Question

how to calculate the mass of earth

Answer 1

Newton’s equation for gravity is F = m1 * m2 * G / r^2

Once you know the mass of a test object, say a 1 kg mass, and the distance to the center of the Earth you have everything you need.

(It is straightforward to prove that for r > the radius of earth, all the mass of earth acts like it was concentrated at the center)

So in the above situation, at sea level at the north pole, we have

r = 6.356E6 m , and

G= 6.67408E-11 m^3 kg^-1 s^-2

F = 9.832 N = 9.832 kg m s^-2

which gives the mass of the earth as 5.951E24 kg

which isn’t too bad, since the internet says 5.972E24 kg

I chose the north pole for this experiment because there is no correction for centrifugal force.