Kepler's Third Law Calculator
Orbital period and speed of a body from its orbital radius and the mass it orbits.
Results
Orbital period
1.880790
a
Days
686.958
Orbital velocity
24.1298
km/s
Distance
227,939,134
km
What this tool does
Written in years, astronomical units and solar masses the law collapses to T² = a³/M, which is why it was discovered from observation long before anyone knew why it was true. The default is Mars: 1.52 AU out and a year of 687 days. Anything orbiting the Sun, from Mercury to a comet, follows the same rule.
Formula
T² = a³ ÷ M (T in years, a in AU, M in solar masses)
Variables
| Symbol | Meaning | Unit |
|---|---|---|
a | Orbital radius | AU |
ms | Mass of the central body | M☉ |
T | Orbital period | a |
TD | Days | — |
V | Orbital velocity | km/s |
KM | Distance | km |
Worked example
- Orbital radius1.52368 AU
- Mass of the central body1 M☉
- Orbital period1.880790 a
- Days686.958
- Orbital velocity24.1298 km/s
- Distance227,939,134 km
Limitations
- The formula assumes ideal conditions: no friction losses, no air resistance and no efficiency losses unless you enter them.
- The default values are typical reference figures, not measurements of your situation. Replace them with your own data whenever you have it.