A spacecraft of mass 500kg is to be launched from the surface of a planet that has mass 6.0×1024kg and radius 6.4×106m. Take the zero of gravitational potential energy at an infinite distance from the planet’s center and neglect any atmospheric effects.
(a) Calculate the gravitational potential energy of the spacecraft when it is at rest on the planet’s surface.
(b) Determine the minimum launch speed the spacecraft must have at the surface in order to escape the planet’s gravitational influence (that is, so that it can reach infinitely large r with zero speed).
(c) On a set of axes with radial distance r on the horizontal axis (from r=R to r=4R) and potential energy U on the vertical axis, sketch the gravitational potential energy curve for the spacecraft–planet system. Draw a horizontal line representing the total mechanical energy corresponding to the threshold escape condition found in part (b) and explain how the graph illustrates the requirement for escape.