If I have a body $\text{A}$, which is orbiting a more massive body $\text{B}$, and I increase $\text{A}$'s velocity, I'd like to be able to calculate $\text{A}$'s new position after some time.
I have all the orbital elements of the previous orbit, and I can calculate orbital period $T$, semi-major axis $a$, eccentricity $e$ of the new orbit from the new initial position and increased velocity vectors $V$.
So, given ...
- a known position along a planet's orbit $P$,
- a velocity vector $V$,
- the semi-major axis $a$,
- the eccentricity of the orbit $e$, and
- the period of orbit $T$
... is it possible to calculate the new position of $\text{A}$ given its old position in the orbit and after some time $t$?