Two satelites of a planet have period 32 days and 256 days. If the radius of orbit of former is R, find the orbital radius of the latter.

Explanation

As `T^(2) prop R^(3)` or `R prop T^(2//3)`
`:. (R_(2))/(R_(1)) = ((r_(2))/(r_(1)))^(3//2)` or `R_(2) = R ((256)/(32))^(3//2)` = 4R`