determining sidereal rate for tracking

[alistairsam]

Hi,

I'm trying to work out the stepping required for a stepper motor to track at the sidereal rate after gear reduction.
But i don't really understand sidereal rate and its relationship with tracking speed.
is the motor speed or tracking rate of a scope or mount dependent on field of view of the telescope?
as per this reference http://www.dur.ac.uk/paul.clark/Tele...otorDrives.pdf , the moon would take under 2 minutes to cross from one side of the scope to the other with a field of view of half a degree.
what happens if the field of view is different, for example with different eyepieces or different f ratios?

I just need to determine the rate at which my RA shaft needs to rotate, that way i can work out the gears required and then the steps required.

Is the sidereal rate 0.00418 deg per sec or 15.04 arc secs? does the RA shaft therefore have to turn at this rate?

[adman (Adam)]

the sidereal rate is the rate at which the earth spins on its axis, and consequently the rate at which the 'fixed' stars appear to move in the sky. This is the rate which you must match with your RA axis. The point of an equatorial mount is that the RA axis is set up to be parallel to the earths north/south axis, and spins at the same rate (in the opposite direction) so that it keeps the apparently-moving stars still in your eyepiece.

The focal length of the scope and eyepieces make no difference to the rate at which the earth turns so you do not need to alter the rate of spin of your RA axis. Imagine a snail that always moves at 1 cm per minute. You stick him on the edge of a large dinner plate and point him towards the opposite edge. The plate is 30 cm across, so it will take him 30 minutes to get across. Same snail, smaller plate - 15 cms this time - it will take him 15 minutes to cross. In case you were wondering, the snail is a star, and the dinner plate represents your FOV....

The field of view of your scope will just determine how big a patch of sky you see, and the stars will traverse your field of view quickly if it is a small FOV and more slowly for a larger FOV, but they are still 'moving' at the same speed.

By the way -relative to the stars - the earth rotates on its axis once every 23.93447 hours (23 hours, 56 minutes, 4.091 seconds), so you have to get your motor / gears to turn you RA axis once every 23.93447 hours.

there is a good explanation here

Hope this helps.

Adam

[alistairsam]

Thanks for that.
your analogy of the snail on a plate was brilliant.

I worked out the clock freq required for a 1.8deg stepper motor using a worm and 360tooth gear as below.

would this be correct?

Earth's Rotation 23h 56m 4s = 86164.091 secs
Thats 360 deg of the RA shaft in 86164.091 secs


360 tooth gear requires 360revs of the worm to turn 360 deg

I need to turn 360 deg of the gear in 86164.091 secs
Thats 0.004178075 deg in 1 sec of the gear
that’s 1.504106856 deg in 1 sec of the worm

with 1/16 stepping of a 1.8 deg stepper, 1 step turns 0.1125 deg
I need 1.5041086856 deg in 1 sec
which is 13.36983872 steps in 1 sec

therefore clock freq should be 13.36985 Hz.

I presume further gear reduction is required to achieve this rate, mechanical errors, clock drift, etc will all add to accuracy errors.

[adman (Adam)]

without actually sitting down with a calculator, your logic appears to be correct

I am not sure whether it is advantageous to get the required frequency to be a whole number of Hz? Probably not but might be worth investigating?

Adam

[rcheshire (Rowland)]

You are using a crystal oscillator to set the clock frequency? Are you micro stepping?

You have probably considered this. An alternative method is to use a programmable microprocessor, such as an Atmega 168, and control stepper speed. Gear reduction and careful choice of the final gear ratio may produce good results.

[alistairsam]

Hi,
At the moment, I'm using a precision silicon oscillator LTC6900, from tests, its not that precise, drifts by +-1hz for frequencies between 100hz and 2khz
I did try a crystal, but noticed the same drift, perhaps the capacitors are causing this? i tried with tantalum, but got the same.
moreover, the LTC6900 is variable which is a great help for me to arrive at the optimum frequency once i've established my gear ratios.
I am using microstepping with 1/16th stepping using the A4983 stepper driver from Allegro and switching to half step digitally for high speed slew. that way i may get away with the need for higher gear reduction

[alistairsam]

Originally Posted by rcheshire

You are using a crystal oscillator to set the clock frequency? Are you micro stepping?

You have probably considered this. An alternative method is to use a programmable microprocessor, such as an Atmega 168, and control stepper speed. Gear reduction and careful choice of the final gear ratio may produce good results.

I'm learning how to program the picaxe microcontroller which i've read is the easiest to learn as it uses BASIC.
I'm very new to microcontrollers, but it looks a lot more efficient than using discrete digital chips.
i came across a document using an S6 compumotor stepper controller that has dip switches for upto 50000 microsteps. wonder how they achieve that.

[rcheshire (Rowland)]

I've been using an Arduino and depended on gearing rather than micro stepping, but motor resonance can be a problem at low RPM, as you know. I don't think that torque reduction is such an issue when micro stepping if gear ratios are significant. Stepping accuracy is also not as critical as far as I can tell. Interested to see the final product. Sounds like an interesting project.

[alistairsam]

Am planning on sticking to timing belts as much as possible but downside is reduction is not easy hence more reliance on microstepping
The a4983 stepper driver has 3 logic inputs to choose from full to 1/16 step' so I've wired spst switches to a 20 key encoder and I thus switch from 1/16 to half step for slew
Torque needs to be tested
The mcu approach would be better as acceleration and deceleration can be incorporated
Will post progress
I bought a digital compass so hopefully polar alignment should be close enough
Mount is a home built fork for a newt

[rcheshire (Rowland)]

I found this article very helpful. http://www.dfmengineering.com/news_t...ing.html#other

[alistairsam]

Originally Posted by rcheshire

I found this article very helpful. http://www.dfmengineering.com/news_t...ing.html#other

that is a very nice article, but in friction drive how is slippage handled as its just smooth metal against metal. is a lot of pressure required to keep the rollers slipping?

[gary]

Originally Posted by adman

the sidereal rate is the rate at which the earth spins on its axis ...

Not quite.

The Earth rotates around its own axis very nearly once every 24 hours.
This determines civil time.

However, the Earth is orbiting around the Sun as well and this changes the apparent
position of the stars every day. During the course of the year, the Earth will thus
rotate exactly one more time with respect to the stars that it does to the Sun.
This determines sidereal time and it results in a solar day being approximately
3 minutes, 54.6 seconds longer than a sidereal day.

To make matters more complex, the tracking rate is simply not the first
differential. The effects of atmospheric refraction distort things and the tracking
rate varies continually from horizon to zenith and then from zenith back down
to the horizon. Some older telescopes attempted to kludge for this by what is
known as the King Rate.

Best Regards

Gary Kopff
Mt. Kuring-Gai NSW

[rcheshire (Rowland)]

Looking at how others have implemented friction drives it's difficult to say. The DFM article suggests that significant pressure is required. How much, I'm not sure. Some builders rough up the surfaces to increase friction. Depending on the materials used there would be a weight limitation - counterweights will help there. A bit more reading will clarify the details - I'm working on a similar project, but it's only on paper at the moment.

[alistairsam]

Originally Posted by gary

Not quite.

To make matters more complex, the tracking rate is simply not the first
differential. The effects of atmospheric refraction distort things and the tracking
rate varies continually from horizon to zenith and then from zenith back down
to the horizon. Some older telescopes attempted to kludge for this by what is
known as the King Rate.

Best Regards

Gary Kopff
Mt. Kuring-Gai NSW

Hi,
what are the upper and lower limits between which the tracking rate varies from zenith to horizon and back, or is the offset dependent on the angle in question, eg, 40 deg above horizon has higher refraction and causes an additional 0.005 secs to sidereal rate, but 60deg adds only 0.001 secs (just an example)

in that case, is autoguiding the only option to counter this drift by autocorrecting the tracking rate? how do mounts with argo navis or other automated controllers with tracking options counter this variation in sidereal rate? is the change in sidereal rate significant?

[gary]

Originally Posted by alistairsam

Hi,
what are the upper and lower limits between which the tracking rate varies from zenith to horizon and back, or is the offset dependent on the angle in question, eg, 40 deg above horizon has higher refraction and causes an additional 0.005 secs to sidereal rate, but 60deg adds only 0.001 secs (just an example)

Hi,

It is a function of the observing latitude, the Hour Angle of the part of the
sky being observed and strictly speaking also a function of barometric pressure
and temperature.

So if one were observing from a latitude of around near Sydney, at 4 hours HA
and one were aligned with the 'true' pole, the rate might be around
15.035 arc minutes/ minute and slightly faster, but still below the nominal
rate at the meridian.

in that case, is autoguiding the only option to counter this drift by autocorrecting the tracking rate? how do mounts with argo navis or other automated controllers with tracking options counter this variation in sidereal rate? is the change in sidereal rate significant?

Most modern large telescopes since the 1970's use computer control to
update the tracking rate on-the-fly in real time. Argo Navis uses this approach.

Generic amateur mounts often come with one fixed rate and the best approach
with these is to align with the refracted pole rather than the 'true' pole. As it turns out, the
nominal sidereal rate then provides a good compromise across the whole sky.
Autoguiding on amateur scopes is most often used for helping iron out
periodic error in worm drives and the sort but since most exposure times by
amateur astrophotographers tends to be relatively short, autoguiding will
assist in helping smooth out the continually varying tracking rate.

When we speak of the 'true' pole it should be made clear that there is
no one point in the sky to which one can align the RA axis of the scope
and not have some field rotation. There is a different 'ideal' pole for every
value of HA. However, again since imaging times are kept short and because the
field of view of most amateur rigs are small, it is usually not a problem for most
practitioners. Again, the best compromise is to align with the refracted pole
above the 'true' pole and for most practical purposes you are likely to achieve
a useful outcome.

Best regards

Gary

[alistairsam]

Originally Posted by gary

Hi,


Generic amateur mounts often come with one fixed rate and the best approach with these is to align with the refracted pole rather than the 'true' pole.

There is a different 'ideal' pole for every value of HA.

Again, the best compromise is to align with the refracted pole
above the 'true' pole and for most practical purposes you are likely to achieve
a useful outcome.

Best regards

Gary

Hi,

I did some reading about the "King Rate" and was surprised at what I found as compensation for effects of refraction is not very commonly found in amateur guides, or maybe just the ones I used.

Is there any guide that correlates HA and the refracted pole.
how do we calculate the "offset from true north" to get the refracted pole if we know the Latitude?

when you say there is a different ideal pole for every HA, does this mean RA Axis alignment needs to be adjusted depending on HA?

Do Argo Navis or other automated systems use feedback from the Dec Axis to correct the tracking rate?
again, is there some sort of table or guide to calculate variance in sidereal rate for various points between horizon and zenith?
or is it just sufficient to point to the refracted pole to compensate.
I'm aiming for exposures between 15 and 30 minutes.

For DSO's with mag 12, would this exposure time be sufficient to capture nominal detail?

[gary]

Originally Posted by alistairsam

I did some reading about the "King Rate" and was surprised at what I found as compensation for effects of refraction is not very commonly found in amateur guides, or maybe just the ones I used.

The concept of polar alignment is commonly misunderstood by many.
A common misconception is that there is some magic point in the sky to
which one can align the RA axis and achieve "perfect polar alignment".

Is there any guide that correlates HA and the refracted pole.
how do we calculate the "offset from true north" to get the refracted pole if we know the Latitude?

See pp 29-30 of this Manual for a handy lookup table.
http://www.bisque.com/sc/media/p/28002/download.aspx

when you say there is a different ideal pole for every HA, does this mean RA Axis alignment needs to be adjusted depending on HA?

Strictly speaking, yes. However, in practice, there are very few telescopes
in the world that go to the trouble of adjusting their elevation as a function of
HA as they track. One that comes to mind that can do this trick is
the U.K. Schmidt, however, it has a FOV of 6.6 degrees by 6.6 degrees
and was originally designed to accommodate 14 inch survey plates.

These days, most large professional telescopes are driven Alt/Az with
a field de-rotator.

Do Argo Navis or other automated systems use feedback from the Dec Axis to correct the tracking rate?

As they are in total control of the pointing of the telescope, they "know" where
it is pointing in an Alt/Az sense and can make the necessary corrections.

again, is there some sort of table or guide to calculate variance in sidereal rate for various points between horizon and zenith?
or is it just sufficient to point to the refracted pole to compensate.

Given it is primarily of interest when aligning scopes in fixed observatories and
since it is dependent on latitude, it tends to get computed from first principals
on a case by case basis or as is more common now, it is embedded within the
telescope control system and the operator enters the latitude, longitude and
time and it is computed automatically. So I am not aware of a handy lookup
table. However, in your circumstance which will be typical of most amateurs,
pointing to the refracted pole will be more than sufficient to meet your tracking
demands.

What I hope you, or any other interested reader, might take away from this
dialog is the knowledge that going in pursuit of a "perfect" polar alignment or
a "perfect" tracking rate which will be good for all points in the sky is a Holy
Grail that does not exist. For practical purposes, there will be some compromise
with the alignment and tracking and the types of compromise we are talking
about would not stop one from, in theory, still winning first prize in an astrophotography
competition. For example, the remnant field rotation could be at the sub-pixel level.

I'm aiming for exposures between 15 and 30 minutes.
For DSO's with mag 12, would this exposure time be sufficient to capture nominal detail?

As you are probably aware, for extended deep sky objects, it is how fast the
optics are rather than just the aperture. However, for most amateur rigs
those types of exposure times are not untypical and often they are shorter.
Stacking of images is popular and there are many talented imagers in the
astrophotography sections of this Forum that I know will be only too
happy to provide advice on exposure times for the given type of camera
and scope you are using.

Good luck!

[alistairsam]

thanks for all the info. its getting very interesting and challenging.
still have more questions, but I think i've got enough data to process and improve on for a while.

[alistairsam]

Originally Posted by gary

As you are probably aware, for extended deep sky objects, it is how fast the
optics are rather than just the aperture.

Good luck!

Hi Gary,

I've been making progress on my drive, I've now completed the code for the picaxe microcontroller to use acceleration, deceleration etc. just waiting for the chip to arrive to test.
also working on a quadrature decoder using the mcu similar to ek's box.

regarding what you mentioned above, i have read that scopes with higher F rations (slower) are suited for planetary imaging, and scopes with lower F ratios (faster) for DSO's. is this due to field of view? have searched and read a bit on faster and slower optics but did'nt really understand how they relate to DSO's and planets.

[gary]

Originally Posted by alistairsam

regarding what you mentioned above, i have read that scopes with higher F rations (slower) are suited for planetary imaging, and scopes with lower F ratios (faster) for DSO's. is this due to field of view? have searched and read a bit on faster and slower optics but did'nt really understand how they relate to DSO's and planets.

Indeed, it is a result of the FOV.

As you would have read, the focal ratio is the focal length divided by the aperture.
Longer focal length instruments have smaller FOV's. So a scope with a long focal
length and large (slow) f/ratio works fine for photographing bright objects such as
the Moon and Jupiter as exposure times can be kept short. For extended objects,
the better choice is a scope with a smaller f/ratio (faster) as the imaging time
for these types of objects becomes smaller.

Fred Watson gives an interesting historical treatment of this topic in his book, Stargazer.
George Willis Ritchey was head of instrument construction at the Yerkes
Observatory in Chicago in 1901. Interested in astrophography, particularly that
of nebulae,

Originally Posted by Fred Watson, Stargazer, page 252

"Richey was aware of a curious and recently discovered (1882)
attribute of photographic image detection - namely that the speed with which
an extended object like a nebula or a comet can be recorded depends not on
the aperture of the telescope but only on is focal ratio, or f/number."

Fred goes on to write -

"It seems almost impossible to believe that the sensitivity could be independent of
aperture, but it is true - the lower the focal ratio (and therefore the stubbier
the telescope), the greater the speed with which the image of the nebula will
be detected. That is why low focal-ratio lenses or mirrors are often called 'fast'.
There are still very good reasons for making them as large as possible, however,
for their diameter determines both the amount of detail that is recorded and their
sensitivity to point like sources such as stars."