(a) If an object of mass \(m\) is released from rest a distance \(r\) from a star of mass \(M \gg m\) and radius \(R_{s}\), is the mechanical energy of the star-object system \(E_{\text {mech }}\) positive, negative, or zero?

(b) Describe the motion of the object, and determine the maximum and minimum values of its kinetic energy during its motion.

(c) Does the motion you described in part \(b\) satisfy conservation of angular momentum about the center of the star?

(d) Suppose the object is now launched with nonzero velocity in a direction perpendicular to the straight line joining it and the center of the star. Is \(E_{\text {mech }}\) positive, negative, or zero?