Suppose a body of mass m_o is placed on the surface of earth. If r_E is the radius of the earth, then the distance between the centers of earth and the object is approximately r_E. According to Newton’s law of universal gravitation, the force with which earth attracts the object is

However, the earth attracts the body with a force equal to the weight W of the object = m_og. Therefore,

Cancel m_o on both sides,

Simplify for the mass of the earth, m_E.

Now we already know that, G = 6.67 × 10^-11 N m² kg^-2, r_E= 6.4 × 10⁶ m and 9.8 ms^-2. Put these values in the above equation,