What is Kepler's Third Law?

Kepler's Third Law states that the square of the orbital period (T²) is proportional to the cube of the semi-major axis (a³): T² = 4π²a³ / GM, where G is the gravitational constant and M is the mass of the central body.

What is the semi-major axis?

For an elliptical orbit, the semi-major axis is half the length of the longest diameter of the ellipse. For a circular orbit it equals the orbital radius — the constant distance from the center of the central body.

Does this work for moons and artificial satellites?

Yes. As long as the orbiting body's mass is much smaller than the central body's mass (which is true for nearly all practical cases), Kepler's Third Law applies to moons, satellites, and spacecraft alike.

Why does the mass of the orbiting body not matter?

Kepler's Third Law in its Newtonian form (T² = 4π²a³/GM) depends only on the central body's mass M. The orbiting body's mass is negligible when it is much smaller than M, which holds for planets around stars and satellites around planets.

How accurate are the results?

The formula gives exact results within Newtonian gravity. For very massive orbiting bodies, extremely high velocities (relativistic), or very strong gravitational fields, general relativistic corrections would apply.

Orbital Period Calculator (Kepler's Third Law)

Calculate the orbital period of any body around a star or planet using Kepler's Third Law (T² = 4π²a³/GM).

Orbital Parameters

Central Body Preset

Central Body Mass (kg)

Use scientific notation: 1.989e30

Semi-Major Axis

Enter orbital parameters and click Calculate

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Summary

This tool applies Kepler's Third Law of planetary motion to compute the orbital period of a satellite, planet, moon, or artificial body given the semi-major axis of its orbit and the mass of the central body. Enter any two known values and the calculator returns the period in seconds, minutes, hours, days, and years. Results are computed entirely in your browser using standard gravitational constants.

How it works

Enter the semi-major axis (average orbital radius) in your chosen unit.
Enter the mass of the central body (star, planet, etc.) or select a preset.
The calculator applies T = 2π × √(a³ / GM) using Newton's gravitational constant G = 6.674 × 10⁻¹¹ N·m²/kg².
Results are displayed instantly in multiple time units for convenience.
You can also work in reverse: enter a known period to find the required semi-major axis.

Use cases

Estimate the orbital period of exoplanets around their host stars.
Verify satellite orbit parameters for aerospace or physics coursework.
Calculate how long a spacecraft takes to complete one orbit around Earth or Mars.
Explore the relationship between orbital distance and period for solar system bodies.
Cross-check textbook problems involving Kepler's Third Law.
Design hypothetical orbits for science fiction world-building.

Frequently Asked Questions

Last updated: 2026-06-13 · Reviewed by Nham Vu