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I just came across a question on skeptics.SE that asked whether it is possible to sail a boat from the coast of Pakistan to the east coast of Russia in an uninterrupted straight line. A quick glance at a globe suggests that there's nothing to be really skeptical about (the OP may have been misled by the planar nature of map projections). But while thinking about the question, I realized that I don't know the right terminology to describe the changes to the bearing on board of the ship.

As a rough estimate, a ship sailing from Karachi to the Kamchatka Peninsula will start with a bearing of perhaps 210° (relative to true north). If it continues its course in a straight line, it will be sailing basically parallel to the meridians with a bearing of 270° roughly by the time the ship has reached the South Sandwich Islands. The bearing at the Equator will be somewhere in the vicinity of 330°, and it will arrive at Kamchatka with a bearing of about 290°.

What is the right term to refer to this phenomenon that the true bearing changes if you move in a straight line in a non-cardinal direction on a globe? I keep thinking of "declination", but this is probably because I'm aware of what magnetic declination is.

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  • $\begingroup$ Note that even if you do go a cardinal direction, I believe your bearing will change (easiest example, heading north over or even near the North Pole... but the reality is, aside from moving around the equator, I don't believe you can ever stay on the same heading without adjustment by moving in a "straight" path) $\endgroup$ Commented Apr 25, 2022 at 13:46

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I would refer to it as "geodesic curvature", because this is exactly what happens. On a sphere all distinct geodesics curve everywhere towards each other except for perpendicular pairs. That includes curving towards the Equator except for the Equator itself (meaning not a distinct geodesic) or a meridian (perpendicular to the Equator). Curving towards the Equator is then what registers as the change in bearing.

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The only (non NS) path that maintains a fixed bearing relative to true north is a "rhumb line". By contrast, all other straight line paths will see their bearing change relative to north: mark any (non rhumb line) straight line over a globe and see that the angle between longitudes and your path changes. Note that this hard to visualize on a 2D map or computer monitor, though you might see it with Google Earth.

As for declination, it is the angular correction made for the difference between magnetic north and true north and it varies over time and especially place. The declination changes with geographic position and must be accounted for when moving anywhere over the earth. Sailors must be especially vigilant about knowing exactly what the declination is for their position when traveling great distances using a compass; declination is irrelevant if using strictly GPS.

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