Great Circles

The straightest lines on a sphere

An interactive lesson with 7 steps, about 6 minutes: you predict, drag and solve, with instant feedback on every answer. It runs in your browser and needs JavaScript.

What you’ll learn

• The shortest path on a sphere follows a great circle.
• Great-circle distance $d = R\theta$, with $\theta$ in radians.
• Parallels (except the equator) aren’t great circles, so following them is longer.

Steps

1. What is a straight line?
2. Along a meridian
3. Over the top
4. The polar route
5. Where the shortcut pays most
6. Walking due east
7. As far as possible