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Movie of elliptical motion
Plots of elliptical Kepler motion

The JavaScript form is preset to the values: eccentricity e=0.5 mean anomaly M=27° or t/T=0.075. The results are, as shown in the figure below: true anomaly phi=75.84° eccentric anomaly E=48.43° A series expansion of the true anomaly φ can be found here or in Meeus (Astronomical Algorithms, Chapter 3):   It is suitable only for small values of the eccentricity e.

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(c) 2006 J. Giesen