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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).

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Answer:

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.

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