Here's a very simple model of planetary motion or, more precisely, motion through a
central field. If you use the checkbox to stop the motion, several fields will reveal
themselves with information about the current state. The first field tells you
the instantaneous speed of the object at that time. You can also use the sliders
to move the starting and
stopping points in an attempt to estimate the
instantaneous speed with average speed.
Running
Starting point:
Stopping point:
Instantaneous speed:
Distance traveled:
Time span:
Average speed:
More information on the motion
Technically, the animation illustrates a numerical solution to the system
$$
\begin{align}
x''(t) &= -G \frac{x(t)}{(x(t)^2 + y(t)^2)^{3/2}} \\
y''(t) &= -G \frac{y(t)}{(x(t)^2 + y(t)^2)^{3/2}}.
\end{align}
$$
with $G=3$ and initial conditions $x(0)=1$, $y(0)=0$, $x'(0)=0$, and $y'(0)=1$.
For more information, have a look at this python code in
IPython notebook or HTML
formats.