As we know that gravitational force of Sun will provide the centripetal force to all planets
so here we will have
[tex]F_g = F_c[/tex]
[tex]\frac{GMm}{r^2} = m\omega^2 r[/tex]
here we know that
[tex]\omega = \frac{2\pi}{T}[/tex]
[tex]\omega = \frac{2\pi}{3.79 \times 10^8}[/tex]
[tex]\omega = 1.66 \times 10^{-8}[/tex]
now from above equation
[tex]\frac{GM}{r^2} = \omega^2 r[/tex]
[tex]\frac{GM}{\omega^2} = r^3[/tex]
[tex]\frac{(6.67 \times 10^{-11})(1.99\times 10^{30})}{(1.66\times 10^{-8})^2} = r^3[/tex]
[tex]r = 7.8 \times 10^{11} m[/tex]
