Chapter 5, Section 5.4, Figure 5.9

Create a graphics object to denote the Sun.

sun=Graphics[{PointSize[0.05],Point[{0,0}]}]

Define a function ksolve to be used to solve Kepler's equation.

ksolve[ma_,e_]:=
FindRoot[ea - e Sin[ea] == ma, {ea,ma}];

Define a function position to be used to calculate an object's position vector for a given mean anomaly, semi-major axis and eccentricity.

position[ma_,a_,e_]:=
(eca=ea/.ksolve[ma,e];
x=N[a(Cos[eca]-e)]; y=N[a Sqrt[1-e^2] Sin[eca]];
{x,y})

Set the values of the semi-major axis (a = 1.0) and eccentricity (e = 0.3).  Note that the diagram is not intended to be an accurate representation of the orbit.

a=1.0; e=0.3;

Create a graphics objects for the points denoting the location of the object at equal intervals in mean anomaly around the orbit.

spoints = 
Graphics[Map[Disk[#,0.05]&,
   Table[position[t,a,e],{t,0,2Pi,Pi/3}]]];

Draw the obit of the object.

planetorbit =
ListPlot[
Table[position[t,a,e],{t,0,2Pi,Pi/20}],
PlotJoined->True,AspectRatio->Automatic,Axes->None]

Show the planet's orbit and the position at fixed intervals.

Show[planetorbit,sun,spoints]