5

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?

2 Answers 2

6

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.

2
  • Ah, and an arc would be the difference between two points on the same line of lat or lon?
    – RickyA
    Nov 29, 2012 at 14:09
  • 1
    (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, 2012 at 16:39
0

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

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge that you have read and understand our privacy policy and code of conduct.

Not the answer you're looking for? Browse other questions tagged or ask your own question.