AP® Physics C: Mechanics · Unit 2 · Topic 2.6
Gravitational Fields
A gravitational field is the force per unit mass that a planet or star sets up at every point in space around it, with g = GM/r2 pointing toward the source.
Instead of tracking a separate force for every object that might wander near a planet, you can ask what the planet does to space itself. Define the gravitational field as g = GM/r2, the force per unit mass at a point a distance r from a mass M. Any test mass placed there feels a force F = mg, but the field exists whether or not you put something there to feel it. This is the same move you will make later with electric fields: separate the source from whatever happens to be sitting in it.
Picture arrows drawn all around a planet, every arrow pointing straight at the center, shrinking in length as you move outward. The direction of the arrow is the direction gravity pulls anything placed there. The length encodes strength: because g falls off as 1/r2, doubling your distance from the center cuts the field to a quarter. Near the surface the arrows are dense and long; far away they thin out and shrink, but never quite vanish.
This is the same field you already know as free-fall acceleration. On Earth's surface g = 9.8 N/kg = 9.8 m/s2, and that is not a coincidence — the two expressions are dimensionally identical. Later, when you get to orbits and gravitational potential energy, this field is exactly what you integrate or combine with orbital speed to find how fast a satellite must move to stay in a circular path, or how much energy it takes to escape a planet entirely.
Key terms
- Gravitational field
- The force per unit mass a source mass creates at each point in space, g = GM/r2, directed toward the source.
- Field line
- An arrow representing the direction and relative strength of a field at a given location.
- Inverse-square law
- A relationship where a quantity falls off in proportion to one over the square of the distance from its source.
- Free-fall acceleration
- The acceleration an object experiences under gravity alone, numerically equal to the local gravitational field.
Watch it explained
- How it worksHow do field arrows around a planet encode both the strength and the direction of gravity?
- Worked exampleFind the surface gravitational field of a planet with twice Earth's mass and 1.5 times its radius.
- Common mistakeWhy isn't a field strength in newtons per kilogram a different thing from an acceleration in m/s2?
- Going furtherWhat does the gravitational field look like in the region between the Earth and the Moon?
Check yourself
End of topic.