Orbital Period Calculator
A moon or satellite that circles a larger body takes a set time to go once around. Kepler's third law links that time to the size of the orbit and the mass of the body it circles.
- Free
- Works offline after your first visit
- Saves on this device
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- Updated
How it works
The period is two pi times the square root of the orbit radius cubed, divided by the gravitational constant times the body's mass. The gravitational constant is about 6.674 times ten to the minus eleven in SI units.
Enter the radius from the centre of the body, not the height above its surface. Add the body's radius to the altitude to get it. A round orbit uses its radius, and an oval orbit uses half its longest width.
Worked example
An orbit with a radius of 4,207 mi from the centre of the body, around the one you chose, takes 1 h 32 min 24 s for one full turn.
Questions
Why measure from the centre?
Gravity pulls toward the centre of the body, so the orbit is measured from there. Adding the body's radius to the height above the surface gives that distance.
Does this work for oval orbits?
Use half the longest width of the orbit as the radius. That gives the same period as a round orbit of that size.
Why does a closer orbit take less time?
Close to a body, gravity is stronger and the path is shorter, so one turn is quicker. Farther out, the path is longer and the pull is weaker, so a turn is slower.
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