Physics

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Kepler's Third Law Calculator.

Calculate two-body orbital period from semi-major axis and central mass.

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Set your values

Results update as you type.

Orbital period: 31,557,718.872966 s

Orbital period

0.000000s
Orbital period: 365.251376 days

Orbital period

0.000000days

Results update automatically as you type.

Use Cases

Astronomy Education

Students and educators can quickly compute orbital periods for hypothetical or real systems, reinforcing understanding of Kepler's laws.

Example: Calculate the orbital period of a satellite with semi-major axis 7,000 km around Earth (mass 5.972 × 10^24 kg).

Mission Planning

Spacecraft engineers can estimate orbital periods for mission design, such as determining the period of a satellite at a given altitude.

Example: Find the period of a geostationary satellite with semi-major axis 42,164 km from Earth's center.

Frequently Asked Questions

What does Kepler's Third Law Calculator do?
This calculator computes the orbital period of a two-body system using Kepler's Third Law. You input the semi-major axis (in meters) and the central mass (in kilograms), and it returns the time required for one complete orbit.
What is the formula used?
The calculator uses the equation T = 2π√(a³/(GM)), where T is the orbital period, a is the semi-major axis, G is the gravitational constant, and M is the central mass. It assumes the orbiting body's mass is negligible compared to the central mass.
Can I use this for any two-body system?
Yes, as long as the central mass is much larger than the orbiting body. It works for planets orbiting stars, moons orbiting planets, and artificial satellites around Earth, provided you input the correct semi-major axis and central mass.

Tips & Common Mistakes

Tips

  • Ensure the semi-major axis is in meters; convert from kilometers by multiplying by 1,000.
  • Use the central mass in kilograms; for Earth, use 5.972 × 10^24 kg.
  • For elliptical orbits, use the semi-major axis (average of periapsis and apoapsis distances).
  • The result is the orbital period in seconds; convert to hours or days by dividing by 3,600 or 86,400.

Common Mistakes to Avoid

  • Forgetting to convert units to meters and kilograms, leading to incorrect results.
  • Using the sum of both masses instead of just the central mass when the orbiting body is not negligible.
  • Confusing semi-major axis with orbital radius for circular orbits; they are the same only for circular orbits.

Last updated: August 13, 2026