Question

calculate the period of revolution of neptune around sun given that diameter of its orbit is 30 times the diameter of earths orbit around the sun,both orbits assumed to be circular.

Answer 1

Kepler's Third law states that
T²∝R³
Let T be time taken by neptune and t be time taken by Earth.
Let R be time taken by Neptune and r be time taken by Earth.
(T/t)²∝(R/r)³
(T/t)²∝(30r/r)³
(T/t)²∝30³
(T/t)²∝27000
T²=27000×365²
T²=√(27000×365²)
T=√27000×365
T=59975 days
T=164 Years