Law of Universal Gravitation

This formula gives the gravitational force between two masses: bigger masses pull more strongly, and the pull gets much weaker as the distance between their centres increases. The inverse-square dependence happens because gravity spreads out through space, so doubling the separation makes the field spread over four times the area, reducing the force to one-quarter. The constant G is the universal proportionality factor measured experimentally, which lets the same law work for objects from stones to planets.

Use this when you need the gravitational force between two objects, especially in astronomy, orbital motion, and problems involving planets, moons, satellites, or separated objects on Earth. It is also useful for estimating how changing mass or distance affects attraction.

• Using the distance between edges instead of the distance between the objects’ centres
• Forgetting that the force decreases with the square of distance, not just distance
• Mixing up mass and weight, or using grams instead of kilograms