Skip to main content
Physics LibreTexts

S10. A Newtonian Homogeneous Expanding Universe - SOLUTIONS

  • Page ID
    7727
  • [ "article:topic", "Box Solutions", "authorname:knoxl" ]

    Box \(\PageIndex{1}\)

    Exercise 10.1.1: Derive Hubble's Law in this universe, \(v = H d\), where \(H = \dot a/a\)

    Solution \(\PageIndex{1.1}\)

    \[\begin{equation*}
      \begin{aligned}
            d = a\ell \quad \Longrightarrow \quad \ell = \frac{d}{a}
      \end{aligned}
    \end{equation*}\]

    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

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