Interactive Physics

This is our special case of GM = 1, m = 1, L = 1. If we start with the mass at y = 0 then:

All this for our very special case

The choice v = 1.0 yields E = -0.5 J and a circle of radius r = 1 m. Note that the starting position of the planet is x = 1 m consistent with a mass of 1 kg and L = 1 kg-m/sec. Note that the period is 6.28 sec.

circle

When we choose v = 1.75 (E approximately -0.2 J) the turning points are at (1/1.75) m and 4 m.

ellipse

Finally, if we choose v = 2 m/sec, E = 0 and we do not have a closed trajectory. There is a distance of closest approach.

parabola