Calculating Gravitational Potential (AQA A Level Physics): Revision Note

Calculating gravitational potential

• The equation for gravitational potential $V$ is defined by the mass $M$ and distance $r$:

$V=-\frac{GM}{r}$

• Where:

  • $V$ = gravitational potential (J kg^-1)

  • $G$ = Newton’s gravitational constant

  • M = mass of the body producing the gravitational field (kg)

  • $r$ = distance from the centre of the mass to the point mass (m)

• The gravitational potential is always negative near an isolated mass, such as a planet, because:

  • the potential when $r$ is at infinity (∞) is defined as zero

  • work must be done to move a mass away from a planet ($V$ becomes less negative)

• It is also a scalar quantity, unlike the gravitational field strength which is a vector quantity

• Gravitational forces are always attractive, this means as $r$ decreases, positive work is done by the mass when moving from infinity to that point

  • When a mass is closer to a planet, its gravitational potential becomes smaller (more negative)

  • As a mass moves away from a planet, its gravitational potential becomes larger (less negative) until it reaches zero at infinity

• This means when the distance ($r$) becomes very large, the gravitational force tends rapidly towards zero at a point further away from a planet