### What multiple of distance between the centre of the earth and that of the moon is the distance between the centre of the earth and the geostationary satelite which always stays above the fixed location on the equator ? take the cycle of revolution of the moomn around the earth to be 27 days ?

According to Kepler’s third law of planetary motion

T

^{2}=R^{3}( For geo stationary satellite)-------1
T’

^{2}=R’^{3}( For Moon)----------------------------2
Dividing eq(2) by eq(1), we get

T’

^{2 }/ T^{2}=R’^{3}/ R^{3}
Since T’=27 T

Then we can write as

27 ~~T~~ /~~T~~= R’

^{2}

^{2}

^{3}/ R^{3}
Or

R’

^{3}=27 R^{3}
Or

R’=3 R

or

R= 1/3 R'

so the distance between the centre of the earth and the geostationary satellite which always stays above the fixed location on the equator is 1/3 times distance between the centre of the earth and that of the moon .

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