Answer:
11.9 years
Explanation:
We can find the orbital period by using Kepler's third law, which states that the ratio between the square of the orbital period and the cube of the average distance of a planet from the Sun is constant for every planet orbiting aroudn the Sun:
[tex]\frac{T^2}{r^3}=const.[/tex]
Using the Earth as reference, we can re-write the law as
[tex]\frac{T_e^2}{r_e^2}=\frac{T_j^2}{r_j^3}[/tex]
where
Te = 1 year is the orbital period of the Earth
re = 1 AU is the average distance of the Earth from the Sun
Tj = ? is the orbital period of Jupiter
rj = 5.20 AU is the average distance of Jupiter from the Sun
Substituting the numbers and re-arranging the equation, we find:
[tex]T_j=\sqrt{\frac{T_e^2 r_j^3}{T_j^2}}=\sqrt{\frac{(1 y)^2 (5.2 AU)^3}{(1 AU)^3}}=11.9 y[/tex]
