a) Show that the torque on a planet orbiting the Sun due to the gravitational attraction of the Sun is zero. b) Show that the area swept out by a planet in time dt is proportional to its angular momentum. c) Using your answers above derive Kepler’s 2nd law.

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a) Show that the torque on a planet orbiting the Sun due to the gravitational attraction of the
Sun is zero.

b) Show that the area swept out by a planet in time dt is proportional to its angular momentum.

c) Using your answers above derive Kepler’s 2nd law.

d) If a planet is in a circular orbit of radius, R, determine the potential energy due to gravity,
its kinetic energy due to the motion of the planet, and the total energy.

e) A satelite is in geostationary orbit. How much energy is required to move it to a circular
orbit where it orbits the Earth once in 8 days? You may express your answer in terms of
the total energy of the initial geostationary orbit. 

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