Question

The expansion rate of the Universe is usually given as something like 70 km s−1 Mpc−1. If you convert this quantity to SI base units of kg, m, s, what is this number and in what units? What do you think this means for the age of the Universe? Give an estimate for the age of the Universe, in s and in billions of years.

Answer 1

Given Hubble constant = 70 km/sec/Mpc

1Mpc = 3.0857*10¹⁹ km

converting Mpc to km then

Hubble constant = 70 km/sec/Mpc / 3.0857*10¹⁹km

Hubble constant = 22.683*10^-19 sec^-1

^{hence number is 22.683*10^-19 and unit is per sec orsec-1}

Velocity = Hubble constant/ distance

Hubble constant = Velocity / distance

Time =distance / velocity

Age of universe is the inversely proportional to hubble constant.

Time =1/ Hubble constant

Time =1/ 22.683 *10^-19 sec^-1

Time = 4.41*10¹⁷ sec

We know 1 sec = 3.17098*10^-8 years

4.41*10¹⁷ sec = 13.98 *10^9 years

Time = 13.98 billion of years

Hence age of universe

Age of universe , t = 4.41 *10^17 sec

Age of universe =13.98 billion of years