I am looking on how to find out how many stages are needed to reach a certain orbit. I come across equations to compute the height reach by a stage of a certain time. On the other hand I don't find material on how to plan a launch, if I choose an orbit, how long should each stage be and how many would there be to reach this orbit ? I would like to develop a model being able to launch a rocket at different orbits. Thus during the launch I'd have accelerations computed for x,y and angular, and an integrator to find velocity and position state vectors.
Thanks in advance for any reference recommendations