Kepler's Third Law Calculator
Calculate orbital periods, distances, and masses using Kepler's laws of planetary motion
Kepler's Third Law Calculator
Mass of the central star (default: 1 Solar mass = Sun)
Average distance from the star (1 AU = Earth-Sun distance)
Usually negligible compared to star mass (Earth = 1 Earth mass)
Calculation Results
Kepler's Third Law: T² ∝ a³, or more precisely: a³/T² = GM/(4π²)
Kepler Constant: 3.363e+18 m³/s²
Solar System Planets
| Planet | Period (years) | Distance (AU) | Mass (Earth masses) | a³/T² |
|---|---|---|---|---|
| Mercury | 0.241 | 0.387 | 0.055 | 0.998 |
| Venus | 0.615 | 0.723 | 0.815 | 0.999 |
| Earth | 1 | 1 | 1 | 1.000 |
| Mars | 1.881 | 1.524 | 0.107 | 1.000 |
| Jupiter | 11.862 | 5.203 | 317.83 | 1.001 |
| Saturn | 29.457 | 9.537 | 95.159 | 1.000 |
| Uranus | 84.021 | 19.191 | 14.536 | 1.001 |
| Neptune | 164.8 | 30.069 | 17.147 | 1.001 |
Notice how the a³/T² ratio is nearly constant for all planets, confirming Kepler's Third Law
Kepler's Three Laws
First Law (Ellipses)
Planets orbit in elliptical paths with the Sun at one focus
Second Law (Equal Areas)
Planets sweep equal areas in equal time intervals
Third Law (Periods)
T² ∝ a³ - Period squared proportional to distance cubed
Key Formulas
Kepler's Third Law
With Planet Mass
Period Formula
Distance Formula
Quick Examples
Earth
1 AU distance → 1 year period
Mars
1.52 AU → 1.88 years
Jupiter
5.2 AU → 11.86 years
Exoplanet Example
0.05 AU → 4.2 days (hot Jupiter)
Understanding Kepler's Third Law
What is Kepler's Third Law?
Kepler's Third Law states that the square of a planet's orbital period is directly proportional to the cube of its semi-major axis. In simple terms: planets farther from their star take longer to complete their orbits, following a precise mathematical relationship.
Historical Context
- •Discovered by Johannes Kepler in 1619
- •Based on Tycho Brahe's precise observations
- •Later explained by Newton's law of gravitation
- •Applies to all gravitationally bound systems
Modern Applications
Exoplanet Discovery
Astronomers use Kepler's laws to determine orbital characteristics of planets around other stars, helping to identify potentially habitable worlds.
Satellite Engineering
Engineers calculate orbital periods for satellites, space stations, and spacecraft missions using these fundamental relationships.
Stellar Mass Measurement
By observing planetary orbits, astronomers can determine the mass of distant stars and even detect binary star systems.
Universal Law: Kepler's Third Law applies to any two objects orbiting under gravitational attraction, from planets to moons to galaxies.