The V-r and g-r graphs are linked by gradient and area

Gravitational Fields & Orbits — AQA A-Level Physics

g = -\frac{\Delta V}{\Delta r}

$g$: 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)
$ΔV$: change in gravitational potentialThe work doneEnergy transferred when a force moves an object. In electrical circuits, W = QV (chargeA property of matter that causes it to experience a force in an electromagnetic field. Measured in coulombs (C). times potential difference). per unit mass in bringing a small test mass from infinity to that point. Always negative. Measured in J kg⁻¹. (J kg⁻¹)
$Δr$: change in distance (m)

The gradient of a V-r graph at any point gives the value of g at that point. Draw a tangent and calculate the slope.
The area under a g-r graph between two radii gives the change in gravitational potentialThe work doneEnergy transferred when a force moves an object. In electrical circuits, W = QV (chargeA property of matter that causes it to experience a force in an electromagnetic field. Measured in coulombs (C). times potential difference). per unit mass in bringing a small test mass from infinity to that point. Always negative. Measured in J kg⁻¹. ΔV between those radii.
The V-r graph follows a -1/r curve. All values of V are negative. The curve has a shallow increase as r increases.
The g-r graph follows a 1/r² curve. All values of g are positive. The curve has a steep decline as r increases.
To estimate the area under a g-r graph: count squares on graph paper or split into trapeziums.

Examiner Tips and Tricks

The g-r graph (1/r²) should start steeper and decay faster than the V-r graph (1/r).
In sketch questions, make this distinction clear or you will lose marks.