# Motion in a central field

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:

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 $y'(0)=1$.