Why is the weight of an object on the moon is 1/6 its weight on the earth prove by equation?
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Show that weight of an object on the moon is 1/6 of its weight on the earth. [Given : mass of earth = 5.98 x 1024 kg, mass of moon = 7.36 x 1022 kg, radius of earth = 6.37 x 106 m, radius of moon = 1.74 x 106 m]
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F = G M m / R^2 gravitational attraction between masses M & m
a = F / m = G M / R^2 acceleration of mass m due to mass M
aE / aM = (ME / Mm) * (Rm / RE)^2 dividing equations for earth and moon
The mass of the moon Mm = .0123 ME mass of the earth
Radius of earth = 3963 mi
Radius of moon = 1080n mi
aE / aM = 1 / .0123 * (1080 / 3963)^2 = 6.04
acceleration due to gravity of earth is 6.04 times that of the moon
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