# Newton's law of gravitation

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## gravitation

gravitation, the attractive force existing between any two particles of matter.

### The Law of Universal Gravitation

Since the gravitational force is experienced by all matter in the universe, from the largest galaxies down to the smallest particles, it is often called universal gravitation. (Based upon observations of distant supernovas around the turn of the 21st cent., a repulsive force, termed dark energy, that opposes the self-attraction of matter has been proposed to explain the accelerated expansion of the universe.) Sir Isaac Newton was the first to fully recognize that the force holding any object to the earth is the same as the force holding the moon, the planets, and other heavenly bodies in their orbits. According to Newton's law of universal gravitation, the force between any two bodies is directly proportional to the product of their masses (see mass) and inversely proportional to the square of the distance between them. The constant of proportionality in this law is known as the gravitational constant; it is usually represented by the symbol G and has the value 6.670 × 10−11 N-m2/kg2 in the meter-kilogram-second (mks) system of units. Very accurate early measurements of the value of G were made by Henry Cavendish.

### The Relativistic Explanation of Gravitation

Newton's theory of gravitation was long able to explain all observable gravitational phenomena, from the falling of objects on the earth to the motions of the planets. However, as centuries passed, very slight discrepancies were observed between the predictions of Newtonian theory and actual events, most notably in the motions of the planet Mercury. The general theory of relativity proposed in 1916 by Albert Einstein explained these differences and provided a geometric explanation for gravitational phenomena, holding that matter causes a curvature of the space-time framework in its immediate neighborhood.

### The Search for Gravity Waves

Analogous to electromagnetic waves, gravity waves were predicted by Einstein's general theory of relativity. A hypothetical particle, given the name graviton, has been suggested as the mediator of the gravitational force; it is analogous to the photon, the particle embodying the quantum properties of electromagnetic waves (see quantum theory). Tantalizing evidence for the existence of gravity waves came from astronomical observations of a binary pulsar designated 1913+16. The rate at which the two neutron stars in the binary rotate around each other changes in a manner that is consistent with the emission of gravity waves. The subsequent search for gravity waves has involved the building of large interferometers sensitive enough to detect the faint waves directly (see interference). The Laser Interferometer Gravitational Wave Observatory (LIGO), supported by the National Science Foundation, consists of two interferometers constructed in the 1990s, one in Hanford, Wash., the other in Livingston, La.; each has two 2.5-mi-long (4-km) arms at a right angle to each other. LIGO begin its work in 2002, but did not detect any gravitational waves until after an upgrade completed in 2015. Beginning in late 2015, LIGO several times detected gravitational waves that resulted from the merging of two black holes. The European Gravitational Observatory's Virgo gravitational wave detector, near Pisa, Italy, became operational in 2017. Begun by French and Italian scientific research organizations and now including personnel from institutes in other European nations, Virgo has a design similar to LIGO's, with two arms 1.86 mi (3 km) long. Later in 2017 it and LIGO detected gravitational waves from another black-hole merger and from a neutron-star merger, and detections by LIGO and Virgo increased in subsequent years. The proposed, even more ambitious Laser Interferometer Space Antenna (LISA) was originally a NASA–European Space Agency project but NASA withdrew in 2011 due to a lack of funding.

### The Force of Gravity

The term gravity is commonly used synonymously with gravitation, but in correct usage a definite distinction is made. Whereas gravitation is the attractive force acting to draw any bodies together, gravity indicates that force in operation between the earth and other bodies, i.e., the force acting to draw bodies toward the earth. The force tending to hold objects to the earth's surface depends not only on the earth's gravitational field but also on other factors, such as the earth's rotation. The measure of the force of gravity on a given body is the weight of that body; although the mass of a body does not vary with location, its weight does vary. It is found that at any given location, all objects are accelerated equally by the force of gravity, observed differences being due to differences in air resistance, etc. Thus, the acceleration due to gravity, symbolized as g, provides a convenient measure of the strength of the earth's gravitational field at different locations. The value of g varies from about 9.832 meters per second per second (m/sec2) at the poles to about 9.780 m/sec2 at the equator. Its value generally decreases with increasing altitude. Because variations in the value of g are not large, for ordinary calculations a value of 9.8 m/sec2, or 32 ft/sec2, is commonly used.

### Bibliography

See A. S. Eddington, Space, Time and Gravitation (1920); J. A. Wheeler, A Journey into Gravity and Spacetime (1990); M. Bartusiak, Einstein's Unfinished Symphony: Listening to the Sounds of Space-Time (2000).

## Newton's law of gravitation

See gravitation.
Collins Dictionary of Astronomy © Market House Books Ltd, 2006
The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.

## Newton’s Law of Gravitation

one of the universal laws of nature. According to Newton’s law of gravitation, all physical bodies attract one another, and the magnitude of the force of attraction is independent of the physical and chemical properties of the bodies, the state of motion of the bodies, and the properties of the medium in which the bodies are located. On the earth, gravitation is manifested primarily in the existence of a gravitational force, which is a result of the attraction of any physical body by the earth.

Newton’s law of gravitation, which was discovered in the 17th century by I. Newton, may be stated in the following way. Any two mass points attract each other with a force F that is directly proportional to their masses m1 and m2 and inversely proportional to the square of the distance r between them:

Here, the force F is directed along the line that connects these points. The proportionality factor G, which is a constant, is called the constant of gravitation. In the cgs system, G ≈ 6.7 × 10−8 dyne · cm2 · g−2. Here, the term “mass points” is understood to mean bodies whose dimensions are negligibly small in comparison with the distances between the bodies. Newton’s law of gravitation may be interpreted differently, if we assume that any mass point with a mass m1 creates around itself a field of attraction (a gravitational field) in which any other free mass point located at a distance r from the center of the field receives an acceleration that is independent of the mass of this second particle and that is equal to

and is directed toward the center of the field.

The gravitational forces and gravitational fields of separate particles possess the property of additivity; that is, the force acting on a certain particle produced by several other particles is equal to the geometric sum of the forces produced by each particle. It follows that the attraction between real physical bodies, taking into account the size, shape, and density distribution of the bodies, can be determined by calculating the sum of the attractive forces of separate small particles into which the bodies may be mentally divided; in such a calculation, the direction of the components of the forces is taken into account. It has been established in this manner that a spherical body, homogeneous or having a spherical distribution of mass density, has precisely the same force of attraction as that of a mass point if the distance r is measured from the center of the sphere.

The nature of the motion of celestial bodies in space is determined primarily by gravitational forces. Indeed, Newton’s law of gravitation was discovered and subsequently rigorously substantiated in the study of the motion of the planets and planetary satellites. In the early 17th century, J. Kepler empirically established the fundamental laws governing planetary motion, which are called Kepler’s laws. Proceeding from these laws, Newton’s contemporaries, such as the French astronomer I. Boullian, the Italian physicist G. A. Borelli, and the British physicist R. Hooke, reasoned that planetary motions may be attributed to the action of a force that attracts every planet to the sun and that decreases in inverse proportion to the square of the distance from the sun. However, this was not rigorously proved until Newton did so in 1687 in the Philosophiae naturalis principia mathematical, his proof was based on his first two laws of motion and his newly devised mathematical methods that constituted the foundation of the differential and integral calculi. Newton proved that the motion of every planet must obey Kepler’s first two laws if it moves under the gravitational force of the sun in accordance with formula (1). Newton further showed that the motion of the moon can be approximately explained by using an analogous force field for the earth and that the gravitational force of the earth results from the action of this force field on physical bodies near the surface of the earth. Newton concluded, on the basis of his third law of motion, that attraction is a reciprocal property, and he formulated his law of gravitation for all physical bodies. Derived from empirical data based on necessarily approximate observational results, Newton’s law of gravitation was originally a working hypothesis. An enormous amount of work over a period of 200 years was subsequently required in order to rigorously substantiate this law.

Newton’s law of gravitation was the foundation for celestial mechanics. In the 17th to 19th centuries, one of the fundamental tasks of celestial mechanics was to prove that gravitational interaction according to Newton’s law explains precisely the observed motions of celestial bodies in the solar system. Newton himself showed that the mutual attraction among the earth, moon, and sun explains quite accurately a number of peculiarities in the motion of the moon that had been observed much earlier, such as the lunar variations, the regression of the nodes, the motion of the perigee, and fluctuations in the inclination of the lunar orbit; he also showed that the earth, because of its rotation and the action of gravitational forces between the particles that make up the earth, should be flattened at the poles. Newton also attributed to gravitational forces such phenomena as the tides and the precession of the earth’s axis. One of the most brilliant confirmations of the validity of the law of universal gravitation in the history of astronomy was the discovery in 1845–46 of the planet Neptune as a result of preliminary theoretical calculations that predicted the planet’s position. Modern theories of the motion of the earth, moon, and planets that are based on Newton’s law of gravitation account for the observed motions of these bodies in all details, except for certain effects, such as the motions of the perihelia of Mercury, Venus, and Mars; these effects are explained in relativistic celestial mechanics, which is based on Einstein’s theory of gravitation.

According to Newton’s law of gravitation, gravitational interaction plays the primary role in the motion of such stellar systems as binary and multiple stars and within star clusters and galaxies. However, the gravitational fields within star clusters and galaxies are quite complex and have not yet been adequately studied. Consequently, the motions within these clusters are studied by methods that differ from those of celestial mechanics (seeSTELLAR ASTRONOMY). Gravitational interaction also plays a significant role in all cosmic processes in which concentration of large masses takes part. Newton’s law of gravitation is the basis for the study of the motion of artificial celestial bodies, in particular, space probes and artificial earth and lunar satellites. Gravimetry is based on Newton’s law of gravitation. The attractive forces between ordinary macroscopic bodies on the earth can be detected and measured but do not have any significant practical role. In a microcosm, gravitational forces are negligibly small in comparison with intramolecular and intranuclear forces.

Newton left unanswered the question of the nature of gravitation and did not explain the hypothesis of instantaneous propagation of gravitation in space, that is, the hypothesis that as the positions of bodies change there is an instantaneous change in the gravitational force between the bodies. This hypothesis is closely related to the nature of gravitation. The associated difficulties were not eliminated until Einstein’s theory of gravitation, which represents a new stage in the understanding of objective natural laws.

### REFERENCES

Isaak N’iuton, 1643–1727 (a collection of articles commemorating Newton’s 300th birthday). Edited by Academician S. I. Vavilov. Moscow-Leningrad, 1943.
Berry, A. Kratkaia istoriia astronomii. Moscow-Leningrad, 1946. (Translated from English.)
Subbotin, M. F. Vvedenie ν teoreticheskuiu astronomiiu. Moscow, 1968.

IU. A. RIABOV

## Newton's law of gravitation

[′nüt·ənz ′lȯ əv ‚grav·ə′tā·shən]
(mechanics)
The law that every two particles of matter in the universe attract each other with a force that acts along the line joining them, and has a magnitude proportional to the product of their masses and inversely proportional to the square of the distance between them. Also known as law of gravitation.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
References in periodicals archive ?
And since the dynamics of the Earth is determined by Newton's law of gravitation any change in G would affect it.
Since the Newton's law of gravitation was published in 1687 [33], this action-at-a-distance theory was criticized by the French Cartesian [9].
Inspired by the aforementioned thoughts and others [52-56], we show that the Newton's law of gravitation is derived based on the assumption that all the particles are made of singularities of a kind of ideal fluid.
The Newton's law of gravitation is arrived if we introduce an assumption that G and the masses of particles are changing so slowly that they can be treated as constants.
Newton's law of gravitation is based a priori on the interaction of two masses; Einstein's theory of gravitation is not.

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