Why Could Newton Not Calculate the Gravitational Constant G?

Isaac Newton, one of the greatest minds in the field of physics, formulated his law of universal gravitation in the late 17th century. However, he did not calculate the gravitational constant G due to several reasons. This article explores the historical context, the limitations of scientific knowledge, and the measurement techniques at the time.

Lack of Measurement Techniques

The technology and methods required to accurately measure gravitational forces and masses in Newton's time (1642-1727) were not sufficiently developed. The measurements of mass, distance, and the force of gravity were rudimentary compared to modern standards. For example, Newton described the gravitational force between two objects as proportional to their masses and inversely proportional to the distance between them. He did not use an equation with a constant of proportionality, as the concept of a universal constant like G was not fully understood at the time. His formulation was based on his observations and mathematical reasoning rather than empirical determination.

Understanding of Gravity

Newton's law of gravitation is expressed as:

F G frac{m_1 m_2}{r^2}

Where:

F is the gravitational force m_1 and m_2 are the masses r is the distance between their centers G is the gravitational constant

At the time, the concept of a universal constant like G was not fully understood. Newton based his formulation on his observations and mathematical reasoning rather than empirical determination of G.

Historical Context

The gravitational constant G was not introduced until the 18th century, long after Newton's death. It was first measured by Henry Cavendish in 1798 using a torsion balance, which allowed for much more precise measurements of gravitational attraction between masses. Cavendish's experiment marked a significant step forward in the understanding of gravity and the measurement of G.

In summary, Newton's inability to calculate G was due to the limitations of scientific knowledge, measurement techniques, and the historical context of his work. Newton's observations and mathematical reasoning laid the foundation for our modern understanding of gravity, but the precise determination of G required advancements in scientific instruments and techniques.