Kepler laws

This applet shows the motion of a body once you choose its starting position and starting velocity.
If you want to browse the source, download the following files:,,,


Clicking with the left button in the black area it will appear a blue circle (the body), a green and a blue constant length vectors (a coordinate frame along the radial and tangent directions) and a white vector (the starting speed). Just drag the mouse around keeping pressed the left mouse button to change the vector length.
As you move the vector it will automatically appear the orbit of the body according to the gravity laws discovered empirically by J. Kepler:

First Law
Planets move around the sun describing elliptic paths. The center of the sun lies over a focus of the ellipse.

Second Law
The area spanned by the vector connecting the sun with the planet in a fixed time is constant, i.e it does not depend on the time chosen to start counting.

Third Law
The squares of planets revolution periods are proportional to the cubes of the half length of the greater axis of the orbit.