For very far objects beyond about 1 billion light-years none of the above methods work. Scientists must move from direct observation to using observations in conjunction with a theory.
The theory used to determine these very great distances in the universe is based on the discovery by Edwin Hubble that the universe is expanding.
In , Edwin Hubble announced that almost all galaxies appeared to be moving away from us. In fact, he found that the universe was expanding - with all of the galaxies moving away from each other. This phenomenon was observed as a redshift of a galaxy's spectrum. This redshift appeared to be larger for faint, presumably further, galaxies. When this metric was applied to the Einstein equations, the so-called Friedmann equations emerged which characterized the expansion of the universe based on a parameter known today as the scale factor which can be considered a scale invariant form of the proportionality constant of Hubble's Law.
This idea of an expanding spacetime would eventually lead to the Big Bang and to the Steady State theories. Before the advent of modern cosmology , there was considerable talk as to what was the size and shape of the universe. Hubble's finding built on the work of Vesto M. Slipher who, in , discovered that light from nearly all of the "spiral nebulae" he observed, regardless of the direction he looked, appeared to be redshifted.
This meant they were moving away. In Hubble discovered that the "spiral nebulae" were actually galaxies outside our Milky Way galaxy. If the universe is static and unchanging, there should be no correlation between distance and velocity. However, if the universe is expanding , we expect a correlation between distance and velocity.
The usual analogy used here is that of an explosion — the fragments of shrapnel produced are moving with a range of velocities, and the most distant objects from the source of the explosion have the largest velocities. Astronomers believe that Hubble's law is a direct consequence of the ongoing expansion of the universe and that the evidence suggests that the universe began in an explosion, which we call the Big Bang.
You can consider Hubble's Law to be the final rung in the distance ladder. If you know Hubble's constant accurately, then you can calculate the distance to any galaxy in the Universe simply by measuring its velocity which is reasonably easy to do for any galaxy for which you can observe its spectrum.
To calibrate Hubble's constant, though, you need to be able to plot the distances for a number of galaxies as obtained using other methods. While that may seem like an easy statement to make, it was an incredibly difficult task to accomplish.
For decades, astronomers have argued over the precise value of Hubble's constant. This measurement was, in fact, one of the major reasons for building and launching the Hubble Space Telescope.
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