Newtonian gravitation
Every pair of masses attracts each other with a force proportional to the product of their masses and inversely proportional to the square of the distance between them.
Practise this conceptEvery object with mass pulls on every other object with mass — you, this screen, and a distant star are all tugging on each other, just with forces too small to notice in most cases. Newton's insight was that a single formula describes all of it, from falling apples to orbiting planets.
The force depends on the product of the two masses and falls off with the square of the distance between them: double the distance and the force drops to a quarter, not a half — a common trip-up, since "inverse square" often gets misremembered as "inverse."
Weight and mass get confused here too. Your mass stays the same everywhere, but your weight — the gravitational force on you — depends on what you're standing on. A more massive planet doesn't automatically pull harder at its surface than a less massive one; a small, dense planet can have stronger surface gravity than a large, fluffy one, because surface gravity depends on mass and radius together.
Key ideas
Requires: Newton's second law, Conservation of energy
Unlocks: Central force motion and orbits, Dark matter and galactic structure, Kepler's laws of planetary motion, Solar system formation and planetary astronomy
Common misconceptions
- Doubling the distance between two masses halves the gravitational force between them.
- A more massive planet always exerts a stronger surface gravity than a less massive one, regardless of the planet's size.
- Gravitational force depends on an object's weight, not its mass.
Resources
Part of these UT courses
This concept is mapped as covering part of the following course(s) in the University of Tartu curriculum.
- Mechanics and heatLTFY.01.006
- General astronomyLTTO.00.013