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.[br][br]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.[br][br]In particular compare the effect of motion towards and away from O. Also compare small with larger velocities.[br][br]Then change the position P, using the slider for theta_P.[br][br]Also consider the effect of the parameters a (one half of the major axis) and e (the eccentricity).