Single-Impulse Orbital Trajectories

Modern space travel has been enabled through the use of multi-stage rockets, where a large booster stage puts a smaller upper stage on a sub-orbital trajectory, and the upper stage lights a new set of engines that carries it onward to orbit.

In order to better understand the trajectories created by a continuous burn of the rocket's engines, I wanted to simplify things and first take a look at what happens if you had to deliver all of the force at one time in a single impulse.

The simulation below computes trajectories for a "cannonball" that has been launched at a certain altitude above a planet's surface. It accounts for aerodynamic resistance, according to the atmosphere of the specified planet.