Launching of satellite from moving object in space.
Elliptical orbit of planet P (or space shuttle) around sun or planet at O. Satellite S is launched with velocity vector given by magnitude v_S and direction psi_S from P. Black indicates the elliptical orbit of P and green indicates the elliptical or hyperbolic orbit of S.
First use sliders to change the speed v_S and direction psi_S of the launching velocity vector. See how the orbit changes and intersects or bypasses the sun/planet at O. In particular compare the effect of motion towards and away from O. Also compare small with larger velocities. Then change the position P, using the slider for theta_P. Also consider the effect of the parameters a (one half of the major axis) and e (the eccentricity).