Mechanics · Physics

Newton's Cannon and Satellites Simulation

Fire a cannonball from a mountain fast enough to orbit the Earth, or escape it, then launch a satellite at any angle. Watch it sweep equal areas in equal times.

Interactive virtual lab · no download · works on phones and laptops

Chapter: Gravitation
For: Class 11 · JEE · NEET
Time: ~12 min

Newton's Cannon and Satellites is a Pro simulation

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How to use it

1Cannon: set the mountain height and launch speed, then Fire.
2Use the circular and escape speed buttons.
3Satellite: set distance, speed and launch angle, then Launch.
4Turn on the equal-time areas.

What to notice

Below √(GM/r) the ball falls back; at it, a circular orbit (7.9 km/s at the surface).
At √(2GM/r) it escapes (11.2 km/s at the surface).
In between, the path is an ellipse.
Gravity exerts no torque about the Earth's centre, so equal areas are swept in equal times.

For teachers

A ready-made teaching kit comes with this lab

Lesson plan
19 min, 4 steps
Ask the class
3 questions with answers
Quick quiz
5 questions, printable
Key formulas
4 formulas

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About the Newton's Cannon and Satellites simulation

In the Principia Newton imagined a cannon on a very high mountain. Fire the ball slowly and it falls back to Earth; fire it faster and it lands further round the curved planet; fire it at the right speed and the ground curves away beneath it as fast as it falls — it is in orbit. Faster still, it escapes. The Moon and every satellite are cannonballs that keep missing.

This orbital velocity simulation uses real Earth numbers: 7.9 km/s for a circular orbit at the surface and 11.2 km/s to escape. A second tab launches a satellite at any speed and angle and shades the areas it sweeps in equal times, showing Kepler's second law and the constant angular momentum behind it.

Also covers: orbital velocity, escape velocity, newton cannonball, satellite launch, kepler second law, equal areas.