Your weight is Earth's pull on you. But gravity is not something only planets do. Newton realized that every two masses attract each other: you and your desk, the Moon and the oceans, the Sun and Earth.
Key idea
The gravitational force between two masses grows with each mass and shrinks with the square of the distance between their centers. Double one mass: double the force. Double the distance: one quarter of the force.
Why it works
Think of gravity spreading out from a mass in all directions, like light from a bulb. At twice the distance, the same pull is spread over a sphere with $2^2 = 4$ times the area, so each spot gets $\tfrac{1}{4}$ as much. At three times the distance, $\tfrac{1}{3^2} = \tfrac{1}{9}$. Between everyday objects the force is tiny; it takes a planet-sized mass to make it strong.
Worked example: Change the distance
Two asteroids attract each other with 600 N. They drift to three times as far apart. What is the force now?
- Distance × 3 means force ÷ $3^2 = 9$.
- $600 \div 9 \approx 67$ N.
Answer: About 67 N
Worked example: Change both
Two balls attract with force $F$. One ball is replaced by one with twice the mass, and the distance is doubled. What is the new force?
- Mass × 2: force × 2.
- Distance × 2: force ÷ 4.
- Together: $F \times \dfrac{2}{4} = \dfrac{F}{2}$.
Answer: Half the old force
Common mistake
Thinking there is no gravity in space because astronauts float, or that gravity needs air. The space station orbits about 400 km up, where gravity is still about 90% as strong as on the ground. Astronauts float because they and the station fall around Earth together, so nothing presses on them. And gravity crosses empty space: it holds the Moon to Earth and Earth to the Sun.
Fire Newton's cannon yourself in the Orbit Lab.