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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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Fw: Astronomical Refraction: Computational Method for All Zenith Angles
From: Marcel Tschudin
Date: 2005 Aug 22, 18:33 +0300

```Strange things happened to the e-mail just sent. The code at the end of it
got cut off and added into an attachment, which cannot be opened. I tried it
now again by forwarding the copy in the sent-file to my own address and this
worked. I send now a copy of this test and hope it works fine this time.

>> 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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