I recently read that there are more than 100 billion galaxies in the universe.
1. How and what method(s) do scientist use to calculate this figure?
2. How can a scientist state with confidence that there this amount when we cannot access other galaxies? Also how do scientist know where the universe ends and what if where we think it ends, it really does not end or what if the vast magnitude that we perceive is nothing but an illusion and it is not as large as we think it is
3. What really exists on these galaxies and how can we know?
Miramar / Pembroke Pines,Florida
First of all, given the uncertainties all we can do as astronomers is make our best guesses in terms of actual galaxy numbers. Among the ways we can do this is by using data from one of more sky surveys such as the Sloan Digital Sky Survey, see e.g.
Thus, we can try to estimate the overall numbers. For example, the assorted SDSS surveys have found 930,000 galaxies and more than 120,000 quasars. This is for a certain volume of the sky. We can then extrapolate (often usng supercomputers) these numbers to other regions using additional data. But again, the end result will still be more in the way of an estimate than a precise number.
Second, in any science it must be understood that no quantity whether the temperature of the interior of the Sun, or the energy of a star or solar flare, is given with absolute confidence. There is always an uncertainty attached, though for sure - these are seldom shown in student text books (often so as to avoid confusing beginners in science).
The same applies to the extent of the universe, which we now know extends beyond the light cone region we can actually see. Thus, although we can see up to 13.7 billion light years, the actual universe is roughly 46.5 b light years in radius.
Now, having said that, I definitely would not say the "vast magnitudes" we estimate- whether in the size of the cosmos or numbers of galaxies within it- are "illusions". No, they are not! Actual measurements - such as in the Sloan Sky Survey - back them up. Just because we cannot obtain absolute accuracy doesn't mean we have zero accuracy! Just because we cannot precisely tabulate every last single galaxy, doesn't mean the numbers we do arrive at amount to illusion or fantasy! This is really confusing uncertainty in actual numbers with illusion about the nature of the systems themselves.
Uncertainty isn't the same as "illusion" because when we perform such surveys and apply them to try to get numbers of galaxies, say, we are aware of the limitations.....and those uncertainties.
So yes, the universe IS as large as we think it is, it is just that we can't pin down that size to the last centimeter. Because we can't pin it to the last cm doesn't mean the whole estimate goes out.
Finally, one can only speculate on what exists in distant galaxies given the limitations of observation. We can, however, apply certain basic laws and principles - such as the cosmological principle - which states that the same chemical elements we detect in our own region of space (including in our own galaxy) also occur in the more distant ones. In addition, the same physical laws we observe on Earth are also applicable in the most distant galaxies, and their planets - if any. This means the probability is quite high that we'd find on any habitable planets, say, would closely resemble what we find on Earth.
Hopefully this answere provides you some basic insights into how astronmers work, and the limitations of that work- which are not to be confused with pursuing "illusions".