NavList:
A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
Re: Star - Star Observations
From: Peter Hakel
Date: 2010 Mar 9, 19:27 -0800
From: George Huxtable <george@hux.me.uk>
To: NavList@fer3.com
Sent: Tue, March 9, 2010 3:31:05 PM
Subject: [NavList] Re: Star - Star Observations
I suggest that Brad Morris and Peter Hakel are taking the wrong tack.
Their procedure will work only if the two stars have the same (or opposite)
azimuths. Only then can one calculate the angle between them, and then, as
the next step, apply the appropriate correction for refraction by simple
arithmetic.
But in the general case, the job has to be done differently, to get the
right answer.
First, obtain the predicted position of star1, in altitude and azimuth. Add
the appropriate refraction correction, to get the apparent altitude. Then do
the same for star 2. Now, using those two apparent positions, calculate the
angle between them using spherical trig. Then, the result will adjust itself
automatically for refraction, depending on how the two azimuths differ.
There are other ways to make the same calculation, but that' the simplest,
conceptually.
It's a similar process to the clearing of a lunar distance, except that it's
simpler because there are no semidiametrs and limbs to worry about, nor any
effects of parallax to account for.
George.
contact George Huxtable, at george@hux.me.uk
or at +44 1865 820222 (from UK, 01865 820222)
or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.
----- Original Message -----
From: "Brad Morris" <bmorris@tactronics.com>
To: <NavList@fer3.com>
Sent: Tuesday, March 09, 2010 9:48 PM
Subject: [NavList] Star - Star Observations
Gentlemen
I have been playing around with star-star observations to determine the
accuracy of the sextant arc. Calculating the star to star distance, without
refraction is not a challenge, nor is correcting for refraction when both
stars are on the same side as the zenith. Derive GHA Aries for the
observation instant, apply SHA objects, determine instantaneous altitude for
both objects using spherical trig, compute refraction correction based on
altitude for both objects, create delta refraction correction and finally,
subtract from star to star distance to get the observable distance for my
location. It sounds like a lot of work, but I have set up a spreadsheet
that uses the Celestron SkyScout as inputs. I just point at two stars,
enter some data from the SkyScout (in Right Ascension & Declination), and
the observable distance from my location at a known time is the
instantaneous result. All the mindless tabular work is done by the
spreadsheet. I don’t really even need to know which stars they are, as long
as the Celestron does! Of course, I have checked my spreadsheet against
some hand done calculations to check to see if it is working the way I
expect it to…and it is.
Here is the dilemma. When I get to larger angles, I need to go beyond my
zenith. For example, I have been looking at Polaris vs Sirius. My latitude
is about 40 degrees north. So Sirius is to my south, Polaris, naturally, is
to my north. The nominal distance works out to about 106 degrees 20 odd
minutes (forgive me, I don’t have the exact numbers in front of me).
Because each object is on either side of my zenith, both objects will appear
to be lower in the sky compared to the horizon, due to refraction. Yet
because they oppose each other in azimuth, the observable distance between
them should be larger by the sum of the refraction corrections, not reduced
by the difference of the refraction corrections. That is, compute the true
distance without refraction. Since each object is lowered by refraction,
but in opposite directions, shouldn’t we add the refraction corrections to
the nominal distance to obtain the observable distance?
Best Regards
Brad
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From: Peter Hakel
Date: 2010 Mar 9, 19:27 -0800
George,
I was simply commenting on the sign of the refraction correction, i.e. on the question of its "adding" vs. "subtracting," nothing more. This is not "my" procedure. And then, the limitation to stars of opposite azimuth is clearly identified in my (very brief) posting, as well as in Brad's original one.
Peter Hakel
I was simply commenting on the sign of the refraction correction, i.e. on the question of its "adding" vs. "subtracting," nothing more. This is not "my" procedure. And then, the limitation to stars of opposite azimuth is clearly identified in my (very brief) posting, as well as in Brad's original one.
Peter Hakel
From: George Huxtable <george@hux.me.uk>
To: NavList@fer3.com
Sent: Tue, March 9, 2010 3:31:05 PM
Subject: [NavList] Re: Star - Star Observations
I suggest that Brad Morris and Peter Hakel are taking the wrong tack.
Their procedure will work only if the two stars have the same (or opposite)
azimuths. Only then can one calculate the angle between them, and then, as
the next step, apply the appropriate correction for refraction by simple
arithmetic.
But in the general case, the job has to be done differently, to get the
right answer.
First, obtain the predicted position of star1, in altitude and azimuth. Add
the appropriate refraction correction, to get the apparent altitude. Then do
the same for star 2. Now, using those two apparent positions, calculate the
angle between them using spherical trig. Then, the result will adjust itself
automatically for refraction, depending on how the two azimuths differ.
There are other ways to make the same calculation, but that' the simplest,
conceptually.
It's a similar process to the clearing of a lunar distance, except that it's
simpler because there are no semidiametrs and limbs to worry about, nor any
effects of parallax to account for.
George.
contact George Huxtable, at george@hux.me.uk
or at +44 1865 820222 (from UK, 01865 820222)
or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.
----- Original Message -----
From: "Brad Morris" <bmorris@tactronics.com>
To: <NavList@fer3.com>
Sent: Tuesday, March 09, 2010 9:48 PM
Subject: [NavList] Star - Star Observations
Gentlemen
I have been playing around with star-star observations to determine the
accuracy of the sextant arc. Calculating the star to star distance, without
refraction is not a challenge, nor is correcting for refraction when both
stars are on the same side as the zenith. Derive GHA Aries for the
observation instant, apply SHA objects, determine instantaneous altitude for
both objects using spherical trig, compute refraction correction based on
altitude for both objects, create delta refraction correction and finally,
subtract from star to star distance to get the observable distance for my
location. It sounds like a lot of work, but I have set up a spreadsheet
that uses the Celestron SkyScout as inputs. I just point at two stars,
enter some data from the SkyScout (in Right Ascension & Declination), and
the observable distance from my location at a known time is the
instantaneous result. All the mindless tabular work is done by the
spreadsheet. I don’t really even need to know which stars they are, as long
as the Celestron does! Of course, I have checked my spreadsheet against
some hand done calculations to check to see if it is working the way I
expect it to…and it is.
Here is the dilemma. When I get to larger angles, I need to go beyond my
zenith. For example, I have been looking at Polaris vs Sirius. My latitude
is about 40 degrees north. So Sirius is to my south, Polaris, naturally, is
to my north. The nominal distance works out to about 106 degrees 20 odd
minutes (forgive me, I don’t have the exact numbers in front of me).
Because each object is on either side of my zenith, both objects will appear
to be lower in the sky compared to the horizon, due to refraction. Yet
because they oppose each other in azimuth, the observable distance between
them should be larger by the sum of the refraction corrections, not reduced
by the difference of the refraction corrections. That is, compute the true
distance without refraction. Since each object is lowered by refraction,
but in opposite directions, shouldn’t we add the refraction corrections to
the nominal distance to obtain the observable distance?
Best Regards
Brad
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