

MASS OF EARTH


Consider a body of mass ‘m’ placed on the surface of the earth. Let the mass of the earth is ‘M_{e}’ and radius of the earth is ‘R_{e}’ . Neglecting the radius of body if compared with that of the earth.  
Gravitational force of attraction between earth and body is  
F = G m M_{e}/ R_{e}^{2 }^{……..(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 M_{e}/ R_{e}^{2 }


But W = mg  
mg = G m M_{e}/ R_{e}^{2}


or
g = G M_{e}/R_{e}^{2} 

or
M_{e} = g x R_{e}^{2}/G 

From astronomical data: g= 9.8 m/s^{2} R_{e }= 6.38 x 10^{6} m G = 6.67 x 10^{11} Nm^{2}/kg^{2} Putting these values in the above equation. 

M_{e} = 9.8 (6.38 x 10^{6})^{2}/6.67 x 10^{11}
or 
