This is the first telescope that I have ever owned.  In fact, this is the first telescope that I have ever "looked" through (not counting images from Hubble, and yes I'm not actually even looking through this one either).  Anyhow, I don't know what I'm doing...  So much so that it took me a good 15 minutes to even find the Moon with this telescope.  I have no spotting scope, I was just sighting along the barrel and I had trouble.

The problems boiled down to:

1. Vibration / Stability - The whole setup shook while moving it by hand, not because it was unstable, by just because my hand vibrates enough to cause problems.  Also I had difficulty focusing because that would move or jiggle the whole thing.  In reality I am going to have a hard time making a rigid telescope out of paper.
2. Positional Resolution / Repeat-ability - It was very difficult to move the telescope in only one axis or be sure that I was "scooting" it just a little bit and not to much to overshoot my target.
3. Inexperience - I didn't know what I was doing or even how large my view of the moon would be

A little homework was in order...  First, I've been using this site: in-the-sky.org to find the size of the objects that I was interesting in seeing.  On the first day 11 - Dec My telescope was giving me a field of view of about a third of the Moon which was 1770 arc-seconds in size. So my field of view (FOV) is in the neighborhood of 600 arc-seconds.  I'm using the 8MP Raspberry PI Camera v2 (native res of 3280 X 2464).  Rather than do actual math, I figures that I start with some napkin math.  I'm going to consider the my horizontal as equal to the 600 arc-second FOV and just round down a little so 3000 / 600 = somewhere 5 pixels per Arc Second.

Next, I went back to in-the-sky.org and found the sizes of some other things that I wanted to see:

So a day is 23:56:04 or 86,164 seconds to turn a total of 1,296,000 arc seconds in a circle or, 15 arc seconds per second.  Thus, during a one-second exposure Saturn would move 15 pixels (1/5 of its size).  That would be a pretty blurry image!

I will limited to 1/30 of second exposures if I want to limit my blurry to sub-pixel size, but that may be pushing the ISO limits of the camera.  This will be my first experiment.

It would be better if I could move the telescope to keep up with the earth's rotation (like the big boys do).  To do this I would need to be able to generate smooth motion at about 1/120 of a second of earth's rotation (I just made that number up).  So 15/120 that give me 0.125 arc seconds "steps" or 10,368,000 steps per revolution.

A quick google search did not turn up any 9.645 * 10^-8 deg stepper motors.  I think a little reduction is going to be in order.  Likely 1/120 of an arc-second is probably an exaggeration of what I will likely need so to give myself a fighting chance, I'm going to aim for a 1 step per arc-second resolution (not to be confused with accuracy).

That works out to a 6480:1 reduction (3,600 arc-seconds per degree * 1.8 degree stepper motor = 6480).  You can also think about it as 1,296,000 arc-seconds per revolution / 200 steps per revolution stepper = 6480 reduction.

6,480 is the magic number.