Question

Solving Direct Variation Problems For the following exercises, use Kepler's Law, which states that the square of the time, T (measured in Earth years), required for a planet to orbit the Sun varies directly with the cube of the mean distance, a (measured in billions of miles), that the planet is from the Sun. a. Use Jupiter's time of 12 and mean distance of 0.484 billion miles, find the equation relating T and a. (Enter an equation in terms of T and a. Round numbers to the nearest tenth.) b. Use the result from part a. to determine the time required for Mars to orbit the Sun if its mean distance is 0.142 billion miles. It takes Mars approximately years to orbit the Sun. (Round your answer to 3 decimal places.)

Answer 1

a mean Kepler's third law States that square of period of revolution (7) of planet around the sun is directly proportional to the Cube of the distance (a) between sun and planet ... Tha a3 т. ka 0 propor dromelity T a] and 0.484 3 [x= constant T= 12 3 0 k (0.484) K (0.1133 79904) 144 Ka 144 0:113379904 ko 1270.06 634 1270 is Submit k in " The required Equation 2-0 Te 1270-1 (0) 3

b] Now have tie we find Time (T) and given mean distance 0.142. we have as 0.142;; K = 1270:7 Submit in Eq T² = (127001) (0.142)3 T = (1870.1) (0.002863288) 72 3.636 66209 T 3-63666209 T |90700343 T 1.907 years a] 1270.1 a 3 b] T 1.907 years.