Newton's Law of Universal Gravitation

Every object with mass pulls on every other object with mass — an apple falls to Earth for the same reason the Moon stays in orbit around it. The pull gets weaker very quickly with distance: twice as far apart means only a quarter of the force.

F = G · M · m / r²

• F — force (N): the gravitational pull between the two objects
• G — gravitational constant (N·m²/kg²): a fixed tiny number that sets the strength of gravity everywhere
• M — mass one (kg): the mass of the first object, like a planet
• m — mass two (kg): the mass of the second object, like a satellite
• r — distance (m): the distance between the centers of the two objects

A planet pulls on a 1 kg satellite. For this planet, G times M works out to a simple 40 in our units, and the satellite orbits at a distance of 2 meters. What is the gravitational force?

• G · M = 40 N·m²/kg
• m = 1 kg
• r = 2 m

1. F = (G · M) · m / r²
2. F = 40 · 1 / 2² = 40 · 1 / 4

F = 10 N

The same satellite now orbits twice as far away, at 4 meters, with the same G M of 40 and mass of 1 kg. What is the new force?

• 5 N
• 20 N
• 2.5 N

Keep the distance at 2 meters and G M at 40, but swap in a heavier 2 kg satellite. What is the new force?

• 20 N
• 10 N
• 40 N