## 2.8 Shortest Distance between Points on a Parallel

Note: if you cannot remember what parallels of longitude are, revise notes for 2.6 Modelling the World.

Note: if you cannot remember how to find the shortest distance between points on great and small circles, revise notes for 2.5 Distance Between Points on a Sphere.

### Shortest Distance between Points on the Equator

- Locations of equal latitude exist on the same parallel of longitude. By taking the shorter section of that parallel with the locations as the endpoints, we can extract an arc representing the shortest path between the two locations. The length of that path can be found using the longitudinal coordinates of the locations.
- The
**plane of the equator**intersects the centre of the world and so it is a**great circle**. - We can modify the equation for arc length (from notes 2.1 Circles and Arcs) for this situation. There are
**3 situations**with different formulas:- If both locations are given in the same units (
^{o}E or^{o}W) or one or both lie on the Greenwich meridian, the formula is:

- If both locations are given in the same units (