stepper: choosing between steps per second

Hello,

I am starting a new project where a stepper motor moves at the same speed as the earth. Yes, it is an equatorial mount.

So Earth's makes a spin every 23 hours, 56 minutes, 4.0905 seconds which are around 86164.1 seconds (this is called sideral time)

The reduction gears I found for the pulleys are: 50/12, 50/15, 60/12, 60/15
The driver I am going to use is probably the TMC2130 which has a lot of microstepping features.
The library I chose is the good, old AccelStepper.
The motor I would probably use is the 17HS4401 which can do 1.8° per step.

This is the formula I have used to calculate the steps per seconds:
(( 360 / 1.8 ) * microstepping * gear_ratio) / 86164.1

From the above calculation I made this:

The Accelstepper library can accept very low speed, from the documentation:

Very slow speeds may be set (eg 0.00027777)

I am wondering if there is a "better" speed I could choose between these or all would work the same

My goal is a smooth and precise movement

relationship.png

in case everyone needs: better using the minimum number of microstepping possible and use a greater reduction