The dome motor is used to spin the dome (what a surprise).
The most common motor is the Pittmann geared motor.
Common models are GM9413, GM9234 and GM9236. With the correct gearbox, the later two offer much higher torque and speed.
But the cheap chinese geraed motors also work very well. And they are easy to find on EBay etc.
They are Pololu style motors.
The most common used are the 350RPM (gear ratio 29:1) and the 200RPM (gear ratio 50:1) motors.
The dimensions are 36mm diameter and 53mm lenght
They are connected to the Syren10 motor driver and are powered with 12V