Question

A saturn year is 29.5 times the earth year. How far is saturn from the sun(m) if the earth is 1.5 x 108 km away from the sun ?

Answer 1

Answer:

Solution : Here, `T_(s) = 29.5 T_(e) , R_(e) = 1.5 xx 10^(8) km, R_(s) = ?`<br> Using the relation, `(T_(s)^(2))/(T_(s)^(3)) = (T_(e)^(2))/(R_(e)^(3)) `or `R_(s) = R_(e) ((T_(s))/(T_(e)))^(2//3) = 1.5 xx 10^(8) ((29.5 T_(e))/(T_(e)))^(2//3) = 1.43 xx 10^(9) km`

Answer 2

WE KNOW THAT

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

SOLUTION

» 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)

† 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.