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If the Moon were twice the distance from Earth than it currently is, the amount of time it would take to go around Earth would be roughly (the current orbital period of the Moon is four weeks)
A. 8 weeks
B. 11 weeks
C. 6 weeks
D. 88 weeks

Respuesta :

Edufirst

Answer:

  • Option D. 11 weeks

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]

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