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# Formula for the distance between 2 longitude lines on a globe at different latititudes

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My goal: the distance between two lines of longitude on a globe at different latitudes.

Would this be accurate?

cosine(latitude) * pi * radius^2  = latitudinal circumference?

then, that circumference / # of longitude lines  = space between 2 of them at this latitude?

Anything simpler or more efficient in mind?

Thanks..

Working on a globe program

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Commented:
CERTIFIED EXPERT
Top Expert 2009
Commented:
>> cosine(latitude) * pi * radius^2  = latitudinal circumference?
That whould be :

2 * cosine(latitude) * pi * radius = latitudinal circumference

when radius is the radius of the Earth and the Earth is seen as a perfect sphere.

>> then, that circumference / # of longitude lines  = space between 2 of them at this latitude
indeed.

You might want to consult the link JR2003 posted though, because it explains how to calculate the distance between two points on the globe (not necessarily on the same latitude).

I suggest the haversine formula :

http://en.wikipedia.org/wiki/Haversine_formula

It's easy to calculate, and has a nice precision.

Note that the Earth is NOT a perfect sphere, so a good choice of the used radius is important (average radius should be OK for most applications).

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Commented:
If you want to add just that little bit extra of geodetic geekiness, you could make sure that your globe model conforms to the WGS84 ellipsoid.  See http://www.colorado.edu/geography/gcraft/notes/datum/datum.html

You'd probably be most interested in the ECEF <-> WGS84 lat lon height conversions in the "Datum Conversions" section.  They have the actual formulas there.

Commented:
I should have some time tonight to review the comments, thanks for your input

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Most Valuable Expert 2014
Top Expert 2015
Commented:
When you say "the distance between two lines of longitude on a globe at different latitudes"
it sounds like you might not be wanting the great circle distance between two points.
If you are wanting the lenght of the path between two lines of longitude while traveling at a constant latitude, then you could use
cosine(latitude) * pi * radius*2  = latitudinal circumference
assuming the globe in question is a sphere.
Although I'm not sure of the purpose of your goal, since traveling at a constant latitude can be almost pi/2 times longer than a great circle path,
e.g. from 90° East to 90° West when traveling along 89°59' North latitude instead of a direct path from 90° East 89°59' North to  90° West 89°59' North
But then, if you aren't restricted to a particular latitide, then the distance between any two lines of longitude is 0, since they all meet at the poles.
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