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Physics LibreTexts

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

    \[\begin{equation*}
      \begin{aligned}
            v = H d
      \end{aligned}
    \end{equation*}\]