Right, let's work through this properly — Page 247, Lesson 225

Right, let's work through this properly. This is a classic exam-style question, and I want to show you exactly how to think about it, because the method is just as important as the answer. The question is: The initial great circle track from A (40°N 002°W) to B (50°N 010°E) is 060°(T). What is the initial great circle track from B to A? Now, the very first thing I want you to do is draw a sketch. It's only a rough diagram to get the situation into your mind — not a scale drawing. We're in the Northern hemisphere, so I want you to draw a couple of meridians converging northwards, like this. The initial great circle track from one of them is 060°(T). So make it the left-hand one, because if you draw it from the right-hand one, the bearing goes off the diagram. This means that the left-hand intersection must be A and the right-hand one must be B, because the question says the initial great circle track from A is 060°(T). Now, check it out by reference to the latitude and longitude. If we have it right, with an initial track of 060°(T) at A, B should be north of A — and it is, because B is at 50°N and A is at 40°N. And B should be east of A — and it is, because B is at 010°E and A is at 002°W. Now that we have the diagram right, we can calculate the convergency. The formula is: Convergency = Change in Longitude × Sine Mean Latitude The change in longitude is 12°, from 002°W to 010°E. The mean latitude is 45°N, halfway between 40°N and 50°N. Sine 45° is 0.7071. So convergency = 12 × 0.7071, which gives us 8.5. Now, that's the convergency. But the question asks for the initial great circle track from B to A. Let me explain the relationship. The initial great circle track from A to B is 060°(T). The track from B to A is the reciprocal, but for a great circle, it's not simply 180° different — that's only true for a rhumb line. For a great circle, the track from B to A is the track from A to B plus 180°, minus the convergency. So: 060° + 180° = 240°. Then subtract the convergency of 8.5°, which gives us 231.5°(T). So the initial great circle track from B to A is 231.5°(T). Let me just recap the key points. The convergency is the angle between the meridians at the two points, and it's calculated as the change in longitude times the sine of the mean latitude. The change in longitude here is 12°, the mean latitude is 45°N, and sine 45° is 0.7071, giving a convergency of 8.5°. And the track from B to A is the reciprocal of the track from A to B, adjusted for convergency: 060° + 180° − 8.5° = 231.5°(T). That's the complete method. The diagram is essential to get the geometry right, and the formula gives you the convergency, which you then apply to find the reciprocal great circle track.