I am trying to recreate this image: enter image description here

I'm however struggling with the flattened circle shape in the centre as well as getting the curved lines for focusing. My current attempt has allowed me to get this far:

\draw (0,0) circle (2.4);
\draw [red, dashed] (0,0) circle (1.8);
\draw [<-, red, thick] (1.3,1.3) -- (2.3,2.3) node[above] {equilibrium orbit};
\draw    (0,2.4) to[out=-50,in=130] (0,-2.4);
\draw    (1.8,1.6) to[out=-60,in=100] (-1.85,-1.5);
\draw    (-2.1,1.2) to[out=40,in=220] (2.1,-1.2);

This produces the pictures below: enter image description here

However I am struggling to get any further.


Something like this?

    declare function={rr(\t)=1.8*(1+0.01*rnd)*(1+0.1*sin(-45+3*\t));}]
 \draw plot[smooth cycle,variable=\t,samples at={0,10,...,350}] (\t:{rr(\t)});
 \draw (0,0) circle[radius=2.4cm];
 \draw[red, dashed] (0,0) circle[radius=1.8cm];
 \draw[<-, red, thick] (1.3,1.3) -- (3,2) node[right] {equilibrium orbit};
 \foreach \X in {80,200,320}
 {\draw (\X:2.4) to[bend right] (0,0) to[bend left] (\X+180:2.4);
 \path (\X-30:2.5) node[anchor=\X-30+180]{Hill}
 (\X+30:2.5) node[anchor=\X+30+180]{Valley};  }

enter image description here

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