Newton's Cannonball Thought Experiment

Imagine a cannon placed at a very high elevation, with air resistance neglected. A cannonball is fired horizontally. The ball moves forward while gravity pulls it downward. It eventually reaches Earth's surface.

It travels farther before reaching the surface.

Earth's surface curves away beneath the falling object. If the ball has an appropriate horizontal speed, it continuously falls toward Earth while continually missing the surface. It is then in **orbit**.

An orbiting object is not beyond gravity. In fact: **Gravity provides the centripetal acceleration needed for the orbit. For a circular orbit: GMm/r² = mv²/r Cancel `m`: GM/r² = v²r Therefore: v = √(GM/r)**

Launching cannonballs at orbital speed from a mountain was not a practical experiment in Newton's time. The imagined scenario allowed a difficult idea to be reasoned about conceptually.

Gravitational force: **F = GMm/r² Centripetal requirement: F = mv²/r Therefore: v_orbit = √(GM/r)**