Question

Between the 1950s and the early 1990s, two major camps of astronomers disagreed on their measurements of the expansion rate of the Universe, which is now thought to be just under 70 km/s/Mpc. This was largely due to a combination of the difficulties in making these measurements, but there was also some implicit bias in the results from time to time as well. One group, headed by Alan Sandage, thought that Ho = 50 km/s/Mpc. The other group, led by G´erard de Vaucouleurs, through that Ho = 100 km/s/Mpc. Using unit conversions, estimate how old each group thought the Universe was

Answer 1

Mpc means megaparsec i.e 10⁶ parsec.

One parsec is equal to about 3.26 light-years = 3.08*10¹³km

1Mpc=30.84*10¹⁸ km

So, according to Alan Sandage Hubbbles constant (Ho)

=50km/s/Mpc={50/(30.84*10¹⁸ )}/s= 1.62*10^-18 /s= (1.62*10^-18)/(3.178*10^-8) /year=0.509 *10^-10 /year.

So, age of the universe t=1/Ho=19.6*10⁹ years=19.6 billion years

So, according to G'erard's group the Hubble constant Ho

= 100km/s/Mpc={100/(30.84*10¹⁸ )}/s= 3.24*10^-18 /s=(3.24*10^-18)/(3.178*10^-8) /year=1.019 *10^-10 /year.

So, age of the universe t=1/Ho=9.8*10⁹ years=9.8 billion years