# Hubble’s Law, Constant and the Expanding Universe

The Hubble Constant is the ratio of speed of recession of a galaxy due to the expansion of the universe. The problem with measuring the Hubble Constant is that it is extremely difficult to get an accurate number (there are lots of variables we cannot control that will affect the value). However, over the years, due to scientific instruments that are more accurate, we are gaining a more accurate value for the Hubble Constant. Over the years, the Hubble constant keeps decreasing in value. At the moment, the value of Hubble’s Constant is roughly 70 km/s/Mpc.

This can be quite difficult to understand. Therefore, if you want a implied and shorter version of this article, scroll down to the bottom and look for ‘Hubble’s Law and the Age of the Universe’.

A galaxy of distance d from us takes a time d/v to reach us in a reversed universe. From Hubble’s law, we know that v = H0d. Therefore:
• t = d / H0d which equals 1 H0.
This time is the age of the universe. If that was a bit difficult to explain, here is it in simple terms:
We can use the equation speed = distance / time to find how long it will take a galaxy at the speed it is travelling away from us to get to us (at that speed). For example, if a galaxy is travelling away from us at 100km/s, the time it takes for the galaxy to reach us is the the time it takes the galaxy to reach us at the 100km/s.
Using time = distance / speed, we know that the distance (from the graph above) is ‘d’. We also know that the speed or velocity of the galaxy travelling away from us is H0d. Therefore:
• Time for the galaxy to reach us at the speed it’s travelling away from us = d / H0d.
• t = 1 / H0. This is the age of the universe.
Time is an upper limit because we have assumed a constant velocity where the average velocity of the galaxy would have been faster because in a reversed universe where everything is falling together, gravity would accelerate their velocities.

A bigger H0 –> faster expansion –> less time to get to present size –> younger universe.

Taking the value of H0 nowadays of 70 km/s/Mpc…

• 1 Mpc – 3.10×10^19 km.
• H0 = 70 km/s  / 3.10×10^19 km (km cancel each other out).
• H0 = 2.26 x10^-18
• 1 / H0 = universe = 4.43×10^17 seconds  which is 14 billion years.
However, studies have now showed that there are still some galaxies in the universe that are older than 14 billion years. Therefore, we must still not have the true value of the Hubble’s Constant. But, we are getting more accurate over the years!

## Summary

• The graph with Hubble’s Constant as the gradient makes clear that the further away a galaxy is from us, the faster it will be moving away from us. This supports the big bang theory because the graph proves everything is expanding outwards from each other.
• v = H0d where v is the velocity of the galaxy and d is the distance the galaxy is from Earth.
• We can measure the age of the universe with 1/ H0. This is an upper limit because we are implying that the velocity of the galaxies are staying constant.
• The age, at the moment, of the universe is 14 billion years although there are galaxies still older than this.

## Hubble’s Law and the Age of the Universe

• Hubble found that the further away a galaxy is, the larger its red shift.
• He interpreted this to mean that distant galaxies are receding from us.
• For a galaxy a distance ‘d’ from us, Hubble wrote v = H0d where v is the speed of a galaxy away from us and His a constant called the Hubble constant.
Run the Universe back in time…distance galaxies are further away but are moving faster…
…in the past galaxies must have been closer together…
….even further back, all the matter and space in the Universe was concentrated to a single point.
A galaxy of distance ‘d’ from us takes a time t = d/v to reach us in a reversed Universe. From Hubble’s law:

t = d/v = d / H0d = 1 / H0

This time is independent of d and v and tells us how long ago the Universe was a single point – this is the age of the Universe.

Strictly, in a reversed Universe, the galaxies accelerates as they fall together so that the ‘Hubble time’, 1 / H0, gives an upper limit for the age of the universe.

1. David Hine May 12, 2018
2. David Hine August 13, 2018