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Solution for 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? - CBSE (Science) Class 11 - Physics

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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?

Solution 1

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

Time period of the Earth = e

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 = `((4pi^2r^3)/"GM")^(1/2)`

For Saturn and Sun, we can write

`(r_s^3)/(r_e^3) = (T_s^2)/(T_e^2)`

`r_s = r_e (T_s/T_e)^(2/3)`

`=1.5 xx 10^11 ((29.5T_e)/T_e)^(2/3)`

`=1.5 xx  10^11 (29.5)^(2/3)`

`= 1.5 xx 10^11xx 9.55`

`=14.32 xx 10^11` m

Hence, the distance between Saturn and the Sun is `1.43 xx 10^(12)` m.

Solution 2

We know that `T^2 oo R^3`

`:.(T_s^2)/(T_e^2) = (R_s^3)/(R_e^3)`

where subscript s and e refer to the Saturn and Earth respectively.

Now `T_s/T_e = 29.5`[given]; `R_e = 1.50 xx 10^8` km

`(R_s/R_e)^3 = (T_s/T_e)`

`R_s = R_exx [(29.5)^2]^(1/3)`

`= 1.50 xx 10^8 xx (870.25)^"1.3" `km

`= 1.43 xx 10^9 km = 1.43 xx 10^12` m

∴Distance of saturn from Sum  `= 1.43 xx 10^(12)` m

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Solution 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? Concept: Kepler’S Laws.
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