Gravitational Constant

The size of $G$ is what decides how strong gravity actually is between any two given masses -- and it is a very, very small number, which is exactly why gravity between two everyday objects (say, two people standing near each other) is completely unnoticeable, while gravity between planet-sized masses is enormous.

Deriving $g$ from the law of gravitation. Consider a mass $m$ sitting on the Earth's surface. The gravitational force on it from the Earth (mass $M_E$, radius $R_E$) is

Equating this to Newton's second law, $F = mg$, and cancelling $m$ gives

This is a beautifully simple result: the acceleration due to gravity does not depend on the falling object's own mass at all -- only on the mass and radius of the Earth. This is exactly the empirical fact Galileo had already discovered 400 years earlier by rolling and dropping different objects. …