I think the game doesn't use the physics to predict the orbit because of computation and instability of the orbit.
And I think ellipse can do the orbit trajectory with sin cos computation and will influence the rb velocity by the direction of the rocket in the ellipse arc. it also creates a stable orbit since orbit is an ellipse(close).
What I mean of unstable orbit is that when you tried to traject or trailed the orbit, it doesn't close the orbit into ellipse.