Distributing circles along a circular path

A PSTricks solution only for comparison purposes.

One

\documentclass[pstricks,border=12pt]{standalone}
\pstVerb{realtime srand}
\begin{document}
\begin{pspicture}(-6,-6)(6,6)
    \qdisk(0,0){5pt}
    \foreach \i in {1,...,6}{\pscircle[linecolor=blue]{\i}}
    \foreach \i in {0,1,...,7}{\pscircle[fillstyle=solid,fillcolor=red,origin={!3 45 \i\space mul PtoC}]{5pt}}
    \psset{linestyle=dashed}    
    \psline(0,-6)(0,6)
    \psline(-6,0)(6,0)
\end{pspicture}
\end{document}

Two

\documentclass[pstricks,border=12pt]{standalone}
\pstVerb{realtime srand}
\begin{document}
\begin{pspicture}(-6,-6)(6,6)
    \qdisk(0,0){5pt}
    \foreach \i in {1,...,6}{\pscircle[linecolor=blue]{\i}}
    \psLoop{8}{\pscircle[fillstyle=solid,fillcolor=red,origin={-3,-2}](!Rand .5 mul Rand 360 mul PtoC){5pt}}
    \psset{linestyle=dashed}    
    \psline(0,-6)(0,6)
    \psline(-6,0)(6,0)
\end{pspicture}
\end{document}

Three

\documentclass[pstricks,border=12pt]{standalone}
\pstVerb{realtime srand}
\begin{document}
\begin{pspicture}(-6,-6)(6,6)
    \qdisk(0,0){5pt}
    \foreach \i in {1,...,6}{\pscircle[linecolor=blue]{\i}}
    \foreach \i in {0,1,...,7}{\pscircle[fillstyle=solid,fillcolor=red,origin={3;225}](!.5 45 \i\space mul PtoC){5pt}}
    \psset{linestyle=dashed}    
    \psline(0,-6)(0,6)
    \psline(-6,0)(6,0)
\end{pspicture}
\end{document}

Is this what you are lookig for?

\documentclass[border=3mm]{standalone}
\usepackage{tikz}
\begin{document}
\tikzset{pics/.cd,cc/.style={code={\draw [black, thin, fill=red] circle (0.248cm);}}}
\begin{tikzpicture}[scale=.9, transform shape]
\begin{scope}[scale=.4]
\draw[black, thick, fill=black] (0,0)node (o){} circle (0.24cm);
\draw[black, thick, dashdotted] ([shift={(-90.:5.4cm)}]o.center) -- ([shift={(90.:5.4cm)}]o.center) ([shift={(180.:5.4cm)}]o.center) -- ([shift={(0.:5.4cm)}]o.center);
\foreach \r in {1, 2,3,4,5} \draw[blue, thick] (o.center) circle (\r);
\foreach \ang in {0,45,...,315}
    \pic at (\ang:2.5cm) {cc};
\end{scope}
\begin{scope}[scale=.4, xshift=14cm]
\draw[black, thick, fill=black] (0,0)node (o){} circle (0.24cm);
\draw[black, thick, dashdotted] ([shift={(-90.:5.4cm)}]o.center) -- ([shift={(90.:5.4cm)}]o.center) ([shift={(180.:5.4cm)}]o.center) -- ([shift={(0.:5.4cm)}]o.center);
\foreach \r in {1, 2,...,5} \draw[blue, thick] (o.center) circle (\r);
\def\dist{0.7}
\coordinate (p) at (240:3cm);
\foreach \ang in {0,45,...,315}
    \pic at ([shift={(\ang:\dist)}]p) {cc};
\end{scope}
\end{tikzpicture}
\end{document}