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from \cite{1999_Tipler_Llewellyn}, page 9
Eq. \ref{eq:1131405} is an initial equation. \begin{equation} v = \frac{d}{t} \label{eq:1131405} \end{equation} Change variable \(d\) to \(C\) in Eq. \ref{eq:1131405}; yields Eq. \ref{eq:7360652}. \begin{equation} v = \frac{C}{t} \label{eq:7360652} \end{equation} Eq. \ref{eq:7959026} is an initial equation. circumference of a circle \begin{equation} C = 2 \pi r \label{eq:7959026} \end{equation} Change variable \(C\) to \(C_{\rm Earth\ orbit}\) and \(r\) to \(r_{\rm Earth\ orbit}\) in Eq. \ref{eq:7959026}; yields Eq. \ref{eq:5753220}. \begin{equation} C_{\rm Earth\ orbit} = 2 \pi r_{\rm Earth\ orbit} \label{eq:5753220} \end{equation} Change of variable \(C\) to \(C_{\rm Earth\ orbit}\) and \(v\) to \(v_{\rm Earth\ orbit}\) and \(t\) to \(t_{\rm Earth\ orbit}\) in Eq. \ref{eq:7360652}; yields Eq. \ref{eq:5320197}. \begin{equation} v_{\rm Earth\ orbit} = \frac{C_{\rm Earth\ orbit}}{t_{\rm Earth\ orbit}} \label{eq:5320197} \end{equation} Substitute LHS of Eq. \ref{eq:5753220} into Eq. \ref{eq:5320197}; yields Eq. \ref{eq:9129246}. \begin{equation} v_{\rm Earth\ orbit} = \frac{2 \pi r_{\rm Earth\ orbit}}{t_{\rm Earth\ orbit}} \label{eq:9129246} \end{equation} Eq. \ref{eq:9494155} is an assumption. \begin{equation} t_{\rm Earth\ orbit} = 1 {\rm year} \label{eq:9494155} \end{equation} Multiply RHS of Eq. \ref{eq:9494155} by 1, which in this case is \(\frac{365 {\rm days}}{1 {\rm year}} \frac{24 {\rm hours}}{1 {\rm day}} \frac{60 {\rm minutes}}{1 {\rm hour}} \frac{60 {\rm seconds}}{1 {\rm minute}}\); yields Eq. \ref{eq:9417128} \begin{equation} t_{\rm Earth\ orbit} = 3.16 10^7 {\rm seconds} \label{eq:9417128} \end{equation} Substitute LHS of Eq. \ref{eq:9417128} into Eq. \ref{eq:9129246}; yields Eq. \ref{eq:1441436}. \begin{equation} v_{\rm Earth\ orbit} = \frac{2 \pi r_{\rm Earth\ orbit}}{3.16\ 10^7 {\rm seconds}} \label{eq:1441436} \end{equation} Eq. \ref{eq:4133484} is an assumption. \begin{equation} r_{\rm Earth\ orbit} = 1.496\ 10^8 {\rm km} \label{eq:4133484} \end{equation} Substitute LHS of Eq. \ref{eq:4133484} into Eq. \ref{eq:1441436}; yields Eq. \ref{eq:8698819}. \begin{equation} v_{\rm Earth\ orbit} = \frac{2 \pi \left( 1.496\ 10^8 {\rm km} \right)}{3.16\ 10^7 {\rm seconds}} \label{eq:8698819} \end{equation} Simplify Eq. \ref{eq:8698819}; yields Eq. \ref{eq:1001745}. \begin{equation} v_{\rm Earth\ orbit} = 29.8 \frac{{\rm km}}{{\rm sec}} \label{eq:1001745} \end{equation} Eq. \ref{eq:1001745} is one of the final equations.