- International edition
- Australia edition
- Europe edition

## Newton's Universal Law of Gravitation

N ewton's equation first appeared in the Philosophiæ Naturalis Principia Mathematica , July 1687. It describes why that apple fell from that tree in that orchard in Lincolnshire. Whether or not that apple actually landed on Isaac Newton's head, as some stories would have it, this equation describes why you stay rooted to the ground, what locks the Earth in orbit around the sun and was used by Nasa engineers to send men to the moon.

It encapsulates the idea that all the particles of matter in the universe attract each other through the force of gravity – Newton's law tells us how strong that attraction is. The equation says that the force (F) between two objects is proportional to the product of their masses (m 1 and m 2 ), divided by the square of the distance between them. The remaining term in the equation, G, is the gravitational constant, which has to be measured by experiment and, as of 2007, US scientists have measured it at 6.693 × 10 −11 cubic metres per kilogram second squared.

Newton came to the formula after studying the centuries of measurements from astronomers before him. Stargazers had spent millennia cataloguing the positions of the stars and planets in the night sky and, by the 17th century, the German astronomer and mathematician Johannes Kepler had worked out the geometry of these movements. By looking at the movement of Mars, Kepler had calculated that planets orbited the sun in elliptical paths and, in a kind of celestial clockwork, his three laws of planetary motion allowed astronomers to work out the position of the planets in the future based on data from past records.

Kepler's laws explain how the planets moved around the sun but not why. Newton filled in that gap by supposing there was a force acting between the bodies that were moving around each other.

The story goes that Newton saw an apple fall to the ground and it made him wonder why the fruit always fell straight to the ground; why did it not veer off to the left or right? According to his own laws of motion, anything that begins moving from a standing start is undergoing acceleration and, where there is acceleration, there must be a force. The apple started in the tree and landed on the Earth, which means there must be a force of attraction between the apple and the Earth.

And even if the apple were higher up in the tree, it would still feel this force of attraction with the Earth, reasoned Newton. In fact, the attraction shouldn't even stop at the top of a tree but carry on way up into the heavens. Which raised the question: if everything around the Earth should feel this force of attraction, including the moon, why doesn't our nearest neighbour fall and crash onto the surface of our planet in the same way as the apple did?

Newton concluded that the moon did feel the effect of the Earth's attractive force and that it was indeed falling towards Earth, but there was a very good reason why it didn't crash down. He used a thought experiment to explain his thinking: imagine you fired a cannonball horizontally from the top of a mountain on Earth. The ball would follow a curved trajectory as it moved forward and was attracted, by gravity, towards the ground at the same time. Fire the cannonball with more energy and it would land further away from the mountain, but it still would follow a curved trajectory in doing so.

Newton proposed that, if you fired the cannonball with enough energy, it could fly all the way around the Earth and never land, because the Earth would be curving away underneath the ball at the same rate as the ball fell. In other words, the ball would now be in orbit around the Earth.

And this is what happens with the moon – it is in freefall around the Earth but it moves fast enough so that the Earth's surface never quite "catches" it.

Newton's law tells us that the strength of the gravitational force between two objects drops off in the same way that a light gets dimmer as you move away from it, a relationship known mathematically as an inverse square law.

Another way to visualise the drop-off in the field is to imagine the gravitational field around an object as a series of concentric spheres. Each sphere represents the same "amount" of gravitational field but the spheres further from the object are bigger, so that same amount of field is spread thinner, over a larger area. The field thus gets weaker as you move away from the object, in proportion to the surface areas of these spheres.

The m 1 and m 2 could be planets and stars or they could be you and the Earth. Compute the equation using numbers for your mass and that of the Earth, and you will get your weight, measured in Newtons. Weight, in true scientific terms, is the gravitational force acting on your mass (which is measured in kilograms) at any point in time. Your mass will stay the same wherever you go in the universe but your weight will fluctuate depending on the mass and position of the objects around you.

Newton's law of gravitation is simple equation, but devastatingly effective: plug in the numbers and you can predict the positions of all the planets, moons and comets you might ever want to watch, anywhere in the solar system and beyond.

And it allowed us to add to those celestial bodies too, heralding the space age. Newton's formula helped engineers work out how much energy we needed to break the gravitational bonds of Earth. The path of every astronaut and the orbit of every satellite from which we benefit – whether for communications, Earth observation, scientific research around Earth or other planets, global positioning information – was calculated using this simple formula.

- Isaac Newton
- A short history of equations

## The ideal gas law – why bubbles expand if you heat them

## Human Brain Project: Henry Markram plans to spend €1bn building a perfect model of the human brain

## Sound, light and water waves and how scientists worked out the mathematics

## Why millions love Elise Andrew's science page

## Big nanotech: towards post-industrial manufacturing

## Why you can't travel at the speed of light

## What is the second law of thermodynamics?

## Starwatch: The brightening of ISON

## What is Heisenberg's Uncertainty Principle?

## Eating popcorn in the cinema makes people immune to advertising

Comments (…), most viewed.

- Utility Menu

## K. Lee Lerner

Aviator, sailor, writer, and scholar Publication and Research Portfolio | Harvard Projects

- [Harvard Projects]
- [Taking Bearings]
- [Harvard Academia]

## Newton's Law of Universal Gravitation

In 1687 English physicist Sir Isaac Newton (1642-1727) published a law of universal gravitation in his influential work Philosophiae Naturalis Principia Mathematica (Mathematical Principles of Natural Philosophy). In its simplest form, Newton's law of universal gravitation states that bodies with mass attract each other with a force that varies directly as the product of their masses and inversely as the square of the distance between them. This mathematically elegant law, however, offered a remarkably reasoned and profound insight into the mechanics of the natural world because revealed a cosmos bound together by the mutual gravitational attraction of its constituent particles. Moreover, along with Newton's laws of motion, the law of universal gravitation became the guiding model for the future development of physical law. Newton's law of universal gravitation was derived from German mathematician and astronomer Johannes Kepler's (1571-1630) laws of planetary motion, the concept of "action-at-a-distance," and Newton's own laws of motion. Building on Galileo's observations of falling bodies, Newton asserted that gravity is a universal property of all matter. Although the force of gravity can become infinitesimally small at increasing distances between bodies, all bodies of mass exert gravitational force on each other. Newton extrapolated that the force of gravity (later characterized by the gravitational field) extended to infinity and, in so doing, bound the universe together. more

Talk to our experts

1800-120-456-456

- Newton’s Law of Gravity

## Introduction

In the late 1600s, Sir Isaac Newton came up with the law of gravity which is also known as the universal law of gravitation. Sir Isaac Newton’s inspiration for deducing the revolutionary law of gravity was an apple falling from a tree. We are all pretty familiar with the story of Newton and how he discovered gravity. The falling of an apple made him discover Newton's gravity and the law of gravitation. Newton’s law of gravity plays an important role in mechanics .

Newton had a simple question out of curiosity is why an apple was falling instead of either sideways or upward!!! Later Newton realized that the earth must be responsible for the apple to fall downwards perpendicular to the ground. This was the major turning point and then he developed the law of gravity.

Gravity is the force of attraction happening between any two bodies. Basically, all the objects in the universe attract each other with a certain amount of force, but in most cases, the force is either too weak or too small to be observed due to the very large distance of separation.

So Newton’s law of gravitation was introduced, and it states that any particle of matter in the universe attracts any other particle with a force varying directly as the product of the masses and inversely as the square of the distance between them. Newton’s law of gravitation is the magnitude of the attractive force F is equal to G multiplied by the product of the masses (\[m_{1}~and~m_{2}\]) and divided by the square of the distance R :

\[F = \frac{G(m_{1} m_{2})}{R^{2}}\].

(Image Will Be Uploaded Soon)

## What is Newton's Law of Gravitation?

The law of gravity is an important discovery in the field of physics. It gives an insight into the relationship between mass and force. The law of gravitation states that- every object in the universe attracts every other object such that the force exerted will be proportional to the product of the masses and inversely proportional to the square of the distance between them.

## The formula of Newton’s Law of Gravity

Newton’s Law of Gravitation is formulated as :

\[F_{G} = \frac{G(m_{1} m_{2})}{r^{2}}\]

In the above equation, the values are defined as:

Fg is the force of gravity that is typically in newtons.

G is the gravitational constant that adds the proper level of proportionality to the equation.

The value of the gravitational constant is \[6.67259 * 10^{-11} N * m^{2} / kg^{2}\], the value will change if other units are being used.

(\[m_{1}~and~m_{2}\]) are the masses of the two particles that are typically in kilograms.

r is the straight-line distance between the two particles that are typically in meters.

## According to Newton’s Law of Gravitation

The magnitude of the force acting between two point masses is directly proportional to the product of their masses.

The magnitude of the force acting between two point masses decreases rapidly as distance increases.

Mathematically we write ,

Consider two objects having masses \[m_{1}~and~m_{2}\] separated by a distance r, as shown in the figure.

## According to the Statement of the Law of Gravitation ,

The magnitude of the force acting on the body is directly proportional to the product of the masses of interacting bodies, then we get:

\[\Rightarrow F \alpha m_{1}m_{2}.....(1)\]

The value of the proportionality constant is found to be \[G = 6.673 \times 10^{-11} Nm^{2}/kg^{2}\]

Equation (4) is known as the mathematical form of Newton’s law of gravitation or the law of gravitational force. From equation (4) we find that the force acting on each other will be directly proportional to the product of point masses and inversely proportional square of the distance between them. It is also known as the inverse square law. In some articles, it is also referred to as the first law of gravity.

The gravitational force acting between two objects is only due to their masses. The gravitational force is one of the four basic forces of physics. Sometimes it is also referred to as Newton gravity or Newton's gravity. The gravitational force is valid throughout the universe. For significant gravitational force, one among the two objects must be larger than the other.

## Characteristics of Gravitational Force

Following are the characteristics of Gravitational Force :

Gravitational force is a central force.

Gravitational force is a mutual force.

Gravitational force is mass-dependent.

Gravitational force is an attractive force.

Gravitational force is independent of the presence of other mass bodies.

Gravitational force is a long-range force.

Gravitational force is a universal force.

Gravitational force is the weakest among the basic forces of nature.

The gravitational force is always attractive and it is directed along with the line joining of two interacting bodies.

The gravitational force is independent of the medium and the surrounding environment.

The gravitational force is valid for long distances like the distance between two planets and for short distances like interatomic distances.

The force of gravitation is conservative. Thus the work done gravitational force will be zero.

If a particle is acted by n particles then the net force exerted on it will be equal to the vector sum of the forces due to surrounding particles. i.e.,

\[F_{net}~=~\sum_{i}~=~1^{n}F_{i}\] where \[F_{i}\] is the force acting on the object by \[i^{th}\] particle.

From the law of gravity or Newton’s law of gravitation, we understood that mass is a crucial entity. There is always confusion between mass and weight , we consider mass and weight to be the same, but in reality, they are interrelated but are different from each other.

Weight is the gravitational force exerted on any object of a certain mass. The weight of an object can be estimated by multiplying the mass m of the object by the acceleration due to gravity, g, at the surface of the Earth. The measured acceleration due to gravity at the Earth’s surface is found to be about \[9.8 m/s^{2}\] or \[980 cm/s^{2}\].

The measure of how much matter is in an object is known as mass, while weight is the measure of the gravitational force exerted on the material in a given gravitational field; thus, mass and weight are proportional to each other.

m - The mass of the object

g - acceleration due to gravity.

It is observed that the mass of the given object will be constant, but the weight depends on the position of the object.

## Solved Examples

1. Define the force of gravity acting on an object of mass 2000 kg at the Earth’s surface?

Given: Mass of Earth \[m_{1}\] = 5.98 × 1024 kg

Mass of object \[m_{2}\] = 2000 kg

The radius of the Earth r = 6.38 × 106 m

Acceleration due to gravity \[ g = 9.8 m/s^{2}\]

Universal constant \[ G = 6.67 \times 10^{-11} N m^{2} / kg^{2}\]

\[ F = \frac{Gm_{1}m_{2}}{r^{2}}\]

F = \[\frac{(6.67 \times 10^{-11}) (5.98 \times 10^{24})(2\times 10^{3})}{(6.38 \times 10^{6})^{2}}\]

F = \[\frac{(7.978 \times 10^{17})}{(4.07044 \times 10^{13})}\]

F = \[1.959 \times 10^{4}\]

F = 19.59 N

Therefore, the force of attraction between the earth and a man is 882.3N.

2. Why Doesn’t the Moon Crash Into the Earth? What is the Value of Gravity on the Moon in Newtons?

Ans: Moon is the natural satellite of the earth. The forces of speed and gravity keep the moon in a constant orbit around the earth. The Moon seems to revolve around the earth, unaffected by gravity. However, the reason the Moon stays in orbit is precise because of gravity. Now the value of gravity on the moon can be calculated by using Newton’s law of gravitation.

This is all about Newton’s Laws of Gravitational forces explained with solved examples. Focus on how the terms are used to determine the formula and the value of the gravitational constant.

## FAQs on Newton’s Law of Gravity

1. What are the applications of Gravity?

Applications of Gravity are :

The information about the acceleration and the time period of satellites all around the Earth is accurately measured with the help of gravity.

The motion of planets, time period, acceleration, and speed are calculated with the help of gravity.

Gravity helps in predicting the solar eclipse and the lunar eclipse.

The production of electricity from water by building dams is also due to the presence of gravitational force.

Gravity is also helpful in various industrial works like gravity separation and others.

2. What is the importance of Newton’s Universal Law of Gravitation?

The importance of Newton’s Universal Law of Gravitation is:

Newton’s Universal Law of Gravitation has explained that every object on earth is bound to the earth’s surface in spite of it rotating continuously.

Newton’s Universal Law of Gravitation explains the motion of the Satellites like the moon around planets like earth.

Newton’s Universal Law of Gravitation explains the motion of the planets around the Sun.

Newton’s Universal Law of Gravitation helps us to find out the value of g (acceleration due to gravity) for the earth.

Newton’s Universal Law of Gravitation helps in understanding why g on earth is different from g on the moon.

3. What is the Universal Law of Gravitation Statement?

Newton’s Law of Gravitation or Law of Universal Gravitation Newton states that every object in this universe is attracting every other object towards it with a force called the gravitational force of attraction. This gravitational force of attraction is inversely proportional to the square of the distance between the objects and directly proportional to the product of the masses of these two objects involved.

4. What is Gravitational Force?

Each and everybody in this universe attracts other bodies towards itself with a force called the Gravitational Force, since gravitation is the interaction between two masses and out of the two masses, the heavier one is called source mass and the lighter one is called test mass. Gravitational force is also defined as a central force that depends only on the position of test mass from the source mass and always acts along the line joining the centers of the two masses.

\[F(r) = \frac{m_{1} m_{2}}{r.r}\]

5. What is the Law of Gravitation?

The law of gravitation states that- every object in the universe attracts every other object such that the force exerted will be proportional to the product of the masses and inversely proportional to the square of the distance between them.

6. Why is Newton’s Law of Gravitation Universal?

It is known as the universal law because Newton's law of gravitation is valid for every object having mass.

7. Will the Gravitational Force be the Same all Over the Earth?

No, The force of gravity changes according to the distance from the center of the earth. At some places, it will be stronger and at some places, it will be weak, depending on the distance of the object from the center of the earth.

- Random article
- Teaching guide
- Privacy & cookies

by Chris Woodford . Last updated: January 6, 2022.

W hat goes up, must come down. That's one way of looking at the weird phenomenon we call gravity , but it's far from the whole story. Some things— space probes and satellites spinning over our heads—never come down. And the idea of gravity as a simple up-down force happening purely on Earth is very wrong too.

Gravity is like invisible elastic stretched through the whole universe, holding the stars and planets together and pulling them toward one another. Much more significantly, it's a fundamental force between every bit of matter in the universe and every other bit: just like Earth and the Sun, you have your own gravity, and so do I. From Aristotle to Kepler and from Newton to Einstein, understanding gravity has challenged some of the best scientific minds in history. Thanks to their efforts in getting a grip on this tricky topic, we can do all kinds of neat things, from figuring out where we are with GPS satellites to making sure bullets hit the spot. But that still leaves an important question: just what is this thing we call gravity and how does it work? Let's take a closer look!

Photo: Gravity in all its beauty! Gravity's pull varies from place to place, both on Earth and elsewhere. This is a map showing how the strength of gravity varies across the Mare Orientale on the moon. Image courtesy of NASA/JPL-Caltech .

## What is gravity?

Gravity is a pulling force (always a force of attraction) between every object in the universe (every bit of matter, everything that has some mass) and every other object. It's a bit like an invisible magnetic pull, but there's no magnetism involved. Some people like to call this force gravitation and reserve the word gravity for the special kind of gravitation ("what goes up must come down") that we experience here on Earth. To my mind, that's unnecessary and wrong, and I'll explain why when we talk about Isaac Newton in a moment. In this article, I'm going to use the word gravity for everything (both gravity and gravitation).

If you've heard physicists talk about the four fundamental forces (or four fundamental interactions) that control everything that happens around us, you'll know that gravity is one of them—along with the electromagnetic force and the two nuclear forces that work on very small scales inside atoms (known as the strong and weak forces). Gravity is very different from these other forces, however. Most of us can remember playing with magnets in school and one of the first things you learn by doing that is that two magnets can attract or repel. Gravity can certainly attract, but it never repels. While magnetism can be an incredibly strong force over very short distances, gravity is generally a much weaker force, though it works over infinitely long distances. The gravity exerted by your body, right now, is pulling the Sun toward you—just a tiny bit—across a distance of something like 150 million kilometers!

Artwork: Gravity keeps the planets in orbit around the Sun, even at immense, astronomical distances. Spacecraft, like Mariner 10 shown here, sometimes use what's called a "gravity assist" to help them achieve a new orbit or a different velocity. Artwork courtesy of NASA

## Gravity on Earth

Cars, trucks, airplanes, mosquitos, your body and everything around you—it's all stuck to Earth by the force of gravity. If we've just said gravity is a weak force, how is that possible? How can such a weak force pull something like a huge Jumbo jet down toward the ground? Gravity might be weak, but Earth has a lot of it because our planet is so big and we're relatively close to it (compared to our distance from the Sun, anyway). Often it helps to think of Earth's gravity originating at a single point at the center of the planet's core. The amount of gravity you feel at any place on Earth depends how far you are from this point, so it's slightly more at sea level and slightly less when you're up a mountain. Now Earth isn't a perfect sphere: technically, it's what's called an oblate spheroid—it's flattened at the poles and bulges at the equator. That means gravity also lessens with latitude (it's slightly less at the equator than at the poles). Finally, because Earth is spinning around, and people at the poles are moving less quickly (relative to space) than those at the equator, that also slightly reduces the effects of gravity. Add all these things together and you get a variation in gravity between the equator and the poles of much less than 1 percent, so for most everyday purposes, we can say that gravity at sea level is the same right across Earth. [1]

Artwork: The force of gravity is slightly lower at the equator than at the poles. Please note that this figure is not drawn to scale and Earth's bulge is hugely exaggerated!

Why might it matter that gravity varies on Earth? First, and perhaps least importantly, it affects how much you weigh. If gravity is more at sea level, you weigh more there! The quickest way to lose weight is to climb an especially high mountain—not because all the effort makes you lose any body mass, but because the force of gravity is weaker the further you go from the center of the Earth. Second, gravity pulls everything toward Earth (the invisible, gassy atmosphere around us as well as everything else), and that's why we have air pressure (on land) and water pressure (in the oceans). These things vary with altitude (above Earth's surface) and depth (below sea level).

If gravity is a force tugging us toward a point in the center of the planet, why don't we keep on being pulled in? Why doesn't gravity tug you through the floor of your house and the rocks below to suffer a really rather unpleasant death in the heart of Earth's fiery core, deep beneath your feet? If you're sitting still in a chair right now, it means all the forces on your body are balanced. So the downward pull of gravity must be balanced exactly by another, upward-pushing force. As gravity tries to pull you down, the atoms in the chair push back upward—you can't squash atoms that easily—and counteract with what is essentially an electromagnetic force. When someone stands on the floor and goes nowhere, the ground is effectively pushing back up again and saying "I will not be squashed." We call the upward-pushing force from the ground that balances downward-pulling gravity the normal force.

## Gravity in space

Photo: Astronauts train for space in a "vomit comet": It simulates weightlessness by making deep dives toward Earth. Photo courtesy of NASA on The Commons .

Scientists used to think Earth sat at the center of the Universe: theories of astronomy were geocentric , which means Earth-centered. Until the 16th century, most people thought the Sun rotated around Earth, rather than (as we now know) the other way around. There was tremendous religious opposition to the idea that Earth spun around the Sun, which is called the helicentric (Sun-centered theory). That idea was first put forward by the ancient Greek thinker Aristarchus (c.310–250 BCE), revived by Polish astronomer Nicolaus Copernicus (1473–1543), and championed by Galileo Galilei (1564–1642). When it comes to gravity, we now accept that Earth isn't at the center of things: it isn't special and it's no different from anywhere else. That's one reason why it makes no sense to talk about gravity (Earth's "special" gravitation) and gravitation (other kinds of gravitation, in other situations or elsewhere). But you'll still see both of those two words used widely. (Isaac Newton formulated a law of "gravitation," as we'll discover in a moment.)

Photo: Galileo Galilei, an Italian astronomer, investigated how gravity accelerates things on Earth and championed the idea that Earth orbits the Sun. Picture from Carol M. Highsmith's America Project in the Carol M. Highsmith Archive, courtesy of US Library of Congress

Just like Earth, every planet (or moon) has a different amount of gravity; bigger planets (or moons) have more gravity than smaller ones. So our own Moon has gravity, but it's about one sixth as much as Earth's (because the Moon has less mass and it's much smaller). That's why astronauts weigh one sixth as much on the Moon and why they can jump about four times higher in the air when they're there. Jupiter has gravity too and because it's bigger and more massive than Earth, you'd weigh almost three times more there and struggle to jump very far at all.

Gravity also explains why the universe looks and behaves the way it does. If you've ever wondered why planets are nice round shapes (roughly spherical) and not square boxes, gravity is the answer. When the planets were busily forming from fizzing atoms and swirling atomic dust billions of years ago, gravity was the force that tugged them together. If lots of matter is pulled toward a central point from many different directions, a sphere is what you end up with—just like you end up with a snow ball if you pat snow together hard from all sides. Invisible "strings" of gravity also explain why the planets dance around one another in the strange cosmic patterns we call orbits. Although we often think of orbits as circular, they're actually ellipses, which are stretched-out, oval relatives of circles (a circle is a special kind of ellipse).

“ ... one of the theories proposed was that the planets went around because behind them were invisible angels, beating their wings and driving the planets forward. You will see that this theory is now modified! ” Richard Feynman, Six Easy Pieces

## How does gravity work?

Early scientific ideas about gravity were based on watching how things naturally fell toward the ground. Aristotle , the ancient Greek philosopher, who lived about 2350 years ago, famously believed that heavier things fall faster than light ones, so if you drop a stone and a feather at the same time, the stone wins the race and hits the ground first. Meanwhile, the whole question of how planets moved in space was considered an entirely different matter. In Aristotle's mind, Sun, moon, planets, and stars all marched in circular orbits round Earth. Astronomers such as Ptolemy (Claudius Ptolemaeus, 100–170 CE) built on this model, but didn't really connect motion in space with what was happening back on Earth. Like Aristotle, Ptolemy was confident that the Sun and planets spun in circles round Earth. Even though his ideas were wrong, his book of astronomy, The Almagest , was accepted as scientific truth for over 1400 years (until Nicolaus Copernicus came along) because no-one else had any better ideas. "Almagest" actually means "The Greatest": Ptolemy's really was the greatest scientific explanation of the world people had at that time.

Artwork: Before people understood gravity, they had to devise ingenious explanations for why the planets moved. In this 14th-century illuminated manuscript, angels make the planets rotate by cranking giant handles! For more about the development of these ideas, see the fascinating Wikipedia article Dynamics of the celestial spheres . Illustration attributed to the atelier of the Catalan Master of St Mark, Spain, 14th century, courtesy of the British Library and Wikimedia Commons .

Aristotle was correct in one sense (a stone beats a feather in a race to the ground), but we now know that everything falls at exactly the same rate and the feather only loses because air resistance (drag) pushes up against it, slowing it down. The person who figured this out, toward the end of the 16th century, was Italian astronomer Galileo Galilei (1564–1642). According to some historians, Galileo experimented with metal balls on a tilted ramp, quickly concluding that the force of gravity accelerates every object—feathers just like stones—at exactly the same rate, which we now call the acceleration due to gravity (or g). Other science historians claim Galileo figured out his ideas by dropping balls from the Leaning Tower of Pisa, while a third theory is that all these were "thought experiments" that he carried out in his own mind. Either way, we now know that all masses are accelerated in the same way; for most practical purposes, g is a constant value everywhere on Earth (although, as we saw up above, it does vary slightly due to altitude, latitude, and so on).

Photo: Isaac Newton—the man behind our modern understanding of gravity. Picture courtesy of US Library of Congress .

While Galileo was musing over gravity on Earth, other astronomers had been coming up with more detailed accounts of how planets moved in space. Nicolaus Copernicus (1473–1543) and Galileo advanced the idea that Earth moved around the Sun. The German Johannes Kepler (1571–1630) believed this too—and realized exactly how it might work. He took a treasure trove of very accurate and detailed observations compiled by another astronomer, Tycho Brahe (1546–1601), and used it to figure out three deceptively simple mathematical laws that seemed to sum everything up. Kepler realized that the planets move in ellipses around the Sun, not circles as had long been supposed. He found that they "sweep out equal areas in equal times," which essentially means they move faster when they're nearer the Sun and slower when they're further out—but in a very predictable way. Finally, he showed how the size of a planet's orbit was related to the time it took for the planet to make a complete circuit around the Sun. It's pretty obvious that if a planet has a bigger orbit, it will take longer to go around it, but Kepler figured out the precise relationship between the two things. (Specifically, he showed that the time a planet takes to orbit, squared, is proportional to its distance from the Sun, cubed.)

But the real stroke of genius in understanding gravity came from English scientist Isaac Newton (1642–1727). He realized that the force of gravity that makes things fall to Earth is exactly the same as the force of gravitation that keeps the planets spinning around in space, which is why I prefer to use the same word for both phenomena. According to the popular myth, Newton figured this out when he saw an apple falling in his garden. Whether that really happened, no-one knows—but it was an incredibly impressive insight that changed science forever. Building on Kepler's work, Newton calculated that a falling apple experienced the same gravity as the Moon would experience being pulled toward Earth. That led him to his groundbreaking law of universal gravitation, published in 1687.

Artwork: Three men who revolutionized astronomy: Copernicus (left), Galileo (right), and Kepler (far right) developed our modern view of the universe with the Sun at its center. Illustration by W. Marshall from a book cover c.1640, about a decade after Kepler's death. Artwork courtesy of US Library of Congress .

## The law of universal gravitation

Newton's gravity law is a simple math formula that explains almost everything we need to know about gravity in almost every situation we're ever likely to come across. It says that the force of gravity, F, between two masses, M and m, a distance r apart, is:

What does this actually mean?

“ It is hard to exaggerate the importance of the effect on the history of science produced by this great success of the theory of gravitation. ” Richard Feynman, Six Easy Pieces

What about the mysterious G in this equation? What's that all about? G is called the universal gravitational constant : a constant is simply a magical, fixed number that makes sure equations like this always work. There are many constants in physics equations and they conceal within themselves very deep truths about the world, though what those truths are, no-one really knows. What does the gravitational constant actually mean? Why is it that exact value? No-one knows! The first person to come up with a figure for G (indirectly, because he actually measured something else) was the eccentric British physicist Henry Cavendish (1731–1810). Cavendish is also known for discovering hydrogen and gives his name to the famous Cavendish Laboratory at Cambridge University in England (where I studied physics too). The value his experiment led to (6.75 × 10 −11 Nm 2 /kg 2 ) was almost exactly the same as the value we use today (6.67 × 10 −11 Nm 2 /kg 2 ).

## Einstein meets gravity

The Universal Law of Gravitation was an astounding success, but there was one strange thing it couldn't explain: a slight oddity in the motion of the planet Mercury, known as its perihelion precession. When theories don't explain everything, we know they can't be quite right. And indeed, at the beginning of the 20th century, the brilliant German-born physicist Albert Einstein (1879–1955) realized that the "classical", Newtonian picture of gravity wasn't quite right either.

Photo: Albert Einstein's General Relativity is currently our most comprehensive theory of gravity. Photo courtesy of US Library of Congress .

Einstein had already revolutionized physics with a remarkable new theory called relativity. Newton had shown that there was nothing special about Earth's gravity; it was the same as gravity anywhere. But it didn't really explain what caused gravity or how it passed from one side of the universe to the other through all the things that sat in between. In September 1905, Einstein's original idea, known as the Special Theory of Relativity, set out a new way of looking at three-dimensional space and time, blending them together to make four-dimensional space-time (or the space-time continuum). Einstein also had new ways of looking at light, which traveled at a constant speed and set an effective speed limit for the universe. Putting these ideas together suddenly made the sober science of physics look like a painting by Salvador Dali. If you traveled close to the speed of light, someone watching your progress as you passed by would see you shrink and your time slow down!

All very strange, but where did gravity fit in? In 1915, Einstein extended his ideas to make what he called a new, General Theory of Relativity . One key aspect of this theory is called the principle of equivalence, and it says that the force produced by gravity is exactly the same as the force produced by acceleration. In other words, gravity and acceleration are exactly the same thing. That means, for example, that if you wake up to find yourself inside a space rocket and you feel a force very much like weight, you have no way of knowing whether it's caused by gravity (because the rocket is sitting on the launchpad on Earth) or acceleration (because it's hurtling through space at ever-increasing speed, producing a force identical to what you'd normally think of as gravity). According to Einstein's new model of gravity, big masses (like planets) bend the very fabric of space time, like a heavy ball sitting on a huge rubber mat. That makes other masses, moving nearby, curve in toward them—giving a pulling force or attraction that looks identical to the thing we've always called gravity. In other words, gravity is the curvature of spacetime around mass (or energy, which is the same as mass). This was a weird and revolutionary idea and few people understood it or believed it, to begin with, but it could explain the odd motion of mercury—and much more. In 1919, scientists observing a solar eclipse found the Sun bent light around it exactly as Einstein's theory predicted. (Extending this idea a little bit, we can see that if light was bent in just the right way, it would give optical effects just like a lens. This concept, known as a gravitational lens, was confirmed experimentally in 1979 and 1988.)

Artwork: According to Albert Einstein's General Theory of Relativity, gravity is the curvature of space time around mass or energy. Imagine if the Sun were a heavy metal ball sitting on a rubber mat. If you rolled a marble in a straight line nearby, it would curve inward because the mat is distorted slightly by the heavy ball. This is roughly how a big mass like the Sun curves space-time around it, pulling things like Earth toward it with the force we call gravity.

## How does gravity travel?

Einstein's General Theory completely explains Newton's Universal Law of Gravitation, so you could say that it makes it unnecessary. However, Newton's law is much simpler and works in most everyday situations, so it's still widely used in physics. (The same goes for Newton's "classical" laws of motion and Einstein's Special Theory of Relativity. Newton's laws are perfectly adequate for most everyday situations, so we still those all the time.) And just as Newton's law turned out not to be a complete explanation of gravity, so there are things that Einstein's law doesn't explain. In other words, Einstein's theory isn't complete either.

Photo: Detectors used to help find gravitational waves . Photo courtesy of NASA/JPL-Caltech .

The current way of explaining forces—how they act "invisibly" on things at a distance removed—is to think about particles being exchanged, but this turns out not to be compatible with Einstein's theories. Exactly how gravity works is still not understood. We don't know why it's so weak (compared to other forces) or how it "travels" from one side of the universe to the other. One idea is that it involves the exchange of hypothetical particles known as gravitons, but no-one has ever seen one of those. Despite its incompleteness, we know that much of Einstein's theory is correct, because the predictions it makes have been borne out by experimental observations, like those described up above. Another key prediction from Einstein's theory is that, when large masses are disturbed (for example, when stars explode or black holes swallow one another), they send out rippling waves (gravitational waves) through space-time at the speed of light. That was fully confirmed in September 2015 by scientists at LIGO (Laser Interferometer Gravitational-wave Observatory in the United States—and the discovery earned three scientists the Nobel Prize in Physics in 2017 . Einstein's General Theory also tells us that the color of light can be shifted toward red by the pull of gravity—another prediction confirmed in reality.

From Aristotle to Einstein, we've made great progress, but when will we have a complete theory of gravity? Perhaps tomorrow, perhaps never. Science is a never-ending quest to understand—and that's what makes it so fascinating. Long may its mysteries continue to inspire us!

Artwork: Gravity constantly throws up exciting new discoveries. How about this "black hole tango," in which a supermassive black hole is forming through the merging of smaller black holes drawn together by gravity. Artwork courtesy of NASA .

## A brief history of gravity

References ↑ in geophysics: a very short introduction , p.72, william lowrie quotes a common estimate of 0.5 percent. --> --> sponsored links (adsbygoogle = window.adsbygoogle || []).push({}); if you liked this article..., find out more, on this website.

- Bullets : An understanding of gravity is essential if you want to know how to fire a bullet accurately.
- Energy : Energy powers forces like gravity.
- Motion : How Isaac Newton revolutionized our understanding of force and motion.
- Science of sport : In many ways, sport is a battle against gravity.

## For younger readers

- A Crash Course in Forces and Motion by Emily Sohn. Capstone, 2019. A graphic/comic introduction to forces.
- Can you Feel the Force? by Richard Hammond. New York/London: Dorling Kindersley, 2007/2015. A simple, fun introduction to physics for ages 8–10.
- Fatal Forces by Nick Arnold. Scholastic, 2014. A more wordy introduction from the Horrible Science series. For ages 10–12, 128 pages.
- Gravity: Scientific Pathways by Chris Woodford. Rosen, 2013. My own little introduction to the history of gravity, from ancient science to Einstein and modern gravity. For ages 9–12, 64 pages.

## For older readers

- Six Easy Pieces by Richard Feynman. Basic Books/Penguin, 2011. Chapter 5, The Theory of Gravitation, is a short overview that covers much the same ground as this article, but with a bit more detail about Kepler and planetary motion.
- Newtonian Mechanics by A.P. French. W. W. Norton, 1971. A classic introduction for undergraduates and bright high-school students.
- Physics: Algebra/Trig by Eugene Hecht. Thomson-Brooks/Cole, 2003.

Text copyright © Chris Woodford 2021. All rights reserved. Full copyright notice and terms of use .

## Rate this page

Tell your friends, cite this page, more to explore on our website....

- Get the book
- Send feedback

- Test React Account
- TPC and eLearning
- What's NEW at TPC?
- Read Watch Interact
- Practice Review Test
- Teacher-Tools
- Subscription Selection
- Seat Calculator
- Ad Free Account
- Edit Profile Settings
- Student Progress Edit
- Task Properties
- Export Student Progress
- Task, Activities, and Scores
- Metric Conversions Questions
- Metric System Questions
- Metric Estimation Questions
- Significant Digits Questions
- Proportional Reasoning
- Acceleration
- Distance-Displacement
- Dots and Graphs
- Graph That Motion
- Match That Graph
- Name That Motion
- Motion Diagrams
- Pos'n Time Graphs Numerical
- Pos'n Time Graphs Conceptual
- Up And Down - Questions
- Balanced vs. Unbalanced Forces
- Change of State
- Force and Motion
- Mass and Weight
- Match That Free-Body Diagram
- Net Force (and Acceleration) Ranking Tasks
- Newton's Second Law
- Normal Force Card Sort
- Recognizing Forces
- Air Resistance and Skydiving
- Solve It! with Newton's Second Law
- Which One Doesn't Belong?
- Component Addition Questions
- Head-to-Tail Vector Addition
- Projectile Mathematics
- Trajectory - Angle Launched Projectiles
- Trajectory - Horizontally Launched Projectiles
- Vector Addition
- Vector Direction
- Which One Doesn't Belong? Projectile Motion
- Forces in 2-Dimensions
- Being Impulsive About Momentum
- Explosions - Law Breakers
- Hit and Stick Collisions - Law Breakers
- Case Studies: Impulse and Force
- Impulse-Momentum Change Table
- Keeping Track of Momentum - Hit and Stick
- Keeping Track of Momentum - Hit and Bounce
- What's Up (and Down) with KE and PE?
- Energy Conservation Questions
- Energy Dissipation Questions
- Energy Ranking Tasks
- LOL Charts (a.k.a., Energy Bar Charts)
- Match That Bar Chart
- Words and Charts Questions
- Name That Energy
- Stepping Up with PE and KE Questions
- Case Studies - Circular Motion
- Circular Logic
- Forces and Free-Body Diagrams in Circular Motion
- Gravitational Field Strength
- Universal Gravitation
- Angular Position and Displacement
- Linear and Angular Velocity
- Angular Acceleration
- Rotational Inertia
- Balanced vs. Unbalanced Torques
- Getting a Handle on Torque
- Torque-ing About Rotation
- Properties of Matter
- Fluid Pressure
- Buoyant Force
- Balloon Interactions
- Charge and Charging
- Charge Interactions
- Charging by Induction
- Conductors and Insulators
- Coulombs Law
- Electric Field
- Electric Field Intensity
- Polarization
- Case Studies: Electric Power
- Know Your Potential
- Light Bulb Anatomy
- I = ∆V/R Equations as a Guide to Thinking
- Parallel Circuits - ∆V = I•R Calculations
- Resistance Ranking Tasks
- Series Circuits - ∆V = I•R Calculations
- Series vs. Parallel Circuits
- Equivalent Resistance
- Period and Frequency of a Pendulum
- Pendulum Motion: Velocity and Force
- Energy of a Pendulum
- Period and Frequency of a Mass on a Spring
- Horizontal Springs: Velocity and Force
- Vertical Springs: Velocity and Force
- Energy of a Mass on a Spring
- Decibel Scale
- Frequency and Period
- Closed-End Air Columns
- Name That Harmonic: Strings
- Rocking the Boat
- Wave Basics
- Matching Pairs: Wave Characteristics
- Wave Interference
- Waves - Case Studies
- Color Addition and Subtraction
- Color Filters
- If This, Then That: Color Subtraction
- Light Intensity
- Color Pigments
- Converging Lenses
- Curved Mirror Images
- Law of Reflection
- Refraction and Lenses
- Total Internal Reflection
- Who Can See Who?
- Formulas and Atom Counting
- Atomic Models
- Bond Polarity
- Entropy Questions
- Cell Voltage Questions
- Heat of Formation Questions
- Reduction Potential Questions
- Oxidation States Questions
- Measuring the Quantity of Heat
- Hess's Law
- Oxidation-Reduction Questions
- Galvanic Cells Questions
- Thermal Stoichiometry
- Molecular Polarity
- Quantum Mechanics
- Balancing Chemical Equations
- Bronsted-Lowry Model of Acids and Bases
- Classification of Matter
- Collision Model of Reaction Rates
- Density Ranking Tasks
- Dissociation Reactions
- Complete Electron Configurations
- Enthalpy Change Questions
- Equilibrium Concept
- Equilibrium Constant Expression
- Equilibrium Calculations - Questions
- Equilibrium ICE Table
- Ionic Bonding
- Lewis Electron Dot Structures
- Line Spectra Questions
- Measurement and Numbers
- Metals, Nonmetals, and Metalloids
- Metric Estimations
- Metric System
- Molarity Ranking Tasks
- Mole Conversions
- Name That Element
- Names to Formulas
- Names to Formulas 2
- Nuclear Decay
- Particles, Words, and Formulas
- Periodic Trends
- Precipitation Reactions and Net Ionic Equations
- Pressure Concepts
- Pressure-Temperature Gas Law
- Pressure-Volume Gas Law
- Chemical Reaction Types
- Significant Digits and Measurement
- States Of Matter Exercise
- Stoichiometry - Math Relationships
- Subatomic Particles
- Spontaneity and Driving Forces
- Gibbs Free Energy
- Volume-Temperature Gas Law
- Acid-Base Properties
- Energy and Chemical Reactions
- Chemical and Physical Properties
- Valence Shell Electron Pair Repulsion Theory
- Writing Balanced Chemical Equations
- Mission CG1
- Mission CG10
- Mission CG2
- Mission CG3
- Mission CG4
- Mission CG5
- Mission CG6
- Mission CG7
- Mission CG8
- Mission CG9
- Mission EC1
- Mission EC10
- Mission EC11
- Mission EC12
- Mission EC2
- Mission EC3
- Mission EC4
- Mission EC5
- Mission EC6
- Mission EC7
- Mission EC8
- Mission EC9
- Mission RL1
- Mission RL2
- Mission RL3
- Mission RL4
- Mission RL5
- Mission RL6
- Mission KG7
- Mission RL8
- Mission KG9
- Mission RL10
- Mission RL11
- Mission RM1
- Mission RM2
- Mission RM3
- Mission RM4
- Mission RM5
- Mission RM6
- Mission RM8
- Mission RM10
- Mission LC1
- Mission RM11
- Mission LC2
- Mission LC3
- Mission LC4
- Mission LC5
- Mission LC6
- Mission LC8
- Mission SM1
- Mission SM2
- Mission SM3
- Mission SM4
- Mission SM5
- Mission SM6
- Mission SM8
- Mission SM10
- Mission KG10
- Mission SM11
- Mission KG2
- Mission KG3
- Mission KG4
- Mission KG5
- Mission KG6
- Mission KG8
- Mission KG11
- Mission F2D1
- Mission F2D2
- Mission F2D3
- Mission F2D4
- Mission F2D5
- Mission F2D6
- Mission KC1
- Mission KC2
- Mission KC3
- Mission KC4
- Mission KC5
- Mission KC6
- Mission KC7
- Mission KC8
- Mission AAA
- Mission SM9
- Mission LC7
- Mission LC9
- Mission NL1
- Mission NL2
- Mission NL3
- Mission NL4
- Mission NL5
- Mission NL6
- Mission NL7
- Mission NL8
- Mission NL9
- Mission NL10
- Mission NL11
- Mission NL12
- Mission MC1
- Mission MC10
- Mission MC2
- Mission MC3
- Mission MC4
- Mission MC5
- Mission MC6
- Mission MC7
- Mission MC8
- Mission MC9
- Mission RM7
- Mission RM9
- Mission RL7
- Mission RL9
- Mission SM7
- Mission SE1
- Mission SE10
- Mission SE11
- Mission SE12
- Mission SE2
- Mission SE3
- Mission SE4
- Mission SE5
- Mission SE6
- Mission SE7
- Mission SE8
- Mission SE9
- Mission VP1
- Mission VP10
- Mission VP2
- Mission VP3
- Mission VP4
- Mission VP5
- Mission VP6
- Mission VP7
- Mission VP8
- Mission VP9
- Mission WM1
- Mission WM2
- Mission WM3
- Mission WM4
- Mission WM5
- Mission WM6
- Mission WM7
- Mission WM8
- Mission WE1
- Mission WE10
- Mission WE2
- Mission WE3
- Mission WE4
- Mission WE5
- Mission WE6
- Mission WE7
- Mission WE8
- Mission WE9
- Vector Walk Interactive
- Name That Motion Interactive
- Kinematic Graphing 1 Concept Checker
- Kinematic Graphing 2 Concept Checker
- Graph That Motion Interactive
- Rocket Sled Concept Checker
- Force Concept Checker
- Free-Body Diagrams Concept Checker
- Free-Body Diagrams The Sequel Concept Checker
- Skydiving Concept Checker
- Elevator Ride Concept Checker
- Vector Addition Concept Checker
- Vector Walk in Two Dimensions Interactive
- Name That Vector Interactive
- River Boat Simulator Concept Checker
- Projectile Simulator 2 Concept Checker
- Projectile Simulator 3 Concept Checker
- Turd the Target 1 Interactive
- Turd the Target 2 Interactive
- Balance It Interactive
- Go For The Gold Interactive
- Egg Drop Concept Checker
- Fish Catch Concept Checker
- Exploding Carts Concept Checker
- Collision Carts - Inelastic Collisions Concept Checker
- Its All Uphill Concept Checker
- Stopping Distance Concept Checker
- Chart That Motion Interactive
- Roller Coaster Model Concept Checker
- Uniform Circular Motion Concept Checker
- Horizontal Circle Simulation Concept Checker
- Vertical Circle Simulation Concept Checker
- Race Track Concept Checker
- Gravitational Fields Concept Checker
- Orbital Motion Concept Checker
- Balance Beam Concept Checker
- Torque Balancer Concept Checker
- Aluminum Can Polarization Concept Checker
- Charging Concept Checker
- Name That Charge Simulation
- Coulomb's Law Concept Checker
- Electric Field Lines Concept Checker
- Put the Charge in the Goal Concept Checker
- Circuit Builder Concept Checker (Series Circuits)
- Circuit Builder Concept Checker (Parallel Circuits)
- Circuit Builder Concept Checker (∆V-I-R)
- Circuit Builder Concept Checker (Voltage Drop)
- Equivalent Resistance Interactive
- Pendulum Motion Simulation Concept Checker
- Mass on a Spring Simulation Concept Checker
- Particle Wave Simulation Concept Checker
- Boundary Behavior Simulation Concept Checker
- Slinky Wave Simulator Concept Checker
- Simple Wave Simulator Concept Checker
- Wave Addition Simulation Concept Checker
- Standing Wave Maker Simulation Concept Checker
- Color Addition Concept Checker
- Painting With CMY Concept Checker
- Stage Lighting Concept Checker
- Filtering Away Concept Checker
- Young's Experiment Interactive
- Plane Mirror Images Interactive
- Who Can See Who Concept Checker
- Optics Bench (Mirrors) Concept Checker
- Name That Image (Mirrors) Interactive
- Refraction Concept Checker
- Total Internal Reflection Concept Checker
- Optics Bench (Lenses) Concept Checker
- Kinematics Preview
- Velocity Time Graphs Preview
- Moving Cart on an Inclined Plane Preview
- Stopping Distance Preview
- Cart, Bricks, and Bands Preview
- Fan Cart Study Preview
- Friction Preview
- Coffee Filter Lab Preview
- Friction, Speed, and Stopping Distance Preview
- Up and Down Preview
- Projectile Range Preview
- Ballistics Preview
- Juggling Preview
- Marshmallow Launcher Preview
- Air Bag Safety Preview
- Colliding Carts Preview
- Collisions Preview
- Engineering Safer Helmets Preview
- Push the Plow Preview
- Its All Uphill Preview
- Energy on an Incline Preview
- Modeling Roller Coasters Preview
- Hot Wheels Stopping Distance Preview
- Ball Bat Collision Preview
- Energy in Fields Preview
- Weightlessness Training Preview
- Roller Coaster Loops Preview
- Universal Gravitation Preview
- Keplers Laws Preview
- Kepler's Third Law Preview
- Charge Interactions Preview
- Sticky Tape Experiments Preview
- Wire Gauge Preview
- Voltage, Current, and Resistance Preview
- Light Bulb Resistance Preview
- Series and Parallel Circuits Preview
- Thermal Equilibrium Preview
- Linear Expansion Preview
- Heating Curves Preview
- Electricity and Magnetism - Part 1 Preview
- Electricity and Magnetism - Part 2 Preview
- Vibrating Mass on a Spring Preview
- Period of a Pendulum Preview
- Wave Speed Preview
- Slinky-Experiments Preview
- Standing Waves in a Rope Preview
- Sound as a Pressure Wave Preview
- DeciBel Scale Preview
- DeciBels, Phons, and Sones Preview
- Sound of Music Preview
- Shedding Light on Light Bulbs Preview
- Models of Light Preview
- Electromagnetic Radiation Preview
- Electromagnetic Spectrum Preview
- EM Wave Communication Preview
- Digitized Data Preview
- Light Intensity Preview
- Concave Mirrors Preview
- Object Image Relations Preview
- Snells Law Preview
- Reflection vs. Transmission Preview
- Magnification Lab Preview
- Reactivity Preview
- Ions and the Periodic Table Preview
- Periodic Trends Preview
- Gaining Teacher Access
- Tasks and Classes
- Tasks - Classic
- Subscription
- Subscription Locator
- 1-D Kinematics
- Newton's Laws
- Vectors - Motion and Forces in Two Dimensions
- Momentum and Its Conservation
- Work and Energy
- Circular Motion and Satellite Motion
- Thermal Physics
- Static Electricity
- Electric Circuits
- Vibrations and Waves
- Sound Waves and Music
- Light and Color
- Reflection and Mirrors
- About the Physics Interactives
- Task Tracker
- Usage Policy
- Newtons Laws
- Vectors and Projectiles
- Forces in 2D
- Momentum and Collisions
- Circular and Satellite Motion
- Balance and Rotation
- Waves and Sound
- Forces in Two Dimensions
- Work, Energy, and Power
- Circular Motion and Gravitation
- Sound Waves
- 1-Dimensional Kinematics
- Circular, Satellite, and Rotational Motion
- Einstein's Theory of Special Relativity
- Waves, Sound and Light
- QuickTime Movies
- About the Concept Builders
- Pricing For Schools
- Directions for Version 2
- Measurement and Units
- Relationships and Graphs
- Rotation and Balance
- Vibrational Motion
- Reflection and Refraction
- Teacher Accounts
- Task Tracker Directions
- Kinematic Concepts
- Kinematic Graphing
- Wave Motion
- Sound and Music
- About CalcPad
- 1D Kinematics
- Vectors and Forces in 2D
- Simple Harmonic Motion
- Rotational Kinematics
- Rotation and Torque
- Rotational Dynamics
- Electric Fields, Potential, and Capacitance
- Transient RC Circuits
- Electromagnetism
- Light Waves
- Units and Measurement
- Stoichiometry
- Molarity and Solutions
- Thermal Chemistry
- Acids and Bases
- Kinetics and Equilibrium
- Solution Equilibria
- Oxidation-Reduction
- Nuclear Chemistry
- NGSS Alignments
- 1D-Kinematics
- Projectiles
- Circular Motion
- Magnetism and Electromagnetism
- Graphing Practice
- About the ACT
- ACT Preparation
- For Teachers
- Other Resources
- Newton's Laws of Motion
- Work and Energy Packet
- Static Electricity Review
- Solutions Guide
- Solutions Guide Digital Download
- Motion in One Dimension
- Work, Energy and Power
- Purchasing the CD
- Purchasing the Digital Download
- About the NGSS Corner
- NGSS Search
- Force and Motion DCIs - High School
- Energy DCIs - High School
- Wave Applications DCIs - High School
- Force and Motion PEs - High School
- Energy PEs - High School
- Wave Applications PEs - High School
- Crosscutting Concepts
- The Practices
- Physics Topics
- NGSS Corner: Activity List
- NGSS Corner: Infographics
- About the Toolkits
- Position-Velocity-Acceleration
- Position-Time Graphs
- Velocity-Time Graphs
- Newton's First Law
- Newton's Second Law
- Newton's Third Law
- Terminal Velocity
- Projectile Motion
- Forces in 2 Dimensions
- Impulse and Momentum Change
- Momentum Conservation
- Work-Energy Fundamentals
- Work-Energy Relationship
- Roller Coaster Physics
- Satellite Motion
- Electric Fields
- Circuit Concepts
- Series Circuits
- Parallel Circuits
- Describing-Waves
- Wave Behavior Toolkit
- Standing Wave Patterns
- Resonating Air Columns
- Wave Model of Light
- Plane Mirrors
- Curved Mirrors
- Teacher Guide
- Using Lab Notebooks
- Current Electricity
- Light Waves and Color
- Reflection and Ray Model of Light
- Refraction and Ray Model of Light
- Teacher Resources
- Subscriptions

- Newton's Laws
- Einstein's Theory of Special Relativity
- About Concept Checkers
- School Pricing
- Newton's Laws of Motion
- Newton's First Law
- Newton's Third Law

## Newton's Law of Universal Gravitation

- Gravity is More Than a Name
- The Apple, the Moon, and the Inverse Square Law
- Newton's Law of Universal Gravitation
- Cavendish and the Value of G
- The Value of g

Newton knew that the force that caused the apple's acceleration (gravity) must be dependent upon the mass of the apple. And since the force acting to cause the apple's downward acceleration also causes the earth's upward acceleration (Newton's third law), that force must also depend upon the mass of the earth. So for Newton, the force of gravity acting between the earth and any other object is directly proportional to the mass of the earth, directly proportional to the mass of the object, and inversely proportional to the square of the distance that separates the centers of the earth and the object.

## The UNIVERSAL Gravitation Equation

But Newton's law of universal gravitation extends gravity beyond earth. Newton's law of universal gravitation is about the universality of gravity. Newton's place in the Gravity Hall of Fame is not due to his discovery of gravity, but rather due to his discovery that gravitation is universal. ALL objects attract each other with a force of gravitational attraction. Gravity is universal. This force of gravitational attraction is directly dependent upon the masses of both objects and inversely proportional to the square of the distance that separates their centers. Newton's conclusion about the magnitude of gravitational forces is summarized symbolically as

Since the gravitational force is directly proportional to the mass of both interacting objects, more massive objects will attract each other with a greater gravitational force. So as the mass of either object increases, the force of gravitational attraction between them also increases. If the mass of one of the objects is doubled, then the force of gravity between them is doubled. If the mass of one of the objects is tripled, then the force of gravity between them is tripled. If the mass of both of the objects is doubled, then the force of gravity between them is quadrupled; and so on.

Since gravitational force is inversely proportional to the square of the separation distance between the two interacting objects, more separation distance will result in weaker gravitational forces. So as two objects are separated from each other, the force of gravitational attraction between them also decreases. If the separation distance between two objects is doubled (increased by a factor of 2), then the force of gravitational attraction is decreased by a factor of 4 (2 raised to the second power). If the separation distance between any two objects is tripled (increased by a factor of 3), then the force of gravitational attraction is decreased by a factor of 9 (3 raised to the second power).

## Thinking Proportionally About Newton's Equation

The proportionalities expressed by Newton's universal law of gravitation are represented graphically by the following illustration. Observe how the force of gravity is directly proportional to the product of the two masses and inversely proportional to the square of the distance of separation.

Another means of representing the proportionalities is to express the relationships in the form of an equation using a constant of proportionality. This equation is shown below.

The constant of proportionality (G) in the above equation is known as the universal gravitation constant . The precise value of G was determined experimentally by Henry Cavendish in the century after Newton's death. (This experiment will be discussed later in Lesson 3 .) The value of G is found to be

The units on G may seem rather odd; nonetheless they are sensible. When the units on G are substituted into the equation above and multiplied by m 1 • m 2 units and divided by d 2 units, the result will be Newtons - the unit of force.

## Using Newton's Gravitation Equation to Solve Problems

Knowing the value of G allows us to calculate the force of gravitational attraction between any two objects of known mass and known separation distance. As a first example, consider the following problem.

The solution of the problem involves substituting known values of G ( 6.673 x 10 -11 N m 2 /kg 2 ), m 1 (5.98 x 10 24 kg), m 2 (70 kg) and d (6.38 x 10 6 m) into the universal gravitation equation and solving for F grav . The solution is as follows:

The solution of the problem involves substituting known values of G ( 6.673 x 10 -11 N m 2 /kg 2 ), m 1 (5.98 x 10 24 kg), m 2 (70 kg) and d (6.39 x 10 6 m) into the universal gravitation equation and solving for F grav . The solution is as follows:

Two general conceptual comments can be made about the results of the two sample calculations above. First, observe that the force of gravity acting upon the student (a.k.a. the student's weight) is less on an airplane at 40 000 feet than at sea level. This illustrates the inverse relationship between separation distance and the force of gravity (or in this case, the weight of the student). The student weighs less at the higher altitude. However, a mere change of 40 000 feet further from the center of the Earth is virtually negligible. This altitude change altered the student's weight changed by 2 N that is much less than 1% of the original weight. A distance of 40 000 feet (from the earth's surface to a high altitude airplane) is not very far when compared to a distance of 6.38 x 10 6 m (equivalent to nearly 20 000 000 feet from the center of the earth to the surface of the earth). This alteration of distance is like a drop in a bucket when compared to the large radius of the Earth. As shown in the diagram below, distance of separation becomes much more influential when a significant variation is made.

The second conceptual comment to be made about the above sample calculations is that the use of Newton's universal gravitation equation to calculate the force of gravity (or weight) yields the same result as when calculating it using the equation presented in Unit 2:

Both equations accomplish the same result because (as we will study later in Lesson 3 ) the value of g is equivalent to the ratio of (G•M earth )/(R earth ) 2 .

## The Universality of Gravity

Gravitational interactions do not simply exist between the earth and other objects; and not simply between the sun and other planets. Gravitational interactions exist between all objects with an intensity that is directly proportional to the product of their masses. So as you sit in your seat in the physics classroom, you are gravitationally attracted to your lab partner, to the desk you are working at, and even to your physics book. Newton's revolutionary idea was that gravity is universal - ALL objects attract in proportion to the product of their masses. Gravity is universal. Of course, most gravitational forces are so minimal to be noticed. Gravitational forces are only recognizable as the masses of objects become large. To illustrate this, use Newton's universal gravitation equation to calculate the force of gravity between the following familiar objects. Click the buttons to check answers.

Today, Newton's law of universal gravitation is a widely accepted theory. It guides the efforts of scientists in their study of planetary orbits. Knowing that all objects exert gravitational influences on each other, the small perturbations in a planet's elliptical motion can be easily explained. As the planet Jupiter approaches the planet Saturn in its orbit, it tends to deviate from its otherwise smooth path; this deviation, or perturbation , is easily explained when considering the effect of the gravitational pull between Saturn and Jupiter. Newton's comparison of the acceleration of the apple to that of the moon led to a surprisingly simple conclusion about the nature of gravity that is woven into the entire universe. All objects attract each other with a force that is directly proportional to the product of their masses and inversely proportional to their distance of separation.

## Investigate!

We would like to suggest ....

## Check Your Understanding

1. Suppose that two objects attract each other with a gravitational force of 16 units. If the distance between the two objects is doubled, what is the new force of attraction between the two objects?

Answer: F = 4 units

If the distance is increased by a factor of 2, then force will be decreased by a factor of 4 (2 2 ). The new force is then 1/4 of the original 16 units.

F = (16 units ) / 4 = 4 units

2. Suppose that two objects attract each other with a gravitational force of 16 units. If the distance between the two objects is reduced in half, then what is the new force of attraction between the two objects?

Answer: F = 64 units

If the distance is decreased by a factor of 2, then force will be increased by a factor of 4 (2 2 ). The new force is then 4 times the original 16 units.

F = (16 units) • 4 = 64 units

3. Suppose that two objects attract each other with a gravitational force of 16 units. If the mass of both objects was doubled, and if the distance between the objects remained the same, then what would be the new force of attraction between the two objects?

If each mass is increased by a factor of 2, then force will be increased by a factor of 4 (2*2). The new force is then 4 times the original 16 units.

F = (16 units ) • 4 = 64 units

4. Suppose that two objects attract each other with a gravitational force of 16 units. If the mass of both objects was doubled, and if the distance between the objects was doubled, then what would be the new force of attraction between the two objects?

Answer: F = 16 units

If each mass is increased by a factor of 2, then force will be increased by a factor of 4 (2*2). But this affect is offset by the doubling of the distance. Doubling the distance would cause the force to be decreased by a factor of 4 (2 2 ); the result is that there is no net affect on force.

F = (16 units) • 4 / 4 = 16 units

5. Suppose that two objects attract each other with a gravitational force of 16 units. If the mass of both objects was tripled, and if the distance between the objects was doubled, then what would be the new force of attraction between the two objects?

Answer: F = 36 units

If each mass is increased by a factor of 3, then force will be increased by a factor of 9 (3*3). But this affect is partly offset by the doubling of the distance. Doubling the distance would cause the force to be decreased by a factor of 4 (2 2 ). the net affect on force is that it increased by 9/4.

F = (16 units) * 9 / 4 = 36 units

6. Suppose that two objects attract each other with a gravitational force of 16 units. If the mass of object 1 was doubled, and if the distance between the objects was tripled, then what would be the new force of attraction between the two objects?

Answer: F = 3.56 units

If the mass of one object is doubled. then the force of attraction will be doubled as well. But this affect is more than offset by the tripling of the separation distance. Tripling the distance would cause the force to be decreased by a factor of 9 (3 2 ). The net affect on force is that it decreased by a factor of 2/9.

F = (16 units) • 2 / 9 = 3.56 units

7. As a star ages, it is believed to undergo a variety of changes. One of the last phases of a star's life is to gravitationally collapse into a black hole. What will happen to the orbit of the planets of the solar system if our star (the Sun shrinks into a black hole)? (And of course, this assumes that the planets are unaffected by prior stages of the Sun's evolving stages.)

Answer: No affect

The shrinking of the sun into a black hole would not influence the amount of force with which the sun attracted the Earth since neither the mass of the sun nor the distance between the Earth's and sun's centers would change.

8. Having recently completed her first Physics course, Dawn Well has devised a new business plan based on her teacher's Physics for Better Living theme. Dawn learned that objects weigh different amounts at different distances from Earth's center. Her plan involves buying gold by the weight at one altitude and then selling it at another altitude at the same price per weight. Should Dawn buy at a high altitude and sell at a low altitude or vice versa?

Answer: Buy high and sell low

The mass of the purchased gold would be the same at both altitudes. Yet it would weight less at higher altitudes. So to make a profit, Dawn should buy at high altitudes and sell at low altitudes. She would have more gold (by weight) to sell at the lower altitudes.

9. Fred is very concerned about his weight but seldom does anything about it. After learning about Newton's law of universal gravitation in Physics class, he becomes all concerned about the possible effect of a change in Earth's mass upon his weight. During a (rare) free moment at the lunch table, he speaks up "How would my weight change if the mass of the Earth increased by 10%?" How would you answer Fred?

Answer: "Fred - that's a great question! Since your weight is directly dependent upon the mass of the Earth, you would weigh 10% more . But no worries bro. You wouldn't look any different than you do now since your mass would remain as is."

10. When comparing mass and size data for the planets Earth and Jupiter, it is observed that Jupiter is about 300 times more massive than Earth. One might quickly conclude that an object on the surface of Jupiter would weigh 300 times more than on the surface of the Earth. For instance, one might expect a person who weighs 500 N on Earth would weigh 150000 N on the surface of Jupiter. Yet this is not the case. In fact, a 500-N person on Earth weighs about 1500 N on the surface of Jupiter. Explain how this can be.

The affect of the greater mass of Jupiter is partly offset by the fact that the radius of Jupiter is larger. An object on Jupiter's surface is 10 times farther from Jupiter's center than it would be if on Earth's surface. So the 300-fold increase in force (due to the greater mass) must be divided by 100 since the separation distance is 10 times greater.

- Kepler's Three Laws

Help | Advanced Search

## High Energy Physics - Theory

Title: on the origin of gravity and the laws of newton.

Abstract: Starting from first principles and general assumptions Newton's law of gravitation is shown to arise naturally and unavoidably in a theory in which space is emergent through a holographic scenario. Gravity is explained as an entropic force caused by changes in the information associated with the positions of material bodies. A relativistic generalization of the presented arguments directly leads to the Einstein equations. When space is emergent even Newton's law of inertia needs to be explained. The equivalence principle leads us to conclude that it is actually this law of inertia whose origin is entropic.

## Submission history

Access paper:.

- Download PDF
- Other Formats

## References & Citations

- INSPIRE HEP
- Google Scholar
- Semantic Scholar

## 37 blog links

Bibtex formatted citation.

## Bibliographic and Citation Tools

Code, data and media associated with this article, recommenders and search tools.

- Institution

## arXivLabs: experimental projects with community collaborators

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs .

## Law Of Gravitation Essay

Newton’s Law of Universal Gravitation states that every object in the universe attracts every other object with a force that is directly proportional to the mass of the objects and inversely proportional to the square of the distance between them. This law was first proposed by Sir Isaac Newton in 1687 and has since been proven correct through extensive experimental evidence.

Gravity is the force by which a planet or other body draws objects toward its center. The force of gravity keeps all of the planets in orbit around the sun. Earth’s gravity is what keeps you on the ground and what makes things fall.

The strength of gravity between two masses is given by:

F = G * (m1 * m2) / d2

where F is the force of gravity in Newtons, m1 and m2 are the masses of the two objects in kilograms, d is the distance between the two objects in meters, and G is the gravitational constant.

The value of the gravitational constant is:

G = 6.67 x 10-11 N * m2 / kg2

Sir Isaac Newton was an English physicist and mathematician who lived from 1642 to 1727. He is considered one of the most important scientists in history for his work on mechanics, optics, and calculus. Newton’s Law of Universal Gravitation was just one of his many contributions to science.

Gravity is a little hard to define since it combines four forces—gravity, magnetism, electricity and nuclear fusion—which are all said to be mysterious. Gravity is one of the four fundamental forces in the universe, according to popular belief. According to Sir Isaac Newton’s research in 1687, gravity is an effect caused by attraction between two bodies (Eddington 93).

Without gravity, everything would stay put unless something acted on it; therefore, it would move indefinitely because there would be no force to stop it. Perhaps the best place to start when trying to understand this topic would be with a simple item such as an apple (after all, it was what “sparked” Newton’s creativity).

An apple falls from a tree at a velocity of 9.8 m/s^2 (32.2 ft/s^2) due to the pull of gravity. The force of gravity is equal to the mass of the object times the acceleration of gravity. F=mg, where m is the mass in kg and g is the acceleration of gravity, which is 9.8 N/kg (about 32 ft/lbsec^2). This value is constant at the Earth’s surface regardless of an object’s mass. So, a 1 kg apple falling at 9.8m/s^2 will have the same weight as a 10 kg boulder falling at 9.8m/s^2; they will both have a weight of about 98 Newtons.

An object’s weight is the force of gravity on that object. The value of gravity (acceleration) is different on other planets and even satellites; for example, the acceleration of gravity is only 3.7 m/s^2 (about 12 ft/sec^2) on Mars. This means that an object that has a mass of 1 kg on Earth would only have a weight of 3.7 N on Mars (about one-third its weight on Earth).

Gravity also affects fluids; in particular, it affects how fluids flow. Fluids are composed of molecules that are in constant motion. The motion of the fluid molecules is affected by gravity and the molecules’ interactions with each other. Gravity affects the motion of fluid molecules in two ways: it pulls them down, and it slows them down.

Gravity pulls fluid molecules down because they have mass. The force of gravity on a fluid molecule is proportional to its mass. So, the more massive a fluid molecule is, the more gravity pulls on it.

Gravity also slows fluid molecules down. When a fluid molecule moves, it collides with other molecules in the fluid. These collisions transfer energy from the moving molecule to the other molecules in the fluid. Gravity slows down moving molecules because it makes them collide more often with other molecules.

The combined effect of these two forces (the force of gravity and the force of collisions) is to make fluid molecules move slower at the bottom of a container than they do at the top. This difference in speed is called a velocity gradient, and it is caused by gravity.

The velocity gradient is important because it determines how fluids flow. The steeper the velocity gradient, the faster the fluid flows. Gravity makes the velocity gradient steeper near the surface of a planet, so fluids tend to flow faster near the surface than they do deep underground.

Gravity also affects the motion of objects in space. Objects in space are not affected by air resistance, so they can move much faster than objects on Earth. Gravity still affects their motion, however. Gravity pulls objects toward the center of a planet or satellite. The closer an object is to the center of a planet, the stronger the force of gravity on it.

The force of gravity also affects the orbit of a satellite. A satellite is any object that orbits another object in space. The most familiar type of satellite is a moon, which orbits a planet. Gravity pulls satellites toward the center of their orbit. The closer a satellite is to the center of its orbit, the stronger the force of gravity on it.

The apple was one of the two curiosities (the other being the moon) that prompted Isaac Newton to develop The Law of Universal Gravitation in 1666 (Eddington 93). It is the tale of an apple falling to the ground, according as Newton later wrote, that caused him to ask if this same force was also keeping the moon in position (Gamow 41). As Galileo had observed, objects descended at a rate of about 9. 8 meters per second seconds.

He also knew that the moon’s orbit was much larger and took about 27. 3 days to complete one revolution. From this, he reasoned that there must be a force that decreases with distance between two masses (Eddington 93).

The Third Law of Motion states that every force exerted by one object on another is equal to a force, but in the opposite direction (every reaction has an equal but opposite eaction). So the pull of the earth on the apple is comparable to the push of the apple back on the earth.

But he didn’t know why. It wasn’t until Newton that we understood the reason for elliptical orbits, and it has to do with his famous Law of Gravity.

Anything that has mass also has gravity. Objects with more mass have more gravity. Gravity also gets weaker with distance. So, the closer objects are to each other, the stronger their gravitational pull is.

Earth’s gravity comes from all its mass. All its mass makes a combined gravitational pull on all the mass in your body. That’s what gives you weight. And if you were on a planet with less mass than Earth, you would weigh less than you do here.

## More Essays

- Isaac Newton
- Sir Isaac Newton
- Sir Isaac Newton’s Three Laws That Changed The World Essay
- Three Types Of Collisions Essay
- The Role Of Physics In Soccer Essay
- Lord Of The Flies Characteristics Essay
- Essay on Identity Shifting Movement In Dance
- John Locke Secondary Qualities Essay
- Air Resistance In Snow Skiing Essay
- The Revolutions Of The Heavenly Bodies Summary Essay

## Leave a Comment Cancel reply

Save my name, email, and website in this browser for the next time I comment.

- IIT JEE Study Material
- Gravitation

## Gravitation - Gravitational Force and Newton's Law of Gravitation

Gravitation or gravity is the force of attraction between any two bodies. All the objects in the universe attract each other with a certain amount of force, but in most cases, the force is too weak to be observed due to the very large distance of separation. Besides, gravity’s range is infinite, but the effect becomes weaker as objects move away.

Download Complete Chapter Notes of Gravitation Download Now

This force of attraction was first observed by Sir Isaac Newton and was presented as Newton’s law of gravitation in the year 1680. However, gravitation can generally exist in two main instances.

1. Gravitation may be the attraction of objects by the earth

For example,

If a body (ball) is thrown upwards, it reaches a certain height and falls downwards because of the gravity of the earth.

2. Gravitation may be the attraction of objects in outer space.

The force of attraction between the other planets and the sun.

## Table of Contents

- Gravitational Force

## Newton’s Law of Gravitation

- Vector Form
- Derivation from Kepler’s Law

## What Is Gravitational Force?

Each body in this universe attracts other bodies towards itself with a force known as Gravitational Force. Thus, gravitation is a study of the interaction between two masses. Out of the two masses, the heavier one is called source mass, and the lighter one is called test mass.

Gravitational force is a central force which depends only on the position of the test mass from the source mass and always acts along the line joining the centres of the two masses.

The core problem of gravitation has always been in understanding the interaction between the two masses and their relativistic effects.

⇒ Also, Check: Gravitational field intensity

## History of Gravitational Theory

Ptolemy proposed the geocentric model, which failed to understand planetary motions, and led to the development of the heliocentric model by Nicholas Copernicus. His idea is based on the rotation of a test mass around the source mass in circular orbits; although the model correctly predicts the position of planets and their motions but has failed to explain many aspects, like the occurrence of seasons, which led to the construction of a model based on Kepler’s laws of planetary motion .

According to Newton’s law of gravitation, every particle in the universe attracts every other particle with a force whose magnitude is,

- Directly proportional to the product of their masses, i.e., F ∝ (M 1 M 2 ) . . . . (1)
- Inversely proportional to the square of the distance between their centre, i.e., (F ∝ 1/r 2 ) . . . . (2)

On combining equations (1) and (2), we get,

F ∝ M 1 M 2 /r 2

F = G × [M 1 M 2 ]/r 2 . . . . (7)

As f(r) varies inversely as a square of ‘r,’ it is also known as the inverse square law force. The proportionality constant (G) in the above equation is known as the gravitational constant.

The dimension formula of G is [M -1 L 3 T -2 ]. Also, the value of the gravitational constant,

- In SI units: 6.67 × 10 -11 Nm 2 kg -2 ,
- In CGS units: 6.67×10 -8 dyne cm 2 g -2

## Vector Form of Newton’s Law of Gravitation

The vector form of Newton’s law of gravitation signifies that the gravitational forces acting between the two particles form action-reaction pair.

From the above figure, it can be seen that the two particles of masses are placed at a distance.

The direction of the vector is from M 1 to M 2

Therefore, the force applied on M 2 by M 1 is

The negative sign indicates the attractive nature of the force.

Similarly, force on M 1 and M 2

Hence, the applied forces are equal and opposite. Also, the gravitational force follows Newton’s third law.

## Gravitational Force Formula

Gravitational force is explained using Newton’s law of gravitation. Gravitational force decides how much we weigh and how far a ball travels when thrown before it lands on the ground.

Also Read: Important Gravitation Formulas for JEE

According to Newton’s law of gravitation, every particle in the universe attracts every other particle with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.

Mathematically, it can be represented as,

F = Gm 1 m 2 /r 2 Where,

- F is the gravitational force between two objects measured in Newton (N).
- G is the universal gravitational constant with a value of 6.674 × 10 -11 Nm 2 kg -2 .
- m 1 is the mass of one massive body measured in kg.
- m 2 is the mass of another massive body measured in kg.
- r is the separation between them measured in kilometre (Km).

## Principle of Superposition of Gravitational Forces

Newton’s law of gravitation answers only the interaction between two particles; if the system contains ‘n’ particles, there are n(n – 1)/2 such interactions.

According to the principle of superposition , if each of these interactions acts independently and uninfluenced by the other bodies, the results can be expressed as the vector summation of these interactions:

F = F 12 + F 13 + F 14 . . . . . . + F 1n .

It states that:

“The resultant gravitational force F acting on a particle due to the number of point masses is equal to the vector sum of forces exerted by the individual masses on the given particle”.

## Derivation of Newton’s law of Gravitation from Kepler’s Law

Suppose a test mass is revolving around a source mass in a nearly circular orbit of radius ‘r’ with a constant angular speed (ω). Then, the centripetal force acting on the test mass for its circular motion is,

F = mrω 2 = mr × (2π/T) 2

According to Kepler’s 3rd law, T 2 ∝ r 3

Using this in force equation, we get,

⇒ F = GMm/r 2 , which is the equation of Newton’s law of gravitation.

## Solved Examples

1. What is the force of gravity acting on an object of mass 2000 kg at the Earth’s surface?

Mass of Earth (m 1 ) = 5.98 × 10 24 kg

Mass of object (m 2 ) = 2000kg

The radius of the Earth (r)= 6.38 × 10 6 m

Acceleration due to gravity (g) = 9.8 m/s 2

Universal constant (G) = 6.67 x 10 -11 N m 2 / kg 2

F = Gm 1 m 2 /r 2

F = ( 6.67 x 10 -11 ) (5.98 × 10 24 )(2 x 10 3 )/(6.38 × 10 6 ) 2

F = (7.978 x 10 17 )/ (4.07044 × 10 13 )

F = 1.959 x 10 4 or F = 19.59 N

2. What is the force of gravity acting on an object of mass 1000 kg at 20,000 meters above the Earth’s surface?

Mass of object (m 2 ) = 1000kg

h = 2 x 10 4 m

F = Gm 1 m 2 /(r +h) 2

F = ( 6.67 x 10 -11 ) (5.98 × 10 24 )(1 x 10 3 )/(6.38 × 10 6 + 2 x 10 4 ) 2

F = (3.988 x 10 17 )/(4.058 x 10 13 )

F = 9,827.50

F = 0.9827 x 10 4

Related Links

Acceleration due to gravity

Gravitational potential energy

- Centre of Gravity
- Practice JEE Previous Years’ Problems on Gravitation

## Gravitation Rapid Revision for JEE

## What Is Gravitation? – Video Lesson

## Gravitation – Top 10 Most Important and Expected JEE Questions

## Frequently Asked Questions on Gravitation

Will your weight be constant when you are travelling to greenland from brazil, can you screen the effect of gravitation by any material medium, why are space rockets launched eastward, why does a bouncing ball bounce higher on hills than on planes, the gravitational potential energy is negative. why, why is newton’s law of gravitation called universal law.

Newton’s law of gravitation holds good irrespective of the nature of the interacting bodies at all places and at all times.

## What is the weight of the body at the centre of the Earth?

The weight of the body at the centre of the earth is zero. W = mg = 0 (g at the centre of the earth is zero).

## Does friction arise due to gravitation?

Friction does not arise due to gravitation. Its origin is electrical in nature.

Put your understanding of this concept to test by answering a few MCQs. Click ‘Start Quiz’ to begin!

Select the correct answer and click on the “Finish” button Check your score and answers at the end of the quiz

Visit BYJU’S for all JEE related queries and study materials

Your result is as below

Request OTP on Voice Call

## Leave a Comment Cancel reply

Your Mobile number and Email id will not be published. Required fields are marked *

Post My Comment

- Share Share

## Register with Aakash BYJU'S & Download Free PDFs

Register with byju's & watch live videos.

## Newton's Universal Law of Gravitation

Format: APA

Academic level: College

Paper type: Essay (Any Type)

Downloads: 0

Newton’s universal law of gravitation did emanate from his desire to create a connection between astronomical movements and falling bodies. This was in connection to a fallen apple. The apple is part of the worldwide folklore and it comes with so much importance because Newton’s work did manage to answer very pertinent old questions on the simplicity and the unity that exists within nature. The gravitational law and laws of motion as advanced by Newton in his work are very instrumental even to this age.

Newton’s universal law of gravitation is simply and states that every particle in the universe is constantly attracting the other using a force that exists along the line that joins them. This force has a direct proportion connection when it comes to the product of their masses but is inverse in terms of proportion when it comes to the square of the distance between the two objects. Universal law of gravitation explains several phenomenon including the motion of planets around the sun and the motion of moon around the earth.

Delegate your assignment to our experts and they will do the rest.

The earth has a gravitational force that makes the moon to move in curved path and this gravitational force is what scientists call the centripetal force. The earth in itself does not remain stationary as the moon orbits it because it exerts some force towards the moon and although the moon exerts and equal opposite force on the earth, those on earth do not feel the force as the gravity from the moon moves our bodies along the earth. This means that as the moon orbits the earth, the earth being a planet also orbits the sun. The sun is an elliptical orbit and forms the center mass orbit for both the moon and the earth. The sun and the earth therefore just like the moon and the earth exert pressure towards each other in a continuous movement as the earth rotates the orbit of the sun and it is the gravitational pull that keeps the two in check.

- Why Did The BP Oil Spill Happen?
- How to Make Your Own Magnet

Select style:

StudyBounty. (2023, September 16). Newton's Universal Law of Gravitation . https://studybounty.com/newtons-universal-law-of-gravitation-essay

Hire an expert to write you a 100% unique paper aligned to your needs.

## Related essays

We post free essay examples for college on a regular basis. Stay in the know!

## Human Populations and the Environment

Water quality and contamination: lab report.

Words: 1039

## Climate Change and Global Warming

Words: 1213

## Nobel Prize Winners: A List of Nobel Laureates

Environmental disaster of the aral sea, the atmosphere of earth: a layer of gases surrounding the planet.

Words: 1435

## Running out of time ?

Entrust your assignment to proficient writers and receive TOP-quality paper before the deadline is over.

## What Is The Importance Of Universal Law Of Gravitation?

Gravitation is a force that is present in all objects in this universe. This force exerts on each and every object irrespective of its size, and shape. Whether it is a subatomic particle, or a cluster of galaxies, the universal law of gravitation applies on every particle. In this article we will learn more about this force, and its importance.

## What is Gravitational Force?

This is a powerful force that attracts every object to its gravitation center. This force is exerted by the object due to its mass. According to the Universal Law of Gravitation, every object of mass present in the Universe has the power to attract every other object of mass.

The force with which it attracts is inversely proportional to the square of the distance between their centers and directly proportional to the product of the masses. Newton’s third law of gravitation also states that the amount of the force exerted on both the objects is same and remains consistent.

This law is represented as: F∝m1m2/r2

It can also be written as F=G(m1m2)/r2 where, G= Universal Gravitation Constant F = Force of gravitation that exist between two bodies m1 = Mass of one object m2 = Mass of the second object r = Distance between the mid-point of one object and the mid-point of another object

The value of Gravitational Constant is 6.67 x 10−11 m3⋅kg−1⋅s−2N. Its value remains constant throughout the universe.

## Importance of Universal Law of Gravitation

After looking at the apple falling from the tree to the ground, Newton got motivated to establish the connection between astronomical motions, and falling bodies. As a result of this observation he realized that there must be some force exerted by the ground that is attracting the apple towards itself. The length of this force can even surpass the length of the tree. It can even reach the Sun .

A lot of importance is linked to Newton’s universal law of gravitation. The conclusion of this law gives us the answer why a person stays rooted to the ground. It also tells us what force makes the Earth revolves around the sun in its orbit. The conclusion derived from this law is not just limited to daily life objects but also helps in understanding the power by which heavenly bodies work. The law summarizes the idea that every particle of matter in this universe has the ability to attract each other by the gravitation force.

Newton’s law conveys us the strength of this attraction. Based on the conclusion derived from the law, it is clear that it is the gravitational force of the earth that binds the different terrestrial objects towards the Earth. It is the force of attraction that lies between two objects of mass. The law also explains about the force that keeps us attached to the Earth. It explains the revolution of planets around the sun and revolution of moon around the Earth. Prediction of lunar, and solar eclipse and the tides arising due to the sun and the moon are also based on the Universal Law of Gravitation.

Newton derived this formula after extensive study of the eras of measurements from stargazers before him. As per his gravitational law, anything that starts to move from a stationary position undergoes an acceleration. If there is an acceleration, there has to be a force. The process of falling of apple from the tree and reaching the Earth is due to the presence of force of attraction between both these entities/objects.

The extent to which the Earth exerts the force is not just limited to the height of the tree, it can even reach the galaxies. Newton also determined that the moon also experience the impact of the planet’s force of attraction that’s the reason it remains in its position and doesn’t fall down.

According to Newton, weight is the gravitational force that exerts on the mass of the object at any instant of time and is measured in terms of kilograms. As a result, he concluded that the mass of the object remains same at different places, but its weight will change depending on the mass and placement of objects around it. With the universal gravitational law, scientists can estimate the positions of celestial bodies anywhere in the solar system.

Newton’s Universal law of Gravitation has assisted scientists to figure out how much energy is required to disrupt the gravitational bonds of planet. The path of astronaut and the satellite’s orbit that are helpful for communications, planet observation, global positioning information, and scientific research around Earth and other planets are computed with this law.

## Leave a Reply Cancel reply

Your email address will not be published. Required fields are marked *

Save my name, email, and website in this browser for the next time I comment.

Captcha: 4484

## Essay on Gravity

Students are often asked to write an essay on Gravity in their schools and colleges. And if you’re also looking for the same, we have created 100-word, 250-word, and 500-word essays on the topic.

Let’s take a look…

## 100 Words Essay on Gravity

Understanding gravity.

Gravity is a force that attracts two objects toward each other. The earth’s gravity pulls us down, keeping us on the ground. It’s why when you jump, you come back down.

## Gravity in Space

In space, gravity keeps planets in orbit around the sun. It’s also why astronauts float in space – they’re falling toward earth but moving forward too fast, creating a constant fall!

## Importance of Gravity

Without gravity, we’d float off into space. It also shapes the universe, forming stars, planets and galaxies. So, gravity is a key force that makes the universe work.

## 250 Words Essay on Gravity

Gravity, a fundamental force in the universe, governs the motion of all celestial bodies. It’s an invisible force that pulls objects toward each other. The more massive an object, the stronger its gravitational pull.

## The Law of Universal Gravitation

Sir Isaac Newton’s Law of Universal Gravitation states that every particle of matter in the universe attracts every other particle with a force directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers. This law explains not only the downward force that keeps us grounded on Earth but also the motion of planets around the Sun.

## Gravity in Einstein’s Theory of Relativity

Einstein’s General Theory of Relativity, however, provides a more comprehensive understanding of gravity. He proposed that gravity is not a force but a curvature in the fabric of space-time caused by mass and energy. This revolutionary perspective has been confirmed by numerous experiments and observations, including the bending of light by massive objects and the precession of Mercury’s orbit.

## Gravity: A Mystery Yet to Unfold

Despite our understanding, gravity remains a mystery in many ways. For instance, it is the weakest of the four fundamental forces, yet it dominates on a cosmic scale. Also, it’s incompatible with quantum mechanics, the theory that excellently describes three other forces. This incompatibility has led to the quest for a theory of quantum gravity, a unified model that can reconcile these disparities.

In conclusion, gravity, while seemingly simple, is a complex and intriguing aspect of our universe, driving the motion of celestial bodies and shaping the cosmos. Understanding it is fundamental to unravelling the mysteries of the universe.

## 500 Words Essay on Gravity

Introduction to gravity.

Gravity is one of the four fundamental forces in the universe, alongside electromagnetism, and the strong and weak nuclear forces. It is the force that attracts two bodies towards each other, the force that gives weight to physical objects, and the force that drives the dynamics of the universe.

## The Concept of Gravity

The concept of gravity was first systematically studied by the great scientist Sir Isaac Newton in the 17th century. Newton’s law of universal gravitation states that every particle of matter in the universe attracts every other particle with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.

## Gravity and Einstein’s Theory of Relativity

However, Newton’s theory was superseded by Albert Einstein’s theory of General Relativity. According to Einstein, gravity is not a force transmitted through space, but a curvature of space-time caused by mass and energy. Objects moving in this curved space-time follow geodesics, paths of least resistance, which we perceive as the force of gravity.

## Gravity and Quantum Mechanics

One of the great unsolved problems in physics is the reconciliation of gravity with quantum mechanics, the theory that describes the behavior of particles at the smallest scales. In quantum mechanics, forces are mediated by particles, but no such particle for gravity has been conclusively identified. This hypothetical particle, the graviton, is the subject of ongoing research.

## Gravity and the Expansion of the Universe

Gravity also plays a crucial role in our understanding of the universe at the largest scales. It is the force that causes matter to clump together into stars, galaxies, and galaxy clusters. However, despite the pull of gravity, the universe is not contracting, but expanding. This expansion is thought to be driven by dark energy, a mysterious form of energy that counteracts gravity and is spread uniformly throughout the universe.

## Gravity and the Future of Physics

The study of gravity is at the forefront of modern physics. It is intimately connected with some of the deepest questions about the nature of the universe and our place in it. The search for a quantum theory of gravity, the study of black holes, and the quest to understand dark energy are all areas where gravity plays a central role. The answers to these questions may well lead to a new revolution in our understanding of the physical world.

In conclusion, gravity is a fundamental force of nature that shapes the universe at all scales, from the smallest particles to the largest cosmic structures. It is a subject of intense research and a source of profound questions about the nature of reality. As we delve deeper into the mysteries of gravity, we are likely to uncover new insights about the universe and our place within it.

That’s it! I hope the essay helped you.

If you’re looking for more, here are essays on other interesting topics:

- Essay on Government
- Essay on Gopabandhu Das
- Essay on Google

Apart from these, you can look at all the essays by clicking here .

Happy studying!

## Leave a Reply Cancel reply

Your email address will not be published. Required fields are marked *

Save my name, email, and website in this browser for the next time I comment.

Study Like a Boss

- Newton’s Law of Universal Gravitation

Gravity if one of the four fundamental forces in the universe. Though the fundamental principles of it eluded scientists until Sir Isaac Newton was able to mathematically describe it in 1687 (Eddington 93). Gravity plays a serious part in everyday actions as it keeps everything on the ground; without gravity everything would be immobile unless a force was applied (then it would move infinitely because there would be no force to stop it). Perhaps, the best place to start then would be with such a simple item as an apple (after all it is what “sparked” Newton’s creativity).

The apple is ne of the two curiosities (the other being the moon) that led Newton to discover The Law of Universal Gravitation in 1666 (Eddington 93). As Newton later wrote, it is the story of the sight of an apple falling to the ground (he was resting at Woolsthorpe because of the plague at Cambridge) that caused Newton to wonder if this same force was what held the moon in place (Gamow 41). Newton knew that an object fell to the earth at a rate of about 9. 8 meters (32 feet) per second second as pointed out by Galileo.

Thus “the apple that fell from the tree” fell to Earth at about this rate. For the first basic xplanation of this we will assume a linear plane, one in which all forces act in only one direction. Therefore when the apple fell it went straight towards the center of the earth (accelerating at about 9. 8 meters per second second). Newton then figured that the same force that pulled the apple to Earth also pulls the moon to the earth. But what force keeps the moon from flying into the earth or the earth flying into the sun (Edwards 493)?

To better understand this, one other aspect must first be understood. Galileo showed that all objects fall to the earth at the same rate (the classic annonball and feather proved this). But why? If a piano and a saxophone were both dropped from the top of the Empire State Building then they would both slam into the ground at the same rate. Newton realized then that the moon and the apple were both being pulled towards Earth at the same rate but yet the moon was the only one who resisted the force and stayed in its elliptical orbit (Eddington 94).

Newton’s Third Law of Motion says that every force exerted by one object on another is equal to a force, but opposite in direction, exerted be the second object on the first (every reaction has an equal but opposite eaction). So the force of the earth pulling the apple to the ground is proportionally the same as the force the apple exerts back on the earth. Now Johannes Kepler lived some forty-five years before Isaac Newton. And he showed that the orbits of the planets in our solar system were elliptical.

When the time of Newton came around he mathematically proved that, if Kepler’s First Law was true, then the force on a planet varied inversely with the square of the distance between the planet and the sun. He did this using Kepler’s Third Law (Zitzewitz 160). The distance in this formula is from the center of the masses and is the average distance over their entire period. It is also important to note that the force acted in the direction of this line (an important factor when dealing with vectors) (Zitzewitz 160). Newton, confident that his idea of all objects exerting a force back on Earth, devised a formula for Universal Gravitation.

It is important to note that Newton was not the first to think of Universal Gravitation, he was just the first one to make considerable and remarkable proofs for it based on mathematical explanations. He said that if force is relative to the mass of an object and it’s acceleration then the force between two objects must also be the same. Thus he came up with the first part of the equation. Also, as he had proved earlier using Kepler’s Third Law of Motion, that the force between two objects is inversely proportional to their distances squared (an inverse square law), then that must also be part of the Universal Gravitation equation.

Thus we know that the two masses and the distance are related to the force; and because the distance is inversely proportional then the product of the masses ivided by the distance between their centers squared must equal the force between the two objects (Zitzewitz 161). Now earlier, Newton had proved that the force on an object was proportional to an object’s mass and its acceleration. And the equation that he had formulated so far did not include anything that would resemble the acceleration. Thus he knew that a gravitational constant must be present and that it should be the same throughout all of the universe.

However, due to scientific limitations he was never able to figure out the exact value of this constant (Zitzewitz 161). One hundred years later, though, an young engineer by the name of Cavendish devised a complex apparatus that was able to measure this gravitational constant. Basically by using very sensitive telescopes and known angles he was able to determine the distance one ball moved another ball. This is often known as “weighing the earth” (Zitzewitz 162-163). The effects of Newton’s Law of Universal Gravitation were varied; but the most common use for his law was the prediction of several planets beyond Jupiter and Saturn.

In 1830, it appeared that Newton’s Law of Universal Gravitation had not been correct because the orbit of Saturn did not follow his law. Some astronomers thought that the force of an undiscovered planet may be changing its course and in 1845 a couple of scientists at the Berlin Observatory began searching for this hidden planet. It did not take very long. The massive planet now known as Neptune was found on the first night of searching (Zitzewitz 164). Perhaps one of the most key things about any theory of gravity prior to Einstein was the fact that none of them proposed the origin of gravity.

Newton’s law always proved to be true in the common world but did not explain he source of the force (Eddington 95). Albert Einstein proposed his Theory of Gravity in his General Theory of Relativity. In this he said that space was a three dimensional plane and that masses curved this plane in one way or another (Eddington 95). Thus a massive object would cause a large “hole” and smaller objects would “orbit” it. It is interesting to note that in either case, Newton’s or Einstein’s law, both prove to be true in the common world. Massive universal objects, such as black holes, are an exception but that’s another story in itself (Edwards 498).

To export a reference to this article please select a referencing style below:

## Related posts:

- Stars And Galaxies
- Sir Isaac Newton
- Sir Isaac Newton Paper
- Sir Isaac Newton – English Mathematician And Physicist
- Sir Isaac Newton Biography
- Isaac Newton – one of the greatest scientists of all time
- Biography of Isaac Newton
- Isaac Newton Biography

## Leave a Comment Cancel reply

Save my name, email, and website in this browser for the next time I comment.

## Scotland's papers: Asylum 'fast-track' and FM's in-law on drug charge

- Published 16 January 2024

## More from Scotland's papers

The Scotsman

Daily Record

The Scottish Sun

Scottish Daily Express

The Telegraph

The National

The Courier

The P&J

Glasgow Times

Edinburgh News

## 'Law & Order: SVU' star Mariska Hargitay shares essay on her experience with sexual assault

"Law & Order: Special Victims Unit" star Mariska Hargitay opened up for the first time about her experience with sexual assault, writing in a first-person essay for People magazine that she was raped in her 30s.

"It wasn’t sexual at all. It was dominance and control. Overpowering control," she wrote in an essay published Wednesday.

"He was a friend. Then he wasn’t. I tried all the ways I knew to get out of it. I tried to make jokes, to be charming, to set a boundary, to reason, to say no. He grabbed me by the arms and held me down. I was terrified. I didn’t want it to escalate to violence. I now know it was already sexual violence, but I was afraid he would become physically violent. I went into freeze mode, a common trauma response when there is no option to escape. I checked out of my body," the actor wrote.

Hargitay, who created the Joyful Heart Foundation in 2004 to help survivors of sexual violence and abuse, said she could not process what happened to her so she "removed it from my narrative."

She wrote that she views that as a survival technique.

"I now have so much empathy for the part of me that made that choice because that part got me through it. It never happened. Now I honor that part: I did what I had to do to survive," she said in her essay.

Over the years, Hargitay, 59, started telling those closest to her what happened. She said "they were the first ones to call it what it was. They were gentle and kind and careful, but their naming it was important."

"Now I’m able to see clearly what was done to me. I understand the neurobiology of trauma. Trauma fractures our mind and our memory. The way a mirror fractures," she wrote.

Hargitay, who plays squad captain Olivia Benson on "Law & Order: SVU," said survivors often tell her how the show has helped them heal, but she now realizes that they have been "the ones who’ve been a source of strength for me."

"They’ve experienced darkness and cruelty, an utter disregard for another human being, and they’ve done what they needed to survive. For some, that means making Olivia Benson a big part of their lives — which is an honor beyond measure — for others, it means building a foundation. We’re strong, and we find a way through," she wrote.

The actor said her hope is that sexual violence will end and the power structures put in place that allow it to happen will change. As for justice, she wants an "acknowledgment and an apology."

"That is a beginning. I don’t know what is on the other side of it, and it won’t undo what happened, but I know it plays a role in how I will work through this," Hargitay wrote.

If you or someone you know is in crisis, these resources can help https://www.nbcnews.com/news/us-news/if-you-or-someone-you-know-crisis-these-resources-can-n1267774

Minyvonne Burke is a senior breaking news reporter for NBC News.

## Scotland's papers: Rwanda appeals fast-track and FM's brother-in-law on drug charge

Posted: January 16, 2024 | Last updated: January 16, 2024

## More for You

US Air Force lieutenant crowned Miss America 2024

Doctor Strange In The Multiverse of Madness' - Cast Interview

30 lovely large-engined classic cars

Here Are The Top Guard Dogs For Home Security

Mauritius: Cyclone Belal – Severe Flooding Hits Port Louis

German firms supply Ukraine as Russia ups arms production

Hair loss: how do I stop my hair from falling out?

Jose Mourinho sacked: the Special One by the numbers – the wins, the defeats, the signings…

The meaning behind major car nameplates

Science shows there are six key behaviors that kill relationships

Over 100 million Americans under wind chill warnings as Arctic blast hits US

Brown accuses Fujitsu of misleading ministers over Horizon

Here Are 6 Of The Most Beautiful Small Towns In Europe

What happened to the advanced tanks Putin sent to Ukraine?

Legendary Musicians With Incredibly Long Careers

15 cool classics with vinyl roofs

New Zealand MP resigns following shoplifting allegations

Korean Air and Cathay Pacific flights collide in a second plane crash in Japan within weeks

A look at the most devalued football players this year

Russia dismisses Davos discussion on Ukrainian president’s peace plan

## IMAGES

## VIDEO

## COMMENTS

Newton's law of gravitation, statement that any particle of matter in the universe attracts any other with a force varying directly as the product of the masses and inversely as the square of the distance between them.

Newton's law of universal gravitation says that every particle attracts every other particle in the universe with a force that is proportional to the product of their masses and inversely proportional to the square of the distance between their centers.

Newton's law of gravitation is simple equation, but devastatingly effective: plug in the numbers and you can predict the positions of all the planets, moons and comets you might ever want to watch ...

The force is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. Figure 2.9.2 2.9. 2: Gravitational attraction is along a line joining the centers of mass of these two bodies. The magnitude of the force is the same on each, consistent with Newton's third law.

Thomson Gale,. 2001. Download Citation Abstract: In 1687 English physicist Sir Isaac Newton (1642-1727) published a law of universal gravitation in his influential work Philosophiae Naturalis Principia Mathematica (Mathematical Principles of Natural Philosophy).

Newton's Law of Universal Gravitation states that every particle attracts every other particle in the universe with force directly proportional to the product of the masses and inversely proportional to the square of the distance between them. The universal gravitation equation thus takes the form

The formula of Newton's Law of Gravity. Newton's Law of Gravitation is formulated as : FG = G(m1m2) r2 F G = G ( m 1 m 2) r 2. In the above equation, the values are defined as: Fg is the force of gravity that is typically in newtons. G is the gravitational constant that adds the proper level of proportionality to the equation.

Gravity is a pulling force (always a force of attraction) between every object in the universe (every bit of matter, everything that has some mass) and every other object. It's a bit like an invisible magnetic pull, but there's no magnetism involved. Some people like to call this force gravitation and reserve the word gravity for the special ...

F grav = 1823 N. Today, Newton's law of universal gravitation is a widely accepted theory. It guides the efforts of scientists in their study of planetary orbits. Knowing that all objects exert gravitational influences on each other, the small perturbations in a planet's elliptical motion can be easily explained.

Every object in the universe attracts every other object with a force along a line joining them. The equation for Newton's law of gravitation is: F g = G m 1 m 2 r 2. Where: F g is the gravitational force between m 1 and m 2 , G is the gravitational constant equal to 6.67 × 10 − 11 m 3 kg ⋅ s 2 , and. m 1 and m 2 are masses.

Newton's law of the universal gravitation states that, "Any two bodies in the universe attract each other with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them." The law of universal gravitation was find by Newton because of an apple.

The equation for Newton's law of gravitation is: F g = G m 1 m 2 r 2. where: F g is the gravitational force between m 1 and m 2 , G is the gravitational constant equal to 6.67 × 10 − 11 m 3 kg ⋅ s 2 , and. m 1 and m 2 are masses. The force is directly proportional to the product of the masses. It is also inversely proportional to the ...

Newton's Law of Universal Gravitation. Newton noted that objects at Earth's surface (hence at a distance of R E from the center of Earth) have an acceleration of g, but the Moon, at a distance of about 60 R E, has a centripetal acceleration about (60) 2 times smaller than g. He could explain this by postulating that a force exists between any two objects, whose magnitude is given by the ...

Starting from first principles and general assumptions Newton's law of gravitation is shown to arise naturally and unavoidably in a theory in which space is emergent through a holographic scenario. Gravity is explained as an entropic force caused by changes in the information associated with the positions of material bodies. A relativistic generalization of the presented arguments directly ...

Newton's Law of Universal Gravitation states that every object in the universe attracts every other object with a force that is directly proportional to the mass of the objects and inversely proportional to the square of the distance between them.

Gravitation - Gravitational Force and Newton's Law of Gravitation Gravitation or gravity is the force of attraction between any two bodies. All the objects in the universe attract each other with a certain amount of force, but in most cases, the force is too weak to be observed due to the very large distance of separation.

Sciences Physics Format: APA Academic level: College Paper type: Essay (Any Type) Words: 317 Pages: 1 Downloads: 0 Newton's universal law of gravitation did emanate from his desire to create a connection between astronomical movements and falling bodies. This was in connection to a fallen apple.

Sir Isaac Newton's Law Of Universal Gravitation Essay Decent Essays 1229 Words 5 Pages 2 Works Cited Open Document Gravity if one of the four fundamental forces in the universe. Though the fundamental principles of it eluded scientists until Sir Isaac Newton was able to mathematically describe it in 1687 (Eddington 93).

According to the Universal Law of Gravitation, every object of mass present in the Universe has the power to attract every other object of mass. The force with which it attracts is inversely proportional to the square of the distance between their centers and directly proportional to the product of the masses.

Sir Isaac Newton's Law of Universal Gravitation states that every particle of matter in the universe attracts every other particle with a force directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.

Newton's first law: the law of inertia. When a basketball player shoots a jump shot, the ball always follows an arcing path. The ball follows this path because its motion obeys Isaac Newton's laws of motion. Newton's first law states that if a body is at rest or moving at a constant speed in a straight line, it will remain at rest or keep ...

Newton's Law of Universal Gravitation Gravity if one of the four fundamental forces in the universe. Though the fundamental principles of it eluded scientists until Sir Isaac Newton was able to mathematically describe it in 1687 (Eddington 93).

Sir Isaac Newton's Law of Universal Gravitation provides the hard scientific theory to parallel the philosophy of my interests. Everything invokes me, though some ideas or objects may provide a stronger attractive force. Only upon separation from the defining aspects of my life may I experience the rest of my world, the attraction of the ...

Fani Willis, the district attorney spearheading the Georgia racketeering case against former President Donald Trump and his associates stemming from their actions following the 2020 election, has ...

Gotham/GC Images/Getty Images. CNN —. Mariska Hargitay revealed in a moving personal essay that decades ago, she was raped - but the "Law & Order: SVU" star wrote that she won't let the ...

Scotland's papers: Rwanda appeals fast-track and FM's brother-in-law on drug charge. Sunak's offer to halt MP's asylum rebellion and Yousaf's in-law accused of dealing heroin make the papers.

"A man raped me in my thirties," Hargitay, 59, opened the essay before detailing the encounter. "I tried to make jokes, to be charming, to set a boundary, to reason, to say no," Hargitay wrote ...

By Minyvonne Burke. "Law & Order: Special Victims Unit" star Mariska Hargitay opened up for the first time about her experience with sexual assault, writing in a first-person essay for People ...

Sunak's offer to halt MP's asylum rebellion and Yousaf's in-law accused of dealing heroin make the papers. BBC. Scotland's papers: Rwanda appeals fast-track and FM's brother-in-law on drug charge.