Answer:
Explanation:
Given
Distance between Pluto and sun is 39.1 times more than the distance between earth and sun
According to Kepler's Law
[tex]T^2=kR^3[/tex]
where k=constant
T=time period
R=Radius of orbit
Suppose [tex]R_1[/tex] is the radius of orbit of earth and sun
so Distance between Pluto and sun is [tex]R_2=39.1\cdot R_1[/tex]
[tex]T_1[/tex] and [tex]T_2[/tex] is the time period corresponding to [tex]R_1[/tex] and R_2[/tex]
[tex](T_1)^2=k(R_1)^3---1[/tex]
[tex](T_2)^2=k(R_2)^3---2[/tex]
divide 1 and 2
[tex](\frac{365}{T_2})^2=(\frac{R_1}{39.1})^3[/tex]
[tex]T_2^2=365^2\times 39.1^3[/tex]
[tex]T_2=89239.67\ Earth\ days[/tex]
