----------------------------Original message----------------------------
re:distance formulas. start here? LC
How far is it?
Welcome to indo.com, the new home of the distance service. Please note the new
URL:
http://www.indo.com/distance/
This service uses the University of Michigan Geographic Name Server and a
supplementary database of
world cities to find the latitude and longitude of two places, and then
calculates the distance between them
(as the crow flies). It also provides a map showing the two places, using the
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Various query formats are allowed; for example:
Chicago, IL
90210
Waikiki
40:26:26N 79:59:46W
Athens, Greece
NEW! We've added over 500 cities around the world!
----------------------------Original message----------------------------
> ----------------------------Original message----------------------------
> Has anyone come across a mathematical formula for the distance between two
points calculated from latitude and logitude coordinates?
>
> Joseph M. Winkler, St. Louis Public Library, [log in to unmask]
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Message-----------------------------
I've become interested in this problem and have given it some, but
not enough yet, thought. First is that the equation below works OK but only
as long as the coordinates are both positive numbers, (or corrected to be
so). Also, as far as I could test, DLo must be less than 90-degrees and the
resulting answer, D, must be less than 90-degrees. On the other hand, I've
not tried the equation in "radians". Actually, the equation should be
written as follows:
D = ArcCos[(sinL1 x sinL2) + (cosL1 x cosL2 x cosDLo)]
*******************************One Answer to Original
Message************************************
Cos D = (sinL1 x SinL2) + (CosL1 x CosL2 x CosDlo)
where L1 = the latitude of place A
L2 =the latitude of place B
DLo = the difference in longitude between places A and B
D = the arc distance (in degrees) between places A and B
taken from "Direct line distances" by Gary Fitzpatrick and Marilyn Modlin
Jim Coombs
Map Librarian
Southwest Missouri State University
******************************End of Answer to Original
Message***********************************
Then, in answer to the suggestion that the accuracy would be as much
as 200miles, I submitt the following.
The Earth is an ellipsoid with an eccentricity of about one part in
300. At the equator, the Earth's radius is 6378 kilometers, (3963 statute
miles & 3487.6 nautical miles), and, at the poles, 6357 kilometers or,
respectively, Earth's circumference is 40,074,(around the equator), or
39,942, (around the poles). Thus, even for a complete circle around the
Earth, the error would be no more than 132 kilometers and, if the average
radius was used, no more than 66 kilometers, much less than the 200+ miles
suggested by another replier. The Earth also has local "highs" and "lows"
but these are on the order of less than 100 meters and are insignificant.
Thus, if one simply finds the angle, D, between the two
coordinates, say 90-degrees, the surface distance is 40,000 times 90/360
equal 10,000 kilometers to within about 90/360 of 66 equal to 16/17
kilometers. To do better, then the equations would have to be those of an
ellipsoid rather than a sphere and the latitudes and longnitudes considered
as to their location on the ellipsoid. That would get the answer in values
of tens of meters rather than kilometers.
Certainly the equations exist to convert two coordinates in any
combination of plus or minus latitudes or longnitudes and separations of
greater than 90-degrees exist but I don't have them handy and I'm too lazy
to work it out but, when you get them, the above will give you the distance.
Fred Schaff, Spring Grove, PA, <[log in to unmask]>
Fred Schaff, Spring Grove, PA, <[log in to unmask]
"The Meek shall inherit the Earth. The Rest of Us will go to the Stars."
John W. Campbell
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>From: Schaff-Fred <[log in to unmask]>
>Subject: Distance between two points
>To: Multiple re
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