Variation Word Problem

Question

Keplers Third Law states that the time T needed for a planet to make one complete revolution about the sun is directly proportional to the 3/2 power of the average distance d between the plent and the sun. The earth, which averages 93 million miles from the sun, completes one revolution in 365 days. Find the average distance from the sun to Mars if Mars completes 1 revolution about the sun in 686 days. Round to the nearest million miles.

Answer 1

According to the first sentence of the problem

T = kd^3/2

Using earth's data to find k,

365 = k 93^3/2.

365/(93^1.5) = 0.406975665 = k

Then. T = 0.406975665 d^3/2

plugging in Mars' data we get

686/0.406975665 = d^3/2

then (686/0.406975665)^2/3 = (d^3/2)^2/3 = d

about 142 million miles = d