AP® Physics 1: Algebra-Based · Unit 2 · Topic 2.6
Gravitational Field and Weight
Every object near Earth falls at 9.8 m/s2 because that number is Earth's gravitational field strength, set by Earth's mass and radius, not by the object's own mass.
Drop a bowling ball and a tennis ball and they hit the ground together. That seems strange until you remember Newton's second law: a = F/m. Gravity's pull F on an object is proportional to that object's mass, so when you divide by mass to get acceleration, the mass cancels out. What's left is a number that depends only on the planet: g = GM/r2, where M is the planet's mass and r is its radius (distance from the planet's center to its surface). Plug in Earth's mass and radius and you get 9.8 m/s2, the same for a feather or a truck.
This formula tells you g is a property of space itself around a planet — a gravitational field. Bigger mass packed into the same radius makes a stronger field; spreading the same mass over a bigger radius makes it weaker, and the radius matters more because it's squared. Drawn as a picture, the field looks like arrows pointing straight into the planet's center from every direction, longer (stronger) close to the surface and shorter (weaker) farther out, since the field falls off as 1/r2.
This connects directly to orbits and to the normal force ideas from earlier in the unit. Weight is just the force of gravity, mg, and what you feel as weight is actually the normal force pushing back on you. An orbiting astronaut still has gravity acting on her, bent into a circular path — she and her station are both in continuous free fall toward Earth, just moving sideways fast enough to keep missing it. With no floor pushing up, she feels nothing, which is why it's called apparent weightlessness, not an absence of gravity.
Key terms
- Gravitational field (g)
- The gravitational force per unit mass at a point in space, measured in N/kg or equivalently m/s2.
- Surface gravity
- The value of the gravitational field right at a planet's surface, equal to GM/r2.
- Free fall
- Motion under gravity alone, with no supporting force, so the object accelerates at g.
- Apparent weightlessness
- The sensation of having no weight that occurs in free fall, even though gravity is still fully acting.
- Weight
- The force of gravity on an object, equal to mg, directed toward the planet's center.
Watch it explained
- How it worksHow does the mass of a planet and its radius combine to set the field strength at its surface?
- Worked exampleFind the surface gravity of a planet with twice Earth's mass and twice Earth's radius.
- Common mistakeWhy isn't an astronaut in orbit weightless because gravity has stopped reaching her?
- How it worksWhat does the gravitational field look like drawn as arrows all around a planet?
Check yourself
End of topic.