Kepler's Third Law Calculator
Compute orbital period T = 2π√(a³/(GM)) from semi-major axis.
Input Data
Semi Major Axis M
m
Central Mass Kg
kg
Results
T = 2π√(a³/(GM)).
31,554,187.747615s
v = √(GM/a).
29,788.899321m/s
T²/a³ (constant for given M).
0s²/m³
At a glance:T = 2π√(a³/(GM)); v = √(GM/a). Complements orbital-velocity and gravitational-force.
Formula
T = 2π·√(a³/(G·M)).
$$T = 2\pi\sqrt{\frac{a^3}{GM}}, \quad v = \sqrt{\frac{GM}{a}}, \quad \frac{T^2}{a^3} = \frac{4\pi^2}{GM}$$How to Use
- Enter a and M.
- The tool returns period and velocity.
Case Studies
a=1.5e11, M=1.99e30
T ≈ 3.16e7 s (1 yr).
FAQ
Earth orbit?
a≈1.5e11 m, T≈1 yr (3.16e7 s).
Related Tools
References
Content review: Calculatorism Science Team. Results are for reference only; please refer to the relevant authorities for the official figures.