How do you calculate gravitational field strength?

Gravitational field strength is calculated using the formula g = GM/r², where G is the gravitational constant, M is the mass, and r is the distance.

In more detail, the gravitational field strength is a measure of the force of gravity experienced by a hypothetical test mass placed at that point in the field. It is defined as the force per unit mass exerted on an object due to gravity. The formula to calculate it is g = GM/r², where:

- g is the gravitational field strength, measured in newtons per kilogram (N/kg)
- G is the gravitational constant, which is approximately 6.674 × 10^-11 N(m/kg)²
- M is the mass of the object creating the gravitational field, measured in kilograms (kg)
- r is the distance from the centre of the object to the point where the field strength is being calculated, measured in metres (m)

This formula is derived from Newton's law of universal gravitation, which states that every particle of matter in the universe attracts every other particle with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centres.

In the context of the Earth, the gravitational field strength is approximately 9.8 N/kg at the surface and decreases as you move away from the centre of the Earth. This is because the distance r in the denominator of the formula is increasing.

It's important to note that the gravitational field strength is a vector quantity, which means it has both magnitude and direction. The direction of the gravitational field is always towards the object creating the field.

IB Physics Tutor Summary: The gravitational field strength, measured in N/kg, shows how strong gravity is at a point. It's found with the formula g = GM/r², using the gravitational constant (G), the mass of the object (M), and the distance from its centre (r). This value tells us how much force per unit mass gravity exerts there, decreasing with distance from the object.