Newton, Galileo, Henry Cavendish, and Eratosthenes contributed to this amazing calculation.
* This calculation is done using Newton's Law of Gravity, which formulates the attractive force (gravitational force) that two masses exert on each other:
In Newton's equation, F is the gravitational force, G is a constant of proportionality, M and m are the two masses exerting the forces, and r is the distance between the two objects.
* G was calculated by Henry Cavendish in 1798, and was determined to be 6.67 x 10-11 m3/(kg sec2).
* Also needed is Newton's second law of motion, F=ma, where F is the force applied to an object, m is the mass of the object, and a is its acceleration due to the force.
* Galileo determined that the acceleration due to the force of gravity of Earth was a constant equal to 9.8 m/sec2 near the surface of the Earth.
* Lastly, you need to know the radius of the Earth; this was first calculated by the Greek Eratosthenes thousands of years ago (by comparing shadows in wells during the summer solstice about 230 B.C.).
1. F = GmM/r2 = ma, where F is the gravitational force, G is the gravitational constant, M is the mass of the Earth, r is the radius of the Earth, and m is the mass of another object (near the surface of the Earth).
2. GM/r2= a (The m's canceled out.) Now solve for M, the mass of the Earth.
3. M = ar2/G, where a = 9.8m/sec2, r = 6.4 x 106m, and G = 6.67 x 10-11m3/(kg sec2).
4. M = 9.8 x (6.4 x 106)2/(6.67 x 10-11) = 6.0 x 1024 kg