The formula for the force of attraction between two bodies. The law of universal gravitation. The movement of bodies under the influence of gravity. Observations of the movement of Mercury
Who discovered the law of gravity
It's no secret that the law of universal gravitation was discovered by the great English scientist Isaac Newton, who, according to legend, is walking in the evening garden and pondering the problems of physics. At that moment, an apple fell from a tree (according to one version, right on the physicist's head, according to another, it just fell), which later became Newton's famous apple, as it led the scientist to insight, eureka. The apple that fell on Newton's head and inspired him to discover the law of universal gravitation, because the Moon remained motionless in the night sky, the apple fell, the scientist may have thought that some kind of force acts like the Moon (causing it to orbit), so on the apple, causing it to fall to the ground.
Now, according to the assurances of some historians of science, this whole story about the apple is just a beautiful fiction. In fact, whether the apple fell or not is not so important, it is important that the scientist did indeed discover and formulate the law of universal gravitation, which is now one of the cornerstones of both physics and astronomy.
Of course, long before Newton, people observed both things falling to the ground and stars in the sky, but before him they believed that there were two types of gravity: terrestrial (acting exclusively within the Earth, causing bodies to fall) and celestial (acting on stars and moon). Newton was the first to combine these two types of gravity in his head, the first to understand that there is only one gravity and its action can be described by a universal physical law.
Definition of the law of universal gravitation
According to this law, all material bodies attract each other, while the force of attraction does not depend on the physical or chemical properties of the bodies. It depends, if everything is simplified as much as possible, only on the weight of the bodies and the distance between them. You also need to additionally take into account the fact that all bodies on Earth are affected by the force of attraction of our planet itself, which is called gravity (from Latin the word "gravitas" is translated as gravity).
Let us now try to formulate and write down the law of universal gravitation as briefly as possible: the force of attraction between two bodies with masses m1 and m2 and separated by a distance R is directly proportional to both masses and inversely proportional to the square of the distance between them.
The formula of the law of universal gravitation
Below we present to your attention the formula of the law of universal gravitation.
G in this formula is the gravitational constant, equal to 6.67408(31) 10 −11, this is the value of the impact on any material object of the gravitational force of our planet.
The law of universal gravitation and the weightlessness of bodies
The law of universal gravitation discovered by Newton, as well as the accompanying mathematical apparatus, later formed the basis of celestial mechanics and astronomy, because it can be used to explain the nature of the movement of celestial bodies, as well as the phenomenon of weightlessness. Being in outer space at a considerable distance from the force of attraction-gravity of such a large body as a planet, any material object (for example, a spacecraft with astronauts on board) will be in a state of weightlessness, since the force of the gravitational influence of the Earth (G in the formula of the law of gravitation) or some other planet will no longer affect it.
Newton's classical theory of gravitation (Newton's law of universal gravitation)- a law describing gravitational interaction within the framework of classical mechanics. This law was discovered by Newton around 1666. He says that power F (\displaystyle F) gravitational attraction between two material points of mass m 1 (\displaystyle m_(1)) and m 2 (\displaystyle m_(2)) separated by distance r (\displaystyle r), is proportional to both masses and inversely proportional to the square of the distance between them - that is:
F = G ⋅ m 1 ⋅ m 2 r 2 (\displaystyle F=G\cdot (m_(1)\cdot m_(2) \over r^(2)))
Here G (\displaystyle G)- gravitational constant, equal to 6.67408(31) 10 −11 m³/(kg s²) .
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Subtitles
Now let's learn a little about gravitation, or gravity. As you know, gravity, especially in an elementary or even in a fairly advanced physics course, is such a concept that you can calculate and find out the main parameters that determine it, but in fact, gravity is not entirely understandable. Even if you are familiar with the general theory of relativity - if you are asked what gravity is, you can answer: it is the curvature of space-time and the like. However, it is still difficult to get an intuition as to why two objects, just because they have a so-called mass, are attracted to each other. At least for me it's mystical. Having noted this, we proceed to consider the concept of gravitation. We will do this by studying Newton's law of universal gravitation, which is valid for most situations. This law says: the force of mutual gravitational attraction F between two material points with masses m₁ and m₂ is equal to the product of the gravitational constant G times the mass of the first object m₁ and the second object m₂, divided by the square of the distance d between them. This is a pretty simple formula. Let's try to transform it and see if we can get some results that are familiar to us. We use this formula to calculate the free fall acceleration near the Earth's surface. Let's draw the Earth first. Just to understand what we are talking about. This is our Earth. Suppose we need to calculate the gravitational acceleration acting on Sal, that is, on me. Here I am. Let's try to apply this equation to calculate the magnitude of the acceleration of my fall to the center of the Earth, or to the center of mass of the Earth. The value denoted by the capital letter G is the universal gravitational constant. Once again: G is the universal gravitational constant. Although, as far as I know, although I am not an expert in this matter, it seems to me that its value can change, that is, it is not a true constant, and I assume that its value differs with different measurements. But for our needs, as well as in most physics courses, it's a constant, a constant equal to 6.67 * 10^(−11) cubic meters divided by a kilogram per second squared. Yes, its dimension looks strange, but it is enough for you to understand that these are arbitrary units necessary to, as a result of multiplying by the masses of objects and dividing by the square of the distance, get the dimension of force - a newton, or a kilogram per meter divided by a second squared. So don't worry about these units, just know that we will have to work with meters, seconds and kilograms. Substitute this number into the formula for force: 6.67 * 10^(−11). Since we need to know the acceleration acting on Sal, then m₁ is equal to the mass of Sal, that is, me. I don't want to expose in this story how much I weigh, so let's leave this weight as a variable, denoting ms. The second mass in the equation is the mass of the Earth. Let's write out its meaning by looking at Wikipedia. So, the mass of the Earth is 5.97 * 10^24 kilograms. Yes, the Earth is more massive than Sal. By the way, weight and mass are different concepts. So, the force F is equal to the product of the gravitational constant G times the mass ms, then the mass of the Earth, and all this is divided by the square of the distance. You may object: what is the distance between the Earth and what stands on it? After all, if objects are in contact, the distance is zero. It is important to understand here: the distance between two objects in this formula is the distance between their centers of mass. In most cases, a person's center of mass is located about three feet above surface of the earth if the person is not too tall. Whatever the case, my center of mass may be three feet above the ground. Where is the Earth's center of mass? Obviously at the center of the earth. What is the Earth's radius? 6371 kilometers, or approximately 6 million meters. Since the height of my center of mass is about one millionth of the distance from the center of mass of the Earth, in this case it can be neglected. Then the distance will be equal to 6 and so on, like all other values, you need to write it in the standard form - 6.371 * 10^6, since 6000 km is 6 million meters, and a million is 10^6. We write, rounding all fractions to the second decimal place, the distance is 6.37 * 10 ^ 6 meters. The formula is the square of the distance, so let's square everything. Let's try to simplify now. First, we multiply the values in the numerator and bring forward the variable ms. Then the force F is equal to the mass of Sal for the whole upper part, we calculate it separately. So 6.67 times 5.97 equals 39.82. 39.82. This is the product of the significant parts, which should now be multiplied by 10 to the desired power. 10^(−11) and 10^24 have the same base, so to multiply them, just add the exponents. Adding 24 and −11, we get 13, as a result we have 10^13. Let's find the denominator. It is equal to 6.37 squared times 10^6 also squared. As you remember, if a number written as a power is raised to another power, then the exponents are multiplied, which means that 10^6 squared is 10 times 6 times 2, or 10^12. Next, we calculate the square of the number 6.37 using a calculator and get ... We square 6.37. And this is 40.58. 40.58. It remains to divide 39.82 by 40.58. Divide 39.82 by 40.58, which equals 0.981. Then we divide 10^13 by 10^12, which is 10^1, or just 10. And 0.981 times 10 is 9.81. After simplification and simple calculations, it was found that the gravitational force near the surface of the Earth, acting on Sal, is equal to the mass of Sal, multiplied by 9.81. What does this give us? Is it possible now to calculate the gravitational acceleration? It is known that the force is equal to the product of mass and acceleration, therefore, the force of gravity is simply equal to the product of Sal's mass and gravitational acceleration, which is usually denoted by a lowercase letter g. So, on the one hand, the force of attraction is equal to the number 9.81 times the mass of Sal. On the other hand, it is equal to Sal's mass per gravitational acceleration. Dividing both parts of the equation by Sal's mass, we get that the coefficient 9.81 is the gravitational acceleration. And if we included in the calculations the full record of units of dimensions, then, having reduced kilograms, we would see that gravitational acceleration is measured in meters divided by a second squared, like any acceleration. You can also notice that the value obtained is very close to the one we used when solving problems about the motion of an abandoned body: 9.8 meters per second squared. It's impressive. Let's solve another short gravity problem, because we have a couple of minutes left. Suppose we have another planet called Earth Baby. Let Malyshka's radius rS be half the Earth's radius rE, and her mass mS also equal to half the Earth's mass mE. What will be the force of gravity acting here on any object, and how much is it less than the force of the earth's gravity? Although, let's leave the problem for the next time, then I will solve it. See you. Subtitles by the Amara.org community
Properties of Newtonian gravity
In Newtonian theory, each massive body generates a force field of attraction to this body, which is called the gravitational field. This field is potentially , and the function of the gravitational potential for a material point with mass M (\displaystyle M) is determined by the formula:
φ (r) = − G M r . (\displaystyle \varphi (r)=-G(\frac (M)(r)).)In general, when the density of matter ρ (\displaystyle \rho ) randomly distributed, satisfies the Poisson equation:
Δ φ = − 4 π G ρ (r) . (\displaystyle \Delta \varphi =-4\pi G\rho (r).)The solution to this equation is written as:
φ = − G ∫ ρ (r) d V r + C , (\displaystyle \varphi =-G\int (\frac (\rho (r)dV)(r))+C,)where r (\displaystyle r) - distance between volume element dV (\displaystyle dV) and the point at which the potential is determined φ (\displaystyle \varphi ), C (\displaystyle C) is an arbitrary constant.
The force of attraction acting in a gravitational field on a material point with mass m (\displaystyle m), is related to the potential by the formula:
F (r) = − m ∇ φ (r) . (\displaystyle F(r)=-m\nabla \varphi (r).)A spherically symmetric body creates the same field outside its boundaries as a material point of the same mass located in the center of the body.
The trajectory of a material point in a gravitational field created by a much larger mass point obeys the laws of Kepler. In particular, planets and comets in the Solar System move in ellipses or hyperbolas. The influence of other planets, which distorts this picture, can be taken into account using the perturbation theory.
Accuracy of Newton's law of universal gravitation
An experimental assessment of the degree of accuracy of Newton's law of gravitation is one of the confirmations of the general theory of relativity. Experiments on measuring the quadrupole interaction of a rotating body and a fixed antenna showed that the increment δ (\displaystyle \delta ) in the expression for the dependence of the Newtonian potential r − (1 + δ) (\displaystyle r^(-(1+\delta))) at distances of several meters is within (2 , 1 ± 6 , 2) ∗ 10 − 3 (\displaystyle (2,1\pm 6,2)*10^(-3)). Other experiments also confirmed the absence of modifications in the law of universal gravitation.
Newton's law of universal gravitation was tested in 2007 at distances less than one centimeter (from 55 microns to 9.53 mm). Taking into account the experimental errors, no deviations from Newton's law were found in the investigated range of distances.
Precise laser ranging observations of the Moon's orbit confirm the law of universal gravitation at a distance from the Earth to the Moon with accuracy 3 ⋅ 10 − 11 (\displaystyle 3\cdot 10^(-11)).
Relationship with the geometry of Euclidean space
The fact of equality with very high precision 10 − 9 (\displaystyle 10^(-9)) the exponent of the distance in the denominator of the expression for the force of gravity to the number 2 (\displaystyle 2) reflects the Euclidean nature of the three-dimensional physical space of Newtonian mechanics. In three-dimensional Euclidean space, the surface area of a sphere is exactly proportional to the square of its radius.
Historical outline
The very idea of a universal gravitational force was repeatedly expressed even before Newton. Earlier, Epicurus, Gassendi, Kepler, Borelli, Descartes, Roberval, Huygens and others thought about it. Kepler believed that gravity is inversely proportional to the distance to the Sun and extends only in the plane of the ecliptic; Descartes considered it to be the result of vortices in the ether. There were, however, guesses with a correct dependence on distance; Newton, in a letter to Halley, mentions Bulliald, Wren, and Hooke as his predecessors. But before Newton, no one was able to clearly and mathematically conclusively link the law of gravitation (a force inversely proportional to the square of distance) and the laws of planetary motion (Kepler's laws).
- law of gravitation;
- the law of motion (Newton's second law);
- system of methods for mathematical research (mathematical analysis).
Taken together, this triad is sufficient for a complete study of the most complex movements of celestial bodies, thereby creating the foundations of celestial mechanics. Prior to Einstein, no fundamental amendments to this model were needed, although the mathematical apparatus turned out to be necessary to be significantly developed.
Note that Newton's theory of gravity was no longer, strictly speaking, heliocentric. Already in the two-body problem, the planet does not rotate around the Sun, but around a common center of gravity, since not only the Sun attracts the planet, but the planet also attracts the Sun. Finally, it turned out to be necessary to take into account the influence of the planets on each other.
During the 18th century, the law of universal gravitation was the subject of active discussion (opposed by supporters of the school of Descartes) and careful testing. By the end of the century, it became generally recognized that the law of universal gravitation makes it possible to explain and predict the movements of celestial bodies with great accuracy. Henry Cavendish in 1798 carried out a direct verification of the validity of the law of gravity in terrestrial conditions, using extremely sensitive torsion balances. An important step was the introduction by Poisson in 1813 of the concept of the gravitational potential and the Poisson equation for this potential; this model made it possible to investigate the gravitational field with an arbitrary distribution of matter. After that, Newton's law began to be regarded as a fundamental law of nature.
At the same time, Newton's theory contained a number of difficulties. The main one is an inexplicable long-range action: the force of gravity was transmitted incomprehensibly how through a completely empty space, and infinitely quickly. Essentially, the Newtonian model was purely mathematical, without any physical content. In addition, if the Universe, as was then assumed, is Euclidean and infinite, and at the same time the average density of matter in it is nonzero, then a gravitational paradox arises. At the end of the 19th century, another problem was discovered: the discrepancy between the theoretical and observed displacement perihelion Mercury.
Further development
General theory of relativity
For more than two hundred years after Newton, physicists have proposed various ways to improve Newton's theory of gravity. These efforts were crowned with success in 1915, with the creation of Einstein's general theory of relativity, in which all these difficulties were overcome. Newton's theory, in full agreement with the correspondence principle, turned out to be an approximation of a more general theory, applicable under two conditions:
In weak stationary gravitational fields, the equations of motion become Newtonian (gravitational potential). To prove this, we show that the scalar gravitational potential in weak stationary gravitational fields satisfies the Poisson equation
Δ Φ = − 4 π G ρ (\displaystyle \Delta \Phi =-4\pi G\rho ).It is known (Gravitational potential) that in this case the gravitational potential has the form:
Φ = − 1 2 c 2 (g 44 + 1) (\displaystyle \Phi =-(\frac (1)(2))c^(2)(g_(44)+1)).Let us find the component of the energy-momentum tensor from the equations of the gravitational field of the general theory of relativity:
R i k = − ϰ (T i k − 1 2 g i k T) (\displaystyle R_(ik)=-\varkappa (T_(ik)-(\frac (1)(2))g_(ik)T)),where R i k (\displaystyle R_(ik)) is the curvature tensor. For we can introduce the kinetic energy-momentum tensor ρ u i u k (\displaystyle \rho u_(i)u_(k)). Neglecting quantities of the order u/c (\displaystyle u/c), you can put all the components T i k (\displaystyle T_(ik)), Besides T 44 (\displaystyle T_(44)), equal to zero. Component T 44 (\displaystyle T_(44)) is equal to T 44 = ρ c 2 (\displaystyle T_(44)=\rho c^(2)) and therefore T = g i k T i k = g 44 T 44 = − ρ c 2 (\displaystyle T=g^(ik)T_(ik)=g^(44)T_(44)=-\rho c^(2)). So the equations gravitational field take the form R 44 = − 1 2 ϰ ρ c 2 (\displaystyle R_(44)=-(\frac (1)(2))\varkappa \rho c^(2)). Due to the formula
R i k = ∂ Γ i α α ∂ x k − ∂ Γ i k α ∂ x α + Γ i α β Γ k β α − Γ i k α Γ α β β (\displaystyle R_(ik)=(\frac (\partial \ Gamma _(i\alpha )^(\alpha ))(\partial x^(k)))-(\frac (\partial \Gamma _(ik)^(\alpha ))(\partial x^(\alpha )))+\Gamma _(i\alpha )^(\beta )\Gamma _(k\beta )^(\alpha )-\Gamma _(ik)^(\alpha )\Gamma _(\alpha \beta )^(\beta ))value of the curvature tensor component R44 (\displaystyle R_(44)) can be taken equal R 44 = − ∂ Γ 44 α ∂ x α (\displaystyle R_(44)=-(\frac (\partial \Gamma _(44)^(\alpha ))(\partial x^(\alpha )))) and since Γ 44 α ≈ − 1 2 ∂ g 44 ∂ x α (\displaystyle \Gamma _(44)^(\alpha )\approx -(\frac (1)(2))(\frac (\partial g_(44) )(\partial x^(\alpha )))), R 44 = 1 2 ∑ α ∂ 2 g 44 ∂ x α 2 = 1 2 Δ g 44 = − Δ Φ c 2 (\displaystyle R_(44)=(\frac (1)(2))\sum _(\ alpha )(\frac (\partial ^(2)g_(44))(\partial x_(\alpha )^(2)))=(\frac (1)(2))\Delta g_(44)=- (\frac (\Delta \Phi )(c^(2)))). Thus, we arrive at the Poisson equation:
Δ Φ = 1 2 ϰ c 4 ρ (\displaystyle \Delta \Phi =(\frac (1)(2))\varkappa c^(4)\rho ), where ϰ = − 8 π G c 4 (\displaystyle \varkappa =-(\frac (8\pi G)(c^(4))))quantum gravity
However, the general theory of relativity is not the final theory of gravitation either, since it does not adequately describe gravitational processes on quantum scales (at distances of the order of the Planck scale, about 1.6⋅10 −35 ). The construction of a consistent quantum theory of gravity is one of the most important unsolved problems of modern physics.
From the point of view of quantum gravity, gravitational interaction is carried out by exchanging virtual gravitons between interacting bodies. According to the uncertainty principle, the energy of a virtual graviton is inversely proportional to the time of its existence from the moment of emission by one body to the moment of absorption by another body. The lifetime is proportional to the distance between the bodies. Thus, at small distances interacting bodies can exchange virtual gravitons with short and long wavelengths, and at large distances only long-wavelength gravitons. From these considerations, one can obtain the law of inverse proportionality of the Newtonian potential from distance. The analogy between Newton's law and Coulomb's law is explained by the fact that the graviton mass, like the mass
Isaac Newton suggested that between any bodies in nature there are forces of mutual attraction. These forces are called gravity forces or forces of gravity. The force of irrepressible gravity manifests itself in space, the solar system and on Earth.
Law of gravity
Newton generalized the laws of motion of celestial bodies and found out that the force \ (F \) is equal to:
\[ F = G \dfrac(m_1 m_2)(R^2) \]
where \(m_1 \) and \(m_2 \) are the masses of interacting bodies, \(R \) is the distance between them, \(G \) is the proportionality coefficient, which is called gravitational constant. The numerical value of the gravitational constant was experimentally determined by Cavendish, measuring the force of interaction between lead balls.
The physical meaning of the gravitational constant follows from the law of universal gravitation. If a \(m_1 = m_2 = 1 \text(kg) \), \(R = 1 \text(m) \) , then \(G = F \) , i.e. the gravitational constant is equal to the force with which two bodies of 1 kg are attracted at a distance of 1 m.
Numerical value:
\(G = 6.67 \cdot() 10^(-11) N \cdot() m^2/ kg^2 \) .
The forces of universal gravitation act between any bodies in nature, but they become tangible at large masses (or if at least the mass of one of the bodies is large). The law of universal gravitation is fulfilled only for material points and balls (in this case, the distance between the centers of the balls is taken as the distance).
Gravity
A special type of universal gravitational force is the force of attraction of bodies to the Earth (or to another planet). This force is called gravity. Under the action of this force, all bodies acquire free fall acceleration.
According to Newton's second law \(g = F_T /m \) , therefore \(F_T = mg \) .
If M is the mass of the Earth, R is its radius, m is the mass of the given body, then the force of gravity is equal to
\(F = G \dfrac(M)(R^2)m = mg \) .
The force of gravity is always directed towards the center of the Earth. Depending on the height \ (h \) above the Earth's surface and the geographical latitude of the position of the body, the free fall acceleration acquires different values. On the surface of the Earth and in middle latitudes, the free fall acceleration is 9.831 m/s 2 .
Body weight
In technology and everyday life, the concept of body weight is widely used.
Body weight denoted by \(P \) . The unit of weight is newton (N). Since the weight is equal to the force with which the body acts on the support, then, in accordance with Newton's third law, the weight of the body is equal in magnitude to the reaction force of the support. Therefore, in order to find the weight of the body, it is necessary to determine what the reaction force of the support is equal to.
It is assumed that the body is motionless relative to the support or suspension.
Body weight and gravity differ in nature: body weight is a manifestation of the action of intermolecular forces, and gravity has a gravitational nature.
The state of a body in which its weight is zero is called weightlessness. The state of weightlessness is observed in an airplane or spacecraft when moving with the acceleration of free fall, regardless of the direction and value of the speed of their movement. Outside the earth's atmosphere, when the jet engines are turned off, only the force of universal gravitation acts on the spacecraft. Under the action of this force, the spaceship and all the bodies in it move with the same acceleration, so the state of weightlessness is observed in the ship.
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Newton's law of gravity the law of gravity, one of the universal laws of nature; according to N. h. i.e., all material bodies attract each other, and the magnitude of the gravitational force does not depend on the physical and chemical properties of the bodies, on the state of their movement, on the properties of the environment where the bodies are located. On Earth, gravitation manifests itself primarily in the existence of gravity, which is the result of the attraction of any material body by the Earth. Related to this is the term "gravity" (from Latin gravitas - gravity), equivalent to the term "gravitation". Gravitational interaction in accordance with N. h. t. plays the main role in the motion of stellar systems such as binary and multiple stars, inside star clusters and galaxies. However, gravitational fields inside star clusters and galaxies are of a very complex nature and have not yet been studied enough, as a result of which movements inside them are studied by methods different from those of celestial mechanics (see Stellar astronomy). The gravitational interaction also plays an essential role in all cosmic processes involving accumulations of large masses of matter. N. h. t. is the basis for studying the motion of artificial celestial bodies, in particular artificial satellites of the Earth and the Moon, and space probes. On N. h. t. relies on Gravimetry. Forces of attraction between ordinary macroscopic material bodies on Earth can be detected and measured, but do not play any noticeable practical role. In the microcosm, the forces of attraction are negligibly small compared to the intramolecular and intranuclear forces. Newton left open the question of the nature of gravity. The assumption of the instantaneous propagation of gravity in space (i.e., the assumption that with a change in the positions of bodies the force of gravity between them instantly changes), which is closely related to the nature of gravity, was also not explained. The difficulties associated with this were eliminated only in Einstein's theory of gravitation, which represents a new stage in the knowledge of the objective laws of nature. Lit.: Isaac Newton. 1643-1727. Sat. Art. to the tercentenary of his birth, ed. acad. S. I. Vavilova, M. - L., 1943; Berry, A., A Brief History of Astronomy, trans. from English, M. - L., 1946; Subbotin M.F., Introduction to theoretical astronomy, M., 1968. Yu. A. Ryabov. Great Soviet Encyclopedia. - M.: Soviet Encyclopedia.
1969-1978
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See what "Newton's law of gravity" is in other dictionaries:
- (universal gravitation law), see Art. (see GRAVITY). Physical Encyclopedic Dictionary. Moscow: Soviet Encyclopedia. Chief Editor A. M. Prokhorov. 1983... Physical Encyclopedia
NEWTON'S LAW OF GRAVITY, the same as the law of universal gravitation ... Modern Encyclopedia
The same as the law of gravity... Big Encyclopedic Dictionary
Newton's law of gravity- NEWTON'S LAW OF GRAVITATION, the same as universal gravitation law. … Illustrated Encyclopedic Dictionary
NEWTON'S LAW OF GRAVITY- the same as (see) ...
The same as the law of universal gravitation. * * * NEWTON'S LAW OF GRAVATION NEWTON'S LAW OF GRAVITY, the same as the law of universal gravitation (see UNIVERSAL GRAVITATION LAW) ... encyclopedic Dictionary
Newton's law of gravity- Niutono gravitacijos dėsnis statusas T sritis fizika atitikmenys: engl. Newton's law of gravity vok. Newtonsches Gravitationsgesetz, n; Newtonsches Massenanziehungsgesetz, n rus. Newton's law of gravity, m; Newton's law of gravity, m pranc.… … Fizikos terminų žodynas
Gravity (universal gravitation, gravitation) (from Latin gravitas "gravity") is a long-range fundamental interaction in nature, to which all material bodies are subject. According to modern data, it is a universal interaction in that ... ... Wikipedia
THE LAW OF UNIVERSAL GRAVITY- (Newton's law of gravity) all material bodies attract each other with forces directly proportional to their masses and inversely proportional to the square of the distance between them: where F is the gravity force module, m1 and m2, the masses of interacting bodies, R ... ... Great Polytechnic Encyclopedia
Law of gravity- I. Newton's law of gravitation (1643 1727) in classical mechanics, according to which the force of gravitational attraction of two bodies with masses m1 and m2 is inversely proportional to the square of the distance r between them; proportionality factor G gravitational … Concepts of modern natural science. Glossary of basic terms
Law of gravity
Gravity (universal gravitation, gravitation)(from lat. gravitas - “gravity”) - a long-range fundamental interaction in nature, to which all material bodies are subject. According to modern data, it is a universal interaction in the sense that, unlike any other forces, it gives the same acceleration to all bodies without exception, regardless of their mass. Primarily gravity plays a decisive role on a cosmic scale. Term gravity also used as the name of a branch of physics that studies the gravitational interaction. The most successful modern physical theory in classical physics, describing gravity, is the general theory of relativity, the quantum theory of gravitational interaction has not yet been built.
Gravitational interaction
Gravitational interaction is one of the four fundamental interactions in our world. Within classical mechanics, the gravitational interaction is described by law of gravity Newton, who states that the force of gravitational attraction between two material points of mass m 1 and m 2 separated by distance R, is proportional to both masses and inversely proportional to the square of the distance - i.e.
.Here G- gravitational constant, equal to approximately 
m³/(kg s²). The minus sign means that the force acting on the body is always equal in direction to the radius vector directed to the body, that is, the gravitational interaction always leads to the attraction of any bodies.
The law of universal gravitation is one of the applications of the inverse square law, which is also encountered in the study of radiation (see, for example, Light Pressure), and which is a direct consequence of the quadratic increase in the area of the sphere with increasing radius, which leads to a quadratic decrease in the contribution of any unit area to the area of the entire sphere.
The simplest task of celestial mechanics is the gravitational interaction of two bodies in empty space. This problem is solved analytically to the end; the result of its solution is often formulated in three Kepler's laws.
As the number of interacting bodies increases, the problem becomes much more complicated. So, the already famous three-body problem (that is, the motion of three bodies with non-zero masses) cannot be solved analytically in a general form. With a numerical solution, the instability of solutions with respect to the initial conditions sets in rather quickly. When applied to the solar system, this instability makes it impossible to predict the motion of the planets on scales exceeding a hundred million years.
In some special cases, it is possible to find an approximate solution. The most important is the case when the mass of one body is significantly greater than the mass of other bodies (examples: solar system and the dynamics of Saturn's rings). In this case, in the first approximation, we can assume that light bodies do not interact with each other and move along Keplerian trajectories around a massive body. Interactions between them can be taken into account in the framework of perturbation theory, and averaged over time. In this case, non-trivial phenomena can arise, such as resonances, attractors, randomness, etc. illustrative example such phenomena - non-trivial structure of the rings of Saturn.
Despite attempts to describe the behavior of a system of a large number of attracting bodies of approximately the same mass, this cannot be done due to the phenomenon of dynamic chaos.
Strong gravitational fields
In strong gravitational fields, when moving at relativistic speeds, the effects of general relativity begin to appear:
- deviation of the law of gravity from Newtonian;
- potential delay associated with the finite propagation velocity of gravitational perturbations; the appearance of gravitational waves;
- non-linear effects: gravitational waves tend to interact with each other, so the principle of superposition of waves in strong fields is no longer valid;
- change in the geometry of space-time;
- the emergence of black holes;
Gravitational radiation
One of the important predictions of general relativity is gravitational radiation, the presence of which has not yet been confirmed by direct observations. However, there is indirect observational evidence in favor of its existence, namely: the energy loss in the binary system with the PSR B1913+16 pulsar - the Hulse-Taylor pulsar - is in good agreement with the model in which this energy is carried away by gravitational radiation.
Gravitational radiation can only be generated by systems with variable quadrupole or higher multipole moments, this fact suggests that the gravitational radiation of most natural sources is directional, which greatly complicates its detection. Gravity power l-poly source is proportional (v / c) 2l + 2 , if the multipole is of electric type, and (v / c) 2l + 4 - if the multipole is magnetic type , where v is the characteristic velocity of sources in the radiating system, and c is the speed of light. Thus, the dominant moment will be the quadrupole moment electric type, and the power of the corresponding radiation is equal to:
where Q ij is the tensor of the quadrupole moment of the mass distribution of the radiating system. Constant 
(1/W) makes it possible to estimate the order of magnitude of the radiation power.
Since 1969 (Weber's experiments (English)) and up to the present (February 2007), attempts have been made to directly detect gravitational radiation. In the USA, Europe and Japan, there are currently several operating ground-based detectors (GEO 600), as well as a project for a space gravitational detector of the Republic of Tatarstan.
Subtle effects of gravity
In addition to the classical effects of gravitational attraction and time dilation, the general theory of relativity predicts the existence of other manifestations of gravity, which are very weak under terrestrial conditions and therefore their detection and experimental verification are therefore very difficult. Until recently, overcoming these difficulties seemed beyond the capabilities of experimenters.
Among them, in particular, one can name the drag of inertial reference frames (or the Lense-Thirring effect) and the gravitomagnetic field. In 2005, NASA's Gravity Probe B conducted an experiment of unprecedented accuracy to measure these effects near the Earth, but the full results have not yet been published.
quantum theory of gravity
Despite more than half a century of attempts, gravity is the only fundamental interaction for which a consistent renormalizable quantum theory has not yet been built. However, at low energies, in the spirit of quantum field theory, the gravitational interaction can be represented as an exchange of gravitons - gauge bosons with spin 2.
Standard Theories of Gravity
Due to the fact that the quantum effects of gravity are extremely small even under the most extreme experimental and observational conditions, there are still no reliable observations of them. Theoretical estimates show that in the vast majority of cases it is possible to restrict classic description gravitational interaction.
There is a modern canonical classical theory of gravity - the general theory of relativity, and many hypotheses that refine it and theories of varying degrees of development that compete with each other (see the article Alternative theories of gravity). All of these theories give very similar predictions within the approximation in which experimental tests are currently being carried out. The following are some of the major, most well developed or known theories of gravity.
- Gravity is not a geometric field, but a real physical force field described by a tensor.
- Gravitational phenomena should be considered within the framework of the flat Minkowski space, in which the laws of conservation of energy-momentum and angular momentum are unambiguously fulfilled. Then the motion of bodies in the Minkowski space is equivalent to the motion of these bodies in the effective Riemannian space.
- In tensor equations, to determine the metric, one should take into account the mass of the graviton, and also use the gauge conditions associated with the metric of the Minkowski space. This does not allow destroying the gravitational field even locally by choosing some suitable frame of reference.
As in general relativity, in RTG, matter refers to all forms of matter (including the electromagnetic field), with the exception of the gravitational field itself. The consequences of the RTG theory are as follows: black holes as physical objects predicted in general relativity do not exist; The universe is flat, homogeneous, isotropic, immobile and Euclidean.
On the other hand, there are no less convincing arguments of RTG opponents, which boil down to the following points:
A similar thing happens in RTG, where the second tensor equation is introduced to take into account the connection between the non-Euclidean space and the Minkowski space. Due to the presence of a dimensionless fitting parameter in the Jordan-Brans-Dicke theory, it becomes possible to choose it so that the results of the theory coincide with the results of gravitational experiments.
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Sources and notes
Literature
- Vizgin V.P. Relativistic theory of gravity (origins and formation, 1900-1915). M.: Nauka, 1981. - 352c.
- Vizgin V.P. Unified theories in the 1st third of the twentieth century. M.: Nauka, 1985. - 304c.
- Ivanenko D. D., Sardanashvili G. A. Gravity, 3rd ed. M.: URSS, 2008. - 200p.
see also
- gravimeter
Links
- The law of universal gravitation or "Why does the moon not fall to the Earth?" - Just about the complex
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