|MadSci Network: Astronomy|
The difficulty with Earth is that there is topography - for the Rocky Mountains you would have to be higher than over the ocean. With no atmosphere, it would be possible to see your horizon deviate from a straight line fairly easily as long as there is nothing in the way (such as a mountain, or an ocean wave) no matter what height you are at. However, seeing your horizon curve doesn't give you a sense as to whether or not you are in fact standing on a sphere. You could be at the center of a disk, which would also look as though your horizon curved. There are ways to test, of course, that this is not the case - an obvious one would be to go to a stationary point above the earth (if you can find one!) and watch it rotate around one complete rotation. If you are on a spherical planet instead of a disk, the horizon you see should remain the same size through the whole rotation. If you were on a disk, it would instead decrease as an oval to a straight line, and then increase as an oval again to a round circle.
Try the links in the MadSci Library for more information on Astronomy.