Question

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

Answer 1

Hey mate,

◆ Answer- 1.43×10^12 m

◆ Explaination-
# Given-
Ts = 29.5 Te
re = 1.5×10^11 m

# Formula-
Period of planet revolving around sun is
T^2 ∝ r^3

So we can infer,
(Ts / Te)^2 = (rs / re)^3
(29.5)^2 = (rs / 1.5×10^11)^3
rs = 1.5×10^11 × (29.5)^(2/3)
rs = 1.42×10^12 m

Saturn's orbit around sun is at 1.42×10^12 m.

Hope this helps you...

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.