With TikZ
I don't know how random your asteroids have to be, so this is maybe not good enough. It uses the dots pattern, so the 'asteroids' are evenly distributed. The border of the belt is randomized with the random steps decoration.
\documentclass{standalone}
\usepackage{tikz}
\usetikzlibrary{patterns,decorations.pathmorphing}
\begin{document}
\begin{tikzpicture}[decoration={random steps,segment length=5pt}]
\draw [black!40] circle[radius=2.65cm];
\fill [pattern color=black,pattern=dots,even odd rule,decorate] circle[radius=2.5cm] circle[radius=2.8cm];
\end{tikzpicture}
\end{document}
With Metapost
The following examples uses the luamplib package, and must be compiled with lualatex.
White asteroids, varying size, on black background:
\documentclass{standalone}
\usepackage{luamplib}
\begin{document}
\begin{mplibcode}
beginfig(1);
r=2cm;
fill unitsquare scaled 4.8cm shifted (-1.2*r,-1.2*r) withcolor black;
for i=0 upto 720:
pickup pencircle scaled 1pt scaled uniformdeviate(1.5);
drawdot (r*cosd(i) + 2*normaldeviate, r*sind(i) + 2*normaldeviate) withcolor white;
endfor;
endfig
\end{mplibcode}
\end{document}
\documentclass{standalone}
\usepackage{luamplib}
\begin{document}
\begin{mplibcode}
beginfig(1);
r=2cm;
pickup pencircle scaled 1pt;
for i=0 upto 360:
drawdot (r*cosd(i) + 2*normaldeviate, r*sind(i) + 2*normaldeviate);
endfor;
endfig
\end{mplibcode}
\end{document}
