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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: Star - Star Observations
From: Brad Morris
Date: 2010 Mar 12, 16:25 -0500

Here is what IS true

For all altitudes above 15 degrees,

Hc = f(B,L,Dec, GHA)

R0 =  f(Hc)

Ha0 = Hc + R0

R1= f(Ha0)

But Ha0 - R1 is within  1.0  seconds of Hc for altitudes greater than 15 degrees

diminishing to             0.1   seconds by 32 degrees,

further to                    0.01 seconds by 59 degrees & etc.

For practical purposes, if the altitudes are above 15 degrees, the computation will provide sufficient accuracy.

Best Regards

Brad

From: navlist-bounce@fer3.com [mailto:navlist-bounce@fer3.com] On Behalf Of Brad Morris
Sent: Friday, March 12, 2010 4:02 PM
To: NavList@fer3.com
Subject: [NavList] Re: Star - Star Observations

Ignore this last….

It is simply wrong

From: navlist-bounce@fer3.com [mailto:navlist-bounce@fer3.com] On Behalf Of Brad Morris
Sent: Friday, March 12, 2010 3:59 PM
To: NavList@fer3.com
Subject: [NavList] Re: Star - Star Observations

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

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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