Wunderbar. Danke für die Hilfe. Hier kommt meine vollständige Lösung:
\documentclass{standalone}
\usepackage{pgfplots}
\pgfplotsset{compat=newest,
every extra y tick/.append style={major tick length=2pt}
}
\usepackage{amsmath}
\begin{document}
\begin{tikzpicture}
\begin{semilogxaxis}[
scaled ticks=false,
xtick pos=left, ytick pos=left,
ymin=0,ymax=8000,
xmin=100, xmax=819200,
/pgf/number format/1000 sep={\,},
ticklabel style={font=\footnotesize},
tick align=outside,
grid=both,
grid style={dotted},
ylabel=\footnotesize{Bahngeschwindigkeit \emph{v} / m\;$\cdot{}\;\text{s}^{-1}$},
xlabel=\footnotesize{Flugh\"ohe \emph{h} / km},
xticklabel style={/pgf/number format/fixed, rotate=45, anchor=east},
xtick={100,200,400,800,1600,3200,6400,12800,25600,51200,102400,204800,409600,819200},
xtick={100,200,400,800,1600,3200,6400,12800,25600,
51200,102400,204800,409600,819200},
x tick label style={yshift=-0.7em},
y tick label style={xshift=-0.3em},
extra y ticks = {1000,3000,5000,7000},
extra y tick labels=\empty,
log ticks with fixed point,
height=7cm,width=12.2cm,
log basis x=2,
]
\node[rotate=90] at (404.5,610) {\footnotesize{ISS}};
\node[rotate=90] at (35880,800) {\footnotesize{GEO}};
\node[rotate=90] at (384400,850) {\footnotesize{Mond}};
\addplot[smooth] coordinates {
(100,7850)
(200,7800)
(400,7661)
(800,7425)
(1600,7000)
(3200,6350)
(6400,5500)
(12800,4500)
(25600,3500)
(51200,2550)
(102400,1825)
(204800,1270)
(409600,900)
(819200,600)};
\end{semilogxaxis}
\end{tikzpicture}
\end{document}
