Answer:
(a) Radius = 4.6 x 10^11 m
(b) speed = 16.96 km/s
Explanation:
Time period, T = 5.4 earth years
mass of sun, M = 1.989 x 10^30 kg
(a) Let the orbital radius is R.
use the formula of period
[tex]T^2 = \frac{4 \pi^2 R^3}{G M}\\\\\left ( 5.4\times 365\times 24\times 3600 \right )^2 = \frac{4\times3.14\times 3.14\times R^3}{6.67\times10^{-11}\times 1.989\times 10^{30}}\\\\R = 4.6\times 10^{11} m[/tex]
(b) Let the speed is v.
[tex]v=\frac{2 \pi\times R}{T}\\\\v=\frac{2\times 3.14\times 4.6\times 10^{11}}{5.4\times 365\times 24\times 3600}\\\\v = 16963.6 m/s =16.96 km/s[/tex]
