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MathGroup Archive 2002

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Re: calculating the azimuth between two lat/lon's

  • To: mathgroup at smc.vnet.net
  • Subject: [mg34790] Re: calculating the azimuth between two lat/lon's
  • From: rainer <rainer.gruber at gmx.at>
  • Date: Fri, 7 Jun 2002 01:08:52 -0400 (EDT)
  • Organization: Johannes Kepler Universitaet Linz
  • References: <adkg5p$a0h$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

rad0 wrote:

> Is there a built in way to calculate the azimuth between
> two points given by their latitude and longitude?
> 


Hi rad0,

I don't think that there's a "built in way" in Mathematica but you easy 
can calculate that angle.

If we have two vectors

  v1 = r1 {Sin[theta1] Cos[phi1], Sin[theta1] Sin[phi1], Cos[theta1]}
  v2 = r2 {Sin[theta2] Cos[phi2], Sin[theta2] Sin[phi2], Cos[theta2]}

(where the phi's are the longitudes and the theta's are the latitudes, 
measured from the z-axis)

you can use the relation of the product of two vectors to get theta12, 
the angle between the two vectors:

  Solve[v1.v2 == r1 r2 Cos[theta12], Cos[theta12]]

Solving and Simplifying yields something like

  Cos[theta12] ->
  Sin[theta1] Sin[theta2] Cos[phi1-phi2] + Cos[theta1] Cos[theta2]

Rainer Gruber

JOHANNES KEPLER UNIVERSITY LINZ
Institute of Experimental Physics
Atomic Physics and Surface Science




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