Universal Gravitation

Universal gravitation explains why planets orbit stars, why moons orbit planets, and why objects fall toward Earth. Newton's law of gravitation says every mass attracts every other mass, and the strength of that attraction depends on mass and distance. This idea connects motion in the sky with motion on Earth using one simple rule. It is one of the foundations of classical physics and astronomy.

The gravitational force gets weaker with distance according to an inverse square law, so doubling the distance makes the force four times smaller. Orbits happen when gravity continuously pulls an object inward while the object's velocity carries it forward. This balance creates circular or elliptical paths instead of straight-line motion. The same physics can be used to calculate satellite motion, planetary periods, and escape speed.

Key Facts

Newton's law of gravitation: F = Gm1m2/r^2
The gravitational constant is G = 6.67 x 10^-11 N·m^2/kg^2
Weight near a planet is F = mg, where g = GM/r^2
For a circular orbit, gravitational force provides centripetal force: G Mm/r^2 = mv^2/r
Orbital speed for a circular orbit is v = sqrt(GM/r)
If distance doubles, gravitational force becomes 1/4 as large; if distance triples, it becomes 1/9 as large

Vocabulary

Universal gravitation: The principle that every object with mass attracts every other object with a force.
Inverse square law: A rule stating that a quantity decreases in proportion to 1/r^2 as distance r increases.
Orbit: The path an object follows around another object because of gravity.
Gravitational field: The region around a mass where another mass experiences a gravitational force.
Centripetal force: The inward net force that keeps an object moving in a curved path.

Common Mistakes to Avoid

Using distance instead of distance squared in the denominator, which is wrong because gravity follows F = Gm1m2/r^2, not 1/r.
Thinking heavier objects fall faster because of a larger gravitational force, which is wrong because larger mass also means larger inertia, so the acceleration can be the same.
Assuming astronauts in orbit feel no gravity, which is wrong because gravity is still strong in orbit and is what keeps the spacecraft moving around Earth.
Mixing up mass and weight, which is wrong because mass is the amount of matter while weight is the gravitational force acting on that mass.

Practice Questions

1 Two objects have masses 4 kg and 6 kg and are 2 m apart. Using G = 6.67 x 10^-11 N·m^2/kg^2, calculate the gravitational force between them.
2 A satellite orbits a planet of mass 8.0 x 10^24 kg at a radius of 2.0 x 10^7 m from the planet's center. Find the satellite's circular orbital speed using v = sqrt(GM/r).
3 A spacecraft moves from a distance r from a planet to a distance 3r. Explain how the gravitational force changes and why this follows the inverse square law.