Answer :
Answer:
Orbital period, T = 1.00074 years
Explanation:
It is given that,
Orbital radius of a solar system planet, [tex]r=4\ AU=1.496\times 10^{11}\ m[/tex]
The orbital period of the planet can be calculated using third law of Kepler's. It is as follows :
[tex]T^2=\dfrac{4\pi^2}{GM}r^3[/tex]
M is the mass of the sun
[tex]T^2=\dfrac{4\pi^2}{6.67\times 10^{-11}\times 1.989\times 10^{30}}\times (1.496\times 10^{11})^3[/tex]
[tex]T^2=\sqrt{9.96\times 10^{14}}\ s[/tex]
T = 31559467.6761 s
T = 1.00074 years
So, a solar-system planet that has an orbital radius of 4 AU would have an orbital period of about 1.00074 years.