Gravitational field strength g is force per unit mass

Gravitational Fields & Orbits — AQA A-Level Physics

Key Definition

Gravitational field strength — The force per unit mass experienced by a small test mass placed at that point. Symbol: g. Units: N kg⁻¹.

$$\begin{aligned} g &= \frac{F}{m} \\ &= -\frac{GM}{$r^{2}$} \end{aligned}$$

g = \frac{F}{m}

$g$: gravitational field strengthThe gravitational force per unit mass at a point in a gravitational fieldA region of space in which a mass experiences a gravitational force.. Measured in N kg⁻¹. (N kg⁻¹)
$F$: force due to gravity / weight (N)
$m$: mass of the object (kg)

An object's mass is constant everywhere. Its weight depends on the local value of g.
On Earth's surface, g = 9.81 N kg⁻¹. On Jupiter, g ≈ 25 N kg⁻¹.
g is also called the 'accelerationThe rate of change of velocityThe rate of change of displacement. A vector quantity. Measured in m s⁻¹.. A vector quantity. Measured in m s⁻². due to gravity' with units m s⁻². The two units are equivalent: 1 N kg⁻¹ = 1 m s⁻².
Factors affecting g at a planet's surface: the mass of the planet and the radius of the planet.

Worked Example

Calculate the mass of an object with weight 10 N on Earth.

Show Solution

Write the equation

$$g = \frac{F}{m}$$

Rearrange for mass

$$m = \frac{F}{g}$$

Substitute values

$$m = \frac{10}{9.81} = 1.0 \text{ kg}$$

Answer

$m = 1.0$ kg

Examiner Tips and Tricks

There is a big difference between g (gravitational field strengthThe gravitational force per unit mass at a point in a gravitational fieldA region of space in which a mass experiences a gravitational force.. Measured in N kg⁻¹., lower case) and G (Newton's gravitational constant, upper case).
They are not interchangeable.
Also remember $densityMass per unit volume of a material. Measured in kg m⁻³. = mass / volume$, which often comes up alongside these calculations.