Kepler’s third law states that the square of a planet’s orbital speed is proportional to the cube of its average orbital radius. Use Kepler’s third law to answer each of the following questions. 

(a) The Moon’s orbital radius is 3.84 x 10⁵ km and it orbits Earth once every 27.3 d. Neglecting the moon’s mass, compute the mass of Earth.  

(b) Io (one of Jupiter’s moons) orbits Jupiter once every 42.5 h in a near-circular orbit of average radius 4.22 x 10⁵ km. Neglecting Io’s mass, compute the mass of Jupiter. 

(c) Compute the orbital period of the International Space Station as it orbits 300 km above Earth’s surface.

(d) Charon, a moon of Pluto, orbits that body once every 6.4 d at an average distance of 1.97 x 10⁴ km. Compute the total mass of Pluto and Charon. What fraction of Earth’s mass is this?