The same Sir Isaac Newton who gave us his Three Laws of Motion also developed the Law of Universal Gravitation,
Newton's Law of Universal Gravitation was initially accepted -- and is accepted today -- because it predicts Kepler's Laws of Planetary Motion.
This ability to predict measurable results is the heart and soul of modern Science.
We already know that the weight of an object is the mass of an object multiplied by the acceleration due to gravity, g = 9.8 m/s/s. This means
From this we can solve for M, the mass of the Earth,
"Weighing the Earth"
This is an inverse square force.
What does that mean?
The surface of a sphere increases as the square of the radius of the sphere.
(C) 2005, Doug Davis; all rights reserved