Calculate orbital period, semi-major axis, or central body mass using Kepler's Third Law: T² = (4π² ÷ GM) × a³
| Body | Axis (AU) | Period |
|---|---|---|
| Mercury | 0.387 | 88.0 days |
| Venus | 0.723 | 224.7 days |
| Earth | 1.000 | 365.25 days |
| Mars | 1.524 | 686.9 days |
| Jupiter | 5.203 | 11.86 years |
| Saturn | 9.537 | 29.46 years |
| Uranus | 19.19 | 84.01 years |
| Neptune | 30.07 | 164.8 years |
| Moon (Earth) | 384,400 km | 27.32 days |
| ISS (Earth) | ~6,780 km | ~92 min |
Kepler's Third Law, published by Johannes Kepler in 1619, states that the square of an object's orbital period is proportional to the cube of the semi-major axis of its orbit. In its modern Newtonian form, T² = (4π² ÷ GM) × a³, where G is the gravitational constant and M is the mass of the central body. This law applies to any two bodies in a gravitational orbit — planets around stars, moons around planets, and artificial satellites around Earth.
For an elliptical orbit, the semi-major axis is half the longest diameter of the ellipse. For a circular orbit, it equals the radius. For Earth's orbit around the Sun, the semi-major axis is defined as exactly 1 Astronomical Unit (AU) — approximately 149.6 million kilometers. The semi-major axis determines both the orbital period and the total energy of the orbit.
A larger orbit has a greater circumference to travel, and the orbital velocity is also lower because gravity is weaker at greater distances. Both effects combine to dramatically increase the period — which is why Neptune takes 165 years to orbit the Sun while Mercury takes only 88 days.
Yes — simply set the central body mass to Earth's mass (5.972 × 10²⁴ kg or 1 Earth mass) and enter the orbital radius. The ISS orbits at about 408 km altitude, giving a total orbital radius of about 6,780 km and a period of roughly 92 minutes.
Geostationary orbit is a circular orbit where the satellite's orbital period exactly matches Earth's rotation period of 24 hours. This places the satellite at an altitude of approximately 35,786 km above the equator, appearing stationary in the sky — which is why communication and weather satellites use this orbit.
Yes — for a binary star system, use the combined mass of both stars as the central body mass and the separation between the two stars as the semi-major axis. The formula gives the orbital period of each star around their common center of mass.