AP® Physics 1: Algebra-Based · Unit 6 · Topic 6.6
Circular Orbits
A satellite orbits because gravity supplies exactly the centripetal force needed to keep it curving around Earth instead of flying straight or falling in. Setting those two forces equal pins down one required speed for any given orbital radius.
A satellite in circular orbit is falling the whole time. Gravity pulls it toward Earth's center, but the satellite is also moving sideways fast enough that as it falls, the curve of its path matches the curve of the Earth falling away beneath it. It never gets closer because it's always missing. That's free fall with sideways motion built in, not an absence of gravity.
To find the required speed, set the gravitational force equal to the centripetal force: G M m / r2 = m v2 / r. The satellite's mass m appears on both sides and cancels, leaving v = √(G M / r). Since surface gravity relates to G M by g = G M / Re2, you can also write G M = g Re2, giving v = √(g Re2 / r) when r is measured from Earth's center. Only the mass of the body being orbited and the orbital radius matter.
Because mass cancels, a heavy satellite and a light one at the same altitude need the identical speed to stay in orbit; drop that speed and gravity wins, pulling the orbit inward, raise it and the satellite drifts outward. This same balance explains why outer planets move slower than inner ones and why period grows with radius: since v = 2 π r / T, combining with v = √(G M / r) gives T2 proportional to r3, a relationship that connects directly to the energy trade-offs of elliptical orbits and transfers covered nearby in this unit.
Key terms
- Centripetal force
- The net inward force needed to keep an object moving on a circular path at constant speed.
- Orbital radius
- The distance from the center of the body being orbited to the satellite, not the altitude above its surface.
- G M
- The product of the gravitational constant and the central body's mass, equal to g times the body's radius squared at its surface.
- Orbital period
- The time for one full trip around the orbit, related to radius by T2 proportional to r3.
Watch it explained
- How it worksHow does setting gravity equal to the centripetal requirement pin down the orbital speed?
- Worked exampleFind the orbital speed of a satellite 400 km over Earth's surface in a circular orbit.
- Common mistakeWhy isn't a heavier satellite required to orbit at a different speed than a light one?
- Going furtherWhat happens to orbital period as the orbit radius grows?
Check yourself
End of topic.