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 ?
Given: The distance of the earth from the sun is 1.5 × 10 8 km and the time period of Saturn is 29.5 times of the time period of the earth.
From Kepler’s third law, the square of time period is proportional to the cube of the orbital radius.
T 2 ∝ r 3
Thus, we can write,
r S 3 r E 3 = T S 2 T E 2
Where, r E is the orbital radius of the earth, r S is the orbital radius of the Saturn, T E is the time period of earth and T S is the time period of the Saturn.
By substituting the given values in the above equation, we get
r S 3 ( 1.5 × 10 11 ) 3 = ( 29.5 T E ) 2 T E 2 r S = 1.5 × 10 11 × ( 29.5 ) 2 3 = 1.5 × 10 11 × 9.55 = 1.43 × 10 12 m
Thus, the distance between Saturn and the sun is 1.43 × 10 12 m .
Given: The distance of the earth from the sun is
From Kepler’s third law, the square of time period is proportional to the cube of the orbital radius.
Thus, we can write,
Where,
By substituting the given values in the above equation, we get
Thus, the distance between Saturn and the sun is
