On 09/19/2020 4:20 PM Roland Christen via groups.io <chris1011@...> wrote:
During my recent imaging sessions I have been gathering a lot of data to better understand how the mount is actually tracking an object over a long time period. I can do this with the Mach2 thanks to the built-in encoders. The scope I'm using is the 160 EDF which yields approximately 1 arc second per pixel on my QSI camera sensor.
I have read on other user sites many posts by people who don't seem to understand that the stars do not move evenly across the sky at the sidereal rate. Some claim that with their inexpensive mounts they can do 5, 10 or even 20 minute unguided imaging. This is with mounts that have no modeling capabilities or even just custom rates in both axes. So that excites others who are having problems with guide scopes, off-axis guiders, guiding software etc., to believe that perhaps there is an easy way to set up a mount for unguided imaging. Back when I first started some umpteen years ago, it was well understood by all that running a mount, even with superb sidereal tracking, that it was not going to guarantee 1 hour exposures on our film negatives. And film is 10 times more forgiving than CCDs today.
So, as that for a background, I would like to share a few observations. These last couple of nights I was shooting NGC7635, the Bubble Nebula, along with star sprinkled M57 nearby. This object is circumpolar, so it is well above the horizon even when 8 hours away from the meridian line overhead. I observed that when the object is between 5 to 8 hours in the east, the RA tracking rate has to be slowed down considerably to avoid trailing, even for 60 second exposures at the focal length of my refractor. Compensating for that drift is exactly what modeling will do.
I spent some time yesterday before sunset getting good drift data and creating a model for the path of NGC7635. The model spans about 5 hours of RA motion, which is about the time it takes for the object to reach the meridian at around midnight. The data shows the following:
At 5 hrs east, the RA un-compensated drift rate was 73 arc-sec/hour, or about 1.2 arc sec per minute. At 3 hours from the zenith the drift rate is 54 arc-sec/hr. At 1 hour from the zenith the rate drops to 13 arc-sec/hr. At the zenith the drift rate drops to zero and begins climbing back up on the other side of the meridian. The Dec rate runs from around 11/hr down to zero and back up on the other side.
For each object the drift rate will be different and depends on the declination that it sits on. There is no one-size-fits-all tracking rate. The rates are variable depending where you are in the sky. People knew that back in the late 1800's. Astronomers at large observatories were actually able to take unguided images up to 1 hour and more by simply adjusting their mechanical clock drives according to charts that they painstakingly created using hand calculations.
The King rate will compensate the RA drive rate to some degree over a large swath of sky, but cannot compensate for Dec drift, nor can it compensate for small amounts of polar misalignment. The above data was for a well aligned mount and matches quite closely to what the King rate produces in RA (only in RA of course).
I did some experiments with small polar misalignments and the RA drift rate can easily double if you are off only a small amount. A decent model will easily compensate for that, along with the inevitable flexure of a large imaging rig.
As far as doing unguided imaging with a mount that runs sidereal rate and no model? Well if the object is drifting at 1.2 arc sec per minute, and you take a 5 minute exposure, I suppose that you can get round stars if your pixel scale is around 6 arc sec per pixel. Anything less than that and you will see trailing. If you are shooting at +60 Degrees Dec, I suppose you can get away with a 3 arc sec per pixel scale and achieve round stars - because of RA foreshortening as you approach the pole.