How do we Know a Galaxy or Star is 13 Billion Light Years Away?
Most recent answer: 07/21/2015
You can tell by looking at the properties of the light from the stars. Stars are made of atoms which are constantly emitting light. That light is composed of specific colors, and is called the star's spectrum. If the star is moving away from you the colors look more red than they would if they were sitting still, an effect called the red shift. Stellar spectrums and red shift has explained more clearly by Ask the Van . Stars moving away more quickly have more red shift.
The star's spectrum and understanding of the red shift give us a measure of the velocity of a star. How does this relate to your question? One of the most awesome discoveries in physics was made by Edwin Hubble when he found that the universe was expanding in every direction. Space itself between the stars and galaxies is continually growing. Because of this outward expansion, if you look at any distant star, its spectrum will red shifted. The amount the spectrum is red shifted depends on how far away from Earth it is, because stars farther away from us are moving away faster. Think of it this way: If space itself is expanding, the more space there is between two points, the more expansion occurs over the same amount of time, which means the points will be moving away from each other at a higher velocity. For example, if a star a distance D away expanded to be 2D away in time T, then a star at distance 2D would be expand to be 4D away in the same T. The second start would appear to be moving twice as fast.
Given all this information, you can look at the spectrum of a star, see how far the spectrum is red shifted, and from that find its distance from Earth.
PS is a link to a plot showing you the relation between distance from earth and velocity of stars.
(published on 07/21/2015)