Investigating the role of 'G' in Newton's Universal Law of Gravitation

Here on our pale blue dot, which we call home, gravity is a constant force that we feel every moment of our lives. We're much more aware of it thanks to Newton's Universal Law of Gravitation.

"Gravity is the force that causes diffuse matter in the space between stars to gradually collapse and form new stars that undergo hydrogen fusion," explains University of Connecticut astrophysicist Cara Battersby. "It is the force that holds galaxies together and ensures our Earth orbits the Sun every year."

Gravity played a pivotal role in the well-known "apple" story of Sir Isaac Newton. One day in Lincolnshire, England, Newton allegedly observed an apple fall from a tree. Over time, he shared this simple event with people like Voltaire and biographer William Stukeley, claiming it sparked his groundbreaking insights into the nature of gravity.

This laid the foundation for Newton's Law of Universal Gravitation, which prominently features the universal gravitational constant, often referred to as 'Big G' or simply 'G.' In this article, we'll delve into Newton's law, examine the challenges posed by Albert Einstein's theory, and explore the concept of gravitational force.

The Origins of Newton's Law of Universal Gravitation

A lot has been speculated about the infamous apple in Newton's story. While the celebrated physicist shared this tale with Stukeley many years after it supposedly happened, many scholars question its authenticity. Regardless, the true significance of Newton's universal law isn't about whether the apple struck him, but rather the force that pulled it straight down.

As Newton's assistant John Conduitt noted:

The Universal Gravitation Constant: The Equation

Before diving into Big G, let's first step back and break down Newton's law of universal gravitation. This equation continues to have profound consequences on how we understand the gravitational field that holds us firmly to the Earth's surface.

As Katie Mack — an astrophysicist and author of "The End of Everything (Astrophysically Speaking)" — mentioned in an email, gravity is "the force by which objects with mass are attracted to one another." Newton was the first to establish that objects exert gravitational pulls on each other.

Newton recognized that the strength of gravitational attraction between any two objects depends on (a) their masses and (b) the distance between them. The inverse square law is central here, stating that gravitational force is inversely proportional to the distance separating objects. This dynamic is captured mathematically in Newton's Law of Universal Gravitation.

Here is the key formula for understanding the concept of gravity:

In this equation, "F" represents the gravitational force; "m1" is the mass of the first object, while "m2" stands for the mass of the second object; "r2" signifies the square of the distance between the centers of mass of both objects. And as for "G", that's the gravitational constant, also known as Big G.

The Exact Value of Gravitational Force

"Whether dealing with simple objects like bowling balls or large celestial bodies like planets, the gravitational force between them is influenced by their masses, the distance separating them, and the gravitational constant G," explains Mack. Thanks to the work of Henry Cavendish in the 1790s, we now know that the value of G is approximately 6.67 x 10^-11 Newtons (m^2/kg^2).

In this case, "Newtons" refers to a unit of force. One Newton is the amount of force required to accelerate an object with a mass of 2.2 pounds (1 kilogram) at 3.28 feet (1 meter) per second. Like Anders Celsius and Charles F. Richter, Sir Isaac Newton is one of the renowned scientists honored with a unit named after him.

Newton vs. Einstein on Gravitational Force

There is an important nuance here. The Law of Universal Gravitation isn't as universally applicable as its name suggests. As Battersby explains, "Newton's classical view of gravity," formulated in the 17th century, provides a reliable approximation of the laws of physics for most of the universe, especially on Earth.

"However," she explains, "this theory has been replaced by Einstein's Theory of General Relativity, which builds upon 'Newtonian Gravity' and introduces the idea that matter actually curves space-time itself (similar to how a heavy ball creates a dent on a rubber sheet)."

This brings us to black holes. These incredibly dense objects can be over a million times more massive than our sun and influence gravity in ways that Newton's laws can't fully explain. General Relativity has proven to offer more precise predictions about their behavior.

"You need to account for the fact that Newton's model of gravity doesn't perfectly apply to extreme gravity or extremely fast motion," says Mack. "In such situations, we must switch to Einstein's theory of gravity... But outside of these extreme circumstances, the equation that Isaac Newton developed in 1686 for what he called 'the Law of Universal Gravitation' is truly universal."

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