Question

According to Kepler's Third Law, a solar-system planet that has an orbital radius of 4 AU would have an orbital period of about _________ year(s).

Answer 1

Orbital period, T = 1.00074 years

Step-by-step explanation:

It is given that,

Orbital radius of a solar system planet,
`r=4\ AU=1.496* 10^(11)\ m`

The orbital period of the planet can be calculated using third law of Kepler's. It is as follows :

`T^2=(4\pi^2)/(GM)r^3`

M is the mass of the sun

`T^2=(4\pi^2)/(6.67* 10^(-11)* 1.989* 10^(30))* (1.496* 10^(11))^3`

`T^2=\sqrt{9.96* 10^(14)}\ s`

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.