The period of the moon revolving under the gravitational force of the earth is $27.3$ days. Find the distance of the moon from the center of the earth if the mass of the earth is $5.97 \;*\;10^{24}kg$.

Given,

Time $(T) = 27.3$ days = $27.3 \; * \; 24 \; * \; 60 \; * \; 60  = 2358720 \; Sec$

Mass of earth $(M) = 5.97 \; *\; 10^{24}\; kg$

Height of the Moon from the center of the earth $(h) = \;?$

We know that,

$h =$ $\left ( \frac{T^2 \; * \; R^2\; * \;g}{4\; \pi^2} \right )^{1/3}$ $- \;R$

$h =$ $\left ( \frac{(2358720)^2 \; * \; {6400000}^2\; * \; 9.8}{4\; \pi^2} \right )^{1/3}$ $- \; 6400000 = 3.77 * 10^8 \; m$

∴ Height of the Moon from the center of the earth $(h) = \;3.77 * 10^8 \; m$

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