What Is Newton's Law of Universal Gravitation?

Newton’s law of universal gravitation states that two bodies in space pull on each other with a force proportional to their masses and the distance between them. For large objects orbiting one another—the moon and Earth, for example—this means that they actually exert noticeable force on one another. It may seem like the moon is orbiting a relatively static Earth, but actually the moon and Earth are rotating around a third point between them. That point is called the barycenter.

Per the terms of Newton’s law, every object in the universe attracts every other object with a measurable force (however slight). The force is:

• Directly proportional to the product of two objects’ masses
• Inversely proportional to the square of the distance between the objects

This principle can be expressed in the equation: F = G mM / r^2

Within this equation:

• F is the magnitude of force
• m is the mass of the smaller object
• M is the mass of the larger object
• r is the distance between the objects’ centers of mass
• G is the gravitational constant

Sir Isaac Newton was the first scientist to specifically articulate the concept of gravitational force, and his writings detailed how gravitational attraction affects both falling objects and the motions of celestial bodies.

However, Newton piggybacked on the observations and theories of other mathematicians and physicists, including: Max Kepler; Robert Hooke; Edmund Halley; and Christopher Wren.

Over 100 years after Newton published his work, the English physicist Henry Cavendish articulated the concept of the gravitational constant G. Among other things, Cavendish’s work helped establish an accurate value for the total mass of Earth. (When using Newton’s equation to measure the gravitational effects of Earth on an Earthbound object, M would represent Earth’s mass and m would represent the mass of the Earthbound object.)

The law of universal gravitation applies to many topics within modern-day science. These topics include:

• Tides (created by the moon’s gravitational pull on Earth)
• The interaction between two earthbound objects
• The interaction between one earthbound object and the Earth itself
• Astrophysics, including how celestial bodies exert force upon one another and upon much smaller objects, such as spacecraft.

For a spaceship orbiting or leaving Earth, since the mass of the spaceship relative to Earth is tiny, the ship doesn’t exert much force on Earth. The primary implication for spaceflight is that the force of gravity on the spaceship decreases as the distance between the spaceship and Earth increases. In fact, the force decreases rapidly, as it’s divided by the distance squared.

Learn more about space exploration in former astronaut Chris Hadfield’s MasterClass.