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
• 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?
>

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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