Question

The distance of two planet from the sun are in the ratio 10:1 meter. find the ratio of speed of two planet​. please send answer with whole solution.

Answer 1

Given data : The distance of two planet from the sun are in the ratio 10:1 meter.

Solution : To find out the ratio of speed of revolution of two planet;

Let, the distance between two planets be R and R' respectively.

Hence,

➜ R/R' = 10/1

Now, by Kepler's Third Law

The Law states that; the square of the planet's period

is proportional to cube of it's mean distance from the sun. ∴ T² ∝ R²

Hence,

➜ [T/T']² = [R/R']³

Here we know that the period of revolution of the planet's is T and T' respectively.

Now,

➜ [T/T']² = [R/R']³

➜ [T/T']² = [10/1]³

➜ [T/T']² = [10³/1³]

➜ [T/T']² = [10³/1]

➜ T/T' = √[10³/1]

➜ T/T' = √(10³)/√1

➜ T/T' = (10√10)/1

Hence, T : T' = 10√10 : 1

Answer : Hence, the ratio of speed of revolution of two planet is T : T' = 10√10 : 1.