Question

A saturn year is 29.5 times the earth year. How far is the saturn from the sun if the earth is 1.50 x 10⁸ km away from the sun?

Answer 1

Distance of the Earth from the Sun, re = 1.5 × 108 km = 1.5 × 1011 m

Time period of the Earth = T­e

Time period of Saturn, Ts = 29. 5 Te

Distance of Saturn from the Sun = rs

From Kepler’s third law of planetary motion, we have



For Saturn and Sun, we can write



Hence, the distance between Saturn and the Sun is 1.43 into 10 power12

Answer 2

Answer:

Distance of the Earth from the Sun, re = 1.5 × 108 km = 1.5 × 1011 m

Time period of the Earth = T­e

Time period of Saturn, Ts = 29. 5 Te

Distance of Saturn from the Sun = rs

From Kepler’s third law of planetary motion, we have

T = (4π2r3 / GM)1/2

For Saturn and Sun, we can write

rs3 / re3 = Ts2 / Te2

rs = re(Ts / Te)2/3

= 1.5 × 1011 (29.5 Te / Te)2/3

= 1.5 × 1011 (29.5)2/3

= 14.32 × 1011 m

Hence, the distance between Saturn and the Sun is 1.43 × 1012 m.