A-level Physics (Advancing Physics)/Big Bang Theory/Worked Solutions

1. What is the Hubble Constant in s−1?

$$H_0 = 70\mbox{ kms}^{-1}\mbox{Mpc}^{-1} = 0.07 \mbox{ ms}^{-1}\mbox{pc}^{-1}$$

1 pc = 3.09 x 1016 m

$$H_0 = \frac{0.07}{3.09 \times 10^{16}} = 2.27 \times 10^{-18}\mbox{ s}^{-1}$$

2. How old is the universe?

$$\frac{1}{H_0} = 4.41 \times 10^{17}\mbox{ s} = 14.0\mbox{ bn years}$$

3. What effect might gravity have had on this figure?

Gravity would slow the expansion of the universe, so the age of the universe would actually be lower than 14.0 billion years.

'''4. Polaris is 132pc away. What is its velocity of recession, according to Hubble's Law?'''

$$v = H_0d = 70 \times 132 \times 10^{-6} = 9.24\mbox{ ms}^{-1}$$