Question

How was the presumed age of the Universe determined?

Answer 1

Hubble's law states that the further away a galaxy is, the faster it is moving:

$v\propto d$

Because of this law, if it is extrapolated backward, it is implied that everything in the universe was once concentrated at one point- supporting the idea of the big bang and also makes it possible to estimate how long ago it was when everything was in one place- i.e the birth of the universe.

However, this is not using SI units, but rather the units for velocity is $km{s}^{-1}$ and distance is measured in Mega-parsecs $MPc$.

This equation, being linear must have a constant- Hubble's constant:

$H_o$

Making the equation:

$v=H_{o}d$

The value of the constant varies throughout the universe but on a VERY rough estimate we can say that the value of the constant is :

$H_o=70km{s}^{-1}MP{c}^{-1}$This constant allows us to estimate the age of the universe using the equation:

$\frac{1}{H_0}\approx T$

However, the Hubble constant must be transferred into SI units for this to work ....

So let's find the value of the constant:

$70km{s}^{-1}=70000m{s}^{-1}$

$1parsec=3.25ly=3.08\times {10}^{16}m$

$1$ Mega-parsec $\left(1millionparsecs\right)=(3.08\times {10}^{16}\times {10}^{6}m)$

$H_0=70km{s}^{-1}MP{c}^{-1}=\frac{70\times {10}^3}{{10}^6\times 3.08\times {10}^{16}}=2.27\times {10}^{-18}$

Inverse it to find Hubble time:

$\frac{1}{2.27\times {10}^{-18}}\approx T$

$T\approx 4.4\times {10}^{17}s$

$T\approx 1.4\times {10}^{10}years$

Which is almost $14$ billion years, but scientists often say that the value is $13.8$ with an uncertainty of $\pm 0.2$ billion years, so we are within the acceptable range.

And that is basically how the age of the universe can be estimated.