Alex, I am hesitant to recommend a motor until you have measurements of the force necessary to rotate the dome. If you had the same rings and wheels as I do, I could recommend one based on my measurements. But I would recommend getting it all assembled and measuring your actual force required.
Earlier in this thread, you linked to a motor that produced something in the ballpark of 800 oz-in of torque. I am working with a 416 oz-in motor, so the 800 ought to be plenty if you have to get one ahead of time.
You will need an Arduino to control things, and a stepper controller. I used this controller: https://www.robotshop.com/ca/en/tb6600- ... river.html
For the shutters, you will want a relay shield to plug into the Arduino. This is the one I used: https://www.robotshop.com/ca/en/relay-s ... duino.html
. I have a couple of external components to operate the shutters. The important one is the door sequencer. It is a home-brew contraption of relays and diodes. If you choose to bypass this, you could operate each door independently from the Arduino, with some reprogramming. The hard part of doing that, though, is not the reprogramming, but getting the signals to the door motors in the rotating dome. Two contacts are not hard to arrange, but more than two is difficult.
If you don't have shutter motors already, you will need to get them. I didn't include them in my $200 figure, since I already had them.
If that sounds like biting off more than you can chew, you might want to investigate an off-the-shelf dome controller.
Orion 200mm f/4 Newtonian Astrograph; ATIK 383L+; EFW2 filter wheel; Astrodon Ha,Oiii,LRGB filters; KWIQ/QHY5 guide scope; Planetary AP:
Celestron C-11; ZWO ASI120MC; Portable:
Celestron C-8 on HEQ5 pro; C-90 on wedge; 20x80 binos; Etc:
Canon 350D; Various EPs, etc. Obs:
8' Exploradome; iOptron CEM60 (pier); Hall's Harbour Observatory (H2O)