Comprehensive Question 2: Determine the mass of Earth by applying law of gravitation.
Suppose a body of mass mo is placed on the surface of earth. If rE is the radius of the earth, then the distance between the centers of earth and the object is approximately rE. 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 = mog. Therefore,
Cancel mo on both sides,
Simplify for the mass of the earth, mE.
Now we already know that, G = 6.67 × 10-11 N m2 kg-2, rE= 6.4 × 106 m and 9.8 ms-2. Put these values in the above equation,