AP Physics C: Mechanics / Unit 6: Energy and Momentum of Rotating Systems
6.6 Motion of Orbiting Satellites
Notes
For a circular orbit, gravity provides the centripetal force: $\displaystyle \frac{GMm}{r^2}=\frac{mv^2}{r}$, so $\displaystyle v=\sqrt{\frac{GM}{r}}$.
- Orbital speed doesn't depend on the satellite's mass.
- In elliptical orbits, angular momentum is conserved: faster when closer.
Practice
A satellite in a larger orbit moves:
$\displaystyle v\propto\frac{1}{\sqrt r}$.
Doubling a satellite's mass changes its orbital speed:
Mass cancels.
In an elliptical orbit, a planet moves fastest:
Angular momentum conservation.
The escape speed from a planet's surface is:
Total energy zero: $\displaystyle \frac{1}{2}v^2=\frac{GM}{R}$.
Ready for more? Take the Unit 6 test.