Final answer:
To find how long it takes Satellite K to orbit the Earth, working with Kepler's Third Law, we find that Satellite K's period is 2.5 weeks, because Satellite J, which is 4 times further away, orbits in 20 weeks.
Step-by-step explanation:
The question pertains to Kepler's Third Law, which relates the period of a celestial body's orbit to its distance from the central body. In the context of the question, Satellite J orbits the Earth in 20 weeks and is 4 times further from the Earth than Satellite K. To determine how long it takes for Satellite K to orbit the Earth, we must consider that Kepler's Third Law states that the orbital period of a planet is proportional to the 3/2 power of the semi-major axis of its orbit.
Applying this to our satellites, if Satellite J is 4 times further away from the Earth than Satellite K, then its orbital period would be 4^(3/2) = 8 times that of Satellite K. Therefore, since Satellite J's period is 20 weeks, to find Satellite K's period, we divide 20 weeks by 8, yielding a period of 2.5 weeks for Satellite K to complete an orbit around the Earth.