Kepler's First Law of Planetary Motion
In this demonstration of Kepler's First Law (as done in Math 1B), the orbit of the planet, the position vector, and the velocity vector are displayed together. Use the theta slider to adjust the angle $\theta$ to move the planet around the orbit, and observe how the velocity vector changes with the angle. Use the $c_1$ and $c_2$ sliders to adjust the velocity constant to see how it affects eccentricity and shape of the orbit. The d slider adjusts the directrix that controls the scale of the orbit.