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
- The gravitational field strength unit is N kg-1
Gravitational Field Strength Formula:
- 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:
- Cancelling mass m, the equation becomes:
- 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 from the mass where you are calculating the field strength (m)