# Newton's law of universal gravitation

law of universal gravitationuniversal gravitationNewtonian gravityNewton's law of gravitationNewton's law of gravitylaw of gravitationNewton's theory of gravitationNewtonian gravitationgravitygravitation
Newton's law of universal gravitation is usually stated that every particle attracts every other particle in the universe with a force which is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.wikipedia
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### Isaac Newton

NewtonSir Isaac NewtonNewtonian
This is a general physical law derived from empirical observations by what Isaac Newton called inductive reasoning.
In Principia, Newton formulated the laws of motion and universal gravitation that formed the dominant scientific viewpoint until it was superseded by the theory of relativity.

### Scientific law

laws of physicsphysical lawlaws of nature
This is a general physical law derived from empirical observations by what Isaac Newton called inductive reasoning.
Ohm's law only applies to linear networks, Newton's law of universal gravitation only applies in weak gravitational fields, the early laws of aerodynamics such as Bernoulli's principle do not apply in case of compressible flow such as occurs in transonic and supersonic flight, Hooke's law only applies to strain below the elastic limit, Boyle's law applies with perfect accuracy only to the ideal gas, etc. These laws remain useful, but only under the conditions where they apply.

### Philosophiæ Naturalis Principia Mathematica

PrincipiaPhilosophiae Naturalis Principia MathematicaPrincipia Mathematica
It is a part of classical mechanics and was formulated in Newton's work Philosophiæ Naturalis Principia Mathematica ("the Principia"), first published on 5 July 1687.
The Principia states Newton's laws of motion, forming the foundation of classical mechanics; Newton's law of universal gravitation; and a derivation of Kepler's laws of planetary motion (which Kepler first obtained empirically).

### Gravitational constant

Newton's constantGuniversal gravitational constant
:where F is the gravitational force acting between two objects, m 1 and m 2 are the masses of the objects, r is the distance between the centers of their masses, and G is the gravitational constant.
is a key quantity in Newton's law of universal gravitation.]]

### Coulomb's law

Coulomb forceelectrostatic forceCoulomb interaction
Newton's law of gravitation resembles Coulomb's law of electrical forces, which is used to calculate the magnitude of the electrical force arising between two charged bodies.
Being an inverse-square law, the law is analogous to Isaac Newton's inverse-square law of universal gravitation, but gravitational forces are always attractive, while electrostatic forces can be attractive or repulsive.

### Inductive reasoning

inductioninductiveinductive logic
This is a general physical law derived from empirical observations by what Isaac Newton called inductive reasoning.
Kant thus saved both metaphysics and Newton's law of universal gravitation, but as a consequence discarded scientific realism and developed transcendental idealism.

### Force

forcesattractiveelastic force
Newton's law of universal gravitation is usually stated that every particle attracts every other particle in the universe with a force which is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers. In today's language, the law states that every point mass attracts every other point mass by a force acting along the line intersecting the two points.
He proposed a law of gravity that could account for the celestial motions that had been described earlier using Kepler's laws of planetary motion.

### Inverse-square law

inverse square lawinverse squareinverse-square
Both are inverse-square laws, where force is inversely proportional to the square of the distance between the bodies.
Newton's law of universal gravitation follows an inverse-square law, as do the effects of electric, magnetic, light, sound, and radiation phenomena.

### Johannes Kepler

KeplerDioptriceJohan Kepler
It was later on, in writing on 6 January 1679|80 to Newton, that Hooke communicated his "supposition ... that the Attraction always is in a duplicate proportion to the Distance from the Center Reciprocall, and Consequently that the Velocity will be in a subduplicate proportion to the Attraction and Consequently as Kepler Supposes Reciprocall to the Distance."
These works also provided one of the foundations for Newton's theory of universal gravitation.

### Cavendish experiment

Torsion bar experiment1798 experimentCavendish pendulum
The first test of Newton's theory of gravitation between masses in the laboratory was the Cavendish experiment conducted by the British scientist Henry Cavendish in 1798.
Since the gravitational force of the Earth on the small ball could be measured directly by weighing it, the ratio of the two forces allowed the density of the Earth to be calculated, using Newton's law of gravitation.

### Celestial mechanics

celestialcelestial dynamicscelestial mechanician
He points instead to the idea of "compounding the celestial motions" and the conversion of Newton's thinking away from "centrifugal" and towards "centripetal" force as Hooke's significant contributions.
Kepler's model greatly improved the accuracy of predictions of planetary motion, years before Isaac Newton developed his law of gravitation in 1686.

### Mass

inertial massgravitational massweight
In today's language, the law states that every point mass attracts every other point mass by a force acting along the line intersecting the two points.
In contrast to earlier theories (e.g. celestial spheres) which stated that the heavens were made of entirely different material, Newton's theory of mass was groundbreaking partly because it introduced universal gravitational mass: every object has gravitational mass, and therefore, every object generates a gravitational field.

### Classical mechanics

Newtonian mechanicsNewtonian physicsclassical
It is a part of classical mechanics and was formulated in Newton's work Philosophiæ Naturalis Principia Mathematica ("the Principia"), first published on 5 July 1687.
In mechanics, Newton was also the first to provide the first correct scientific and mathematical formulation of gravity in Newton's law of universal gravitation.

### Gauss's law for gravity

Gauss's lawfor gravityGauss' law for gravity
As per Gauss's law, field in a symmetric body can be found by the mathematical equation:
In physics, Gauss's law for gravity, also known as Gauss's flux theorem for gravity, is a law of physics that is essentially equivalent to Newton's law of universal gravitation.

### Point particle

point chargepoint massparticle
In today's language, the law states that every point mass attracts every other point mass by a force acting along the line intersecting the two points.
In Newtonian gravitation and classical electromagnetism, for example, the respective fields outside a spherical object are identical to those of a point particle of equal charge/mass located at the center of the sphere.

### Action at a distance

action-at-a-distancenonlocalityAction at a distance (physics)
For example, Coulomb's law and Newton's law of universal gravitation are such early theories.

### Albert Einstein

EinsteinEinsteinianA. Einstein
Newton's law has since been superseded by Albert Einstein's theory of general relativity, but it continues to be used as an excellent approximation of the effects of gravity in most applications.
By contrast, gravitational waves cannot exist in the Newtonian theory of gravitation, which postulates that the physical interactions of gravity propagate at infinite speed.

### Free fall

free-fallfreefallfree-falling
The relation of the distance of objects in free fall to the square of the time taken had recently been confirmed by Grimaldi and Riccioli between 1640 and 1650.
Assuming spherical objects means that the equation of motion is governed by Newton's Law of Universal Gravitation, with solutions to the gravitational two-body problem being elliptic orbits obeying Kepler's laws of planetary motion.

### General relativity

general theory of relativitygeneral relativity theoryrelativity
Newton's law has since been superseded by Albert Einstein's theory of general relativity, but it continues to be used as an excellent approximation of the effects of gravity in most applications.
General relativity generalizes special relativity and refines Newton's law of universal gravitation, providing a unified description of gravity as a geometric property of space and time, or spacetime.

### Shell theorem

homogeneous spherespherically symmetrical Earthuniform hollow sphere
For points inside a spherically-symmetric distribution of matter, Newton's Shell theorem can be used to find the gravitational force.
Applying Newton's Universal Law of Gravitation, the sum of the forces due to mass elements in the shaded band is

### Gravitational acceleration

acceleration due to gravityacceleration of gravityg
The gravitational field is a vector field that describes the gravitational force which would be applied on an object in any given point in space, per unit mass. It is actually equal to the gravitational acceleration at that point.
Newton's law of universal gravitation states that there is a gravitational force between any two masses that is equal in magnitude for each mass, and is aligned to draw the two masses toward each other.

### Physical object

physical bodyobjectbody
In the limit, as the component point masses become "infinitely small", this entails integrating the force (in vector form, see below) over the extents of the two bodies.
Under Newtonian gravity the gravitational field further away than the furthest extent of an object is determined only by the mass and the position of the center of mass.

### Theory of everything

theories of everythingeverythingattempt to explain all
Newton's work in his Mathematical Principles of Natural Philosophy dealt with this in a further example of unification, in this case unifying Galileo's work on terrestrial gravity, Kepler's laws of planetary motion and the phenomenon of tides by explaining these apparent actions at a distance under one single law: the law of universal gravitation.

### Gravity

gravitationgravitationalgravitational force
Newton's law of gravitation resembles Coulomb's law of electrical forces, which is used to calculate the magnitude of the electrical force arising between two charged bodies.
However, for most applications, gravity is well approximated by Newton's law of universal gravitation, which describes gravity as a force which causes any two bodies to be attracted to each other, with the force proportional to the product of their masses and inversely proportional to the square of the distance between them.

### Three-body problem

restricted three-body problem3-body problemcircular restricted three-body problem
The two-body problem has been completely solved, as has the restricted three-body problem.
In physics and classical mechanics, the three-body problem is the problem of taking the initial positions and velocities (or momenta) of three point masses and solving for their subsequent motion according to Newton's laws of motion and Newton's law of universal gravitation.