Question

Let the period of revolution of a planet at a distance 'R' from a star be 'T'
Prove that if it was at a distance of '2R'
from the star its period of revolution will 'under root 8 ,T.
pls answer if u know the correct answer.............

Answer 1

You Can try doing this 8 x 2r=? or 2rx 8= you can do it any way And it will have to be like this when you get the answer T= ? with r

Answer 2

According to the Kepler’s third law:

                   T^2=R^3

where T is the time period of revolution and R is the distance of the planet from the star.

Therefore,

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

Let the time period of revolution of a planet at a distance 2R from star be t

so, R2 = 2R and T2 = t

   and R1 = R and T1 = T

T^2 / R^3 = t^2 / (2R)^3

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

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

T^2 / t^2 = 1/8

t^2 = 8 T^2

t = under root 8 * T