Gravitational Field Strength in a Radial Field (AQA A Level Physics): Revision Note

Gravitational field strength in a radial field

• The gravitational field strength at a point describes how strong or weak a gravitational field is at that point

• The equation for gravitational field strength due to a point mass is:

$g=\frac{GM}{r^2}$

• Where:

  • $g$ = gravitational field strength (N kg^-1)

  • $G$ = Newton’s gravitational constant

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

  • $r$ = distance between point source (mass, $m$) and position in field (m)

• Gravitational field strength, $g$, is a vector quantity

• The direction of $g$ is always towards the centre of the body creating the gravitational field

  • This is the same direction as the gravitational field lines

  • On the Earth’s surface, $g$ has a constant value of 9.81 N kg^-1

• However, outside the Earth’s surface, $g$ is not constant

  • $g$ decreases as $r$ increases by a factor of $\frac{1}{r^2}$

  • This is an inverse square law relationship with distance

• When $g$ is plotted against the distance $r$ from the centre of a planet, the graph has two parts:

  • when $r<R$, the radius of the planet, $g$ is directly proportional to $r$

  • when $r>R$, $g$ is inversely proportional to $r^2$ (this is an ‘L’ shaped curve and shows that $g$ decreases rapidly with increasing distance $r$)

• Sometimes, $g$ is referred to as the ‘acceleration due to gravity’ with units of m s^-2

  • Any object that falls freely in a uniform gravitational field on Earth has an acceleration of 9.81 m s^-2