\documentclass[a4paper]{article}
\usepackage{amsmath}
\DeclareMathOperator{\artanh}{artanh}
\begin{document}
\begin{eqnarray*}
\mbox{(1)} \qquad \Delta t
 & = & \frac{2 R_{s}}{c} \left (
 \artanh \sqrt{\frac{r}{R_{s}}} - \artanh \sqrt{\frac{r_{\infty}}{R_{s}}}
 + \sqrt{\frac{r_{\infty}}{R_{s}}} \left ( \frac{1}{3} \frac{r_{\infty}}{R_{s}} + 1 \right )
 - \sqrt{\frac{r}{R_{s}}} \left ( \frac{1}{3} \frac{r}{R_{s}} + 1 \right ) \, \right ) \\
\end{eqnarray*}
\newpage
\begin{eqnarray*}
\mbox{(2)} \qquad \Delta t
 & = & \frac{2}{3 c \sqrt{R_{s}}} \left ( r_{\infty}^{\frac{3}{2}} - r^{\frac{3}{2}} \right ) \\
\end{eqnarray*}
\newpage
\begin{eqnarray*}
\mbox{(3)} \qquad \Delta t
 & = & \frac{2 R_{s}}{c} \left (
 \artanh \sqrt{\frac{r}{R_{s}}} - \artanh \sqrt{\frac{r_{k}}{R_{s}}}
 + \sqrt{\frac{r_{k}}{R_{s}}} \left ( \frac{1}{3} \frac{r_{k}}{R_{s}} + 1 \right )
 - \sqrt{\frac{r}{R_{s}}} \left ( \frac{1}{3} \frac{r}{R_{s}} + 1 \right ) \, \right ) \\
\end{eqnarray*}
\newpage
\begin{eqnarray*}
\mbox{(4)} \qquad \Delta t
 & = & \frac{2}{3 c \sqrt{R_{s}}} \left ( r_{k}^{\frac{3}{2}} - r^{\frac{3}{2}} \right ) \\
\end{eqnarray*}
\end{document}
