Artist project: rotating table top

To keep it short: I am trying to make a table with a rotating top that moves very very slowly- exactly one rotation per 10hr and 39 mins. It’s important to the project that the movement is both accurate and imperceptible.

I have put together the gears and mechanics for the table (see pics attached) but need someone to assist me with putting together the electronics + programme the arduino. (I’m completely new to all this stuff!)

A quick overview of the mechanics- The turntable plate is attached to a 1” shaft which is connected to a 252:1 reduction worm gear (the sort they use in telescopes), powered by a Hurst (model 3008-002) stepper motor, which has a built in reduction gear box of 150:1. (See pic attached)

Let me know if you think you might be able to help.