I would invite any mathematics enthusiasts among you to attempt to calculate the input : output ratio of this gearbox. With the help of a learned colleague at work I was able to settle on 931.222222 worm revolutions per output shaft revolution.
I am not sure I have calculated this correctly as it seems a little on the high side to me.
My calculation was thus:
1/((1/25)*(10/34)*(9/29)*(10/34)) = 931.2222...
Does that sound right? Time will tell. I am currently awaiting the arrival of some new tools that will enable me to progress with the metalworking aspects of this build and finally affix the stepper motor to the gearbox via a worm screw. Then it will be but a trivial matter to have the stepper motor move a full (931.222222 * 200 = 186244.444444 (full) steps and see if the output shaft does precisely one revolution. If not then I'll have to recalculate!
I obtained this gearbox for about £13 on Ebay, having bought it with the expectation that it would be a cheap piece of flimsy crap that would fall apart after a bit of machining. Turns out it's actually pretty decently made (for it's price) and has metal gears within, which is a bonus. I didn't know what the ratio would be before hand, only that it was fitted with a 12VDC reversible motor and had a rated output shaft speed of 8RPM.
My limited knowledge of 12VDC motors told me that they probably spin at a few thousand RPM at the motor shaft, 8RPM on the output must mean it's got a pretty awesome gear reduction. Such a reduction gives me lots of torque to play with and also a very fine resolution on the positional accuracy of the output shaft. This is increased even more because my stepper motor driver can microstep down to 1/8th of a regular step. 1600 steps per revolution on the input shaft to a gearbox with a 931.2222:1 reduction gives me a mind-meltingly fine resolution of 1 part per 1489955.6.
That is to say, my stepper motor needs to microstep 1489955.6 times per day in order for my celestial camera mount to follow the starfield movement perfectly. That's one microstep every.... (86164.098903691 / 1489955.6) = 0.05782998 seconds. Or one about microstep every 57830 clock cycles when running from a 1MHz crystal.
17.3 micro steps per second or so. Sounds reasonable.