This note will be a solution to the following problem :
Any orbiting object with negligible size which is launched with a velocity at a distance of from the centre a planet and that we know (only) the following values :
Also assume that mass of the orbiting object is very - very smaller than the mass of the planet.
From Kepler's First law we know that the orbit is going to be a conic section, which can be described by the following polar equation :
Let there be some position in this orbit with distance from the centre of the planet and velocity such that angle
between and the line joining the center of the planet and the orbiting object is
Using and we can find