Gravitational Field Strength

Gravitational field — a region in which a mass experiences a force.

Gravitational field strength (g) — the force per unit mass acting on a small test mass placed at a point:

g = F / m

measured in N kg⁻¹. It is a vector, directed towards the mass creating the field.

For a point or spherical mass — substituting F = GMm/r² gives

g = G M / r²

The test mass cancels, so the field strength is a property of the field itself, not of whatever is placed in it.

Radial fields — around a spherical mass the field lines point radially inwards, getting further apart with distance. Their spacing represents the field strength, which is why an inverse square law and a radial geometry go together: the same number of lines spread over a sphere of area 4πr².

Uniform fields — over a region small compared with the Earth's radius, the field lines are effectively parallel and evenly spaced, so g is constant. This is the assumption behind ΔEₚ = mgΔh and every Year 1 projectile question.

Example: at the Earth's surface g = 9.81 N kg⁻¹; at the altitude of the International Space Station, about 400 km up, r has increased by only 6%, so g is still about 8.7 N kg⁻¹ — roughly 89% of its surface value. Astronauts are not weightless because gravity is absent. They are in continuous free fall, orbiting the Earth, and everything around them falls with them.

Field strength and acceleration of free fall are the same quantity — N kg⁻¹ is dimensionally identical to m s⁻², since a newton is kg m s⁻². Force per unit mass is acceleration.

Inside a uniform sphere — the field strength falls linearly to zero at the centre, because only the mass closer to the centre than your position contributes. This is often shown on a graph of g against r: rising linearly from the centre to the surface, then falling as 1/r² beyond it.