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The assumptions of the models above are:

1. Gravitaitonal acceleration is constant. 

2. The rocket experiences an air resistance force which acts antiparallel to the direction of its velocity and is dependent on the square of its velocity (Newton Drag), which dominates only if the Reynold's Number is large. 

3. Fuel is ejected at a constant rate and the exhaust velocity is always constant. 

4. The direction of thrust force is always parallel to the velocity. 


If 3 and 4 hold, then the rocket may eventually reach a point where the vertical component of thrust is no longer able to counter-balance its weight (because the direction is too horizontal) and the rocket will accelerate downwards, into a dive of no return. This is disastrous and we don't want it. 


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You might find solving it numerically with a the fourth order Runge-Kutta method more accurate it converges quickly too.We use it in Vegastrike for each physics frame.This is to calculate the position of about several hundred ships each frame as well as the planets in that solar system.The problem you describe reminds me of an article from early 70's in the "the British Interplanetary Society" journal.

Enjoy the Choice :)    

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