﻿ A Saturn year is 29.5 times the earth year. How far is the Saturn from the sun if the earth is 1.50 ×108 km away from the sun? from Physics Gravitation Class 11 Manipur Board

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

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

Time period of the Earth =

Time period of Saturn, Ts = 29. 5 T

Distance of Saturn from the Sun = r

From Kepler’s third law of planetary motion,

T = (4π2r3 / GM)1/2

For Saturn and Sun,

rs3 / re3  =  Ts2 / Te

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.
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