Newton's Gravitation

Newton’s law of gravitation says that any two objects with mass attract each other, and the strength of that pull depends on how much mass they have and how far apart they are. The force gets larger if either mass increases, and it drops off with the square of the distance, so doubling the separation makes the force only one quarter as large. The constant G is the universal proportionality factor that makes the units come out correctly and matches the measured strength of gravity in nature.

Use this formula whenever you need the gravitational force between two masses, such as a planet and a satellite, two people, or two laboratory masses. It is also the starting point for explaining orbits, weight near a planet’s surface, and why gravity weakens rapidly with distance.

• Forgetting that r must be squared, not just used once
• Using the wrong distance, such as the distance from the surface instead of the center for spheres
• Mixing up the gravitational force between two objects with an object's weight near Earth without checking the situation