I am interested in modelling the trajectory of a rocket from the Earth to the Moon by solving a differential equation numerically. Below are some key facts and assumptions I am using. I want to make sure that I have not made any serious mistakes, nor disregarded any necessary facts.
We will consider the following equation, $$ \vec{T} + \vec{c}(\vec{r})\dot{\vec{x}} + \vec{G}(\vec{r})= m(t) \ddot{\vec{x}}, $$
where $T$ is the constant rocket thrust, $c$ denotes air resistance and is a function of radial distance from the earth, and the rocket has mass that drops at a rate that is constant with respect to time (we are assuming that a constant amount of fuel is always used for constant rocket thrust -- is this a valid assumption?).
Now a question:
- The trajectory of the rocket is not straight; how do we incorporate parabolic motion into the numerics?