Rotation change/ composition manipulation

Hello world! Is someone there know pretty well how to manipulate axes (and other object properties)?
I have an issue with my simplified planet - moon system. I would like to add some dynamic movement of moon displayed in camera frame (from bottom left to upper right) - (in short) animation im trying to prepare. So I’ve started messin’ around with Face Transformation Deformation but result was non precise (kinda wacky). So by visual, this is what I want to achieve this time.


As you can see I want to move the center of moon rotation invard planet center and make it to share same plane as axial section of the sphere which is world center too.

Or other way. Is there possibility to change position (rotation) of axis? like this:

sorry for simple english
Best regards!!

I would use the “follow path” constraint,
here is a quick example. It is make such things easy cause you can change orbits independent.
orbits.blend (217.0 KB)

Thanks for advice i didnt knew about that feature. Beside that I found what im searched for, cheers!

Haha, My mistake (or rather you were right). Youre solution I can see is more comfortable, Cheers!