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Well, people do have good opinions on telescopes like Maksutov Newtonian and Schmidt Newtonian. Granted, those are full aperture correctors and not sub aperture correctors, but can be quite fast systems as well- often F/4-F/5.

For newtonian with single curved mirror - it is true that spherical aberration increases rapidly with faster optics. https://www.telescope-optics.net/reflecting.htm For paraboloid - it's equal to 0 but for spherical with K=0, we can see that it is inverse of third power of F/ratio, so telescope has to be really slow, or have small diameter.

Catadioptric has refractive glass element in optical train next to mirrors - usually as front aperture corrector - making tube closed. Sometimes this element sits inside focuser or in front of secondary - but then you'd have very short tube (Bird-Jones design) or Ruten Maksutov type (but you have newtonian, so it's not that). If it's a longer tube - greater chance that it's spherical mirror. Fast telescopes and spherical mirrors don't get along. If it's F/8 or slower - then it might be spherical.

Two things come to mind - first is to check for off axis coma and second is to get Ronchi eyepiece: https://www.firstlightoptics.com/specialist/gerd-neumann-ronchi-eyepiece.html

Ha-ha! Less nerdy (at least no one is as nerdy as I am - 0% scored the same )

How fast is your slew to position? Looking at the specs - stepper motors could be quite a bit under powered. This can result in skipped steps at high slew speeds. Steppers loose their torque with higher RPMs and since this mount does not use counterweights - it instead relies on stepper motors to provide torque to keep the weight in position. From specs - max amperage when slewing is 0.8A - that is very low, we can say that it uses probably 0.3A per motor (some of current for electronics and some for motors - two of them). Anyway, it slews at max 6 degrees / second - with reduction ratio of 360:1. That makes one whole revolution in 60 seconds - or 1 rpm, so motor needs to spin at 360 rpm. Here is example of 0.4A Nema 17 motor showing dependence of torque to RPM - at 360rpm pull out torque is 1/10th that of slow speed (motor is rated at 26N/cm). This is with 24V and 1600 micro steps (or 1/8th micro stepping) - things get only worse with finer micro stepping and when using lower voltage to power motors - like 12V Anyway - try setting slew speed to 1-2 degrees / second instead to see if that helps with goto accuracy.

I always wondered how large this effect is - particularly on galactic scales. For example - when computing Hubble's law - do we have to take into account relative difference between galaxy masses? Origin galaxy and MW? When light leaves origin galaxy it will be red shifted, but then when it "falls into" MW it will be blue shifted - difference between those two will be some percent of total red shift - but how large is the effect?

I was aiming more on funny side rather than informative, but hey .... (I edited the post and inserted the actual image instead of hot linking it ...)

Just to be sure on terminology there ...

I'm not sure that OP is concerned about origin of motion, but rather the fact that there is no preferred direction. If you look at this post: I believe it shows what is the heart of the question. We tend to study stars from earth and study their motion relative to us. Someone else might see different motion - after all motion is relative, and their Doppler shift would be in agreement with what they observe - as movement is relative.

It does not matter. Consider this case: We have a source of waves moving on a line from our right to left like in image above. At first - it is approaching - so there is component of motion that is in our direction. Source is blue shifted. At the mid point - source is still moving at constant speed - but component of motion in our direction is zero - so we receive normal frequency. After it passes this point - it starts moving away from us - now there is component of motion in our direction that is away from us - source is red shifted. No acceleration takes place in above case - but we have 3 different scenarios happening: from blue shift thru no shift to red shift. This shows that Doppler effect in its essence is not related to acceleration (that once must have happened for object to be moving with respect to us) - but rather to component of its relative speed in our direction. This is regular red shift - and what we observe when we look at for example rotational curves of galaxies (stars moving from/away depending if they are on one side or other side of the galaxy). It also happens when ambulance passes by - we first hear high pitched siren, then regular, then low pitched siren ... There are other two sources of red shift - gravitational (or the one related to acceleration / curvature of space time) and cosmological red shift - which happens due to expansion of space. Last one is "equivalent" to regular red shift - as if galaxy is really moving away from us at certain speed. There are only a few indicators that the space is actually expanding - like fact that we can have different places recede faster than the speed of light - which would not be possible if galaxies were moving thru the space instead of space expanding.

No need for acceleration - just uniform motion is enough to produce Doppler shift. On the other hand, red shift (or blue shift for that matter) - can be due to acceleration - but we might not need force for that either - curvature of space time is enough to produce the effect. Light emitted from vicinity of large mass will be red shifted to observer that is far away, while light produced by observer floating in intergalactic space and observed near massive body (or even inside the galaxy) will be blue shifted due to it "falling" into gravitational potential well of mass concentration. This is closely related to time dilation effects by the way (think of laser producing exact wavelength of light and those oscillations being slowed down due to time dilation and thus producing longer wavelengths - red shift).

Only if you do the analogy with moving train, three people on the train - one seated, one exiting car on one side and other exiting car on the other side versus bystander watching the train go by Who will see what?

Depends on where you put observer. If you stand on earth - then earth is moving with 0 units of speed relative to you and thus star A must move to the left and star B must move to the right. For some external observer, standing near star C - it can indeed appear that all three are moving to the left or to the right or some other combination - because motion is relative to the observer.

That's 150mm F/8 newtonian right? Aluminum has about thermal expansion of about 22um per meter Celsius. You have about a 1.2 meters, so you get something like 26um of expansion for every C. F/8 system has critical focus zone of about 156um, so you should be good for about 3C change in temperature (give or take - it might be even a bit more, depending where you landed with original focus). Slower scopes are harder to get knocked out of focus due to temperature change because critical focus zone grows as square of F/ratio. Btw, Coma free zone of F/8 newtonian is about 5.7mm radius, so 11.4mm diameter circle. That is shy of 16mm diagonal of ASI533, but you'll likely not notice much coma to the edge of the sensor as it is very small at that F/ratio.