Hi all I have been trying to find A set of equations that can allow me to map the movement of a planetary body on a polar coordinate sheet (a 2-D Problem). As well as allow me to find out about information such as the perigee and apogee radaii. So far i have been using Keplers equations and guessing the eccentricity of the orbit. But that is not really a good way of approaching it. However, I couldnt figure out how to do it with Keplers equations so I turned to Projectile Motion. I am currently trying to figure out how to use the basic projectile motion diff eq to map a planets orbital trajectory. Only problem I havent tried to account for yet is that the normal projectile motion equations seem to assume a flat earth. I have attached a screenshot of some of my work.