Posted: Mar 19, 2012 5:53 pm
Here, I've reposted it a few times but I thought I'd save anyone some time and post the maths so you don't have to do it. 
CJ wrote:Let's reverse the question. How would the universe have to behave if the Earth were stationary?
If the Earth were stationary one would still have to account for the movement of the stars around the Earth, which of course they would have to do every 24 hours. They would also be having to orbit the Earth as they turn up in the same place each night, it's not as though stars pass us like they would if we were in a space ship travelling in a straight line.
So a star has to get around the Earth in 24 hours. Firstly the Earth would have to have a gravitational field strong enough to hold the star in orbit (we'll leave that aside for the moment). A star could not travel faster than the speed of light while in orbit around the Earth. So we have a maximum speed that a star could orbit the Earth.
Now lets find out the circumference of a maximum circle made by an object moving at the speed of light orbiting in the equatorial plane. The speed of light is 186,282 miles per second, there are 60 seconds in a minute, 60 minutes in an hour and 24 hours in a day. So the circumference of the orbit of the furthest possible star is 16,094,764,800 miles, this gives a radius of 2,561,561,375 miles. Thus all stars would have to be this distances, or closer, if they were to be able to orbit the Earth in 24 hours and still be travelling at or below the speed of light.
So we have a maximum radius of 2,561,561,375 miles. How long is a light year? It is 5,874,589,152,000 miles. What is the maximum radius as a percentage of a light year? It is 0.0436%. Thus all stars that appear to orbit the Earth in 24 hours must be less than or equal to 0.0436% of a light year away.
As we don't see any stars that do not make an orbit in less or more than 24 hours this means that the universe can only be a maximum 2x0.0436% of a light year across, or approximately 0.09% of a light year. In fact this sphere would have to enclose all the matter in the universe to explain what we see and still obey the laws of relativity.
So which is the more plausible description of what we see? Is it that all we can observe is contained in a non-expanding universe that is rotating at no more than the speed of light and is no more than 0.09% of a light year in diameter. Or is it that we are on a ball of rotating rock. I vote ball of rotating rock.
Here are the maths in detail. circumference = Pi*diameter, so diameter=circumference/Pi and radius=diameter/2
I used Miles (M) to keep the numbers a little bit more manageable and relevant.
Thanks to the person who checked my maths
