Star Tracker

Precisely control my amature telescope's right ascension axis so that (when the telescope is polar aligned) it counteracts the rotation of the Earth, allowing me to take long (>~7s) exposure pictures of planets and deep sky objects (clusters & nebulae). I have an "EQ-2" mount.

It controls the rotation rate of the right-ascenction axis to counteract the Earth's rotation. I use a servo to do this and plan on powering this with a 12V lead acid alarm battery.

The declination axis isn't controlled so it must be pointed at the object of interest (and polar aligned) before use. My telescope's mount is manual (wasn't designed for automation or being motorised like this). It required mechanical modifications (metalworking) inorder to securely fit the stepper motor.

1 rotation of RA must occur each sidreal day (24hrs - 4min + 4sec) and the RA control is connected to the telescope's RA bearing with a 130x reduction worm gear. Thus I need a rotation rate of 130/(86,164.1s) or 0.5 degrees per second. I plan on using a stepper motor and this is smaller than almost all step sizes so I need a reduction gear.

• The speed needs to be 1 rotation per sidreal day on the telescope's right ascension axis
• The motor is attatched to the RA axis through a 130x reduction ratio worm gear on the telescope's mount
• The stepper motor has an (internal) 26.85x planetary reduction gear between it and the worm gear
• Therefore need 360*130/86164.1 = 0.543 deg/s at the output of the motor
• The motor (with gear) has a step angle of 0.067deg
• Therefore I need 0.543/0.067=8.104 steps per second
• Sanity check (step_speedstepangle/(reduction_ratio))sidreal_day = 360deg
  (8.1041.8/(26.85*130))*86164.1 = 360.09 thus maths using these numerical approximations drift is 0.1deg/day
• There is experimental uncertainty on the worm gear ratio, the amount of this is unknown because it's kinda hard to measure....

The torque required to turn the right ascension axis control shaft is about 1.25kg*cm or 0.123Nm or 12.3Ncm, though this is almost a guess.

I've selected a small geared NMEA17 stepper motor with a 27x reduction ratio:
https://www.omc-stepperonline.com/geared-stepper-motor/nema-17-stepper-motor-bipolar-l33mm-w-gear-raio-271-planetary-gearbox-17hs13-0404s-pg27.html
This is a little more expensive than I was hoping for, however it has much better documentation andhigher torque than cheaper alternatives I had been looking at.