## What Is Gravitational Force

Newtons Law of Universal Gravitation is used to explain gravitational force. This law states that every massive particle in the universe attracts every other massive particle with a force which is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. This general, physical law was derived from observations made by induction. Another way, more modern, way to state the law is: every point mass attracts every single other point mass by a force pointing along the line intersecting both points. The force is proportional to the product of the two masses and inversely proportional to the square of the distance between the point masses.

Gravitational force surrounds us. It is what decides how much we weigh and how far a basketball will travel when thrown before it returns to the surface. The gravitational force on Earth is equal to the force the Earth exerts on you. At rest, on or near the surface of the Earth, the gravitational force equals your weight. On a different astronomical body like Venus or the Moon, the acceleration of gravity is different than on Earth, so if you were to stand on a scale, it would show you that you weigh a different amount than on Earth.

Each system in the galaxy, and presumably, the universe, has a barycenter. The push and pull of the gravitational force of the objects is what keeps everything in space from crashing into one another.

## Newton’s Law Of Universal Gravitation

In 1687 Newton published his work on the universal law of gravity in his book Philosophiae Naturalis Principia Mathematica . Newtonâs law of gravitation states that: *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.*If the particles have masses *m1* and *m2* and are separated by a distance *r* , the magnitude of this gravitational force is:

where:

## How To Use The Gravity Formula

*You can enter this large number into the calculator by typing 5.972e24.*

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## Astrophysics Astroparticles & Gravitation

Astrophysics activities at Georgia Tech are devoted to interdisciplinary research and education linking astrophysics, astroparticle physics, cosmology, numerical relativity and gravitational wave physics. Research focuses on extreme astrophysics such as mergers of black holes and neutron stars, central engines of active galactic nuclei, gamma ray bursts and the sources of the highest energy neutrinos. Faculty that conduct astrophysics research at Georgia Tech form the Center for Relativistic Astrophysics .

## What Do You Mean By Gravitational Force

Gravity can be defined as the force which a planet exerts on other objects and draws them towards its center. It is this force of gravity that keeps all the planets in their orbits around the Sun.

Newton explained what is meant by gravitational force in his law of universal gravitation as a force of attraction that exists between any two objects having mass. This force is directly proportional to the masses of the objects and inversely proportional to the distance between them. It is mathematically expressed as:

F = G * / R2

Where F – Force of gravity.

G – Gravitational constant and its value is 6.67 x 10-11 N * m2/kg2.

R – The distance between the objects.

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## History Of Gravitational Theory:

Ptolemy has proposed geocentric model which failed in understanding planetary motions led to the development of the heliocentric model by Nicholas Copernicus whose 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 in explaining many aspects like the occurrence of seasons which led the construction of a model based on Keplers laws of planetary motion.

## Universal Law Of Gravitation

Every object in the universe has the property to attract every other object with a force which is directly proportional to the product of their masses and inversely proportional to the square of the distance between them .

**F**= force of attraction between two the objects A & B**M**= mass of A**d2**= the square of the distance between A & B**G**= is the constant of proportionality and is known as the universal gravitation constant.The SI unit of G is

**N m2 kg2**. It is obtained by substituting the units of force, distance and mass (as given in the following equation

$$G = \frac$$

Henry Cavendish had calculated the value of

**G**as**6.673 × 1011 N m2 kg2**.Henry Cavendish had used a sensitive balance to find the value of G.

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## Newtons Universal Law Of Gravitation

What do aching feet, a falling apple, and the orbit of the Moon have in common? Each is caused by the gravitational force. Our feet are strained by supporting our weightâthe force of Earthâs gravity on us. An apple falls from a tree because of the same force acting a few meters above Earthâs surface. And the Moon orbits Earth because gravity is able to supply the necessary centripetal force at a distance of hundreds of millions of meters. In fact, the same force causes planets to orbit the Sun, stars to orbit the center of the galaxy, and galaxies to cluster together. Gravity is another example of underlying simplicity in nature. It is the weakest of the four basic forces found in nature, and in some ways the least understood. It is a force that acts at a distance, without physical contact, and is expressed by a formula that is valid everywhere in the universe, for masses and distances that vary from the tiny to the immense.

The gravitational force is relatively simple. It is always attractive, and it depends only on the masses involved and the distance between them. Stated in modern language, Newtonâs universal law of gravitation states that every particle in the universe attracts every other particle with a force along a line joining them. The force is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.

## What Is Gravity Made Of

Earths gravity comes from its entire mass. Earths entire mass exerts a combined gravitational pull on your body mass. It is this gravitational pull of the earth which gives you your weight. So if you are on a planet whose mass is less than the earth, then you would weigh less there. You and earth both exert gravitational force on each other, but since earths mass is way more than your weight, your force has no effect on the planet.

A team of scientists based in the South Pole discovered the celestial fingerprint using a telescope, BICEP2. This fingerprint explains the beginning of time and reveals microscopic details of gravity. Quantum particles in an infant universe gave rise to inflation, which is the reason behind why the universe exploded outwards.

It also revealed that gravity is made up of quantum particles called gravitons. A single graviton is too small and massless, but these gravitons’ quantum fluctuations in the infant universe bend pockets of this tiny space-time.

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## What Is The Gravity Equation

Use the following formula to calculate the gravitational force between any two objects:

where:

- F stands for gravitational force. It is measured in newtons and is always positive. It means that two objects of a certain mass always attract each other
- M and m are the masses of two objects in question
- R is the distance between the centers of these two objects and
- G is the gravitational constant. It is equal to 6.674×10-11 N·m²/kg².

Did you notice that this equation is similar to the formula in Coulomb’s law? While Newton’s law of gravity deals with masses, Coulomb’s law describes the attractive or repulsive force between electric charges.

## Newtons Law Of Universal Gravitation

Enter Isaac Newton, who realised there must be a force acting between the planets and the Sun. Whether or not a falling apple really prompted his eureka moment, the equation he came up with to describe the behaviour of this force was revolutionary.

*F* = *Gm*1*m*2 / *r*2

This equation says that gravity is a force that two objects with mass exert on each other simply because they have mass. The strength of the force is proportional to the masses of the two objects divided by the square of the distance between them . The *G* is a constant that measures the basic strength of the force.

It boils down to this: the more massive objects are, the greater the force of attraction between them, but the further they are apart, the weaker the attraction.

Consider the legend associated with Newtons revelation about gravity: an apple falling from a tree. Newtons law of universal gravitation tells us that not only does the Earth tug on the apple, the apple also tugs on the Earth. But the Earths enormous mass means it takes a lot more force to move it an appreciable amount, so the apple comes toppling down while the Earth remains practically motionless. The same is true in a broader context. Every object in the Universe is attracting every other object, but the closer and more massive it is, the greater its gravitational power.

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## Using Equations As A Guide To Thinking

**The inverse square law proposed by Newton suggests that the force of gravity acting between any two objects is inversely proportional to the square of the separation distance between the object’s centers. Altering the separation distance results in an alteration in the force of gravity acting between the objects. Since the two quantities are inversely proportional, an increase in one quantity results in a decrease in the value of the other quantity. That is, an increase in the separation distance causes a decrease in the force of gravity and a decrease in the separation distance causes an increase in the force of gravity. **

**Furthermore, the factor by which the force of gravity is changed is the square of the factor by which the separation distance is changed. So if the separation distance is doubled , then the force of gravity is decreased by a factor of four . And if the separation distance is tripled , then the force of gravity is decreased by a factor of nine . Thinking of the force-distance relationship in this way involves using a mathematical relationship as a guide to thinking about how an alteration in one variable effects the other variable. Equations can be more than merely recipes for algebraic problem-solving they can be “guides to thinking.”**

**Check your understanding of the inverse square law as a guide to thinking by answering the following questions below.**

**Check Your Understanding**

**Check Your Understanding**

## Case : A Hollow Spherical Shell

The gravitational force acting by a spherically symmetric shell upon a point mass *inside *it, is the vector sum of gravitational forces acted by each part of the shell, and this vector sum is equal to zero. That is, a mass \text *within *a spherically symmetric shell of mass \text, will feel no net force .

The net gravitational force that a spherical shell of mass \text exerts on a body *outside *of it, is the vector sum of the gravitational forces acted by each part of the shell on the outside object, which add up to a net force acting as if mass \text is concentrated on a point at the center of the sphere .

**Diagram used in the proof of the Shell Theorem**: This diagram outlines the geometry considered when proving The Shell Theorem. In particular, in this case a spherical shell of mass \text exerts a force on mass \text outside of it. The surface area of a thin slice of the sphere is shown in color.

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## Newton’s Theory Of Gravitation

In 1679, Robert Hooke wrote to English mathematician Isaac Newton of his hypothesis concerning orbital motion, which partly depends on an inverse-square force. In 1684, both Hooke and Newton told Edmond Halley that they had proven the inverse-square law of planetary motion. Hooke refused to produce his proofs, but Newton produced *De motu corporum in gyrum* , in which he derives Kepler’s laws of planetary motion. Halley supported Newton’s expansion of his work into the *Philosophiæ Naturalis Principia Mathematica* , in which he hypothesizes the inverse-square law of universal gravitation.

According to Newton, he “deduced that the forces which keep the planets in their orbs must reciprocally as the squares of their distances from the centers about which they revolve: and thereby compared the force requisite to keep the Moon in her Orb with the force of gravity at the surface of the Earth and found them answer pretty nearly.” The equation is the following:

F m_}}}\ }

Where *F* is the force, *m1* and *m2* are the masses of the objects interacting, *r* is the distance between the centers of the masses and *G* is the gravitational constant.

## Universal Gravitation For Spherically Symmetric Bodies

*The **Law** of Universal Gravitation* states that the gravitational force between two points of mass is proportional to the magnitudes of their masses and the inverse-square of their separation, \text:

\displaystyle \text=\frac}^2}

However, most objects are not point particles. Finding the gravitational force between three-dimensional objects requires treating them as points in space. For highly symmetric shapes such as spheres or spherical shells, finding this point is simple.

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## Weight And The Gravitational Force

**We have seen that in the Universal Law of Gravitation the crucial quantity ismass. In popular language mass and weight are often used to mean the samething in reality they are related but quite different things. What wecommonly call weight is really just the gravitational force exerted on anobject of a certain mass. We can illustrate by choosing the Earth as one of the two massesin the previous illustration of the Law of Gravitation:**

**Thus, the weight of an object of mass**

*m*at the surface of the Earth is obtainedby multiplying the mass*m*by the acceleration due to gravity,*g*, at the surfaceof the Earth. The acceleration due to gravity is approximately the product ofthe universal gravitational constant*G*and the mass of the Earth*M*, divided by the radius of the Earth,*r*, squared. The measured gravitational acceleration at theEarth’s surface is found to be about 980 cm/second/second.## Vector Form Of Newtons Law Of Gravitation

The vector form of Newtons 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 and are placed at a distance

Hence the applied forces are equal and opposite. Hence the gravitational force follows Newtons third law

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## Equations For A Falling Body Near The Surface Of The Earth

Under an assumption of constant gravitational attraction, Newton’s law of universal gravitation simplifies to *F* = *mg*, where *m* is the mass of the body and *g* is a constant vector with an average magnitude of 9.81 m/s2 on Earth. This resulting force is the object’s weight. The acceleration due to gravity is equal to this *g*. An initially stationary object which is allowed to fall freely under gravity drops a distance which is proportional to the square of the elapsed time. The image on the right, spanning half a second, was captured with a stroboscopic flash at 20 flashes per second. During the first 120 of a second the ball drops one unit of distance by 220 it has dropped at total of 4 units by 320, 9 units and so on.

Under the same constant gravity assumptions, the potential energy, *E*p, of a body at height *h* is given by *E*p = *mgh* . This expression is valid only over small distances *h* from the surface of the Earth. Similarly, the expression h g }}} for the maximum height reached by a vertically projected body with initial velocity *v* is useful for small heights and small initial velocities only.

## Relationship Between Gravity And Weight

Weight is defined as the force with which a body is attracted to the earth by gravitation. It is just another word for the force of gravity *F**g*. Weight is a force that acts on all objects near earth. The weight of an object can be calculated by multiplying the mass of the body with the magnitude of the acceleration due to gravity* .*

*Mathematically, it is represented as:*

Fg = mg |

is the force of gravity*F**g*is the mass of the object*m*is the acceleration due to gravity*g*

Many people confuse mass with weight. One has to keep in mind that mass is the measure of how much the body resists velocity, in other words, the inertia of the object. Although they are closely related to each other, they mean different things. The mass has units of kg, whereas, the weight is a force and has units of N.

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