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What is the delta between two lat/lon pairs called? Delta degrees? Arcs?

Is it some quantity of distance but what is its unit of measurement?

And related: Can we use pythagoras to calculate this distance?

eg. d = (0, 3) and (4, 0) = 5?

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2 Answers

up vote 6 down vote accepted

You can't use the simple Pythagorean theorem as that one's for planes whereas the distances you are talking about now are on a curve. For that, you'll have to use spherical trigonometry. From Wikipedia:

Let enter image description here be the geographical latitude and longitude of two points (a base "standpoint" and the destination "forepoint"), respectively, and enter image description here their absolute differences; then enter image description here, the central angle between them, is given by the spherical law of cosines:

enter image description here

The distance d, i.e. the arc length, for a sphere of radius r and enter image description here  given in radians, is then

enter image description here

Note that using r = 6,371.009 metres is appropriate for calculating great-circle distances between points on the Earth's surface, in which case the result d will also be in metres.

It's called a great circle distance btw.

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Ah, and an arc would be the difference between two points on the same line of lat or lon? –  RickyA Nov 29 '12 at 14:09
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(1) The Wikipedia formula is usually not used in practice, due to numerical problems in computing the inverse cosine of small angles: see gis.stackexchange.com/questions/4906. (2) "Arc" is a vague term. In the context of this question, Ricky, you probably mean "geodesic." However, "lines" of latitude are not geodesics (except the Equator itself): that is to say, in traversing from point A to point B (both on a common latitude), you do not stay at a constant latitude. See Why is the 'straight line' path across a continent so curved?. –  whuber Nov 29 '12 at 16:39
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I've seen a Euler Pole plus an angular displacement used to describe "delta". This is used a lot in plate reconstruction, where these deltas are often referred to as "rotations", but I'm not sure if that is a formal definition.

enter image description here

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