I've got proof: When you see a ship approaching from somewhere very far, you don't see it fade in, like it would when exiting fog. No, you see how it first rises, as if climbing a slope, while approaching you.
This has been seen by sailors and related peoples for milleniae. Alternative: Go on a cruise, and watch as the land rises out from the horizon when you approach it.
The earth's rotation around the sun? Just put up a camera somewhere, making sure to get a good view of the night sky, while still having some environment in the shot as a referrence point. If you take a picture every night for about six months, you'll see that the first picture is very different from the first one, and that you can clearly see the night sky "moving" if you can set them up as one frame each in an animation (Flash? MovieMaker?)
Funny thing is, these two experiments are both pretty old, and have been redone millions of times for all kinds of educational films and such.