\documentclass[dvisvgm]{article}
\usepackage{animate}
\usepackage{graphicx}
\pagestyle{empty}
\usepackage{kpfonts}
\usepackage{pstricks}
\usepackage{pst-eucl}
\usepackage{xintexpr}

\newcommand\FloatToFix[1]{\xintieval{[4]\xintfloatexpr\empty#1\relax}}
\newcommand\FloatEdef[2]{\edef#1{\xintfloatexpr\empty#2\relax}}

\xintdefvar Ox, Oy := 7, 2;                                     % Center coordinates of the ellipse
\xintdefvar a_el, b_el := 5, 3;                                 % demi axes
\xintdefvar e_el   := sqrt(a_el^2-b_el^2);                      % eccentricity
\xintdefvar F_1x, F_1y, F_2x, F_2y := Ox-e_el, Oy, Ox+e_el, Oy; % foci
\xintdefvar eps_el := e_el/a_el;                                % numeric eccentricity
\xintdeffloatefunc fK(E) := E - eps_el * oneRadian * sind(E);% oneRadian = 180/Pi in xinttrig.sty
% E <-- E - (f(E)- 360 t/T)/f'(E)
\xintNewFunction{EKepler}[1]{iter(#1;subs((abs(D) < 1e-6)?
                                          {break(@-D)}% stop now
                                          {@ - D} % @ is previous value, replace it with @ -D
                                         , D = (fK(@)- #1)/(1 - eps_el * cosd(@))
                                         )% end of substitution of D value
                                    , i = 1++)}

\xintdeffloatefunc Ellipse_E_x(E) := Ox+a_el*cosd(E);
\xintdeffloatefunc Ellipse_E_y(E) := Oy+b_el*sind(E);

\newcommand\CalculeEtAffichePoint[1]{%
%
  \FloatEdef\EKepler{EKepler(#1)}%
%
  \FloatEdef\PX{Ellipse_E_x(\EKepler)}%
  \FloatEdef\PY{Ellipse_E_y(\EKepler)}%
%
  \psdot[linecolor=blue,dotsize=6pt]
        (\FloatToFix{\PX}, \FloatToFix{\PY})%
}%

\begin{document}

\begin{animateinline}[%
controls,
loop,
begin={\begin{pspicture}(1,-2)(13,6)
            \psset{dotscale=0.8}\psset{plotpoints=600}
            \pnode(\FloatToFix{Ox},\FloatToFix{Oy}){O}
            \pnode(\FloatToFix{F_2x},\FloatToFix{F_2y}){F_2}
            \pscircle[linecolor=yellow,fillcolor=yellow,fillstyle=solid](F_2){0.2}
            \uput{0.35}[-90]{0}(F_2){\footnotesize Soleil}
            \pstEllipse[linecolor=gray,linewidth=1pt](O)(\FloatToFix{a_el},\FloatToFix{b_el})
            \rput(2,-1.5){\tiny\copyright{} 2019~Jean-Fran\c{c}ois Burnol}
      },
 end={\end{pspicture}}]{20}% 20 frames/s (velocity of the animation)
\multiframe{15}{rB=0+1}{% number of frames
\xintFor* #1 in {\xintSeq{0}{23}}\do {%
\CalculeEtAffichePoint{\FloatToFix{\rB+#1*15}}
}}
\end{animateinline}
\end{document} 