Question

What would be your estimate of the age of the universe if you measured a value for Hubble's constant of H0 = 30 km/s/Mly ? You can assume that the expansion rate has remained unchanged during the history of the universe.

Answer 1

The age of the universe would be 9.9 billion years

Step-by-step explanation:

We can calculate an estimate for the age of the Universe from Hubble's Law. Let's suppose the distance between two galaxies is D and the apparent velocity with which they are separating from each other is v. At some point, the galaxies were touching, and we can consider that time the moment of the Big Bang.

Thus, the time it has taken for the galaxies to reach their current separations is:

`\displaystyle{t=D/v}`

and from Hubble's Law:

`v =H_0D`

Therefore:

`\displaystyle{t=D/v=D/(H_0* D)=1/H_0}`

With the given value for the Hubble's constant we have:

`H_0=(30\ km/s/Mly) * (1 Mly/ 9.461 * 10^(18) km) = 3.17* 10^(-18)\ 1/s`

and thus,

`t=1/H_0 = 1/(3.17* 10^(-18) 1/s) = 0.315 * 10^(18)\ s \approx 9988584474.8858\ years \approx 9.9\ billion\ years`