We present a study of the flight path trajectory of a three stage rocket launched from colombian territory with the purpose of placing a small satellite in Low Earth Orbit (LEO). Various forces that affect the motion of the rocket were considered such as thrust, gravity an those that arise from the movement through the atmosphere. Taking into account specific values related with the performance of rockets that could be derived from the output of the national industry, we calculated the mass and size of each one of the three stages by means of an optimization process. The differential equations were integrated using a Fortran code written by the authors which permits to calculate the dynamic state of the payload (and stages when discarged) at the desired time. The integration was extended until orbit insertion which permits to know the orbital elements of the satellite.