Answer:
Explanation:
Third Kepler's law states that the ratio of the squares of the orbital periods of the planets and satellites to the cubes of their average distances from the center of the orbit is constant.
In mathematical terms:
[tex]\dfrac{T_1^2}{R_1^3}=\dfrac{T_2^2}{R_2^3}[/tex]
Substitute T₁ = 4week, R₁ = D, R₂ = 2D, and solve for T₂:
[tex]\dfrac{(4week)^2}{D^3}=\dfrac{T_2^2}{(2D)^3}[/tex]
[tex]T_2=8\times 16week^2 =128week^2\\\\T_2=\sqrt{128week^2}=11.3week\approx 11week[/tex]
