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At What Latitudes Are Polar Alignment Errors More Pronounced ?

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#1 kel123

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Posted 04 August 2020 - 11:09 PM

At What latitudes are the effects of polar alignment errors more pronounced, especially when it comes to imaging and guiding ?
Is it high, middle or low latitudes? What about the equator? And what if you are theoretically set up directly on the north pole (if Santa allows you πŸ˜ƒ)

How does it affect your targets?

Thanks.

Edited by kel123, 04 August 2020 - 11:27 PM.


#2 Alex McConahay

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Posted 04 August 2020 - 11:36 PM

http://celestialwond...xErrorCalc.html

 

Lets you adjust the declination of the target and see how it affects the tracking errors. 

 

I notice it says nothing about your latitude.

 

Since the earth rotates as a whole, I do not believe it matters what latitude you set up.

 

But I am willing to be proven incorrect by somebody who actually knows. 

 

Alex


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#3 jerahian

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Posted 04 August 2020 - 11:57 PM

At What latitudes are the effects of polar alignment errors more pronounced, especially when it comes to imaging and guiding ?
Is it high, middle or low latitudes? What about the equator? And what if you are theoretically set up directly on the north pole (if Santa allows you )

How does it affect your targets?

Thanks.

 

The relative distance a star β€œmovesβ€œ in the sky in one hour is greatest at the celestial equator, and least at the celestial poles.  This is similar to the distance traveled by the spokes on a hub; the ends nearest the hub travel less distance than the outer ends of the same spokes, when rotating.  As such, any polar alignment error will manifest most if your target is at the celestial equator.  Consequently, this is the same reason guiding calibration is performed on a star close to the celestial equator.  Your own latitude does not factor into this.



#4 james7ca

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Posted 05 August 2020 - 12:07 AM

Errors in polar alignment can affect your guided results more as the target gets closer to one of the celestial poles, so that probably means that on average you'll have more error the closer your latitude brings you to either the north or south pole. However, polar alignment using a polar scope is easier (and potentially more accurate) the closer you are to the poles and atmospheric refraction will affect your tracking less as you approach either of the poles. Thus, when directly under one of the celestial poles the altitude of your DSO target will remain unchanged during the night and you'll track using just azimuth (R.A.), no changes in altitude (Dec.).

 

So, in practice it's probably kind of a "wash," since depending upon your latitude some things are likely worse while others are somewhat better (for guided imaging).

 

As for the relative distance that an object moves during a given amount of time that certainly affects your tracking accuracy (or an object's apparent speed across the sky), but when guiding that's not the same as the amount of error that occurs because of any polar alignment error and thus as I noted earlier you actually need a better polar alignment when imaging close to one of the poles than you do when imaging near to the celestial equator.

 

Of course, if your guiding is poor then the question becomes somewhat moot since your errors will come mostly from the failed guiding rather than from your polar alignment error. However, if you had perfect guiding then imaging near to the equator would be "easy" in comparison to imaging near to one of the poles. But, in practice it's impossible to have either perfect guiding or tracking or polar alignment so you'll likely end up with a complete jumble of errors.

 

For a mathematically rigorous treatment on polar alignment accuracy you can reference the following paper:

 

  http://celestialwond...entAccuracy.pdf

 

Particularly, note the statements made on page #8 of this article (under "Declination of the Target"):

Therefore, as we image closer and closer to the celestial pole we will need a smaller and smaller alignment error.

Edited by james7ca, 05 August 2020 - 12:58 AM.


#5 ButterFly

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Posted 05 August 2020 - 12:52 AM

Refraction of the pole based on latitude is the only effect.  So what is polar alignment: aligning to the true pole or the refracted pole?

 

When a scope is polar aligned to the true pole, it is equivalent to a level alt/az mount placed at the pole when there is no atmosphere.  All of the effects of polar alignment error can be derived by considering a tilted alt/az mount at the pole, when atmosphere doesn't exist.  Atmospheric refraction makes things look higher up in the sky than they really are.  That's not just the pole - it's everything that's not at zenith.  The effect is much greater nearer the horizon.  For about 35 latitude, the pole is refracted about one arcminute.  In the tropics, it's tens of minutes.  To answer your question, it depends both on latitude of the scope and the altitude of the target.  At the pole, a given declination is at some altitude, so it's all refracted the same way.  It still stays a circle, but it's higher up in the sky.  At other latitudes, a given declination does not stay a tilted circle.  The parts near the horizon are shifted further upward than closer to meridian.  Refraction is very difficult to model below about ten degrees.  Think fata morganas - they change one moment to the next.

 

Practically speaking, exposures are now on the order of seconds and minutes instead of hours or tens of minutes.  Pictures also aren't taken at very low altitudes.  The guide star distance has a much bigger impact on field rotation than any refraction effect.  Polar alignment (whichever) to a few minutes and a guide star within a few degrees should be good enough for most AP.  So to answer your question practically, there is no real difference because one doesn't expose long enough on low enough targets for it to really matter.



#6 sharkmelley

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Posted 05 August 2020 - 01:28 AM

At What latitudes are the effects of polar alignment errors more pronounced, especially when it comes to imaging and guiding ?
Is it high, middle or low latitudes? What about the equator? And what if you are theoretically set up directly on the north pole (if Santa allows you )
 

Latitude makes no difference. 

 

If you image the same target from the north pole and the equator with the same alignment error then the effect will be the same.

 

Mark 


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#7 james7ca

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Posted 05 August 2020 - 01:52 AM

Latitude makes no difference. 

 

If you image the same target from the north pole and the equator with the same alignment error then the effect will be the same.

 

Mark 

While that's true the targets you can image when at the equator are generally at a different declination than what you can image at the pole. That's why I said in my original response "that on average you'll have more error the closer your latitude brings you to either the north or south pole." That's because it's more likely that your targets will be closer to the pole when you are imaging nearer to the poles and thus on average you'll have more issues when near to the pole (for guided imaging).

 

Also, since the altitude of any given target will vary with your latitude you'll "suffer" different amounts of atmospheric refraction depending upon your location. So, it's a complicated set of conditions and thus there is no simple, single answer to the OP's question.



#8 TOMDEY

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Posted 05 August 2020 - 02:51 AM

In the context of the traditional equatorial mount, guide-corrected imagery:

 

All of these matter >>>

 

1) Polar Misalignment

2) Sub-Exposure Duration

3) Imaging Field

4) Observatory Latitude

5) Barometric Pressure

6) Target Altitude

7) Target Azimuth

 

Among us amateurs, #1, #2, and #3 are almost always the dominant affectives, vastly overwhelming the other little nuanced ones. When the pole of your equatorial mount is misaligned, this manifests as cyclic cosinusoidal field rotation about the guide star. I capture those three in my little handout shown below, from a white-paper presentation I gave a few decades ago, at some regional clubs.

 

Beyond that... here is a brief discussion of the nuances: #4 enters into it because the vacuum geometric and atmospheric refracted poles diverge more and more as one migrates the observatory toward the earth's equator. One then must consider whether to align to the one or the other (vacuum unrefracted or atmosphere refracted) pole... or some best compromise. #5 linearly affects the ramifications of #4. #6 throws in target refraction, especially for low altitudes. #7 nuances #6.

 

There are myriad other picayune affectives... aberration of star light (due to the earth's orbital motion and the finite speed of light), plate tectonics, target proper motion, relativistic effects... endless list. These generally only matter to the geodesy, astrometry, and GPS guys... once such accuracies realistically approached e.g. the size of the keys I'm typing on. I got obtusely involved in those when I was working some satellite docking technologies.

 

But, in conclusion... your polar alignment is the only big one... and that is captured in this handout >>>    Tom

 

 

 

 

Attached Thumbnails

  • 10 field rotation Tom's Dec Drift handout p1.jpg
  • 11 field rotation Tom's Dec Drift handout p2.jpg

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#9 ButterFly

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Posted 05 August 2020 - 03:22 AM

Plate tectonics!?  I forgot to consider some latitudes as more prone to earthquakes from glaciers crumbling!

 

Distance to guide star should be made explicit on that wonderful list and placed between 3 and 4.




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