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(meteorobs) Query: Gnomonic Projection




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Date: Thu, 25 May 2000 13:35:51 +0200
From: Szabolcs Kiss <achilles@freemail.hu>
To: meteorobs@jovian.com
Subject: Gnomonic Projection

I am working on a program to transform Atlas Brno gnomonic coordinates
to equatorial system. There is a method on IMO's home page 
(http://www.imodot net/visual/minor05.htm) to do this but does not working well.

x=(X-X_0)/R
y=(Y-Y_0)/R

t=sqrt(1+x*x+y*y)
p=( sin(delta_0)+y*cos(delta_0) ) / t
delta=arcsin(p)

q=-x/t
r=( cos(delta_0)-y*sin(delta_0) ) / t
if q>=0 then   alpha=arccos( r/cos(delta) )+alpha_0
if q<0 then    alpha=360-arccos( r/cos(delta) )+alpha_0

X and Y are gnomonic coordinates in mm. R is the radius of the
projection in mm. X_0 and Y_0 are the position of the center of
the map in mm. alpha_0 and delta_0 are the right ascension and
declination of the center of the map in degree.
The results are alpha and delta (the right ascension and declination
of the object in degree).
Delta is OK, but alpha is wrong.

Where is the error? What is the correct formula?

ps: the equatorial to gnomonic formula is working well.

Thanks,
Szabolcs


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