Question

let the period of revolution of planet at a distance R from a star be T. prove that if it was at distance of 2R from the star, it's period of revolution will be √8T​

Answer 1

According to kepler's 3rd law

T^2 = R^3

T1 = T

T2 = 8^1/2 T

R1 = R

R2 = 2R

(T1/T2)^2 = (R1/R2)^3

(1/8^1/2)^2 = (1/2)^3

1/8 = 1/8

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Answer 2

Answer:

Here's your answer...

Explanation:

Distance from Sun = R

Time of rotation = T

New distance = 2R

New time = Tn = ?

T^2 / R^3 = k......(1)

Tn^2 / (2R)^3 = k.....(2)

From (1) and (2),

Tn^2 / 8R^3 = T^2 / R^3

Tn^2/ 8 = T^2

Tn^2 = 8T^2

Tn = √8T

Hence proved.

Hope it helps you...