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Mechanics
Orbital Period
T
=
2
π
r
3
G
M
T = 2\pi\sqrt{\frac{r^3}{GM}}
T
=
2
π
GM
r
3
T = 2π√(r³/GM)
Kepler's third law for circular orbits.
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Variables
T
Orbital period
Time for one orbit
s
r
Orbital radius
Semi-major axis
m
G
Gravitational constant
6.674×10⁻¹¹
N·m²/kg²
M
Central mass
Mass being orbited
kg
Derivation
T = 2πr/v with v = √(GM/r).
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