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## A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding

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Re: Astronomical Refraction: Computational Method for All Zenith Angles
From: Marcel Tschudin
Date: 2005 Aug 22, 17:40 +0300

```Refering my last mail, where I mention that I can not reproduce the values
shown in the Auer Standish paper using the polytropic atmosphere model:

1) I overlooked the part on the following page: "These values are used to
compute the coefficients for only that associated region of the atmosphere.
In order to ensure continuity, the temperature and the density must be
extrapolated to the boundary, defined by the altitude hB."

2) When introducing what is described there, the results are even worse.

It seems that there is something wrong in my stratospheric part. May I ask
you, Frank, to have a look at it? May be you can see what is going wrong
there.

Thanks, Marcel

>>>>>>>>>>>>>>>>>>>>>
Function getmu (r : Real): Real;  // r = REarth + h
var
...
begin  // getmu
// Poytropic atmospheres:
Tw:=273.15+RefTemp;       // Tw=Temperature at reference point in ?K
RHOw := 273.15/1013.25 * RefPress/Tw;   // RefPress = Pw
Rw := (REarth+RefHeight)/REarth;        // RefHeight = hw
Rrel := r/REarth;           // r relative to REarth
rr := 1.0/Rrel - 1.0/Rw;
// nPoly = Polytropic index = 5
BETAw := g * REarth / ( Rgas * Tw * (1.0 + nPoly) );
Rhb:=(REarth+hB)/REarth;

if R<=Rhb then
begin                                                      // Begin:  T r o
p o s p h e r e

RHOpoly := RHOw * Power( (1.0 + BETAw * rr), nPoly); // Power(x,y)
calculates x**y

end                                                        // End  :  T r o
p o s p h e r e
else
begin                                                      // Begin:  S t r
a t o s p h e r e

Tb:=Tw * ( 1.0 + BETAw*(1.0/Rhb - 1.0/Rw) );
RHOw := 273.15/1013.25 * RefPress/Tb;
GAMMAw := g * REarth / ( Rgas * Tb );
rr := 1.0/Rrel - 1.0/Rhb;
RHOpoly := RHOw * EXP( GAMMAw * rr );

end;                                                       // End  :  S t r
a t o s p h e r e

// Nminus1 ... Refractive index of air minus 1: (n-1)=0.00029241
getmu := 1.0 + Nminus1 * RHOpoly;

end;  // getmu

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