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# Effect of level on ASPA - with figures

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### #276 OzAndrewJ

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Posted 30 November 2013 - 12:29 AM

Gday SPNC

Whew...
No one is saying the system doesn't know how to calculate the actual polar offset, or where the scope is currently pointing, or how to find any other place in the 3D coordinate scheme after aligning.
The initial 2 star aligning process requires no knowledge re how the base is set up, it merely does a process that results in a line in space that represents where the RA axle is truly pointing.

To do the process of ASPA ( not the earlier aligning ), you must use ONLY the controls of the base to move 2 points in space, ie the OTA towards a precalculated target and ( as a byproduct, the RA axle to the true pole ).
As per my photos above, this process gives different results based on the level of the base.
Theoretically calculating 3 points in space is all well and good, but if you cant then "physically" get them to move there in a consistent manner it wont work.

Andrew Johansen Melbourne Australia

### #277 freestar8n

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Posted 30 November 2013 - 04:17 AM

Your diagrams and animation presupposes the star offset is the same for an alignment done with a level and out of level mount

This has to be true because I think everyone agrees that the mount has no idea which way the az axis is oriented. More importantly, some people insist that orientation is irrelevant and superfluous.

What should really be clear is that the alt/az motions needed to center the star will change with pier tilt. A range of pier tilts will have different ra/dec offsets and each will allow some strange combination alt/az to center the star and the pole - but for a given pier tilt, only one ra/dec offset and its one corresponding alt/az motion will align both at the same time.

The motion of the ota pointing at the star is totally weird compared to the nice x/y motion of the polar axis in my figure. The weirdness is due to the orientation of the alt/az axes relative to the star. You need to account for that weirdness when you pre-offset ra/dec. There is no way to do it otherwise.

Frank

### #278 freestar8n

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Posted 30 November 2013 - 04:44 AM

If you can understand or accept that this is the process the 2+4 star alignment and ASPA use, then you can understand or accept the fallacy of the second diagram in this thread showing the pier tilted 10 degrees from level. The statement that everything else is the same except the pier being tilted 10 degrees is not correct because everything else is not the same. The location of the mathematical model for the mount has now changed due to the pier being tilted.

Welcome to CN. Certainly a lengthy post - I wondered if it would end with the shark-eaten carcass of a marlin being hauled into port. Well, I guess in some ways it did.

No, there is no fallacy in the drawing. The mount knows exactly how the polar axis is oriented to the sky and it can point accurately anywhere no matter how the crazy pier is oriented - including hanging off a building.

But that is different from the physical motion of the mount that happens to polar align it.

It is essential to ASPA that the mount move in a deterministic manner during the physical alignment - because it is done "blind" and must be predicted. It involves motion in two specific axes, and that process needs to be predicted exactly so it cannot be done by an arbitrary rotation - hence my earlier example of a ball-socket joint instead of alt/az adjustments. It could not work unless the motions were constrained and deterministic.

Although some of the principles from celestial navigation may apply - the specifics do not - and it's the specifics that matter here.

The mount has no way to know the difference between a pier physically tilted N/S to misalign the polar axis by 40 degrees, and a vertical pier with the latitude set wrong by 40 degrees. They would behave exactly the same during star alignment. But during the physical motion required by ASPA, they would behave differently, and the mount would have no way to know this when it calculated the ra/dec pre-offset.

Frank

### #279 spnc

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Posted 30 November 2013 - 08:54 AM

Your example of a pier tilted out of level by 40 degrees and a level pier with the altitude adjusted out level by 40 degrees is correct only if there is no azimuth error of the two mounts. In that case, and only that case, the only adjustment needed would be in altitude and the movements of the two mounts would be the same to be polar aligned. If there is any error in the azimuth component of either mount, the movements during the 2 star alignment of the mounts will be different and the mounts will compute different mathematical locations which will then require different movements in altitude and azimuth to polar align each mount.

You are correct in stating that the levelness or lack thereof affects the motions of the mount in altitude and azimuth during the polar alignment process. What I have tried to explain is that the degree of levelness of the mount does not matter because during the initial alignment process the mount knows this and corrects for it. In the example above, you are using a specific case and the specifics (formulas) still apply as well as the principals (theory). The specifics have to be correct in all cases if the principals are correct.

### #280 freestar8n

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Posted 30 November 2013 - 09:04 AM

Your example of a pier tilted out of level by 40 degrees and a level pier with the altitude adjusted out level by 40 degrees is correct only if there is no azimuth error of the two mounts. In that case, and only that case, the only adjustment needed would be in altitude and the movements of the two mounts would be the same to be polar aligned.

I can only assume you have not read much of this thread and/or you haven't performed ASPA. The diagrams shown do have the mount misaligned in alt and az. If the mount only knows the polar axis orientation on the celestial sphere, and it knows nothing about the pier axis, then my animation shows a series of exactly identical scenarios - as far as what the mount knows. It has no idea the pier is tilting, so in all cases it has exactly the same sky model, and calculates exactly the same ra/dec offset. That single calculation only works when the mount is level.

The animation shows changing pier tilt but constant polar axis misalignment in both alt and az. It does not work as the pier is tilted. The mount does not know the pier is tilted.

ASPA would have more to do with ship navigation if that ship were on its way to Mars.

Frank

### #281 spnc

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Posted 30 November 2013 - 10:54 AM

"If the mount only knows the polar axis orientation on the celestial sphere, and it knows nothing about the pier axis, then my animation shows a series of exactly identical scenarios - as far as what the mount knows." And I will agree that you are correct that if the mount is oblivious to pier tilt then the effect you are showing is correct.

However my original response was in regards to points 4 and 5 you made in your post at the beginning of this thread and why they are not valid assumptions. Perhaps I wasn't clear on that issue. My point is that the mount does know the amount and direction of tilt of the pier and has all the information needed to compensate for it in the real world. Otherwise ASPA would only work correctly for a level mount that is already polar aligned. And if the mount is already polar aligned, then why would you need the ASPA routine in the first place?

I can see that we are going to continue to agree we disagree. Happy Holidays.

### #282 freestar8n

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Posted 30 November 2013 - 12:33 PM

My point is that the mount does know the amount and direction of tilt of the pier and has all the information needed to compensate for it in the real world.

This appears to be a consequence of joining a long thread late, or perhaps not being familiar with the mounts we are discussing.

They can be perfectly aligned to the sky and know exactly how the polar axis is oriented to the sky, but they have absolutely no clue at all how the pier is oriented. It could be vertical, on its side, or sticking out with some weird angle from a giant martini glass. It would be able to point exactly to stars in the sky and it could tell you exactly where the polar axis is pointing - but knows nothing about how the pier is oriented, or how the eq. head will move when it is adjusted in alt az relative to the pier.

Frank

### #283 GlennLeDrew

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Posted 30 November 2013 - 06:26 PM

spnc,
Your first post, while of a length that *might* otherwise have found me skimming, was very clearly written, and certainly helped to further crystallize some of my own notions on how the system might--nay, should, and hopefully does--work.

To summarize what I've divined...

If the mount had *no* orthogonality and cone error, the initial two-star alignment would suffice for GoTo use, no matter the pier tilt.

The additional stars are used only to model mount errors.

The polar axis alignment star (nominally the final step) will permit to 'dial in' the correct polar alignment for any pier tilt.

As additional ASPA run would be required only to improve GoTo accuracy, particularly if the previous step had significant polar alignment offset to start with.

- - -

This seems to be the logical (and I do believe most achievable) procedure. What is key here is that for the star used for aligning the polar axis, you're simply *reversing the slew made by the mount* so to reacquire the alignment star. This motion is completely independent from the alt/az coordinate system if the slew was made in the RA/Dec coordinate system. Which makes perfect sense to me, as long as pier tilt has remained unchanged throughout.

### #284 freestar8n

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Posted 30 November 2013 - 07:14 PM

This motion is completely independent from the alt/az coordinate system if the slew was made in the RA/Dec coordinate system.

Glenn-

You are completely missing the geometry that is involved.

This has NOTHING to do with cone or orthogonality error. Assume it is a perfect eq. mount. Align it to the sky with 2 or 200 stars - doesn't matter.

Study my examples and Andrew's.

It is NOT TRIVIAL to know the ra/dec offset to pre-offset the mount. That doesn't just come out of the air. It has to be calculated. That calculation requires knowledge of how the alt/az axes are oriented to the celestial sphere. That information is unknown and needs to be assumed.

Sure - go ahead and keep the pier tilt constant. As long as it stays tilted, there will be error after ASPA - because ASPA *has to assume* how the alt/az axes or oriented - or it cannot calculate the ra/dec offset.

If it assumes something about the orientation - e.g. that the pier is vertical - and that is not the case - the alt-az motions made by the user will cause the polar axis to miss its intended destination.

Just because my animation shows the pier tilting - it does not mean I am tilting it during the procedure. It just shows how the resulting error is affected by pier tilt. It is meant to show also that the alt/az adjustments are changing dramatically - from a mixture of alt/az to one of az. If you have not performed ASPA, this part of it may not be as clear as if you had.

Frank

### #285 freestar8n

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Posted 30 November 2013 - 08:35 PM

he system might--nay, should, and hopefully does--work.

And once again - the system does work and it works very well. Because mounts are almost always very nearly level, and if the alignment star is chosen well, and it is close to polar aligned in the first place, level is not critical.

At no point should anyone get the idea special care is needed to level, or that the implementation is not as general as it could be. That is why I am describing everything in terms of fundamental geometry.

Andrew demonstrated it with a little tripod and an antenna - but I don't think it made the geometry any more real, and some people still don't see what is going on.

Frank

### #286 OzAndrewJ

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Posted 30 November 2013 - 09:13 PM

Gday All

Just for my info, as i dont have any celestron gear,
does ASPA "allow" you to use Polaris as your target star????
If so, and you can see it, why would you use anything else???
Ie the error being discussed here due to base tilt
is also proportional to the angle between the target star and the true pole,
so why not use Polaris if you can ????
You will still get rotation of the axes if the base isnt level,
but the process will home in on the pole very quickly.
Just goto a known star afterwards and resynch and you should be sweet.

Andrew Johansen Melbourne Australia

### #287 spnc

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Posted 30 November 2013 - 10:29 PM

Glenn,

Thanks for summarizing my lengthy post into four short highlights. You have the concepts described correctly with only one minor misconception.

If the goto pointing accuracy is not acceptable after performing the ASPA procedure, then another two star alignment will restore the goto pointing accuracy, not repeating the ASPA procedure. The ASPA procedure's only function in this scenario is to allow the user to align the polar axis of the mount with the celestial pole. You should only have to do that one time. Unless of course my better half trips on the tripod. Don't laugh, it's happened. And on more than one occasion!

Steve

### #288 freestar8n

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Posted 01 December 2013 - 03:03 AM

If so, and you can see it, why would you use anything else???

Hi Andrew-

I'm afraid this is where I disagree with you. Again I want to stick to fundamentals.

Although ASPA isn't directly tied to mount imperfections - except you need a good pointing model to know the polar axis direction - mount imperfections would cause problems near Polaris.

One simple issue - which again is fundamental but many people may not realize - is that if you have cone of 1 degree and if your mount is perfectly polar aligned - you cannot physically center polaris in the view no matter how hard you try. This may be surprising to some people, but try as you might, you would not be able to center polaris in view without offsetting the polar axis from perfectly aligned, even if you rotate the ra/dec axes any way you want.

In other words - if you have significant cone and you see polaris centered - ever - you know immediately you are not polar aligned.

Even if you have perhaps 15' of cone, it will challenge the pointing model since it will change the hour angle of approach away from the normal hour angle of polaris. This amounts to the normal challenges of a mechanical system near gimbal lock.

Another reason is for people near the equator, polaris will be high up and you will lose azimuth sensitivity in aligning it due to the cosine altitude term. [I misspoke here, as corrected in subsequent notes. Instead of near the equator it should say at high latitude]. A star down low and near the meridian retains sensitivity in both directions.

So - there would be good reasons not to use polaris even if you could. As long as the pointing model is good and you use a star low down on the opposite side of the sky, it is mechanically stable and accurate. It does require good all sky pointing to some extent to know the polar axis direction in the first place, but you need that for any of these methods that involve pointing the telescope somewhere for some purpose.

Note that even the high end ASA mounts apparently use a similar approach - and they have plate solving and so forth available.

So - I think there are many advantages to being able to use other stars in the sky - especially if polaris is not visible in the first place, which is often the case. But make sure the mount is close to level, of course.

Frank

### #289 freestar8n

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Posted 01 December 2013 - 03:14 AM

f the goto pointing accuracy is not acceptable after performing the ASPA procedure, then another two star alignment will restore the goto pointing accuracy, not repeating the ASPA procedure.

The goal of ASPA is to physically polar align the mount and immediately have good goto after a single iteration. This works well if the mount is level.

If the mount is not level, the polar alignment and goto accuracy will be off after a single iteration. A second star alignment would recover goto accuracy, but without repeating ASPA the polar axis will remain out of alignment - and the key goal of the process will not have been achieved.

You cannot know the rotation matrix corresponding to successive rotations about two arbitrary axes, without knowing those axes.

Frank

### #290 scopefreak

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Posted 01 December 2013 - 04:42 AM

"Another reason is for people near the equator, polaris will be high up and you will lose azimuth sensitivity in aligning it due to the cosine altitude term. A star down low and near the meridian retains sensitivity in both directions. "

Really? The EQUATOR!!

I have agreed with everything you have said so far, but this?? Maybe a typo??

### #291 freestar8n

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Posted 01 December 2013 - 05:21 AM

Whoops. Typo.

Thanks
Frank

### #292 scopefreak

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Posted 01 December 2013 - 05:24 AM

Whoops. Typo.

Thanks
Frank

I kinda figured.

### #293 spnc

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Posted 01 December 2013 - 09:49 AM

The original post in this thread implies that for the ASPA procedure to work correctly the mount has to be close to level since it has no information about how the altitude and azimuth axes of the mount are oriented relative to the Earth’s surface. It is my belief that this is not a correct statement and I have attempted to explain why this is not a correct statement. For those of you that are of the “show me” category, I have an experiment that you can perform using your mount at the start of your next observing session. I could use my CG-5 and post pictures but it is a ’04 vintage and doesn’t have the ASPA routine. Since this discussion is relative to the ASPA and how the mount orientation affects the accuracy of the ASPA routine, it should ideally be performed with a mount that has that capability. The experiment is described as follows:

1 – Set up your mount’s pier/tripod tilted obviously out of level. CAUTION!! Do not use an excessive amount of tilt without first making sure that the mount/ pier/tripod assembly is stable in all positions. I don’t want to be responsible for someone blindly following this experiment and having their equipment damaged by the entire setup suddenly and unexpectedly crashing to the ground. This is the main reason that the instructions state to be “reasonably” level, not from any limitation in the ASPA procedure but because as the angle of tilt increases you are moving the center of mass of the mount/OTA away from the center of the pier/tripod and deceasing the stability of the entire assembly. Several degrees out of level is more than sufficient but it can be performed at any angle as long as the tripod/pier is securely anchored to the ground.

2 – Perform the initial setup and two star alignment. If you want to perform the ASPA routine you can but it is not necessary for the purposes of the experiment.

3 – The hand control has a function called goto alt-az or goto axes. My hand controller says goto alt-az but in reading the current Celestron manuals online it appears to now be called goto axes. Regardless of what it is called, it allows the user to point the telescope at the altitude and azimuth of the user’s choosing. Enter any azimuth you like and an altitude of zero. Slew the mount to those coordinates. At the completion of the slew the telescope should be pointed at the horizon, that is, level along the optical axis of the telescope. This can be confirmed by placing a level on top of the telescope.

4 – Repeat the third step using an azimuth that is 90 degrees more or less than the azimuth used in the third step. The telescope should be again pointing at the horizon but in a direction 90 degrees from the third step.

So what has this demonstrated? Being level in two directions at 90 degrees from each other defines a level plane. If the mount has performed as I have described in the experiment above, then it MUST have the information about how the mount’s altitude and azimuth axes are oriented relative to the Earth’s surface otherwise it could not point correctly in the altitude-azimuth coordinate system. If it doesn’t, then I gladly admit I am wrong in my belief of how Celeston’s two star alignment and ASPA procedures operate.

5 – The final step in our little experiment and the most important one regardless of the outcome above – enjoy the rest of your observing session!

Steve

### #294 GlennLeDrew

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Posted 01 December 2013 - 10:07 AM

Steve,
That certainly seems like a wise first experiment. It tests just the fundamental first alignment step in isolation.

I suppose it should be mentioned that the tilt should be comfortably larger than the cone error. If the latter is extreme, and the former minimal, the OTA could be artificially out-of-level at some azimuths, thus masking the otherwise internal handling of the mount tilt. In any event, I see cone error as manifesting as a sinusoidal term on altitude with azimuth in this test, which effect should be borne in mind when non-zero altitudes are measured.

### #295 freestar8n

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Posted 01 December 2013 - 11:46 AM

It is my belief that this is not a correct statement and I have attempted to explain why this is not a correct statement. For those of you that are of the “show me” category

I have "shown you" with worked examples and mathematics from several different angles. Andrew has "shown you" with a real world example. I would like you to show me - your math and worked example. All I see is words, and claims that the mount has powers to sense the world around it that I do not understand.

As a first step, anyone who has a gut feeling that my illustration is wrong and Andrew's physical tripod is wrong can directly address the issues they present. There is no need for experiment for anyone who thinks they fully understand this - because the first thing they should be able to do is explain to Andrew and me why our examples do not directly convey the impossibility of a system that can do ASPA without relying on level.

Remember - any failed experiment would not prove me right. It would simply fuel the fire that the implementation is not as good as it should be. If that is the case, I will still ask for a complete mathematical description - right now - from anyone who feels they have a good handle on this and how it "should" work.

Ideally they should have taken a course in linear algebra and have experience with rotation matrices, Euler angles, quaternions, etc. I would certainly prefer a description in that language - if you feel it is all worked out.

You have said that the mount can "tell" how the pier is oriented. How does it do that? There certainly isn't something about that in the menu.

The current polar misalignment is available - as alt/az values referenced to the local horizon. Isn't that a hint to you?

How can the mount tell that the pier is tilted 20 degrees north, if the latitude setting on the eq. head can be set fairly arbitrarily relative to the pier? How can it tell?

Frank

### #296 Stew57

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Posted 01 December 2013 - 12:28 PM

Would ASPA mess up if you set your RA home position wrong? Why would it care then if the tripod was out of level east and west?

### #297 Per Frejvall

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Posted 01 December 2013 - 12:50 PM

Just a quick log on the fire...

Isn't it a fact that any software suggesting a correction by offsetting a star must offset it in what it assumes are the axis of movements that the user will use to correct the error (cool senence )

/per

### #298 Alph

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Posted 01 December 2013 - 12:55 PM

Gday All

Just for my info, as i dont have any celestron gear,
does ASPA "allow" you to use Polaris as your target star????
If so, and you can see it, why would you use anything else???
Ie the error being discussed here due to base tilt
is also proportional to the angle between the target star and the true pole,
so why not use Polaris if you can ????
You will still get rotation of the axes if the base isnt level,
but the process will home in on the pole very quickly.
Just goto a known star afterwards and resynch and you should be sweet.

Andrew Johansen Melbourne Australia

This is an interesting observation. You just described the old (prior to 2009) polar alignment method. Here is a quote from the CGE user manual:

After performing an Auto Two-Star Alignment, the telescope will slew to where Polaris should be. By using the equatorial head to center Polaris in the eyepiece, the mount will then be pointed towards the actual North Celestial Pole. Once Polar Align is complete, you must re-align your telescope again using any of the alignment methods described earlier.

Another interesting tidbit of information is rumor has it, when Celestron was working on ASPA, someone did an error analysis showing that a star near the intersection of the meridian and equator gives best results.

BTW. It is not that difficult to include gravity (oops I mean level) in the RA/Dec offset calculations. It just requires additonal coordinate rotation.

### #299 Alph

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Posted 01 December 2013 - 01:04 PM

Ideally they should have taken a course in linear algebra and have experience with rotation matrices, Euler angles, quaternions, etc. I would certainly prefer a description in that language - if you feel it is all worked out.

Very impressive statement. I guess it supposed to intimidate anyone who does not agree with you. Why don’t you apply the same standards to yourself and show the math.

### #300 freestar8n

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Posted 01 December 2013 - 01:06 PM

Isn't it a fact that any software suggesting a correction by offsetting a star must offset it in what it assumes are the axis of movements that the user will use to correct the error

Yes, that's the whole idea. Thanks. If you don't know the axes, the expected motion is indeterminate. Pretty simple.

That's the situation shown by Andrew's and my examples - that no one has directly addressed.

Frank

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