13.1 Gravitational field
- Syllabus
- 9702–2028–2029
- Topic
- 13.1
- Level
- A2
Learning objectives
13.1.1A gravitational field is an example of a field of force and define• understand that a gravitational field is an example of a field of force and define gravitational field as force per unit mass13.1.2A gravitational field by means of field lines• represent a gravitational field by means of field lines
Gravitational field strength is force per unit mass
A gravitational field is a region in which a mass experiences gravitational force. At a point, gravitational field strength g is the gravitational force per unit mass on a small test mass placed there.
g=F/mandF=mg;unitNkg−1(equivalenttoms−2)
g is a vector directed as the force on the test mass. The field is a property of the source masses and exists without the test mass. For several sources, add their field vectors to obtain the resultant.
At g = 9.8 N kg⁻¹ downward, a 2.0 kg mass experiences F = 19.6 N downward. Between Earth and Moon, a point can have g_resultant = 0 when their field contributions have equal magnitudes in opposite directions; neither individual field is zero there.
Field strength is not the force on every object: at one point g is fixed by the sources, while F=mg changes with test mass. g is not universally 9.8 N kg⁻¹.
Field lines encode gravitational direction and relative strength
| Feature of field-line diagram | Meaning |
|---|---|
| tangent to a line at a point | direction of gravitational force and g on a small test mass |
| arrowhead | points in that force direction |
| closer spacing | qualitatively stronger field |
| non-crossing lines | one unique resultant-field direction at each point |
| Source/region | Required pattern |
|---|---|
| isolated point mass or outside a spherical mass | radial lines directed inward toward the centre; symmetrically spaced |
| approximately uniform field | parallel, equally spaced lines with common arrow direction |
To draw a field, identify the direction a small mass would accelerate at several points, sketch smooth lines tangent to those directions, add inward arrowheads and vary spacing only to show relative strength.
Gravitational field lines are a representation, not physical tracks or object trajectories. They refer to a test mass, not a positive test charge, and their density is not an exact numerical scale unless separately calibrated.