From: kovarik@mcmail.cis.McMaster.CA (Zdislav V. Kovarik)
Subject: Re: distance between two points on a sphere?
Date: 9 Dec 2000 05:15:10 -0500
Newsgroups: sci.math
Summary: [missing]

In article <20001209041346.21263.00003428@ng-co1.aol.com>,
MilazzoBobby <milazzobobby@aol.com> wrote:
:What is a general method of computing the distance between two
:points on the surface of any sphere?
:
:Is there an exact formula?
:
:
 On the unit sphere, using spherical coordinates
(from my collection):

Angle beta between vectors

[cos(th1)*cos(phi1) , sin(th1)*cos(phi1) , sin(phi1) ]

and

[cos(th2)*cos(phi2) , sin(th2)*cos(phi2) , sin(phi2) ]

is obtained from

(sin(beta/2))^2 

= (sin((phi1-phi2)/2))^2 

   + (sin((th1-th2)/2))^2 * cos(phi1) * cos(phi2)

or, if you want to see a sum of squares throughout,

(sin(beta/2))^2 

= (sin((phi1-phi2)/2))^2 * (cos((th1-th2)/2))^2

  + (sin((th1-th2)/2))^2 * (cos((phi1+phi2)/2))^2

:Thank You.

You are welcome.

ZVK(Slavek)