I am trying to predict how long a rocket will take to predict its trajectory, given target location, general rocket information, starting position, etc. I am currently in high school and working on my science fair project. I have people who would be willing to explain higher level math/physics to me, so feel free to use advanced math and physics in your answer.

The general equations that will govern the flight of the rocket are:


\Sigma \vec F = \frac {d(m \vec v)} {dt}


where the forces acting on the rocket include the thrust from the engine, gravity, air resistance, and the effects of side winds, and:


\Sigma \vec T = \frac {d (I \vec{\dot \theta})} {dt}


where the torques are due to different positions of the center of pressure versus center of gravity (i.e. the fins causing the rocket to fly a stable course), the effect of side winds, plus any additional steering torque from the fins or steerable rocket exhaust.

So the first task is to develiop a mathemetical model of the rocket's thrust, the air resistance, its mass versus time (as it burns fuel it gets lighter), it's moment of inertia I versus time (which depends on how the fuel is burned), and any torques that may influence its flight.

I think you'll find that developing a single mathemetical equation that takes all this into account is virtually impossible. So instead think about a computer simulation that determines factors such as mass, change in velocity, change in angle of attack, etc in increments of, say, 1/10 second.