|MadSci Network: Astronomy|
The best proof I can think of, off the top of my head, would be the Coriolis Force, which acts over large distances, creating weather systems and dividing our atmosphere into tropical, temperate and polar bands. For a full explanation, take a look at the Coriolis Force web page.
If the Earth didn't rotate, we wouldn't have hurricanes or typhoons. The coriolis effect also affects naval guns, so that ships firing at distant targets have to correct for the Earth's rotation. This affected, for example, a battle near the Falkland Islands in the mid-Nineteenth Century, when Royal Navy ships missed their targets because they were using mathematical tables compiled in the Northern Hemisphere (the coriolis force acts in the opposite direction in the Southern Hemisphere).
An even more extreme example of the coriolis effect can be seen on Jupiter, where Jupiter's rotation period of about 10 hours has divided the atmosphere up into several zones and bands.
Jim O'Donnell, firstname.lastname@example.org
Phil Plait adds the following:
There is no simple way to prove the Earth rotates. As you said, mathematically it's almost always possible to changes your reference frame such that the Universe rotates around the Earth every 24 hours. People that believe the Earth actually is fixed (such as some manners of creationists) use this argument to show their point.
However, they are wrong, because they are forgetting relativity. If the Universe rotates around the Earth every 24 hours, then objects farther away are moving faster because their ``orbit'' is larger. At some distance, an object must be moving faster than light to be able to circle the Earth in one day. That distance is about 4 billion kilometers, or roughly the distance to the planet Pluto. You can see this for yourself: velocity equals the distance traveled divided by time. We set velocity equal to light speed (300,000 kilometers/second), time equal to one day (86,400 seconds) and distance traveled the equal to 2*pi*radius of orbit. Solve for that radius to get 86,400 x 300,000 / (2 x pi) = 4 x 109 kilometers.
To say the Earth is fixed and the Universe spins around us once a day (besides being the height of human arrogance!) is to also deny everything we have learned about relativity, even the most basic premises which we know are correct. Nothing can travel faster than light, and when you travel even close to light speed you get all sorts of weird effects including huge Doppler shifts, mass increase, time dilation and the like. We see none of these effects. Therefore, we throw out that theory and use the much more simple one that it is the Earth itself that spins on its axis.
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