Let’s try to clear up a couple of things.
First off, regarding the orbit of Earth, I always notice a big confusion. There are two aspects: The yearly orbit around the sun, and the daily revolution.
When speaking about how relativity reconciles the two, we must realize that that applies to the yearly orbit. That doesn’t help anybody stick up for Chazal since they are never referring to this orbit. For all you know, they would agree that Earth revolves around the sun once a year.
As far as the daily revolution, dd already (finally) explained that we actually can prove that the earth rotates by testing the effects of centrifugal force.
Now, back to relativity. Let’s understand, that the whole thing started when it was noticed that light always seems to be traveling at the same speed, even when you are traveling away from it.
Based on this, Einstein decided that the speed pertains to how fast it will get to you. Since light, he says, travels at top speed, it will always get to you at the speed of light. This should answer someonesbored and Mod-80.
If it makes sense in our frame of reference then it makes sense. As far as we are concerned, we are going around the sun and everything else stays put.