DETERMINATION OF MASS OF EARTH

Newton, Galileo, Henry Cavendish, and Eratosthenes contributed a lot in this calculation

The mass of the Earth may be determined using Newton's law of gravitation. Newton's law of gravity formulates the gravitational force that two masses exert on each other and is given by

F = GmM/r²

                                                           where,  M and m are the masses  

                                                                        r is the separation between them

                                                                        G is universal gravitational constant                                      

                                                                                  (6.67 × 10⁻¹¹ m³/(kg sec²))

If we assumed that M is the mass of the Earth, and m is the mass of an object on the surface of the Earth, we can solve for M by equating Newton's Law of Gravity with his second law of motion

F = ma

We have:

F = GmM/r² = ma → GM/r² = a

Solving for M, the mass of the Earth,

a = 9.8 m/s²,
r = 6.38 × 10⁶ m, and
G = 6.67 × 10⁻¹¹ m³/(kg sec²)

we obtain:

M = ar²/G = 5.98 × 10²⁴ kg.