Special & General Relativity Questions and Answers
Is our perception of distances and sizes in the universe just an illusion?
In particular, a big object 1000 miles away can look the same size to the eye as a small one 100 feet away, so how in astronomy do we tell whether stars are tiny things a few million miles away, or big things a million light years away?
Well, from Newtonian physics we have determined how far away the Moon and planets are, and with the space program we have actually traversed this predicted distance to find the planets where we expected to find them and with the size we expected to measure. So, there is no problem there.
Then, by using the Earth's orbit as a standard unit of distance, we triangulated to find the distances to the nearest stars. Since there is nothing fishy about the geometry, we find the stars to be light years away, not millions of miles away, and at their distances we deduce that, for some of them, they have sizes that are no bigger than what theory predicts they ought to be. We can even directly measure the sizes to some of these using optical interferometry and find that their angular sizes as seen from Earth are exactly what we would expect given their measured distances and the kind of stars they are, namely, red giant stars ( Betelgeuse, Antares etc).
So, the idea that stars and such things might be very small things at close distances can be proven to be incorrect. That's the best we can do in science. Note, however, some astronomers continue to believe that quasars are objects ejected by our galaxy and are only a few million light years away, not the billions of light years suggested by their redshift and Big Bang cosmology. This is an example of a debate like the one this question suggests.
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All answers are provided by Dr. Sten Odenwald (Raytheon STX) for the NASA Astronomy Cafe, part of the NASA Education and Public Outreach program.