The distance of the dwarf planet pluto from the sun is 40 times the average distance of the earth from the sun. How much time does pluto take to revolve around the sun ?

Explanation

Let `T_1` =time period of pluto,
`T_2`=time period of the earth,
`r_1`= distance of Pluto from the sun and
`r_2`= distance of the earth from the sun
From Kepler.s law,
`(T_1^2)/(T_2^2)=(r_1^3)/(r_2^3)or, (T_1^2)/((1)^2)=((40r_2)/(r_2))^3=40^3`
`therefore T_1^2=40^3 or, T_1=253y` (approx.).