Mass of Earth (by pak physics notes)

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)

thereforeComparing (1) and (2), we get,

W = G m M_e/ R_e²               

                But W = mg

mg = G m M_e/ R_e²

or
g = G M_e/R_e²

or
M_e = g x R_e²/G

From astronomical data:

                                                          g= 9.8 m/s²
                                                      R_e = 6.38 x 10⁶ m
                                                G = 6.67 x 10^-11 N-m²/kg²
                                    Putting these values in the above equation.

M_e = 9.8 (6.38 x 10⁶)²/6.67 x 10^-11
or

  M_e = 6x10²⁴ Kg

(www.pak-physicsnotes.blogspot.com)

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