Answer:
16,400 miles
Explanation:
Kepler's third law states that the ratio between the cube of the distance of a satellite from its planet and the square of its orbital period is constant for all the satellite orbiting around that planet:
[tex]\frac{d^3}{T^2}=const.[/tex]
where d is the distance of the satellite from the planet and T is the orbital period.
By applying this law to the Moon and the other satellite of this problem, we can write
[tex]\frac{d_M^3}{T_M^2}=\frac{d_S^3}{T_S^2}[/tex]
where [tex]d_M=240,000 miles[/tex] is the distance of the Moon from the Earth, [tex]T_M=28 d[/tex] is its orbital period, [tex]T_S=12 h=0.5 d[/tex] is the orbital period of the satellite. Re-arranging the equation and replacing the numbers, we can find dS, the distance of the satellite from the Earth:
[tex]d_S=\sqrt[3]{\frac{d_M^3 T_S^2}{T_M^2}}= \sqrt[3]{\frac{(240,000)^3 (0.5)^2}{(28)^2}}=16,400 miles[/tex]