# S10. A Newtonian Homogeneous Expanding Universe - SOLUTIONS

- Page ID
- 7727

# Exercise 10.1.1

**Answer**-
\[\begin{equation*}

\begin{aligned}

d = a\ell \quad \Longrightarrow \quad \ell = \frac{d}{a}

\end{aligned}

\end{equation*}\]Substituting for \(\ell\) in \(v = \dot a \ell\), we get

\[\begin{equation*}

\begin{aligned}

v = \frac{\dot a}{a}d

\end{aligned}

\end{equation*}\]Now substituting in \(\dot a/a = H\), we get

\[\begin{equation*}

\begin{aligned}

v = H d

\end{aligned}

\end{equation*}\]