Newton's Cannon: Falling Around the Earth

Lesson 1 of 10 · 5 min · Free, no account needed

What you will learn

A ball fired sideways falls toward Earth, and the faster it goes, the farther it lands.
Fast enough, about 7.9 km/s at the ground, the Earth curves away as fast as the ball falls: an orbit.
Higher up gravity is weaker, so a circle orbit needs less speed. A bit faster than that gives a stretched loop.

The ISS is falling toward Earth right now, all the time. Why does it never hit the ground?
Newton imagined a cannon on a giant mountain. Bet: how fast must the ball fly to fall all the way round?
Turn the speed and fire. Faster and faster, until the ball never lands.
This cannon only fires at 7.0 km/s. Drag the mountain until the shot is a circle.
The green dashed ring is a circle at the mountain top's height. Higher up, a circle needs less speed: find the height where it needs exactly 7.0 km/s.
What you saw has a name.
An orbit is falling around a planet: the object falls toward it all the time, but moves sideways so fast that it keeps missing.
At the ground, without air, that takes about 7.9 km/s. The ISS, about 420 km up, flies at about 7.7 km/s and goes round in about 92 minutes.
Simplified model: real cannonballs would be stopped by the air. Real satellites are launched above most of the air first.
Game: Orbit or crash. Put a ball in orbit from each of three mountains.
Drag the arrow tip to set the speed. The ball must stay inside the green band. Fewer misses, more stars.
This ball leaves at 8.4 km/s, a bit faster than the circle speed. Draw its path.
At the cannon the ball moves faster than circle speed, so gravity bends its path less than a circle. It climbs, slows as it climbs, and gravity turns it back. The cannon ends up the lowest point of a stretched loop, an ellipse.
Your last shot from the game. Press Play.

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