UHmm, going back to the very start of this thread, "How can the Earth be an infinite plane"
I do not think it can be an infinite plane at all, because as someone as already stated (just to choose one discussion line and not being lost in 10^3 different lines), this would result in the fact that it has infinite mass, and therefore an infinite amount of atoms and an infinite volume.
If earth would have infinite mass, then there should be almost no other thing in the universe but earth. So unless someone states that stars ( which you can see with your eyes at night ) are nothing but bright parts of the infinite earth, (earth becomes maybe a ring after some time as in Ringworld?), or reflections in the atmosphere of the existing ones in the earth plane or so.. you must conclude that above, there are exactly this, stars. And a moon, and other planets and such.... and all this from my point of view is a substantial amount of matter that does not ( most likely ) belongs to Earth.
The only possible approximation I can see to an "infinite" earth is a Dyson sphere, and again, it is not infinite, and I do not think we are inside one.
Anyway, when you start considering the "infinite" outside the pure mathematical thinking, you face a very slippery territory, where you can throw a lot of things into the "infinite" box of anything. Infinite, from a macroscopic point of view, is simply too much for any specific object.
This would lead as well to discuss if the Universe is an object (in which programming language?..ha ha ha :-P), and if it is infinite ( can it be? )