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Orbital period
Intermediate
Time for one revolution.
T = 2π√(r³/GM)T = 2π√(r³/GM). The period depends only on the orbital radius and the central mass, not the satellite's mass.
At r = 6770 km: T ≈ 92 minutes.
r is measured from Earth's centre.
In more detail
For a circular orbit of radius r, the period is T = 2π sqrt(r³/GM). The period increases with the cube root of the radius, so higher orbits take longer.
Real-world uses
- The Moon's orbital period is about 27.3 days, derived from this relation.
- Designers choose orbit radii for satellites to match required periods.
- GPS and communication satellites follow orbits whose periods are set by their radius, which determines how often they pass over a site.
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Frequently asked questions
Does satellite mass matter for its period?
No, the period depends only on the central mass and radius.
What is Kepler's third law doing here?
It is this same relation, T squared proportional to r cubed, in a different form.
Does a satellite's mass affect its orbital period?
No. The period depends only on the orbit's radius and the planet's mass, not on the satellite's own mass.
Related topics in Gravitation & Orbits
Escape velocity of Earth · Orbital velocity · Satellite energy · Geostationary satellites · Polar and low Earth orbits · Weightlessness in orbit