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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: Angular Distance Between Stars By Camera and Sextant
From: Marcel Tschudin
Date: 2012 Sep 18, 14:46 +0300
In the mean time Andrés was so kind to provide me with his Navigation calculator.  For the purpose of sextant calibration it allows also to calculate star-star distances. Not calibrating a sextant the corresponding values were left 0.0.

For Greg's Alioth-Alkaid-observation his program provides the following output:

* * * * * *

16/09/2012
03:05:00 UT1
Geocentric equatorial coordinates
Alioth
GHA = 208.084158 º = 208º  5.0'
Dec = 55.892403 º =  55º 53.5'
Alkaid
GHA = 194.718161 º = 194º 43.1'
Dec = 49.252840 º =  49º 15.2'

Sextant Error by a Star-Star Distance

Input data:
Star 1: Dec = 55.892403 GHA = 208.084158
Star 2: Dec = 49.252840 GHA = 194.718161
Star-star distance - sextant: DSSs = 0.000000 =   0º  0.0'
Position of the observer:
B = 34.173333 =  34º 10.4'
L = -119.230000 = -119º 13.8'
hEye = 1.830000
Atmospheric parameters:
P = 1015.600000
T = 22.200000

Calculated altitudes:
Hc1 = 28.317414
Z1 = 320.442970
Hc2 = 34.115333
Z2 = 310.248963
Refraction:
R1 = 0.028946
R2 = 0.023032
Apparent altitudes:
Ha1 = 28.347441
Ha2 = 34.139225

Star-star distance: Calculated and Observed
DSSc = 10.460896 =  10º 27.7'

* * * * * *

This compares well with the result obtained using the USNO values but differs by 0.4 moa from Paul's result. Do you, Paul and Andrés have any ideas where this difference originates? May be different epoch data?

Regarding Andrés output: I would have expected that Ha1=Hc1+R1 and Ha2=Hc2+R2 but with the values shown they do not add up. Do the R1 and R2 values shown in the output relate to standard condition, and which then are converted to P and T of the observation for calculating Ha1 and Ha2?

Marcel

On Tue, Sep 18, 2012 at 12:02 PM, Marcel Tschudin wrote:
In the mean time I had a look at possible reasons for the 0.3 moa difference between the calculated distance as resulting from Paul's calculation and the one resulting from the USNO data, noticing the following:

(1) There are some Hc and Zn values which are rounded different to 1/10 of a moa. This means that there are somewhere differences of +/-0.05 moa or +/-3 sec of arc. For navigational purpose this is negligible, but for spherical astronomy calculations it is a lot. Where could this difference have its origin?

(2) The refraction values provided in the USNO almanac are slightly larger than those Paul used. This seems to confirm that the refraction values in the USNO table relate to observed altitudes; those are the refractions to deduct from the sextant measurement to obtain the Hc value resulting from measurements. The refraction values in the USNO table can therefore not be used for calculating the observed star distance from the Hc values, they have to be calculated separately.

(3) Calculating the distance D between the local coordinates of e.g. Alioth and Alkaid using Paul's el and az values to 1/10th of moa  results in D=627.6 moa. Using his el and az values to 1/100th of a moa results in D=627.2 moa. With the full accuracy program values Paul obtained D=627.3 moa.

This example suggests that - independent of the accuracy in measured pixels - the calibration accuracy cannot noticeably be improved by using the distance of two star positions with the local coordinates calculated to 1/10th of a moa (difference in this example is 0.3 moa compared to +/-0.5 moa accuracy from HS observations). Improving the present calibration accuracy would require at least accurate J2000 star positions and a program for converting them to local coordinates to at least 1/100th of a moa (like Paul shows in his output).

However, for those not fortunate to live close to the sea and looking for a mean to calibrate their camera to somewhere around +/- 0.5 moa, measuring star distances and comparing them with the USNO almanac data, corrected with Saemundsson's refraction, may be an option.

Marcel

P.S: Thank you, Paul, for the link.

On Tue, Sep 18, 2012 at 6:49 AM, Paul Hirose wrote:
I'm surprised you could read the message. In the copy of my own message received by email, the link to the file gives a "page not found" error message.

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