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How long would a perfect polar alignment be accurate for?

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#1 shakafell

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Posted 24 April 2024 - 10:38 PM

This is a hypothetical question to try to understand the theory. Lets say theoretically you had a completely stable mount on solid ground that is not affected by ground erosion or atmospheric conditions. And lets say the mount is perfectly accurate and never drifts.

 

And lets say you did a perfect polar alignment on the celestial pole to a 0.000" precision.

 

How long would this alignment last? I know about precession and the J epochs so I assume that means the coordinate system is constantly changing. Or does that only affect the location of objects and not the coordinate system itself. If so would that mean an alignment would last essentially forever?

 

And a bonus question: What about the average continental drift of 1.5cm per year. How long would it take for that to have an affect if any?


Edited by shakafell, 24 April 2024 - 10:59 PM.


#2 WadeH237

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Posted 24 April 2024 - 11:13 PM

First off, there is no such thing as a perfect polar alignment.  By that, I mean that there is no possible alignment of the RA axis that results in zero drift in both axes at all points in the sky.  Any polar alignment is a compromise.  A "traditional" drift alignment, for example, will counter declination drift across a large area of sky, but does not eliminate RA drift (this is because older mounts were driven in RA, but not necessarily dec, so RA drift could be corrected by altering the tracking speed).

 

That said, your question is interesting, and it should be possible to solve it within your given assumption of a "perfect" polar alignment (even though such a thing doesn't actually exist).  I don't know the math off the top of my head, but if you use just about any planetarium software, it's easy to switch between JNow and J2000 coordinates to see the effect of 24 years of precession.  It's surprising how much movement happens, so our hypothetical polar alignment would definitely need to be updated on a time scale probably in single digit years.

 

As for continental drift, I would offer this as a reality check:  The Earth rotates at just over 1,000mph at the equator.  Also, it moves in its orbit at more than 65,000mph.  The entire solar system is moving through space at nearly 450,000mph.  So I doubt that the effect of continental drift could be measured by any means.

 

Now continental drift would potentially change the longitude and latitude of the site.  But it would take centuries to result in the equivalent change you'd get by setting up on the opposite side of a field.  Again, any effect from continental drift would be unmeasurable.

 

Using Polaris as an example, the parallax motion is around 10 milli-arc-seconds.  So that is the effect of moving the observer about 185 million miles (twice the Earth-Sun distance).  Again, not something you could measure with amateur gear (at least not easily).

 

So the question is interesting academically, but has no practical application to amateur astronomers.


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#3 italic

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Posted 24 April 2024 - 11:23 PM

As long as it takes for the Earth's rotational axis to process beyond tolerances. Procession takes about 26,000 years for a complete cycle. Given a tolerance of 30 arcminutes, it looks like you would need to realign every 36 years, give or take. Let's break it down simply: 360 degrees (a full circle per cycle) over 26,000 years gives us ~0.01385 degrees change per year. 30 arcminutes (0.5 degrees) divided by 0.01385 = 36.1 years. This is for the typical tolerance for imaging. If your tolerances for visual/imaging are different, you'd recalculate.

 

EDIT: Let's correct the math a bit (not perfect, but bear with me here). You would need to calculate how much sky would actually be covered per year as the procession doesn't flip the planet's axis upside down (180 degrees), but only wobbles it ~48 degrees (at ~24 degrees from perpendicular to the orbital plane). My geometric math isn't too strong anymore, but a very rough estimate could be a linear relationship. 180/48=3.75, so 36.1*3.75 is 135.375 years to exceed tolerance of 0.5 degrees. I'd love to see an actual breakdown from someone more skilled in geometry than me. It's an interesting question and puts something astronomically-long into the context of a short human time scale.

 

EDIT2: This is an interesting thought experiment because thinking about it again, it shouldn't change because the axis of rotation relative to the Earth's body wouldn't change over time; the whole body wobbles, not just the rotational axis through the body. So you very likely wouldn't need to polar align ever again. Continental drift, however, would certainly change things if you're adding that to the equation. What an interesting thing to think about.


Edited by italic, 24 April 2024 - 11:53 PM.


#4 CharLakeAstro

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Posted 24 April 2024 - 11:56 PM

Geology dependent, localized ground movement would likely be the first cause of a polar alignment change.

Soil is not generally static, factors such as isostatic rebound result in constant movement.

My pier is on precambrian bedrock, but most piers are on or in soil.


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#5 shakafell

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Posted 25 April 2024 - 12:44 AM


 

EDIT2: This is an interesting thought experiment because thinking about it again, it shouldn't change because the axis of rotation relative to the Earth's body wouldn't change over time; the whole body wobbles, not just the rotational axis through the body. So you very likely wouldn't need to polar align ever again. Continental drift, however, would certainly change things if you're adding that to the equation. What an interesting thing to think about.

That was exactly my thought as well. The coordinate system itself never moves. So if you are pointing at the Celestial pole right now you will always be pointing at it regardless of precession. All you need to do is update your object positions by using the latest epoch (and by accounting for the actual movement of objects thru space).

 

So the only thing that would affect alignment is if your physical position on earth changes and you are no longer pointing at the pole.

 

Does anyone else agree with this?


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#6 deSitter

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Posted 25 April 2024 - 12:58 AM

As long as it takes for the Earth's rotational axis to process beyond tolerances. Procession takes about 26,000 years for a complete cycle. Given a tolerance of 30 arcminutes, it looks like you would need to realign every 36 years, give or take. Let's break it down simply: 360 degrees (a full circle per cycle) over 26,000 years gives us ~0.01385 degrees change per year. 30 arcminutes (0.5 degrees) divided by 0.01385 = 36.1 years. This is for the typical tolerance for imaging. If your tolerances for visual/imaging are different, you'd recalculate.

 

EDIT: Let's correct the math a bit (not perfect, but bear with me here). You would need to calculate how much sky would actually be covered per year as the procession doesn't flip the planet's axis upside down (180 degrees), but only wobbles it ~48 degrees (at ~24 degrees from perpendicular to the orbital plane). My geometric math isn't too strong anymore, but a very rough estimate could be a linear relationship. 180/48=3.75, so 36.1*3.75 is 135.375 years to exceed tolerance of 0.5 degrees. I'd love to see an actual breakdown from someone more skilled in geometry than me. It's an interesting question and puts something astronomically-long into the context of a short human time scale.

 

EDIT2: This is an interesting thought experiment because thinking about it again, it shouldn't change because the axis of rotation relative to the Earth's body wouldn't change over time; the whole body wobbles, not just the rotational axis through the body. So you very likely wouldn't need to polar align ever again. Continental drift, however, would certainly change things if you're adding that to the equation. What an interesting thing to think about.

Precession will change the background of stars but would not affect polar alignment. That would require the Earth's axis of rotation to change relative to the alignment. There are small secular changes in the Earth's axis of rotation - the place where the axis meets the surface wanders around irregularly, but the difference is measured in feet, not miles or 10s of miles, so no effect on alignment. So, assuming you live on solid ground and nothing dramatically alters the Earth's angular momentum - e.g. impact of a huge comet! - polar alignment should last as long as the ground beneath the mount is stable. Which means, geological processes like continental drift and seismic activity are the determinant.

 

For reference, the Atlantic Ocean is widening by about 3" per year. You're good to go for a long time :)

 

-drl


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#7 deSitter

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Posted 25 April 2024 - 01:20 AM

I believe I remember reading that seismic activity - and the Loma Prieta earthquake in particular - had knocked one or more of the telescopes at Lick Observatory out of polar alignment - the 120" in particular IIRC.

 

-drl


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#8 vidrazor

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Posted 25 April 2024 - 01:52 AM

I'm reminded of a cartoon showing a $0.00000000000001 increase in airlines fees to compensate for continental drift...


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#9 TOMDEY

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Posted 25 April 2024 - 02:03 AM



This is a hypothetical question to try to understand the theory. Lets say theoretically you had a completely stable mount on solid ground that is not affected by ground erosion or atmospheric conditions. And lets say the mount is perfectly accurate and never drifts.

 

And lets say you did a perfect polar alignment on the celestial pole to a 0.000" precision.

 

How long would this alignment last? I know about precession and the J epochs so I assume that means the coordinate system is constantly changing. Or does that only affect the location of objects and not the coordinate system itself. If so would that mean an alignment would last essentially forever?

 

And a bonus question: What about the average continental drift of 1.5cm per year. How long would it take for that to have an affect if any?

To your hypothetical, it's actually a simple computation, without even looking anything up > 0.00056 arc-sec per year for your continental drift number. But the typical meandering of the earth's axis would be two or three times that.

 

That computation is based on just a couple of common constants that any decent surveyor worth his salt has in his head: a nautical mile is an arc-minute across the earth's surface; a nautical mile is pretty close to a statute mile, and a ten km foot race is about 6.2 statute miles.    Tom

 

[I worked GPS, geodesy, and astrometry at work... so immersed in all those little corrections. Even designed and built little laser-based ~pointing sensors~ that required tiny fractional arc-sec accuracy for --- ten years. This stuff is critical in a few notable applications e.g. gravity wave sensors, satellite docking, GPS, JWST optical alignments and certification.]    Tom


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#10 WadeH237

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Posted 25 April 2024 - 08:16 AM

So the only thing that would affect alignment is if your physical position on earth changes and you are no longer pointing at the pole.

 

Does anyone else agree with this?

I agree with it.  I focused in on precession, when that's not actually relevant to the question.  It's still a fun question, either way.


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#11 Skywatchr

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Posted 25 April 2024 - 10:26 AM

A "perfect enough" polar alignment will outlive any one of us. grin.gif

 

Unless some cataclysmic event changes the Earth's axis.  In which case, polar alignment would be the least of our worries.


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#12 pvdv

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Posted 25 April 2024 - 11:47 AM

In any case, a theoretical perfect geometric alignment with the Earth's axis wouldn't be practicaly perfect as temperature and atmospheric pressure change - the refracted pole will wander around, the lower your latitude is the more so.



#13 jdupton

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Posted 25 April 2024 - 12:12 PM

   Hi,

 

    This is an Interesting and thought-provoking discussion topic.

 

    I have a few random thoughts:

  1. I don't think precession matters at all. 
    It simply shows where in the sky the rotational axis of the Earth points. We do not align telescopes to a particular location in the sky but instead reference to an Alt-Az reference with respect to our location on Earth that coincides with the projection of the Earth's rotational axis into the sky.

    Consider the view 13,000 years into the future. Other considerations aside, the mount will still be pointing to coincide with the rotation of the Earth but the constellations will have precessed to something very different. The sky is moving, not the Earth's rotational axis in this context.
     
  2. We want to keep the mount's rotational axis pointed to coincide with the Earth's rotational axis. That way, the telescope will always follow the stars (to the extent it can given Wade's comments about refraction effects and such.) The point in the sky may change but so did the "pole point."

    Geological events can change the rotational axis of the Earth (as measured by a surface location) by up to a few hundred meters per event. I seem to recall that the earthquake that caused the 2004 tsunami in Asia was said to have made a change in the earth's rotational axis of about that magnitude.
     
  3. As has already been pointed out, geological processes on Earth will change where the fixed-to-the-ground telescope is pointing with reference to the rotational axis of the Earth. This will be a highly localized effect. Some areas may change slowly due mostly to continental drift while other areas near active earthquake zones may change slightly every few years. I think I saw it written somewhere that some points near the California coast can move on average a couple of centimeters per year due to earthquake activity. That can affect where the telescope is pointed.

   There are even more considerations, I am sure. Because of the unpredictable nature of some of the things that change, I don't know if it is even possible to calculate how much "polar alignment accuracy" may change over time.

 

 

John


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#14 PIEJr

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Posted 25 April 2024 - 05:38 PM

Perfect? No such a thing.

It would change as soon as the temperature changes.

Because everything changes with the temperature.

 

And the Earth is better looked at as a giant ball of jello.

Study seismometers. The earth is constantly in motion.

 

Try running a night of Polar Alignments.

Every one will be different from the rest.

I did this with Sharpcap, because I used to try for all zero's PA.

Oh, I got close. Very close. Then run it again.

And again, and again, and again.... every time it is just a smidgen different.

 

Ain't no sucha thing.

 

Polar Alignment is a mechanical setting up of the mount and telescope aim.

 

Have you ever looked into specifications? They all have a tolerance factored in.


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#15 Skywatchr

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Posted 25 April 2024 - 07:21 PM

Perfect? No such a thing.

It would change as soon as the temperature changes.

Because everything changes with the temperature.

 

And the Earth is better looked at as a giant ball of jello.

Study seismometers. The earth is constantly in motion.

 

Try running a night of Polar Alignments.

Every one will be different from the rest.

I did this with Sharpcap, because I used to try for all zero's PA.

Oh, I got close. Very close. Then run it again.

And again, and again, and again.... every time it is just a smidgen different.

 

Ain't no sucha thing.

 

Polar Alignment is a mechanical setting up of the mount and telescope aim.

 

Have you ever looked into specifications? They all have a tolerance factored in.

Because nothing is perfect. grin.gif   Plus in the calculations, many numbers are rounded up, sometimes down (whichever crosses the threshold) which end up as part of the "tolerance".

 

If I can track, guide and get great results, then it is "perfect enough". lol.gif  Also referred to as "nominal" with room for improvement. tongue2.gif 
 


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#16 TOMDEY

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Posted 25 April 2024 - 08:21 PM

In any case, a theoretical perfect geometric alignment with the Earth's axis wouldn't be practicaly perfect as temperature and atmospheric pressure change - the refracted pole will wander around, the lower your latitude is the more so.

And even the refracted pole isn't the optimal best pole to use. Some professionals correct for these things (to the extent possible). The Air Force was the 1st to address these corrections with their early 5-axis satellite tracking cameras.    Tom


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#17 luxo II

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Posted 25 April 2024 - 09:47 PM

How long would this alignment last?

The first thing that will throw it off is the axial precession (ie gradual shift in the orientation of Earth's axis of rotation) which has a cycle of approximately 26,000 years. This will be measurable over a few decades.

 

Geology of the location will also have influences long before continental drift becomes an issue.

 

For example, across much of the USA you're on deep soils - a firm attachment to "bedrock" is unlikely - and on a slope, soil creep will probably tilt whatever you construct, downhill, in much the same way as it tilts trees.  

 

If you're on soft ground, heavy rainfall/flooding may cause sinkholes under, followed by subsidence.

 

If you're on what was once swampy or sandy ground, you may have noticed that parts of houses tend to move a little with time - and this is worse in locations that experience freezing conditions - eg the stumps supporting floors rise/fall relative to walls, and separate foundations (with walls) tend to creep apart. Same will happen to whatever your put your scope on.

 

An earthquake is likely to shift the alignment enough to be measurable.

 

The terrain also undergoes long-term rise/fall as well as drift; for example where I live was once a shallow sea, but is now sandstone approx 500m thick, and the surface is 200m above sea level.

 

Any/all of these will happen.


Edited by luxo II, 25 April 2024 - 10:06 PM.


#18 Skywatchr

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Posted 26 April 2024 - 08:47 AM

The first thing that will throw it off is the axial precession (ie gradual shift in the orientation of Earth's axis of rotation) which has a cycle of approximately 26,000 years. This will be measurable over a few decades.

 


 

Irrelevant. Why? You are polar aligning with the Earth's own Axis no matter what is in the sky. You are on Earth yourself and axis alignment is relative only to Earth.  Realigning because of any variations in your terrain over time, still brings you back to Earth's physical axis. The apparent positions of the pole stars (for alignment) is what changes with precession.  This is why there are updated reticles for x- time periods in polar alignment scopes to remain, or align for the first time for any particular date.
 


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#19 WadeH237

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Posted 26 April 2024 - 09:23 AM

If I can track, guide and get great results, then it is "perfect enough". lol.gif  Also referred to as "nominal" with room for improvement. tongue2.gif

This!

 

And if you are serious about unguided, especially at longer focal lengths, you will want to use a mount that supports a custom tracking model.  Such a model will account for lots of sources of error - including polar misalignment.

 

I've long been an advocate of guiding, even with a premium mount.  But a year or two ago, I started doing some experimenting with my system and unguided imaging with a tracking model.  I found that I can build a target-specific tracking model as part of my automation, and before it's dark enough to do serious imaging.  With such a model, I have tested up to 15 minute exposures at 0.9 arc seconds per pixel without noticeable star elongation.  Since I normally use 5 minute exposures, I've pretty much gone all unguided.  My current imaging scopes don't even have accommodation for guiding anymore.  I removed the OAG's and redid the extensions to have proper spacing without them.

 

I don't even have to be that precise about my polar alignment.  When imaging away from home, I often just use my polar alignment scope, and still get great unguided results.


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#20 shakafell

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Posted 26 April 2024 - 01:00 PM

Thanks for the replies. I have a more intuitive understanding of precession and the coordinate system now.

 

Also you can always tell the people who reply just from reading the title. lol.gif



#21 Jim in PA

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Posted 26 April 2024 - 01:20 PM

Thanks for the replies. I have a more intuitive understanding of precession and the coordinate system now.

 

Also you can always tell the people who reply just from reading the title. lol.gif

lol.gif waytogo.gif
 



#22 deSitter

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Posted 26 April 2024 - 02:33 PM

Something that was so obvious it never occurred to me - do modern go-to mounts account for refraction? That would require slight tweaks in declination tracking as well as RA tracking as the object rose and set. Near the horizon the difference is quite large.

 

-drl



#23 jdupton

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Posted 26 April 2024 - 02:47 PM

drl,

 

Something that was so obvious it never occurred to me - do modern go-to mounts account for refraction? That would require slight tweaks in declination tracking as well as RA tracking as the object rose and set. Near the horizon the difference is quite large.

    I don't think any mounts attempt to do this directly since the magnitude of refraction from the atmosphere varies by not only where in the sky you are pointing, but is also varies as temperature and humidity change.
 
   The way this is compensated for is through the use of Sky Models. You use the telescope and plate solving to scan the sky and record the actual plate solved location versus where the mount says it is physically pointing. That allows you to "model the sky" with enough accuracy to vary RA and DEC pointing and tracking rates. This is easier with some mounts than others but is theoretically possible so long as the mount has repeatable pointing errors. (In other words if the mount can point somewhere in the sky and then slew elsewhere and then come back to exactly the staring point, then modeling should work to counteract any refraction by the atmosphere.)
 
   Some mounts come with firmware and / or software to do this modeling. The coding can also compensate for changes in temperature and humidity at any given time by applying small correction terms to the stored internal model. Mounts such as those from 10Micron, AstroPhysics, and Software Bisque and others are among those that can apply this modeling via firmware and / or software. I think there is also some (more or less) standalone software that can do this modeling for mounts that have repeatable movements. (By the way, repeatable movement applies not only to the mount mechanics but also to the OTA used. Refractors are normally highly repeatable but some SCTs that experience "mirror-flop" while pointing different directions, for example, are much harder to model and may not work quite as well.)
 
 
John


Edited by jdupton, 26 April 2024 - 02:53 PM.

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#24 WadeH237

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Posted 26 April 2024 - 02:56 PM

Something that was so obvious it never occurred to me - do modern go-to mounts account for refraction? That would require slight tweaks in declination tracking as well as RA tracking as the object rose and set. Near the horizon the difference is quite large.

It depends.

 

Mounts that offer sidereal tracking do not account for refraction.  If your mount offers "King" tracking rate, then it does account for refraction.  The King tracking rate was developed by Edward Skinner King specifically for this purpose.  I am not sure, but I believe that the King tracking rate only affects the RA axis.  The declination axis is still fixed in this case (except for guide corrections).  Note that the actual effect of refraction depends on atmospheric conditions, like temperature and humidity.  As a result, the King rate is an approximation.

 

Mounts that offer a custom tracking model, created by sampling many areas of the sky to verify behavior of the system, will apply custom rates to both the RA and declination axis.  The custom rates will account for refraction, as well as about a dozen other factors that can affect tracking.  Note that as far as I know, the only currently offered amateur mounts that can do this are the Paramounts (with ProTrack), Astro-Physics (either with APCC Pro, or separately with the hand controller), and 10Micron (with modeling support built into the mount controller).  And some (maybe all) of these systems have the ability to use a weather sensor to adjust their models to account for temperature and humidity.

 

There is another, much less common, situation.  Some mounts can do declination tracking when in EQ mode (I think that Losmandy mounts with Gemini can do this, but I'm not positive).  Note that it's my understanding that these mounts will keep a target centered, even with poor polar alignment, but that the declination tracking is not accurate enough for imaging, and you should not use declination tracking while imaging.

 

Note that all of the above applies to tracking.  The question is also relevant for goto accuracy.  It's important to understand the goto pointing is a completely separate thing from tracking.  I suspect that many (most?  all?) modern mounts do account for refraction in their pointing algorithms.


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#25 Kolenka

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Posted 26 April 2024 - 04:36 PM

I've long been an advocate of guiding, even with a premium mount.  But a year or two ago, I started doing some experimenting with my system and unguided imaging with a tracking model.  I found that I can build a target-specific tracking model as part of my automation, and before it's dark enough to do serious imaging.  With such a model, I have tested up to 15 minute exposures at 0.9 arc seconds per pixel without noticeable star elongation.  Since I normally use 5 minute exposures, I've pretty much gone all unguided.  My current imaging scopes don't even have accommodation for guiding anymore.  I removed the OAG's and redid the extensions to have proper spacing without them.

 

I don't even have to be that precise about my polar alignment.  When imaging away from home, I often just use my polar alignment scope, and still get great unguided results.

I'll be honest, when I got my Mach2, I looked at my gear, and realized that I'd want to also rethink my guiding options. Then I asked myself, "what about unguided? Let's learn how to make a model and see if it lives up to the hype while I figure out the guiding situation." Had I not done that and waited to rebuild my guiding setup, I probably would eye this statement with suspicion. Except I've done pretty much everything you've listed here with similar results. The difference being that I've only dared 10min exposures for testing (light polluted Bothell/Redmond says hello), and my pixel scale is around 1.4px/arcsec.

 

There are just certain things we take as axioms in this hobby at times. And for some, it can take seeing something actually work to get that they aren't actually axioms, just very well-worn rules of thumb.

 

Have you tried the C14 much just to see how it handles? I assume the not-fixed mirror is a hurdle in this case? 




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