Problem
Why does the Moon not fall? A child asks: “If gravity pulls the Moon toward the Earth, why doesn’t the Moon crash into us?”. Answer in qualitative terms using Newton’s concept of continuous falling and orbital velocity. Why does the same not hold for an apple?
Solution
The Moon really is falling. The Moon does indeed fall toward the Earth: gravity pulls it continuously and its trajectory constantly curves toward the planet. The key is that the Moon also has a large tangential velocity, perpendicular to the direction of the fall.
Newton’s mountain thought experiment. Imagine a cannon on a very tall mountain. With little speed the ball lands not far away; increasing the speed makes it land ever further. At a sufficient speed, the Earth’s surface “curves away” beneath the ball at the same rate it falls: the ball keeps falling but never touches the ground, and circles the Earth. This is exactly an orbit: permanent free fall. Here gravity plays the role of the centripetal force that maintains the circular motion.
Why not the apple? The Moon has the “right” tangential velocity (about ) to always miss the Earth while falling. An apple released from rest has essentially zero tangential velocity: its falling trajectory is almost vertical and meets the ground immediately. Same law of gravity, same “falling,” but different initial conditions.
Links
Topics: Gravitazione Concepts: Orbite · Moto circolare uniforme · Forza centripeta · Legge di gravitazione universale