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Re: Star - Star Observations
From: Brad Morris
Date: 2010 Mar 10, 14:00 -0500
From: Brad Morris
Date: 2010 Mar 10, 14:00 -0500
A big thank you to George and Andres for clarifying the equations. And I did find my error, so I can now compute
what the observed distance should be.
To re-iterate,
d = acos{ [cos(D) +cos (H1 + H2)]*cos(h1)*cos(h2) / (cos(H1)*cos(H2)) -cos(h1+h2) }
where
H1 is the true altitude of object 1, should refraction not exist
H2 is the true altitude of object 2, should refraction not exist
h1 will be the observed altitude of object 1, when refraction is present
h2 will be the observed altitude of object 2, when refraction is present.
d is the observed distance, when refraction is present.
D would be the true distance, should refraction not exist.
Since all objects rise with the tide
h1 = H1 + a1
h2 = H2 + a2
where
a1 is the altitude correction for refraction for object 1
a2 is the altitude correction for refraction for object 2
Now for the fun part, I have two objects already selected.
My location N40d 53.0m W72d 48.0m
GMT 10-March-10 00-57-00
Object 1: RA 6h 45.22m Dec -16.7175
Object 2: RA 9h 27.68m Dec -8.6678
Therefore
D = 40d 21m 12.41s
H1 = 28.63501 d
H2 = 37.80218 d
a1 = 0.03025 d
a2 = 0.02135 d
factor 1 = 0.43592
factor 2 = 0.02371
And consequently
d, Corner Cosines = 40d 22m 1.7s
d, Youngs = 40d 24m 45.84s
I find a difference of 2m 44.14s between the two computations. The first assumption is that I erred again (a too often occurrence IMHO) !
The second assumption is that Young's equations are rigorous while the corner cosines are only an approximation, therefore a small
difference is to be expected and that Young's equations are the ones to follow.
Some further commentary would certainly be helpful!
Best Regards
Brad
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