Archive for September 29th, 2014

Newton’s Law of Gravitation and the Universal Gravitational Constant

Monday, September 29th, 2014

      Last time we introduced the term acceleration of gravity, a physical phenomenon posited by Sir Isaac Newton in his book Philosophia Naturalis Principia Mathematica.   Newton’s Law of Gravitation is also presented in this book.   It provides the basis for his mathematical formula to calculate the acceleration of gravity, g, for any heavenly body in the universe.

      Newton’s formula to compute the acceleration of gravity is,

g = (G × M) ÷ R2

where, g is the acceleration of gravity, M the mass of the heavenly body, R the radius, and G the universal gravitational constant.

      As for the values of the variables in his equation, Newton theorized that G would be a constant, holding the same numerical value throughout the universe.   This universal gravitational constant would be the glue that bound together M, the mass of the object being measured, and R, its radius, and render Newton’s formula a workable equation.   Without these three values, scientists would be unable to determine the acceleration of gravity rate, g, for the heavenly body under study, and Newton’s equation would be useless, relegated to the depths of pure mathematical theory.

      In fact, the value for G wasn’t determined until 1796.   At that time Henry Cavendish derived its value as an adjunct to calculating the mass of Earth.   In the end he was able to arrive at values for Earth’s mass, M, as well as its radius, R.   He also came up with the much needed value for G, the universal gravitational constant.   He was able to accomplish so much by building upon the work of other scientists before him.

      We’ll see who those earlier scientists were and how they contributed to the world’s discoveries concerning gravity next time.

Cavendish and the Universal Gravitation Constant