Center-of-Mass Orbits show variations on a planet orbiting a much more massive central star in Cartesian and polar coordinates. The examples show one circular and two elliptical orbits that begin at the same position, yet have different initial velocities.
~~1. Look at all of the simulations, both in Cartesian and polar coordinates. How does the initial velocity account for the difference in orbital trajectory around the central star?
~~2. In both in Cartesian and polar coordinates, what is the value of GM? Hint: it is easiest to answer this question for the circular orbit example.