Table of Contents
Kepler's Third Law
Kepler's third law of planetary motion states that the square of the orbital period is proportional to the cube of the semi-major axis of the orbit. Combined with Newton's law of gravitation, this gives an exact formula for the orbital period of any object orbiting any central body, from artificial satellites orbiting Earth to planets orbiting stars.
The orbital period depends only on the semi-major axis (average orbital radius) and the mass of the central body. It does not depend on the orbiting object's mass (as long as it is much smaller than the central body). This is why all objects at the same orbital altitude have the same period, regardless of their mass.
Formula
Where T is period (seconds), a is semi-major axis (m), G is gravitational constant (6.674×10⁻¹¹), and M is central body mass (kg).
Common Orbits
| Orbit | Altitude (km) | Period |
|---|---|---|
| ISS (LEO) | 408 | 92.7 min |
| GPS (MEO) | 20,200 | 11.97 hrs |
| Geostationary (GEO) | 35,786 | 23.93 hrs |
| Moon | 384,400 | 27.32 days |
Frequently Asked Questions
What is a geostationary orbit?
A geostationary orbit has a period exactly equal to Earth's rotation period (23 hours 56 minutes), at an altitude of 35,786 km. A satellite in this orbit appears stationary above a fixed point on the equator, making it ideal for communication and weather satellites.
Does orbit shape matter?
The period depends only on the semi-major axis, not the eccentricity. A highly elliptical orbit with the same semi-major axis as a circular orbit has the same period. However, the velocity varies along the elliptical path (faster at perigee, slower at apogee) per Kepler's second law.