[Espressosaurus]

Fancy astrophotography tripods--really, the mount--do that rotation for you. That's why they exist. Even fancier ones exist that permit close-to-arbitrary slewing. Those can be used as a go-to-mount where with the right software, it can image wherever in the sky you're pointed, take the current time, and plate solve for where it's pointed, then finally point at whatever target you actually want to shoot.

For the very long exposure times, you can also hook a second camera up and run closed loop control on a specific star to keep your primary image sensor trained on the correct target to even tighter tolerances. There's companies making cameras that combine both the primary and secondary camera into a single housing so you don't need to fit a second camera + lens to your setup, or insert a prism to pick off part of the image to go to a second camera.

Amateur astrophotography today does tricks you needed access to a dedicated lab to do in previous decades. It's amazing!