MASS OF EARTH



MASS OF EARTH
MASS OF EARTH
Consider a body of mass ‘m’ placed on the surface of the earth. Let the mass of the earth is ‘Me’ and radius of the earth is ‘Re’ . Neglecting the radius of body if compared with that of the earth.
determining mass of earth 
Gravitational force of attraction between earth and body is
F = G m Me/ Re2 ……..(1)
We know that the force of attraction of the earth on a body is equal to weight the weight of body.
i.e
F = W ……………………(2)
therefore
Comparing (1) and (2), we get,
W = G m Me/ Re2
But W = mg
mg = G m Me/ Re2
or
g = G Me/Re2
or
Me = g x Re2/G
From astronomical data:
g= 9.8 m/s2
Re = 6.38 x 106 m
G = 6.67 x 10-11 N-m2/kg2
Putting these values in the above equation.
Me = 9.8 (6.38 x 106)2/6.67 x 10-11
or

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