Answer the following conceptual questions related to gravitational potential energy and the energy of orbital motion.
a. (i) Why is the gravitational potential energy U of a two–body system expressed with a negative sign when the separation between the bodies is finite?
b. (ii) A satellite of mass m is moving around a planet of mass M in a closed orbit. Using general energy considerations, state the condition on the sign of the total mechanical energy E=K+U for the orbit to remain bound.
c. (iii) Explain qualitatively why a satellite must be given additional kinetic energy in order to escape from its orbit around the planet.