What constant is used in Newton's Law of Universal Gravitation?

Newton's Law of Universal Gravitation describes the gravitational force between two masses and is expressed by the formula ( F = G \frac{m_1 m_2}{r^2} ), where ( F ) is the gravitational force, ( m_1 ) and ( m_2 ) are the two masses involved, ( r ) is the distance between the centers of the two masses, and ( G ) is the gravitational constant. This constant is crucial because it quantifies the strength of the gravitational interaction in the universe. Without this constant, the equation would not yield meaningful or universally applicable results for the force of gravity.

The gravitational constant, typically denoted as ( G ), has a value of approximately ( 6.674 \times 10^{-11} , \text{N m}^2/\text{kg}^2 ), reflecting the weakness of gravity compared to other fundamental forces. Its presence in the formula allows scientists to calculate the gravitational force between masses accurately, regardless of their size or distance apart, provided the values for mass and distance are known. This is a fundamental aspect of both classical and modern physics.