\documentclass[a4paper]{article}
\begin{document}
\begin{eqnarray*}
\mbox{(1)} \qquad F_{g}
 & = & G \, \frac{m_{1} m_{2}}{r^{2}} \\
\end{eqnarray*}
\newpage
\begin{eqnarray*}
\mbox{(2)} \qquad F_{g, onder}
 & = & G \, \frac{m_{A} m_{b, onder}}{r_{A}^{2}} \\
& = & G \, \frac{m_{A} \cdot 1}{r_{A}^{2}} \\
& = & G \, \frac{m_{A}}{r_{A}^{2}} \\
\end{eqnarray*}
\newpage
\begin{eqnarray*}
\mbox{(3)} \qquad F_{g, boven}
 & = & G \, \frac{m_{A} m_{b, boven}}{(r_{A} + 1)^{2}} \\
& = & G \, \frac{m_{A} \cdot 1}{(r_{A} + 1)^{2}} \\
& = & G \, \frac{m_{A}}{(r_{A} + 1)^{2}} \\
\end{eqnarray*}
\newpage
\begin{eqnarray*}
\mbox{(4)} \qquad \Delta F_{g}
 & = & F_{g, boven} - F_{g, onder} \\
& = & G \, \frac{m_{A}}{(r_{A} + 1)^{2}} - G \, \frac{m_{A}}{r_{A}^{2}} \\
& = & G m_{A} \left ( \frac{1}{(r_{A} + 1)^{2}} - \frac{1}{r_{A}^{2}} \right ) \\
\end{eqnarray*}
\newpage
\begin{eqnarray*}
\Delta F_{g}
 & = & -3.073 \cdot 10^{-6} \mbox{ N} \\
\end{eqnarray*}
\newpage
\begin{eqnarray*}
\mbox{(5)} \qquad \frac{\mbox{d}F_{g}}{\mbox{d}r}
 & = & \frac{\mbox{d}}{\mbox{d}r} \left ( G \, \frac{m_{A} m_{b}}{r_{A}^{2}} \right ) \\
& = & - 2 G \, \frac{m_{A} m_{b}}{r_{A}^{3}} \\
\end{eqnarray*}
\newpage
\begin{eqnarray*}
\mbox{(6)} \qquad \frac{\Delta F_{g}}{\Delta r}
 & = & - 2 G \, \frac{m_{A} m_{b}}{r_{A}^{3}} \\
\Delta F_{g}
 & = & - 2 G \, \frac{m_{A} m_{b}}{r_{A}^{3}} \, \Delta r \\
\end{eqnarray*}
\newpage
\begin{eqnarray*}
\mbox{(7)} \qquad \frac{d}{O}
 & = & \frac{\alpha}{2 \pi} \\
\frac{d}{2 \pi r_{A}}
 & = & \frac{\alpha}{2 \pi} \\
\alpha
 & = & \frac{d}{r_{A}} \\
\end{eqnarray*}
\newpage
\begin{eqnarray*}
\mbox{(8)} \qquad F_{g,hori}
 & = & F_{g} \cos \beta \\
\end{eqnarray*}
\newpage
\begin{eqnarray*}
\mbox{(9)} \qquad \alpha + \beta + \beta
 & = & \pi \\
\alpha + 2 \beta
 & = & \pi \\
2 \beta
 & = & \pi - \alpha \\
\beta
 & = & \frac{1}{2} \pi - \frac{1}{2} \alpha \\
\end{eqnarray*}
\newpage
\begin{eqnarray*}
\mbox{(10)} \qquad \cos (\xi - \eta)
 & = & \cos \xi \cos \eta + \sin \xi \sin \eta \\
\end{eqnarray*}
\newpage
\begin{eqnarray*}
\mbox{(11)} \qquad F_{g,hori}
 & = & F_{g} \cos \beta \\
& = & F_{g} \cos \left ( \frac{1}{2} \pi - \frac{1}{2} \alpha \right ) \\
& = & F_{g} \left ( \cos \left ( \frac{1}{2} \pi \right ) \cos \left ( \frac{1}{2} \alpha \right ) +
 \sin \left ( \frac{1}{2} \pi \right ) \sin \left ( \frac{1}{2} \alpha \right ) \right ) \\
& = & F_{g} \left ( 0 \cdot \cos \left ( \frac{1}{2} \alpha \right ) + 1 \cdot \sin \left ( \frac{1}{2} \alpha \right ) \right ) \\
& = & F_{g} \sin \left ( \frac{1}{2} \alpha \right ) \\
& = & G \, \frac{m_{A} m_{b}}{r_{A}^{2}} \sin \left ( \frac{1}{2} \alpha \right ) \\
\end{eqnarray*}
\newpage
\begin{eqnarray*}
\mbox{(12)} \qquad \lim_{x \to 0} \frac{\sin x}{x}
 & = & 1 \\
\end{eqnarray*}
\newpage
\begin{eqnarray*}
\mbox{(13)} \qquad F_{g,hori}
 & = & G \, \frac{m_{A} m_{b}}{r_{A}^{2}} \sin \left ( \frac{1}{2} \alpha \right ) \\
& \approx & G \, \frac{m_{A} m_{b}}{r_{A}^{2}} \frac{1}{2} \alpha \\
& = & G \, \frac{m_{A} m_{b}}{r_{A}^{2}} \frac{1}{2} \frac{d}{r_{A}} \\
& = & G \, \frac{m_{A} m_{b}}{2 r_{A}^{3}} d \\
\end{eqnarray*}
\newpage
\begin{eqnarray*}
\mbox{(14)} \qquad F_{g,hori}
 & = & 2 G \, \frac{m_{A} m_{b}}{2 r_{A}^{3}} d \\
& = & G \, \frac{m_{A} \cdot 1}{r_{A}^{3}} \cdot 1 \\
& = & G \, \frac{m_{A}}{r_{A}^{3}} \\
\end{eqnarray*}
\newpage
\begin{eqnarray*}
\Delta F_{g,hori}
 & = & 1.537 \cdot 10^{-6} \mbox{ N} \\
\end{eqnarray*}
\end{document}
