This was a fun project. Programming using advanced function calls and polar coordinates, I determined that a 5 kg Cubesat would require an initial velocity of 9.5 km/s and a launch angle of 89.5 degrees to reach lower earth orbit and orbit as many times as possible without further intervention. The satellite launched from Cape Canaveral (i.e. ϴ = π/4) and made 5.25 revolutions in 11.6 hours before crashing back to earth’s surface. During its voyage it made an elliptical orbit that slowly got smaller due to gravity and atmospheric drag, which both changed as the satellite’s altitude changed. The satellite’s course is plotted here with earth in the middle, showing its altitude and position above the earth.
I took this project a step further by examining the 5 kg satellite’s velocity and altitude. I was surprised when I realized that the satellite’s velocity peaks twice per revolution, but this makes sense once you look at where the velocity peaks; velocity peaks when the satellite travelling parallel to earth’s surface. This phenomena is easily understood by plotting velocity and altitude as functions of time on the same plot.