Moon is the natural satellite of Earth a f it takes 37 days to go once around its orbit. Calculate the distance of the Moon from the surface of the Earth assuming the orbit of the Moon as circular.

Explanation

Time Period T= 27 days = `27 xx 86400 ` sec
Radius of the Earth `R_(E ) = 6.4 xx10^(6)` m
Mass of the Earth `M_(E ) = 6.02 xx10^(24)` kg
Gravitational constant `G = 6.67 xx10^(-11) "Nm"^(2) kg^(-2)`
The distance of the Moon from the surface of The Earth is
`T_(2) = c (R_(E ) +h)^(2) , T^(2//3) = c^(1//3) (R_(E)+h)`
`((T^(2))/c)^(1//3) = (R_(E )+h)`
`((T^(2)GM_(E ))/(4pi^(2))) = (R_(E)+h) , c = (4pi^(2))/(GM_(E ))`
` h = ((T^(2)GM_(E ))/(4pi^(2)))^(1/3) - R_(E )`
` = [((27xx86400)^(2)xx6.67 xx10^(11) xx6.02 xx10^(24))/(4xx(3.14)^(2))]^(1/3) - (6.4 xx10^(6))`
` = 380476187 - 6400000 = 3.74 xx10^(8)` m
` h = 3.74 xx10^(5)` km