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Kepler Applet
This applet is simulating the elliptical motion of a celestial body.
Use
the
third
scrollbar
(blue)
to
increase
uniformly
the
true
anomaly
angle
phi. Select
from
the
menu for details, such as eccentric anomaly. radius,
velocity.
Use the fourth scrollbar (red) to increase uniformly the time (mean
anomaly M).


The
mean
anomaly
M
is
the
angular
distance
from
perihelion
which
a
(fictitious)
planet would have if it moved on the circle of radius a
with a constant angular velocity and with the same orbital
period T as the real planet moving on the ellipse. By definition, M
increases linearly (uniformly) with time. Choose
Show/Hide Velocity v and Show/Hide Vel. Circle: Applet for Mars
As the planet P is moving around the ellipse, the end of the velocity
vector OP' will move around the gray circle (center M), and FP is
always pependicular to to MP'.
The data window of the applet:
Solving Kepler's equation of elliptical motion
E  e*sin(E) = M(t)
Eccentricity of the orbit of the Earth (longperiod variations)

Solution for the motion as a function of time (Wikipedia) Kepler's Equation of Elliptical Motion Kepler's Equation for Elliptical Motion, a Numerical Solution Utility 
Updated: 2011, Jun 24