# 银河系|PHYS11056 Galaxies代写 Edinburgh代写

If the average speeds of the galaxies had always remained constant, they would have been on top of each other at a time $t_{\mathrm{H}}$ before the present, where
$$t_{\mathrm{H}}=\frac{1}{H_{0}}=9.78 h^{-1} \mathrm{Gyr}=15 \mathrm{Gyr} \times \frac{67 \mathrm{~km} \mathrm{~s}^{-1} \mathrm{Mpc}^{-1}}{H_{0}} .$$
This is called the Hubble time; we can use it as a rough estimate of the age of the Universe, the time since the Big Bang.

\begin{aligned} \rho_{\text {crit }}(\text { now })=\frac{3 H_{0}^{2}}{8 \pi G} &=1.9 \times 10^{-29} h^{2} \mathrm{~g} \mathrm{~cm}^{-3} \ &=2.8 \times 10^{11} h^{2} \mathcal{M}{\odot} \mathrm{Mpc}^{-3} \end{aligned} For $H{0}=67 \mathrm{~km} \mathrm{~s}^{-1} \mathrm{Mpc}^{-1}$, this is equivalent to a good-sized galaxy in each megaparsec cube, or about five hydrogen atoms per $\mathrm{m}^{3}$. If matter in the Universe has exactly this density, the time $t_{0}$ from the Big Bang to the present day is
$$t_{0}=\frac{2}{3 H_{0}} \approx 10 \mathrm{Gyr} \times\left(\frac{67 \mathrm{~km} \mathrm{~s}^{-1} \mathrm{Mpc}^{-1}}{H_{0}}\right)$$

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