SOLUTION: Find the mass of Earth by equating the weight of an object near the surface of Earth (Hint: Use Newtons' Second Law of Motion) to the gravitational force found from Newton's Law of

For the given problem, Newton's Law of Gravitation says


 = W = m*g    (1)


where M is the Earth mass (in kilograms), m is the mass of the body at the Earth surface, 

W = mg is the weight of the body, g is the free fall acceleration g = 9.81 m/s^2,

R is the Earth radius = 6.37*10^6 m,

G is universal gravitational constant = 6.67408 × 10-11 m3/(kg*s^2).


In (1), cancel the factor "m" in both sides and express M


M = .


Substitute the given data and calculate.  You will get

M = 5.97*10^24 kg  for the Earth mass.


Wikipedia ( https://en.wikipedia.org/wiki/Earth_mass ) gives the same value.