A physics student might encounter gravity in physics in two different ways: as the acceleration due to gravity on Earth or other celestial bodies, or as the force of attraction between any two objects in the universe. Indeed gravity is one of the most fundamental forces in nature.

Sir Isaac Newton developed laws to describe both. Newton's Second Law (*F _{net} = ma*) applies to any net force acting on an object, including the force of gravity experienced in the locale of any large body, such as a planet. Newton's Law of Universal Gravitation, an inverse square law, explains the gravitational pull or attraction between any two objects.

## Force of Gravity

The gravitational force experienced by an object within a gravitational field is always directed towards the center of the mass that is generating the field, such as the center of the Earth. In the absence of any other forces, it can be described using the Newtonian relationship *F _{net} = ma*, where

*F* is the force of gravity in Newtons (N),

_{net}*m* is mass in kilograms (kg) and

*a* is acceleration due to gravity in m/s

^{2}.

Any objects inside a gravitational field, such as all the rocks on Mars, experience the same *acceleration toward the center of the field* *acting on their masses.* Thus, the only factor that changes the force of gravity felt by different objects on the same planet is their mass: The more mass, the larger the force of gravity and vice versa.

The force of gravity *is* its weight in physics, though colloquially weight is often used differently.

## Acceleration Due to Gravity

Newton's Second Law, *F _{net} = ma*, shows that a

**net force** causes a mass to accelerate. If the net force is from gravity, this acceleration is called acceleration due to gravity; for objects near particular large bodies like planets this acceleration is approximately constant, meaning all objects fall with the same acceleration.

Near the Earth's surface, this constant is given its own special variable: *g*. "Little g," as *g* is often called, always has a constant value of 9.8 m/s^{2}. (The phrase "little g" distinguishes this constant from another important gravitational constant, *G*, or "big G," which applies to the Universal Law of Gravitation.) Any object dropped near the surface of the Earth will fall toward the center of the Earth at an ever-increasing rate, each second going 9.8 m/s faster than the second before.

On Earth, the force of gravity on an object of mass *m* is:

## Example With Gravity

Astronauts reach a distant planet and find it takes eight times as much force to lift objects there than it does on Earth. What is the acceleration due to gravity on this planet?

On this planet the force of gravity is eight times larger. Since the masses of objects are a fundamental property of those objects, they cannot change, that means the value of *g* must be eight times larger as well:

The value of *g* on Earth is 9.8 m/s^{2}, so 8 × 9.8 m/s^{2} = 78.4 m/s^{2}.

## Newton's Universal Law of Gravitation

The second of Newton's laws that apply to understanding gravity in physics resulted from Newton puzzling through another physicist's findings. He was trying to explain why the solar system's planets have elliptical orbits rather than circular orbits, as observed and mathematically described by Johannes Kepler in his set of eponymous laws.

Newton determined that the gravitational attractions between the planets as they got closer and farther from one another were playing into the motion of the planets. These planets were in fact in free fall. He quantified this attraction in his **Universal Law of Gravitation**:

Where *F _{grav }*again is the force of gravity in Newtons (N),

*m* and

_{1}*m* are the masses of the first and second objects, respectively, in kilograms (kg) (for example, the mass of the Earth and the mass of the object near the Earth), and

_{2}*d* is the square of the distance between them in meters (m).

^{2}The variable *G*, called "big G," is the universal gravitational constant. It **has the same value everywhere in the universe**. Newton didn't discover the value of G (Henry Cavendish found it experimentally after Newton's death), but he found the proportionality of force to mass and distance without it.

The equation shows two important relationships:

- The more massive either object is, the larger the attraction. If the moon was suddenly
*twice as massive* as it is now, the force of attraction between the Earth and the moon would *double*. - The closer the objects are, the larger the attraction. Because the masses are related by the distance between them
*squared*, the force of attraction *quadruples* every time the objects are *twice as close*. If the moon was suddenly *half the distance* to Earth as it is now, the force of attraction between the Earth and the moon would be *four times larger.*

Newton's theory is also known as an **inverse square law** because of the second point above. It explains why the gravitational attraction between two objects drops off quickly as they separate, much more quickly than if changing the mass of either or both of them.

## Example with Newton's Universal Law of Gravitation

What is the force of attraction between an 8,000 kg comet that is 70,000 m away from a 200 kg comet?

## Albert Einstein's Theory of General Relativity

Newton did amazing work predicting the motion of objects and quantifying the force of gravity in the 1600s. But roughly 300 years later, another great mind - Albert Einstein - challenged this thinking with a new way and more accurate way of understanding gravity.

According to Einstein, gravity is a distortion of *spacetime*, the fabric of the universe itself. Mass warps space, like a bowling ball creates an indent on a bed sheet, and more massive objects like stars or black holes warp space with effects easily observed in a telescope - the bending of light or a change in motion of objects close to those masses.

Einstein's theory of general relativity famously proved itself by explaining why Mercury, the tiny planet closest to the sun in our solar system, has an orbit with a measurable difference from what is predicted by Newton's Laws.

While general relativity is more accurate in explaining gravity than Newton's Laws, the difference in calculations using either is noticeable for the most part only on "relativistic" scales - looking at extremely massive objects in the cosmos, or a near-light speeds. Therefore Newton's Laws remain useful and relevant today in describing many real-world situations the average human is likely to encounter.

## Gravity is Important

The "universal" part of Newton's Universal Law of Gravitation is not hyperbolic. This law applies to everything in the universe with a mass! Any two particles attract one another, as do any two galaxies. Of course, at large enough distances, the attraction becomes so small as to be effectively zero.

Given how important gravity is to describing *how all matter interacts*, the colloquial English definitions of *gravity* (according to Oxford: "extreme or alarming importance; seriousness") or *gravitas* ("dignity, seriousness or solemnity of manner") take on additional significance. That said, when someone refers to the "gravity of a situation" a physicist might still need clarification: Do they mean in terms of big G or little g?

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About the Author

Amy Dusto is a high school science teacher and a freelance writer. She holds a Bachelor of Arts in Natural Sciences area and a Master of Arts in Science Writing from Johns Hopkins University. She has contributed to Discovery.com, Climate.gov, Science News and Symmetry Magazine, among other outlets.