Question

1. Expansion of the Universe (Hubble)

a) Would the Universe be older if the expansion rate was H₀ = 50 km/s/Mpc or if H₀ = 75 km/s/Mpc? Explain.

b) What is the age of the Universe if the Hubble constant is measured to be 75 km/s/Mpc? Express your answer in billions of years. Would this value be consistent with the range for the Hubble time from the HST Key Project? Explain.

c) On average, how do the velocities of far away galaxies compare to those of closer galaxies? Why?

d) How do you know that the Universe is expanding (stretching) but the individual galaxies are not?

Answer 1

a) Hubble's constant H0 has units of s-1

So, the time t,

So, if H0 is higher, t will be low, and vice versa.

So, the universe would be older at H0 = 50 km/s/Mpc than that of at H0 = 75 km/s/Mpc

b) Hubble time is the reciprocal of H0 = 75 km/s/Mpc

but, 1 Mpc = 3*1019 km

..........(yr = year)

.......(byr = billion years)

Hence the age od the universe is 12.68 billion years.

This age is less than the age estimated by HST Key project ( 14 byr ).

This is because the Hubble constant calculated was 72 km/s/Mpc in their calculation.

c) In general, the speed of recession of distant galaxies is high. It is because of the acceleration due to the continuous expansion of the universe. This is explained by Hubble's law,

where,

v = recession velocity of the galaxy distance d away from us.

d) Yes. We can know this by redshifts. The galaxies are showing redshifts, but there is no change in distance between the stars of the same galaxy.

This suggests the galaxies are moving away and hence the universe is expanding, but the galaxies are not streching.