Mechanics
Orbital Period
Kepler's third law for circular orbits.
Variables
Ts
Orbital period
Time for one orbit
Allowed values: greater than 0
rm
Orbital radius
Semi-major axis
Allowed values: greater than 0
GN·m²/kg²
Gravitational constant
6.674×10⁻¹¹
In SI units: m³/(kg·s²)
Allowed values: greater than 0
Mkg
Central mass
Mass being orbited
Allowed values: greater than 0
Derivation
T = 2πr/v with v = √(GM/r).
Your notes
0/5000
Constants in this formula
Check value
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- r = 2 m (Orbital radius)
- G = 6.674 30 × 10⁻¹¹ N·m²/kg² (Gravitational constant)
- M = 3 kg (Central mass)
Result: T = 1.255918 × 10⁶ s
Other mechanics formulas with the same quantities
- Geosynchronous Orbit Radius (Gravitation) shares Orbital radius, Gravitational constant, Orbital period
- Gravitational Field (Gravitation) shares Gravitational constant
- Gravitational Potential Energy (General) (Gravitation) shares Gravitational constant
- Escape Velocity (Gravitation) shares Gravitational constant
- Surface Gravity (Gravitation) shares Gravitational constant
Where this formula is listed
- Mechanics formulas, under Gravitation.
- In the mechanics list it comes after Orbital Velocity and before Escape Velocity.
- Mechanics formula sheet, one of 58 formulas printed with symbol keys and SI units.
- The full formula index, grouped by category and topic.
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)).