NavList:
A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Brad Morris
Date: 2010 Mar 12, 15:58 -0500
As a follow up, I have been playing with the equations and some numerical examples
Start, of course with:
Hc = f(B,L,Dec, GHA)
We calculate
R0
= f(Hc)
Ha0
= Hc + R0
We can then calculate refraction as a function of apparent altitude:
R1= f(Ha0)
But Ha0 - R1 is within 0.1 seconds of Hc. There is no need for any iteration or loop.
Is this what you meant by “iteration”, Andres?
Best Regards
Brad
From: navlist-bounce@fer3.com [mailto:navlist-bounce@fer3.com]
On Behalf Of Brad Morris
Sent: Friday, March 12, 2010 10:17 AM
To: NavList@fer3.com
Subject: [NavList] Re: Star - Star Observations
Andres, you wrote:
“ I suppose you first calculate Hc = f( B, L, Dec, GHA )”
Yes! And then you wrote:
Refraction is a function of the apparent altitude: R = f(Ha)
True. Finally, you state that
The solution must be obtained with precision by an iterative process.
To help me to understand this iterative process, I must begin with the original computation
Hc = f(B,L,Dec, GHA)
We calculate
R0
= f(Hc)
Ha0
= Hc + R0
We can then calculate refraction as a function of apparent altitude:
R1= f(Ha0)
For nominal atmospheric conditions, R0
cannot not equal R1, as Ha0 does not equal Hc. Excellent!
So
i=0
LOOP
R(i+1) = f(Hai)
Ha(i+1) = Hai
+ R(i+1)
If ( (Ha(i+1) - R(i+1)) = Hc) then
Exit LOOP
Otherwise
i = i+1
LOOP again!
END LOOP
Is this what you mean?
Apologies to all who receive email in plain text form. I recognize that the subscripts are going to look rather odd.
Best Regards
Brad
From: navlist-bounce@fer3.com [mailto:navlist-bounce@fer3.com]
On Behalf Of Andres Ruiz
Sent: Friday, March 12, 2010 8:29 AM
To: NavList@fer3.com
Subject: [NavList] Re: Star - Star Observations
Brad, I suppose you first calculate Hc = f( B, L, Dec, GHA )
Refraction is a function of the apparent altitude: R = f(Ha)
And Ha = Hc + R = Hc + f(Ha)
The solution must be obtained with precision by an iterative process.
I have repeated the calculations with more precise ephemerides, and the solution is the same.
Note the variation of R with Ha:
Ha º |
R ‘ |
30 |
1.68 |
31 |
1.62 |
32 |
1.56 |
33 |
1.50 |
Regards.
---
Andrés Ruiz
Navigational Algorithms
https://sites.google.com/site/navigationalalgorithms/
De: navlist-bounce@fer3.com [mailto:navlist-bounce@fer3.com]
En nombre de Brad Morris
Enviado el: jueves, 11 de marzo de 2010 21:24
Para: NavList@fer3.com
Asunto: [NavList] Re: Star - Star Observations
Hi Andres
Thank you very much for sticking with me on this! I discovered that I had inverted one of the terms in Young’s equation.
For the calculated distance
Morris 40d 21m 20.92s.
Ruiz 40d 21m 17.96s, a trivial difference between us of 3 seconds.
For the observed distance, I now get
Corner Cosines 40d 22m 4.67s
Young’s Equation 40d 22m 4.70s
Now there is no difference between my two results and therefore can readily retract my question about which is better.
Corner Cosines and Young’s Equations yield the same result.
Your result for the observed distance is
Ruiz 40d 21m 55.26s
There is a small discrepancy between our results of about 8 seconds.
In tracing this down, I believe it to be the altitude correction and most likely the atmospheric conditions
USNO 1m 36s Sirius altitude correction
1m 36s Alphard altitude correction
Morris 1m 35.47s Sirius
1m 35.79s Alphard
Ruiz 1m 33.43 Sirius
1m 33.74 Alphard
Not only have I corrected this deficiency in the spreadsheet, I have re-cast the interface to accept GHA Aries, SHA Object 1, SHA Object 2, Declination Object 1 & Declination Object 2. Of course,
these items will now come from the Nautical Almanac, not my Skyscout.
Now on to the calibration of the arc of my sextant!
Best Regards
Brad
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