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 Ā center of the orbit is constant.
In mathematical terms:
Ā Ā Ā Ā Ā Ā [tex]\dfrac{T_1^2}{R_1^3}=\dfrac{T_2^2}{R_2^3}[/tex]
Substitute Tā = 4week, Rā = D, Rā = 2D, and solve for Tā:
Ā Ā Ā Ā Ā [tex]\dfrac{(4week)^2}{D^3}=\dfrac{T_2^2}{(2D)^3}[/tex]
Ā Ā Ā Ā Ā [tex]T_2=8\times 16week^2 =128week^2\\\\T_2=\sqrt{128week^2}=11.3week\approx 11week[/tex]
