In the late 17th century, Isaac Newton devised a brilliant thought experiment to show that the same gravitational force responsible for making objects fall to the ground is also responsible for keeping the Moon in its orbit. This was a revolutionary unification of terrestrial and celestial mechanics.
Imagine a cannon placed on top of an impossibly tall mountain — so high that air resistance can be ignored. The cannon fires a ball horizontally with increasing speeds.
| Launch Speed | Result |
|---|---|
| Low speed | Ball curves down and hits Earth nearby |
| Medium speed | Ball travels farther before hitting Earth |
| At orbital velocity | Ball falls at the same rate Earth curves away — circular orbit |
| Above orbital velocity | Elliptical orbit or escape from Earth |
The force underlying this experiment is described by:
where:
This single law explains both why an apple falls from a tree and why the Moon orbits Earth.
Earth's surface curves downward by approximately 5 m for every 8 km of horizontal distance. If a projectile is launched horizontally fast enough, it falls toward Earth at exactly the rate the surface curves away beneath it. The result is a continuous circular orbit.
This is the key insight: an orbit is perpetual free-fall. The satellite is always falling toward Earth, but its tangential velocity is so large that it never actually reaches the surface.
For a circular orbit, the gravitational force provides the centripetal force:
Cancelling (the satellite mass) from both sides:
where is Earth's mass and is the orbital radius.
Key result: Orbital speed is independent of the satellite's own mass and decreases as orbital radius increases.
Below orbital velocity: The cannonball follows a curved arc and strikes Earth's surface (parabolic approximation for short ranges; technically an ellipse truncated by Earth).
At orbital velocity: Circular orbit — the ball is in perpetual free-fall around Earth.
Above orbital velocity: The orbit becomes elliptical. At a sufficiently high speed (escape velocity), the ball escapes Earth's gravitational field entirely.
A satellite in orbit is not beyond gravity's reach. Gravity is still acting on it — that is precisely what keeps it in a curved path. The satellite is in a state of continuous free-fall, but its high tangential velocity means it moves sideways as fast as it falls, maintaining a constant altitude.