Deriving gravitational field strength (g)
- There are two situations where gravitational field strength is considered:
- at a point
- due to a mass
Gravitational field strength due to a point
- The gravitational field strength at a point describes how strong or weak a gravitational field is at that point
- The gravitational field strength at a point is defined as
The force per unit mass of a gravitational force on an object
- Gravitational field strength at a point is given by the equation:
- Where:
- g = gravitational field strength measured in newtons per kilogram (N/kg)
- F = gravitational force measured in newtons (N)
- m = mass of object in gravitational field measured in kilograms (kg)
Gravitational field strength due to a point mass
- The gravitational field strength due to a point mass within a gravitational field can be derived from
- combining the equations for Newton’s law of gravitation
- the definition of a gravitational field
- Newton’s law of gravitation states that the attractive force FG between two masses M and m with separation r is equal to:
- Rearrange the definition of gravitational field strength at a point to make force F the subject:
- Equate the gravitational force and the force due to gravitational field strength:
- Cancel out the mass, m, on each side:
- The equation for gravitational field strength due to a point mass is:
- 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)
Examiner Tip
It is important to recognise the difference between the two gravitational field strength situations:
- gravitational field strength at a point due to the object creating the gravitational field
- gravitational field strength due to a point mass placed in a the gravitational field of a bigger object is