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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? - 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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#### APPEARS IN

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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