3.7.2.4
Circular orbits: gravitational force provides centripetal force
Gravitational Fields & Orbits — AQA A-Level Physics
- For a planet or satellite in a circular orbit, the gravitational force provides the centripetal forceThe resultant force directed towards the centre of a circular path that causes an object to move in a circle. It is not a separate force but the net force providing circular motion..
- The gravitational force is perpendicular to the direction of travel, so it changes direction but not speed.
Deriving the orbital speed
- Set gravitational force equal to centripetal forceThe resultant force directed towards the centre of a circular path that causes an object to move in a circle. It is not a separate force but the net force providing circular motion.:
$$\frac{GMm}{r^2} = \frac{mv^2}{r}$$
- Cancel m and one factor of r:
$$v^2 = \frac{GM}{r}$$
- $v$: orbital speed (m s⁻¹)
- $G$: Newton's gravitational constant
- $M$: mass of the central body being orbited (kg)
- $r$: orbital radius from centre of central body (m)
- All satellites in the same orbit travel at the same speed, regardless of their own mass.
- Closer orbits have higher speeds. Further orbits have lower speeds.