My minimap mock up

I had the same idea. For planetary view you could have a spherical minimap that shows the exact opposite side of the planet. and for systemic or galactic view you could have something like the far right mini-map in conquest future wars. So you could have something like flashing planets for attack alerts and other colors for economy alerts.:

This seems like the best way to have a mini-map set up. It would be able to alert you to anything going on on the planet selected, and would be centered on where you are currently looking. If you change your main screen the mini-map moves with it.

With multiple planets you can pan through multiple mini-maps, or even have space to view multiple mini-maps at once.

edit: problem with other side of the sphere map is that is make using a mini-map for unit control commands kind of wonky.

edit2: added crappy mock-up. The numbers by the mini-map would be for preset views. These could be locations on one world with a way to switch between worlds too (each world could have it's own set of preset views).

Simple, it disappears. You only need it when you are on a planet.

There are some additional benefits from multi window support. With multi window i mean, that you press something like ctrl + n and you get a new window with exakt the same content. But the new window is independent to its parent window.

1. The new window could be resize very small and be used as minimap for a certain section.
2. The new window could be moved to another monitor for controlling another planet.
3. The new window could enable single pc coop. e.g. you have multiple input devices and screens. http://en.wikipedia.org/wiki/Multi-Pointer_X

+1 to xaseron