Direction, Latitude and Longitude — Page 14, Lesson 23

We’ve covered latitude, so now let’s turn to longitude. This is the east–west coordinate, and I want you to hold onto one image: the Equator is the only line of latitude that’s a great circle, and longitude is measured along that Equator. Here’s the precise definition. The longitude of any point is the shorter distance in the arc along the Equator between the Prime Meridian and the meridian through the point. So we measure along the Equator, in degrees and minutes of arc, and we annotate it East (E) or West (W), depending on whether the point lies east or west of the Prime Meridian, which is Greenwich. Let me make that concrete. In Figure 1.10, you’re looking down on the North Pole from out in space. The meridian of point B crosses the Equator at point Q, say 40° of arc to the east of the Prime Meridian. So point B is at longitude 040°E. Notice the format — four digits, 040°E — that’s the standard way we write it. Now, the real skill in navigation is not just reading a longitude, but finding the difference in longitude between two positions. And here’s the rule. If both positions are the same direction — both East or both West — you subtract the smaller from the larger. So 100°W minus 080°W gives you 20° difference. We call that the change of longitude, abbreviated ch long. But if the two longitudes are opposite — one East and one West — you add them. So 020°W plus 010°E gives you 30° difference, or 30° ch long. Now here’s the trap, and it’s a classic exam question. What happens when the two longitudes are East and West, but they’re close to the Greenwich Anti-Meridian? Let’s work the example. What’s the difference in longitude between 163°E and 152°W? If you blindly follow the rule, you add them: 163 plus 152 gives you 315°. But that’s wrong, because we want the shortest value of difference. So you take 315° away from 360°, and you get 45° ch long. That’s the correct answer. Why does this happen? Because longitude can be measured up to 180°E or 180°W of the Prime Meridian. And those two meridians — 180°E and 180°W — are actually the same line. They’re coincident, and together they’re called the Greenwich Anti-Meridian, normally labelled 180°E or 180°W. So when two points straddle that anti-meridian, the short way around the world is across it, not the long way through Greenwich. So the key takeaway: difference in longitude is always the shorter arc. Same direction, subtract. Opposite directions, add — but if that sum exceeds 180°, subtract it from 360° to get the true shortest change of longitude. That’s the whole game with longitude.