Orbits: Period, Speed and Kepler's Third Law
Setting the gravitational force equal to the centripetal requirement gives orbital speed and period from the central mass and the radius alone. Squaring the period and cubing the radius turns the relationship into a straight line.
What a learner can do afterwards
- Gets orbital speed by equating GMm over r squared with mv squared over r
- Shows that T squared is proportional to r cubed and uses it to compare two satellites
- Says what a geostationary orbit has to fix and works out its radius
1 · Read
A satellite is a projectile falling around Earth. Gravity supplies the inward force that circular motion demands, so G M m over r squared equals m v squared over r. The small mass cancels. Closer satellites race and distant ones drift, since v equals root G M over r.
Period follows from circumference over speed, giving T squared proportional to r cubed. Compare two moons by ratio and G cancels entirely. Make the radius 4 times bigger and the period grows 8 times, since 4 cubed is 64 and its square root is 8.
The prized geostationary slot sits over the equator with a 24 hour period. It turns with Earth and hangs over one spot, perfect for TV relays. It floats about 42,000 km from Earth's centre, far above the surface.
Balance gravity against circular demand, scale periods by radius cubed, and park TV satellites over the equator.
2 · Watch
Take it off screen
Where it sits
Where this leads
Jobs that lean on this skill. Follow one to see everything it is built on.
8 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.