---
title: "Orbits: Period, Speed and Kepler's Third Law"
description: "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 rela"
canonical: https://lightmysky.com/learn/science/orbits-period-speed-and-keplers-third-law-mt_PLKLykGF8Z
source: https://lightmysky.com/learn/science/orbits-period-speed-and-keplers-third-law-mt_PLKLykGF8Z.md
retrieved: 2026-09-12
---

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# 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.

Subject: Science · Area: Space Systems & Earth's History · Ages 17 to 18
Page: https://lightmysky.com/learn/science/orbits-period-speed-and-keplers-third-law-mt_PLKLykGF8Z

## Ready when they can

- 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

## Lesson: Falling around Earth forever

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.

**Recap.** Balance gravity against circular demand, scale periods by radius cubed, and park TV satellites over the equator.

## Practice

8 questions on this page, each with its working shown.

## Needs first

- [Orbital Mechanics](https://lightmysky.com/learn/science/orbital-mechanics-mt_1nl396BaVa)
- [Changing Ideas About Space](https://lightmysky.com/learn/science/changing-ideas-about-space-mt_KiRn5lnRgj)
- [Circular Motion: Angular Speed and Centripetal Force](https://lightmysky.com/learn/science/circular-motion-angular-speed-and-centripetal-force-mt_PW1G6nYStq)
- [Newton's Law of Gravitation and Gravitational Field Strength](https://lightmysky.com/learn/science/newtons-law-of-gravitation-and-gravitational-field-strength-mt_uUYXl3L0oW)

## Opens up

- [The Two-Body Problem, Orbital Energy and Kepler's First Two Laws](https://lightmysky.com/learn/science/the-two-body-problem-orbital-energy-and-keplers-first-two-laws-mt_CjHFftkB6M)
- [Coulomb's Law and the Electric Field of a Point Charge](https://lightmysky.com/learn/science/coulombs-law-and-the-electric-field-of-a-point-charge-mt_p7FuzIsQch)