Gravitation
A short lesson with diagrams, a worked example, a problem to try, and a quick check. Then quiz yourself on 5 practice questions.
Every two masses attract: Fg = Gm1m2 ÷ r². The distance r is measured center to center, and the force follows an inverse square: double the distance and the force drops to a quarter.
1. The inverse square law
2. g, weight, and mass
The gravitational field strength g tells you the force per kilogram at a location. Near Earth’s surface g ≈ 10 N/kg, which is also the free-fall acceleration, 10 m/s².
Farther from the planet’s center, g gets smaller by the same inverse square rule.
Mass shows up two ways: how hard an object is to accelerate (inertial mass, from Fnet = ma) and how strongly gravity pulls it (gravitational mass, from Fg = mg). Every experiment finds these are equal. That’s why all objects fall with the same acceleration.
3. Example, then try it
A 400 kg satellite weighs 4000 N on Earth’s surface. What is the gravitational force on it in orbit at an altitude equal to Earth’s radius?
Altitude R means the distance from Earth’s center is r = R + R = 2R.
Double the distance → one-quarter the force: 4000 ÷ 4 = 1000 N.
Planet X has twice Earth’s mass and twice Earth’s radius. What is g at its surface? (Earth: g = 10 N/kg)
Write the ratio: g = GM/r², so gX ÷ gEarth = (MX/ME) ÷ (rX/rE)².
Plug in: 2 ÷ 2² = 2 ÷ 4 = 1/2.
Scale Earth’s value: gX = (1/2)(10 N/kg) = 5 N/kg.
Answer: 5 N/kg. More mass helps, but the larger radius counts twice because it’s squared.
4. Common mistakes
Two asteroids are a fixed distance apart, center to center. If both of their masses double and the distance stays the same, the gravitational force between them…
F = Gm1m2/r². Doubling both masses multiplies the top by 2 × 2 = 4, so the force becomes four times as large.
Ready to practice?
5 questions on Gravitation, each with a hint and an explanation for every wrong answer.