Back in time
During the time of Albert Einstein, Astronomers only really knew of the existence of our own galaxy and had no idea of other galaxies around us. Like Issac Newton, even Einstein beleived the idea of static infinite universe, he never came up with the idea of dynamic finite universe so he even introduced the term mysterious counteracting force (which he called cosmological constant). Some years later ,American astronomer,Edwin hubble stunned the whole astronomical commity by showing that there are many more other galaxies other than our milky way, thousands of islands of stars ,some close to us, some million light years away from us.
With well sophisticated telescope he observed that light coming from these far away galaxies are shifted towards the red end of spectrum, this showed that galaxies are moving away from us at greater speed. this doesnt mean that we are centre of the universe, galaxies are moving away from us as well as moving away from each other.
Consider an infinite line , let x=0,x=1.x=2 etc. be points or one dimensional galaxies . The distance between 2 neibhouring galaxies be ‘a’. ,a is called the scale factor which depends on time and is same for all galaxies.
let us fix the 2 points in space, we have distance between 2 galaxies as D = aΔx.
dD/dt = v =d(aΔx)/dt
v = åΔx ( where å is da/dt). By dividing and multipying by scale factor a,
v = å Δx a/a = å/a D ( because D = aΔx).
å/a is called Hubbles constant and is constant for all galaxies.therefore we have v = H D.
thus Hubble proved that velocity is directly proportonal to distance, as distance increases velocity increases,this implies that, the farther the galaxies are ,the faster it is moving away.
Origin of space time
Hubbles law not only showed that universe is expanding, but also can give some ideas on origin of universe. If galaxies are flying apart , then clearly at some point of time ,earlier, they were close to each other. Following back logically it might have been extremly tiny and infinitly crowded probably during the time of beginning of space-time. This idea gave rise to the theory of Big Bang. The idea of origin of universe was not immedeatily welcomed by everyone but due to several strands of evidence it was later approved by many. Albert Einstein was also later forced to abandon his theory of force of repultion(cosmological constant) and called it as his biggest blunder. But his theory of general realtivity helped many scientists to bluild ideas on geometry of space-time.