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Kepler's third law
Beginner
Square of the period is proportional to cube of semi-major axis.
T² ∝ a³T² ∝ a³: with T in years and a in AU, T² = a³. More precisely T² = 4π²a³/GM.
Mars: a = 1.52 AU gives T = 1.88 years.
Applies to bodies around the same central mass.
In more detail
Kepler's third law states that the square of the orbital period is proportional to the cube of the semi-major axis, T² ∝ a³. Written exactly, T² = (4π²/GM) a³, so the constant depends on the mass of the central body.
Real-world uses
- Estimating the distances of exoplanets from their orbital periods.
- Calculating the mass of a star from the orbit of a companion.
- Astronomers use the third law to estimate the distance of a newly discovered planet from its orbital period alone.
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Frequently asked questions
Does it apply to moons?
Yes, for a moon orbiting a planet, using the planet's mass.
Is the constant the same for all planets?
No, it depends on the mass of the central body.
Does Kepler's third law apply to moons too?
Yes. For any two bodies orbiting each other, the square of the period is proportional to the cube of the separation.
Related topics in Gravitation & Orbits
Weightlessness in orbit · Kepler's first law · Kepler's second law · Elliptical orbit energy · Eccentricity · Perihelion and aphelion