Question

the time period of earth is taken as T and its distance from sun as R .what will be the distance of a certain planet from sun whoes time period is 64 times that of earth

Answer 1

T^2 = k. R^3 .. 1.

T'2 = k. R^3
= (64T)^2 = k. R'^3 .. 2.

Divide 2. By 1.

= (64T)^2 / T^2 = k. R'^3 / k. R^3

= 64*64 T^2 / T^2 = R'^3 / R^3

= 64*64 = R'^3 / R^3

= under cube root 64*64 = R' / R

= 4*4 = R'/ R

= 16= R'/ R

= 16R = R'.

Hope it's helpful to u.