How To Calculate The Mass Of The Earth

Here is a simple procedure to calculate the mass of the Earth:

• Calculate the radius of the Earth as shown here.
• Calculate the time it takes any rock to fall from a known height.
• Calculate M, the mass of the Earth, using M = 2R²h / (Gt²) where R is the radius of the Earth, h is the height, t is the elapsed time and G is the gravitational constant.

The gravitational force on a rock of mass m, on or near the surface of the Earth, is GMm / R² by Newton's Law Of Gravitation. It is also ma, where a is the acceleration, by Newton's Second Law. The kinematic equations here imply a = 2h / t². Combining these equations gives M = 2R²h / (Gt²).