Direction, Latitude and Longitude — Page 14, Lesson 23

I want to walk you through the concept of longitude, which is the second coordinate we use to fix a position on the Earth's surface, alongside latitude. Let's start with the 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. Let me unpack that. Imagine you have a point on the Earth. The meridian that passes through that point is a great circle running from the North Pole to the South Pole. The Prime Meridian is the reference meridian that passes through Greenwich, England. Now, look at where those two meridians cross the Equator. The shorter arc along the Equator between those two crossing points is the longitude of your point. Longitude is measured in degrees and minutes of arc, and it's annotated East (E) or West (W), depending on whether the point lies East or West of the Prime Meridian. Think of it this way: in Figure 1.10, you are looking 'down' on the North Pole from a point out in space. The meridian of point B crosses the Equator at point Q at, say, 40° of arc to the East of the Prime Meridian. So point B is said to be at longitude 040°E. That's the fundamental idea. Now, a critical skill is calculating the difference in longitude between two positions, sometimes called change of longitude, abbreviated as ch long. The rule depends on whether the two longitudes are on the same side of the Prime Meridian or on opposite sides. If both positions are the same East or West longitude — for example, both West — you subtract the smaller from the larger. So, 100°W minus 080°W gives you a 20° difference, or 20° ch long. Simple enough. If the two longitudes are one East and one West, you add them together. For example, 020°W plus 010°E gives you a 30° difference, or 30° ch long. However, there's an important anomaly you need to watch for. This happens when the two longitudes are East and West and are 'close' to the Greenwich Anti Meridian. Let me give you the example from the book. What is the difference in longitude between 163°E and 152°W? If you follow the basic principle, you'd add them together: 163 plus 152 gives you 315°. But here's the catch — we need to consider the shortest value of difference. The Earth is a sphere, and the shortest arc between two meridians might go the other way around. In this case, if you take that 315° and subtract it from 360°, you get 45° ch long. That 45° is the correct, shortest difference. So always check whether the simple addition gives you more than 180°; if it does, subtract that result from 360° to get the true shortest difference. Finally, let's talk about the limits of longitude. Longitude can be measured up to 180° East or 180° West of the Prime Meridian. These two meridians — 180°E and 180°W — are actually coincident; they are the same line on the opposite side of the Earth from Greenwich. That line is known as the Greenwich Anti-Meridian, and it's normally labelled as either 180°E or 180°W. It's the line where the date changes, but that's a topic for another lesson. So, to summarise: longitude is the angular distance along the Equator from the Prime Meridian, measured up to 180° East or West. When finding the difference, same side means subtract, opposite sides means add, but if that sum exceeds 180°, subtract it from 360° to get the shortest arc.