Kepler Analysis

Explore the relationship between a planet's distance from its star and its orbital period.

Orbital Parameters
Adjust distance and central mass to see how they affect the orbital period.
1.00 AU

1 AU = Distance from Earth to Sun (~150M km)

1.00 M☉
Calculated Results
1.00
Orbital Period (Years)
29.79
Velocity (km/s)
Kepler's Relation: Distance vs Period
Comparison with real Solar System planets.

How it Works

Johannes Kepler discovered that the square of a planet's orbital period ($T$) is directly proportional to the cube of the semi-major axis ($r$) of its orbit.

When using units of Earth Years for time and Astronomical Units (AU) for distance, and assuming a central body with 1 Solar Mass, the equation simplifies to:

Did You Know?

  • Mercury orbits the Sun in just 88 days because it's so close (0.39 AU).
  • Neptune takes about 165 years to complete one orbit (30.07 AU).
  • This law applies to any orbiting body, including moons orbiting planets and artificial satellites orbiting Earth.
  • If the central star were more massive, planets would need to orbit faster to stay in stable orbit!