Optimizing perspective tikz graphic

Question

I could use a little help optimizing the following tikz graphic:

\documentclass[border=3pt]{standalone}
\usepackage{tikz}
\begin{document}

\begin{tikzpicture}
\filldraw[black!5] (-4.5,-1.5)--(1.5,-1.5)--(4.5,1.5)--(-1.5,1.5)--(-4.5,-1.5);
\draw[->] (-1.5,-1.5)--(1.5,1.5);
\draw[->] (-3,0)--(3,0);
\node[right] at (3,0) {$x$};
\node[above] at (1.5,1.5) {$y$};
\def\firstellipse{(0,0) ellipse (2.5 and .7)};
\draw[cyan!80]\firstellipse;
\def\secondellipse{(0,0) ellipse (1.5 and .4)};
\draw[orange]\secondellipse;
\node[circle,inner sep=.5pt,draw=red] at (2,.41) {};
\node[above] at (2.1,.41) {$\color{red}P$};
\node[circle,inner sep=.5pt,draw=red] at (1,.-.298) {};
\node[below] at (1.1,-.3) {$\color{red}Q$};
\end{tikzpicture}

\end{document}

1. I would like some dotted arrows along the ellipses starting at P and Q. Maybe 1cm long. Do I have to figure out the correct arc configurations by trying?
2. As you can see, I've drawn the x- and y-axis, as well as the (supposed to be) circles by estimating. Is there a proper way of drawing circles in a plane without tikz-3D? Or do you think it suffices to do it this way?
3. Any other recommendations as to optimize this graphic? Maybe in terms of color or other details. It's basically about the orbits of points in the euclidean plane $\mathbb R^2$ when acting with the special orthogonal group $SO(2)$. It's supposed to be associated with the planetal orbits.

Answer 1

Just showcasing tikz-3dplot.

So this is essentially what you have drawn.

\documentclass[tikz,border=3pt]{standalone}
\usepackage{tikz-3dplot}

\begin{document}

%% viewing angles %%
\def\angThe{70}
\def\angPhi{55}

\tdplotsetmaincoords{\angThe}{\angPhi}
\begin{tikzpicture}%[tdplot_main_coords,scale=1.5]
  \filldraw[black!5] (-3,-3) -- (-3,3) -- (3,3) -- (3,-3) -- cycle;
  \draw[->] (-3,0)--(3,0) node [at end, above] {$x$};
  \draw[->] (0,-3)--(0,3) node [at end, right] {$y$};
  \def\R{2.5} % big radius
  \def\r{1.5} % smaller one
  \draw[cyan!80] (0,0) circle (\R);
  \draw[orange] (0,0) circle (\r);
  \node [circle,inner sep=.5pt,draw=red,label={[red,above right]$P$}] at (25:\R) {};
  \node [circle,inner sep=.5pt,draw=red,label={[red,below right]$Q$}] at (-25:\r) {};
\end{tikzpicture}

\end{document}

It produces :

We uncomment the options [tdplot_main_coords,scale=1.5] of the tikzpicture.

Everything transforms like so :

Now we have a nice setup : we work the hard stuff in the plane (with tikz-3dplot commented) and once in a while, we check back in 3d how things look.

In particular the ellipse arrows you want to draw are simply arcs (probably much easier to work with.)

With a bit a fiddling around, we can get this :

\documentclass[tikz,border=3pt]{standalone}
\usepackage{tikz-3dplot}

\begin{document}

%% viewing angles %%
\def\angThe{70}
\def\angPhi{55}

\tdplotsetmaincoords{\angThe}{\angPhi}
\begin{tikzpicture}[tdplot_main_coords,scale=1.5]
  \filldraw[black!5] (-3,-3) -- (-3,3) -- (3,3) -- (3,-3) -- cycle;
  \draw[->] (-3,0)--(3,0) node [at end, above right] {$x$};
  \draw[->] (0,-3)--(0,3) node [at end, below right] {$y$};
  \def\R{2.5}
  \def\r{1.5}
  \draw[cyan!80] (0,0) circle (\R);
  \draw[orange] (0,0) circle (\r);
  \node [circle,inner sep=.5pt,draw=red,label={[red,below right]$P$}] (P) at (25:\R) {};
  \node [circle,inner sep=.5pt,draw=red,label={[red,above]$Q$}] at (-25:\r) {};
  \draw [->, thick, red](25:\R-.1) arc [start angle=25,end angle=55,radius=\R-.1] ;
  \draw [->, thick, red](-25:\r+.1) arc [start angle=-25,end angle=05,radius=\r+.1] ;
\end{tikzpicture}

\end{document}

Otherwise, without using tikz-3dplot at all, we set the y unit vector by hand.

\documentclass[tikz,border=3pt]{standalone}
\begin{document}

\begin{tikzpicture}[y={(.5cm,.7cm)}]
  \filldraw[black!5] (-3,-3) -- (-3,3) -- (3,3) -- (3,-3) -- cycle;
  \draw[->] (-3,0)--(3,0) node [at end, above right] {$x$};
  \draw[->] (0,-3)--(0,3) node [at end, below right] {$y$};
  \def\R{2.5}
  \def\r{1.5}
  \draw[cyan!80] (0,0) circle (\R);
  \draw[orange] (0,0) circle (\r);
  \node [circle,inner sep=.5pt,draw=red,label={[red,below right]$P$}] (P) at (25:\R) {};
  \node [circle,inner sep=.5pt,draw=red,label={[red,above]$Q$}] at (-25:\r) {};
  \draw [->, thick, red](25:\R-.1) arc [start angle=25,end angle=55,radius=\R-.1] ;
  \draw [->, thick, red](-25:\r+.1) arc [start angle=-25,end angle=05,radius=\r+.1] ;
\end{tikzpicture}

\end{document}