Mechanics
Orbital Period
Kepler's third law for circular orbits.
Variables
Ts
Orbital period
Time for one orbit
rm
Orbital radius
Semi-major axis
GN·m²/kg²
Gravitational constant
6.674×10⁻¹¹
Mkg
Central mass
Mass being orbited
Derivation
T = 2πr/v with v = √(GM/r).
Your notes
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Common questions
What is the Orbital Period formula?
Orbital Period is written T = 2π√(r³/GM). Kepler's third law for circular orbits. It belongs to Mechanics, under Gravitation.
What are the units in T = 2π√(r³/GM)?
In SI units, T is orbital period, measured in s; r is orbital radius, measured in m; G is gravitational constant, measured in m³/(kg·s²); M is central mass, measured in kg.
How is the Orbital Period formula derived?
T = 2πr/v with v = √(GM/r). The result is T = 2π√(r³/GM).