets orbiting stars, moons orbiting planets, etc.).
• The orbit is a Keplerian ellipse (no perturbations from other bodies).
• For circular orbits the semi-major axis equals the orbital radius.

Orbital Velocity

The mean orbital velocity for a circular orbit is:

Examples

• Earth around the Sun — Semi-major axis 1 AU, period ~365.25 days.
• ISS around Earth — Altitude ~420 km (a ~6,791 km), period ~92 minutes.
• Moon around Earth — Semi-major axis ~384,400 km, period ~27.3 days.