Question

A Saturn year is 29.5 times the earth year. How far is the Saturn from the sun if the earth is 1.50×108 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
$T = (\frac{4 \pi^2 r^3 }{ GM})^{\frac{1}{2}}$

For Saturn and Sun, we can write

$\frac{rs^3}{ re^3 }= \frac{Ts^2 }{ Te ^2}$

$r_s = r_e(\frac{T_s}{ T_e})^{\frac{2}{3}}$

= 1.5 x 1011 $(\frac{29.5T_e}{T_e})^{\frac{2}{3}}$

= 1.5 x 1011$(29.5)^{\frac{2}{3}}$

= 1.5 x 1011 x 9.55
= 14.32 x 1011 m

Hence, the distance between Saturn and the Sun is 1.432 x 1012 m .