Visualizing a Trajectory

basically, what KSP did is taking the liberty of massive difference in mass between your shuttle and the planet itself.
So for most of the case, the orbit you are on, planet are always in one of the 2 focus points of a ellipse.
The tangent speed you applied changes the distance of focus points thus change the result of predicted orbit.
In case of moon landing, it’s more complicated, but I assume similar principle applies.

It really depends on what you want to achieve really, as orbit is kinda special case(where most planet/moon bodies won’t change their existing orbit because of mass difference).
I doubt you can give much detail about what you guys are contracted to do, but not everything has to be simulated to get the results right.
(Of course NASA isn’t going to risk some decade projected launch(like recent probe orbiting a comet) from KSP, it’s a game after all.