Great-Circle Routes

Distances and headings between cities

An interactive lesson with 8 steps, about 7 minutes: you predict, drag and solve, with instant feedback on every answer. It runs in your browser and needs JavaScript.

What you’ll learn

• Spherical law of cosines: $\cos\theta = \sin\varphi_1\sin\varphi_2 + \cos\varphi_1\cos\varphi_2\cos\Delta\lambda$.
• Rhumb lines keep a constant bearing (straight on Mercator); great circles are shorter.
• A great circle’s bearing changes along the way; London to New York starts at 288°.

Steps

1. Distance between any two places
2. London to New York
3. Which way to head?
4. Aim for New York
5. How much shorter?
6. Spiralling
7. The loxodrome
8. The northernmost point