NSW · HSCModule 5
Kepler's third law calculator
Pick a central body (Earth, Sun, Moon, Mars, Jupiter) or enter your own mass. Solve for orbital period given radius, or for radius given period. Orbital speed comes free.
Inputs
Result
Orbital period T
8.628e+4s
≈
23.97hours
Orbital speed v
3073m/s
T²/r³
9.905e-14s²/m³
T²/r³ = 4π²/(GM). Independent of the orbiting body's mass.
How this calculator works
Kepler's third law, T² = 4π²r³/(GM), is the bridge between orbital period and orbital radius. The calculator rearranges the formula for whichever quantity you want. Behind it is Newton's derivation: gravity provides centripetal force, so G M m / r² = m v² / r, which combined with v = 2πr/T gives the law.
See the full derivation in our Kepler's laws dot point answer.
Common questions
- What is Kepler's third law?
- T²/r³ = 4π²/(GM) for any body orbiting a central mass M. The square of the period is proportional to the cube of the semi-major axis.
- What is r in this formula?
- The semi-major axis of the orbit, measured from the centre of the central body. For a circular orbit, this is just the radius.
- Why does mass of the orbiting body not appear?
- Both gravity (Gravitational pull) and centripetal demand scale linearly with the orbiting body's mass m, so m cancels. Kepler's third law constant depends only on the central mass M.
- How do I get orbital speed from this?
- Once you have r, orbital speed v = 2πr/T or v = √(GM/r). The calculator shows both T and v in the result.