So, I'm in the planetarium. I can tell by the map there is an entrance to a secret room here.

I noticed that the different planets have ingrained numbers on them:

Purple planet: 1

Moon: 2

Earth: 3, both symbol versions of it,

Sun: 4, both symbol versions of it

I assume I have to wait for the planets to align in rising order, but is there anything more to it than that? AFAIS, I can't interact with the gears on which the planets spin or anything. Could someone point me in the right direction?

Good eye, that's how the planets are labeled. However, unless I'm mistaken, you're overthinking that room.

so, what is the answer?

edit: nevermind, you just rotate to find another door.