Deriving Gravitational Field Strength (g)
- The gravitational field strength at a point describes how strong or weak a gravitational field is at that point
- The gravitational field strength due to a point mass can be derived from combining the equations for Newton’s law of gravitation and gravitational field strength
- For calculations involving gravitational forces, a spherical mass can be treated as a point mass at the centre of the sphere
- Newton’s law of gravitation states that the attractive force F between two masses M and m with separation r is equal to:
- The gravitational field strength at a point is defined as the force F per unit mass m
- Substituting the force F with the gravitational force FG leads to:
Calculating g
- 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 1/r2
- This is an inverse square law relationship with distance
- When g is plotted against the distance from the centre of a planet, r 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 r2 (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
Worked example: Gravitational field strength

Step 1: Write down the known quantities
gM = gravitational field strength on the Moon, ρM = mean density of the Moon
gE = gravitational field strength on the Earth, ρE = mean density of the Earth
Step 2: The volumes of the Earth and Moon are equal to the volume of a sphere
Step 3: Write the density equation and rearrange for mass M
M = ρV
Step 4: Write the gravitational field strength equation
Step 5: Substitute M in terms of ρ and V
Step 6: Substitute the volume of a sphere equation for V, and simplify