Suppose the gravitational force varies inversely as the nth power of distance. Then the time period of a planet in circular orbit of radius R around the sun will be proportional to

F∝1Rn----(1) ⇒Gravitational force provides centripetal force⇒F=mω2R---(2) From equations (1) and(2) we get ⇒mω2R∝1Rn⇒m4π2T2R∝1Rn∵ω=2πT ⇒1T2R∝1Rn∵m,4,π are constants ⇒RnR∝T2⇒T2∝Rn+1  ∴T∝Rn+12