As per Kepler's third law we know that
[tex]\frac{T_1^2}{T_2^2} = \frac{R_1^3}{R_2^3}[/tex]
now here we know that
[tex]T_1 [/tex] = year of Neptune
[tex]T_2[/tex] = year of Earth
[tex]R_1[/tex] = distance of Neptune from Sun
[tex]R_2[/tex] = Distance of Earth from Sun
so now we will have
[tex]\frac{T_1^2}{1} = \frac{(4.5 \times 10^{12})^3}{(1.5 \times 10^11)^3}[/tex]
[tex]T_1^2 = 27000[/tex]
[tex]T_1 = 164.3 years[/tex]
so length of year of Neptune is 164.3 years
