Newton, who states that the force of gravitational attraction between two material points of mass and , separated by a distance, is proportional to both masses and inversely proportional to the square of the distance - that is:

Here - gravitational constant, equal to approximately 6.6725 × 10 −11 m³ / (kg s²).

The law of universal gravitation is one of the applications of the inverse square law, which also occurs in the study of radiation (see, for example, Light pressure), and 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 gravitational field, as well as the gravity field, is potentially . This means that it is possible to introduce the potential energy of the gravitational attraction of a pair of bodies, and this energy will not change after moving the bodies along a closed contour. The potentiality of the gravitational field entails the law of conservation of the sum of kinetic and potential energy, and when studying the motion of bodies in a gravitational field, it often greatly simplifies the solution. Within the framework of Newtonian mechanics, the gravitational interaction is long-range. This means that no matter how a massive body moves, at any point in space the gravitational potential depends only on the position of the body at a given time.

Large space objects - planets, stars and galaxies have a huge mass and, therefore, create significant gravitational fields.

Gravity is the weakest force. However, since it acts at all distances and all masses are positive, it is nevertheless a very important force in the universe. In particular, the electromagnetic interaction between bodies on a cosmic scale is small, since the total electric charge of these bodies is zero (substance as a whole is electrically neutral).

Also, gravity, unlike other interactions, is universal in its effect on all matter and energy. No objects have been found that have no gravitational interaction at all.

Due to its global nature, gravity is also responsible for such large-scale effects as the structure of galaxies, black holes and the expansion of the Universe, and for elementary astronomical phenomena - the orbits of planets, and for simple attraction to the Earth's surface and falling bodies.

Gravity was the first interaction described by a mathematical theory. Aristotle believed that objects with different masses fall at different speeds. Only much later, Galileo Galilei experimentally determined that this was not the case - if air resistance is eliminated, all bodies accelerate equally. Isaac Newton's law of gravity (1687) was a good description of the general behavior of gravity. In 1915, Albert Einstein created the General Theory of Relativity, which describes gravity more accurately in terms of spacetime geometry.

Celestial mechanics and some of its problems

The simplest task of celestial mechanics is the gravitational interaction of two point or spherical bodies in empty space. This problem within the framework of classical mechanics is solved analytically in a closed form; the result of its solution is often formulated in the form of Kepler's three 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, however, the instability of the solutions with respect to the initial conditions sets in rather quickly. When applied to the solar system, this instability makes it impossible to accurately 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: the 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 may arise, such as resonances, attractors, randomness, etc. A good example of such phenomena is the complex structure of Saturn's rings.

Despite attempts to accurately 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, as well as when moving in a gravitational field with relativistic velocities, the effects of the general theory of relativity (GR) begin to appear:

• change in the geometry of space-time;
  • as a consequence, the deviation of the law of gravity from Newtonian;
  • and in extreme cases - the emergence of black holes;
• potential delay associated with the finite propagation velocity of gravitational perturbations;
  • as a consequence, the appearance of gravitational waves;
• non-linear effects: gravity tends to interact with itself, so the principle of superposition in strong fields is no longer valid.

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 strong indirect evidence in favor of its existence, namely: energy losses in close binary systems containing compact gravitating objects (such as neutron stars or black holes), in particular, in the famous PSR B1913 + 16 system (Hulse-Taylor pulsar) - are in good agreement with the GR model, in which this energy is carried away precisely 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 n-field source is proportional to if the multipole is of electrical type, and - if the multipole is of 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 of the electric type, and the power of the corresponding radiation is equal to:

where is the tensor of the quadrupole moment of the mass distribution of the radiating system. The constant (1/W) makes it possible to estimate the order of magnitude of the radiation power.

Since 1969 (Weber's experiments ( English)), attempts are being made to directly detect gravitational radiation. In the USA, Europe and Japan, there are currently several operating ground-based detectors (LIGO , VIRGO , TAMA ( English), GEO 600), as well as the LISA (Laser Interferometer Space Antenna) space gravitational detector project). The ground-based detector in Russia is being developed at the Scientific Center for Gravitational-Wave Research "Dulkyn" of the Republic of Tatarstan.

Subtle effects of gravity

Measuring the curvature of space in Earth's orbit (artist's drawing)

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. Processing of the obtained data was carried out until May 2011 and confirmed the existence and magnitude of the effects of geodesic precession and drag of inertial frames of reference, although with an accuracy slightly less than originally assumed.

After intensive work on the analysis and extraction of measurement noise, the final results of the mission were announced at a press conference on NASA-TV on May 4, 2011 and published in Physical Review Letters. The measured value of the geodesic precession was −6601.8±18.3 milliseconds arcs per year, and the drag effect - −37.2±7.2 milliseconds arcs per year (compare with the theoretical values ​​of −6606.1 mas/year and −39.2 mas/year).

Classical theories of gravity

See also: 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 overwhelming majority of cases one can confine oneself to the classical description of the gravitational interaction.

There is a modern canonical classical theory of gravity - the general theory of relativity, and many hypotheses and theories of varying degrees of development that refine it, competing with each other. 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.

General theory of relativity

In the standard approach of the general theory of relativity (GR), gravity is initially considered not as a force interaction, but as a manifestation of the curvature of space-time. Thus, in general relativity, gravity is interpreted as a geometric effect, and space-time is considered in the framework of non-Euclidean Riemannian (more precisely, pseudo-Riemannian) geometry. The gravitational field (a generalization of the Newtonian gravitational potential), sometimes also called the gravitational field, in general relativity is identified with the tensor metric field - the metric of four-dimensional space-time, and the gravitational field strength - with the affine connection of space-time, determined by the metric.

The standard task of general relativity is to determine the components of the metric tensor, which together determine the geometric properties of space-time, according to the known distribution of energy-momentum sources in the four-dimensional coordinate system under consideration. In turn, knowledge of the metric allows one to calculate the motion of test particles, which is equivalent to knowing the properties of the gravitational field in a given system. In connection with the tensor nature of the GR equations, as well as with the standard fundamental justification for its formulation, it is believed that gravity also has a tensor character. One of the consequences is that the gravitational radiation must be at least of the quadrupole order.

It is known that there are difficulties in general relativity due to the non-invariance of the energy of the gravitational field, since this energy is not described by a tensor and can be theoretically determined in different ways. In classical general relativity, the problem of describing the spin-orbit interaction also arises (since the spin of an extended object also does not have a unique definition). It is believed that there are certain problems with the uniqueness of the results and the justification of consistency (the problem of gravitational singularities).

However, GR is experimentally confirmed until very recently (2012). In addition, many alternative to Einsteinian, but standard for modern physics, approaches to the formulation of the theory of gravity lead to a result that coincides with general relativity in the low-energy approximation, which is the only one available now for experimental verification.

Einstein-Cartan theory

A similar division of equations into two classes also takes place 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 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. At the same time, as the parameter tends to infinity, the predictions of the theory become closer and closer to general relativity, so that it is impossible to refute the Jordan-Brance-Dicke theory by any experiment confirming the general theory of relativity.

quantum theory of gravity

Despite more than half a century of attempts, gravity is the only fundamental interaction for which a generally accepted consistent quantum theory has not yet been built. At low energies, in the spirit of quantum field theory, the gravitational interaction can be thought of as an exchange of gravitons—gauge bosons with spin 2. However, the resulting theory is not renormalizable, and is therefore considered unsatisfactory.

In recent decades, three promising approaches to solving the gravity quantization problem have been developed: string theory, loop quantum gravity, and causal dynamical triangulation.

String theory

In it, instead of particles and background space-time, strings and their multidimensional counterparts, branes, appear. For high-dimensional problems, branes are high-dimensional particles, but in terms of particles moving inside these branes, they are space-time structures. A variant of string theory is M-theory.

Loop quantum gravity

It attempts to formulate a quantum field theory without reference to the space-time background, space and time, according to this theory, consist of discrete parts. These small quantum cells of space are connected to each other in a certain way, so that on small scales of time and length they create a motley, discrete structure of space, and on large scales they smoothly turn into a continuous smooth space-time. Although many cosmological models can only describe the behavior of the universe from Planck time after the Big Bang, loop quantum gravity can describe the explosion process itself, and even look earlier. Loop quantum gravity makes it possible to describe all standard model particles without requiring the introduction of the Higgs boson to explain their masses.

Main article: Causal dynamic triangulation

In it, the space-time manifold is built from elementary Euclidean simplices (triangle, tetrahedron, pentachore) of dimensions of the Planck order, taking into account the principle of causality. Four-dimensionality and pseudo-Euclidean space-time on a macroscopic scale are not postulated in it, but are a consequence of the theory.

see also

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.
• Mizner C., Thorne K., Wheeler J. Gravity. - M.: Mir, 1977.
• Thorn K. Black holes and folds of time. Einstein's audacious legacy. - M.: State publishing house of physical and mathematical literature, 2009.

Links

• The law of universal gravitation or "Why does the moon not fall to the Earth?" - Just about the complex
• Problems with Gravity (BBC Documentary, Video)
• Earth and Gravity; Relativistic theory of gravity (TV shows Gordon "Dialogues", video)

Theories of gravity
Standard Theories of Gravity

Gravity is the most mysterious force in the universe. Scientists do not know until the end of its nature. It is she who keeps the planets of the solar system in orbit. It is a force that occurs between two objects and depends on mass and distance.

Gravity is called the force of attraction or gravitation. With the help of it, the planet or other body pulls objects to its center. Gravity keeps the planets in orbit around the sun.

What else does gravity do?

Why do you land on the ground when you jump up instead of floating away into space? Why do items fall when you drop them? The answer is an invisible force of gravity that pulls objects towards each other. Earth gravity is what keeps you on the ground and makes things fall.

Everything that has mass has gravity. The power of gravity depends on two factors: the mass of objects and the distance between them. If you pick up a stone and a feather, let them go from the same height, both objects will fall to the ground. A heavy stone will fall faster than a feather. The feather will still hang in the air, because it is lighter. Objects with more mass have a greater force of attraction, which gets weaker with distance: the closer objects are to each other, the stronger their gravitational attraction.

Gravity on Earth and in the Universe

During the flight of the aircraft, people in it remain in place and can move as if on the ground. This happens because of the flight path. There are specially designed aircraft in which there is no gravity at a certain height, weightlessness is formed. The aircraft performs a special maneuver, the mass of objects changes, they briefly rise into the air. After a few seconds, the gravitational field is restored.

Considering the force of gravity in space, it is greater than most of the planets on the globe. It is enough to look at the movement of astronauts during landing on planets. If we walk calmly on the ground, then there the astronauts seem to soar in the air, but do not fly away into space. This means that this planet also has a gravitational force, just a little different than that of the planet Earth.

The force of attraction of the Sun is so great that it holds nine planets, numerous satellites, asteroids and planets.

Gravity plays a crucial role in the development of the universe. In the absence of gravity, there would be no stars, planets, asteroids, black holes, galaxies. Interestingly, black holes are not actually visible. Scientists determine the signs of a black hole by the degree of power of the gravitational field in a certain area. If it is very strong with the strongest vibration, this indicates the existence of a black hole.

Myth 1. There is no gravity in space

Watching documentaries about astronauts, it seems that they are hovering above the surface of the planets. This is due to the fact that gravity on other planets is lower than on Earth, so astronauts walk as if floating in the air.

Myth 2. All bodies approaching a black hole are torn apart.

Black holes have a powerful force and form powerful gravitational fields. The closer an object is to a black hole, the stronger the tidal forces and the power of attraction become. Further development of events depends on the mass of the object, the size of the black hole and the distance between them. A black hole has a mass directly opposite to its size. Interestingly, the larger the hole, the weaker the tidal forces and vice versa. In this way, not all objects are torn apart when they enter the field of a black hole.

Myth 3. Artificial satellites can orbit the Earth forever

Theoretically, one could say so, if it were not for the influence of secondary factors. Much depends on the orbit. In a low orbit, a satellite will not be able to fly forever due to atmospheric braking; in high orbits, it can remain in an unchanged state for quite a long time, but the gravitational forces of other objects come into force here.

If only the Earth existed of all the planets, the satellite would be attracted to it and practically not change the trajectory of movement. But in high orbits, the object is surrounded by many planets, large and small, each with its own gravity.

In this case, the satellite would gradually move away from its orbit and move randomly. And, it is likely that after some time, it would have crashed to the nearest surface or moved to another orbit.

Some facts

1. In some corners of the Earth, the force of gravity is weaker than on the entire planet. For example, in Canada, in the Hudson Bay region, gravity is lower.
2. When astronauts return from space to our planet, at the very beginning it is difficult for them to adapt to the gravitational force of the globe. Sometimes it takes several months.
3. Black holes have the most powerful gravitational force among space objects. One ball-sized black hole has more power than any planet.

Despite the ongoing study of the force of gravity, gravity remains undiscovered. This means that scientific knowledge remains limited and humanity has a lot to learn.

« Physics - Grade 10 "

Why does the moon move around the earth?
What happens if the moon stops?
Why do the planets revolve around the sun?

In Chapter 1, it was discussed in detail that the globe imparts the same acceleration to all bodies near the surface of the Earth - the acceleration of free fall. But if the globe imparts acceleration to the body, then, according to Newton's second law, it acts on the body with some force. The force with which the earth acts on the body is called gravity. First, let's find this force, and then consider the force of universal gravitation.

Modulo acceleration is determined from Newton's second law:

In the general case, it depends on the force acting on the body and its mass. Since the acceleration of free fall does not depend on the mass, it is clear that the force of gravity must be proportional to the mass:

The physical quantity is the free fall acceleration, it is constant for all bodies.

Based on the formula F = mg, you can specify a simple and practically convenient method for measuring the masses of bodies by comparing the mass of a given body with the standard unit of mass. The ratio of the masses of two bodies is equal to the ratio of the forces of gravity acting on the bodies:

This means that the masses of bodies are the same if the forces of gravity acting on them are the same.

This is the basis for the determination of masses by weighing on a spring or balance scale. By ensuring that the force of pressure of the body on the scales, equal to the force of gravity applied to the body, is balanced by the force of pressure of the weights on the other scales, equal to the force of gravity applied to the weights, we thereby determine the mass of the body.

The force of gravity acting on a given body near the Earth can be considered constant only at a certain latitude near the Earth's surface. If the body is lifted or moved to a place with a different latitude, then the acceleration of free fall, and hence the force of gravity, will change.

The force of gravity.

Newton was the first to rigorously prove that the reason that causes the fall of a stone to the Earth, the movement of the Moon around the Earth and the planets around the Sun, is the same. it gravitational force acting between any bodies of the Universe.

Newton came to the conclusion that if it were not for air resistance, then the trajectory of a stone thrown from a high mountain (Fig. 3.1) with a certain speed could become such that it would never reach the Earth's surface at all, but would move around it like how the planets describe their orbits in the sky.

Newton found this reason and was able to accurately express it in the form of one formula - the law of universal gravitation.

Since the force of universal gravitation imparts the same acceleration to all bodies, regardless of their mass, it must be proportional to the mass of the body on which it acts:

“Gravity exists for all bodies in general and is proportional to the mass of each of them ... all planets gravitate towards each other ...” I. Newton

But since, for example, the Earth acts on the Moon with a force proportional to the mass of the Moon, then the Moon, according to Newton's third law, must act on the Earth with the same force. Moreover, this force must be proportional to the mass of the Earth. If the gravitational force is truly universal, then from the side of a given body any other body must be acted upon by a force proportional to the mass of this other body. Consequently, the force of universal gravitation must be proportional to the product of the masses of the interacting bodies. From this follows the formulation of the law of universal gravitation.

Law of gravity:

The force of mutual attraction of two bodies is directly proportional to the product of the masses of these bodies and inversely proportional to the square of the distance between them:

The proportionality factor G is called gravitational constant.

The gravitational constant is numerically equal to the force of attraction between two material points with a mass of 1 kg each, if the distance between them is 1 m. After all, with masses m 1 \u003d m 2 \u003d 1 kg and a distance r \u003d 1 m, we get G \u003d F (numerically).

It must be kept in mind that the law of universal gravitation (3.4) as a universal law is valid for material points. In this case, the forces of gravitational interaction are directed along the line connecting these points (Fig. 3.2, a).

It can be shown that homogeneous bodies having the shape of a ball (even if they cannot be considered material points, Fig. 3.2, b) also interact with the force defined by formula (3.4). In this case, r is the distance between the centers of the balls. The forces of mutual attraction lie on a straight line passing through the centers of the balls. Such forces are called central. The bodies whose fall to the Earth we usually consider are much smaller than the Earth's radius (R ≈ 6400 km).

Such bodies, regardless of their shape, can be considered as material points and the force of their attraction to the Earth can be determined using the law (3.4), bearing in mind that r is the distance from the given body to the center of the Earth.

A stone thrown to the Earth will deviate under the action of gravity from a straight path and, having described a curved trajectory, will finally fall to the Earth. If you throw it with more speed, it will fall further.” I. Newton

Definition of the gravitational constant.

Now let's find out how you can find the gravitational constant. First of all, note that G has a specific name. This is due to the fact that the units (and, accordingly, the names) of all quantities included in the law of universal gravitation have already been established earlier. The law of gravitation gives a new connection between known quantities with certain names of units. That is why the coefficient turns out to be a named value. Using the formula of the law of universal gravitation, it is easy to find the name of the unit of gravitational constant in SI: N m 2 / kg 2 \u003d m 3 / (kg s 2).

To quantify G, it is necessary to independently determine all the quantities included in the law of universal gravitation: both masses, force and distance between bodies.

The difficulty lies in the fact that the gravitational forces between bodies of small masses are extremely small. It is for this reason that we do not notice the attraction of our body to surrounding objects and the mutual attraction of objects to each other, although gravitational forces are the most universal of all forces in nature. Two people weighing 60 kg at a distance of 1 m from each other are attracted with a force of only about 10 -9 N. Therefore, to measure the gravitational constant, rather subtle experiments are needed.

The gravitational constant was first measured by the English physicist G. Cavendish in 1798 using a device called a torsion balance. The scheme of the torsion balance is shown in Figure 3.3. A light rocker with two identical weights at the ends is suspended on a thin elastic thread. Two heavy balls are motionlessly fixed nearby. Gravitational forces act between weights and motionless balls. Under the influence of these forces, the rocker turns and twists the thread until the resulting elastic force becomes equal to the gravitational force. The angle of twist can be used to determine the force of attraction. To do this, you only need to know the elastic properties of the thread. The masses of bodies are known, and the distance between the centers of interacting bodies can be directly measured.

From these experiments, the following value for the gravitational constant was obtained:

G \u003d 6.67 10 -11 N m 2 / kg 2.

Only in the case when bodies of enormous masses interact (or at least the mass of one of the bodies is very large), the gravitational force reaches a large value. For example, the Earth and the Moon are attracted to each other with a force F ≈ 2 10 20 N.

Dependence of free fall acceleration of bodies on geographic latitude.

One of the reasons for the increase in the acceleration of gravity when moving the point where the body is located from the equator to the poles is that the globe is somewhat flattened at the poles and the distance from the center of the Earth to its surface at the poles is less than at the equator. Another reason is the rotation of the Earth.

Equality of inertial and gravitational masses.

The most striking property of gravitational forces is that they impart the same acceleration to all bodies, regardless of their masses. What would you say about a football player whose kick would equally accelerate an ordinary leather ball and a two-pound weight? Everyone will say that it is impossible. But the Earth is just such an “extraordinary football player”, with the only difference that its effect on bodies does not have the character of a short-term impact, but continues continuously for billions of years.

In Newton's theory, mass is the source of the gravitational field. We are in the Earth's gravitational field. At the same time, we are also sources of the gravitational field, but due to the fact that our mass is significantly less than the mass of the Earth, our field is much weaker and the surrounding objects do not react to it.

The unusual property of gravitational forces, as we have already said, is explained by the fact that these forces are proportional to the masses of both interacting bodies. The mass of the body, which is included in Newton's second law, determines the inertial properties of the body, i.e., its ability to acquire a certain acceleration under the action of a given force. it inertial mass m and.

It would seem, what relation can it have to the ability of bodies to attract each other? The mass that determines the ability of bodies to attract each other is the gravitational mass m r .

It does not follow at all from Newtonian mechanics that the inertial and gravitational masses are the same, i.e. that

m and = m r . (3.5)

Equality (3.5) is a direct consequence of experience. It means that one can simply speak of the mass of a body as a quantitative measure of both its inertial and gravitational properties.

Since ancient times, mankind has thought about how the world around us works. Why does grass grow, why does the Sun shine, why can't we fly... The latter, by the way, has always been of particular interest to people. Now we know that the reason for everything is gravity. What it is, and why this phenomenon is so important on the scale of the Universe, we will consider today.

Introduction

Scientists have found that all massive bodies experience mutual attraction to each other. Subsequently, it turned out that this mysterious force also determines the movement of celestial bodies in their constant orbits. The very same theory of gravity was formulated by a genius whose hypotheses predetermined the development of physics for many centuries to come. Developed and continued (albeit in a completely different direction) this teaching was Albert Einstein - one of the greatest minds of the past century.

For centuries, scientists have observed gravity, trying to understand and measure it. Finally, in the last few decades, even such a phenomenon as gravity has been put at the service of mankind (in a certain sense, of course). What is it, what is the definition of the term in question in modern science?

scientific definition

If you study the works of ancient thinkers, you can find out that the Latin word "gravitas" means "gravity", "attraction". Today, scientists so call the universal and constant interaction between material bodies. If this force is relatively weak and acts only on objects that move much more slowly, then Newton's theory is applicable to them. If the opposite is the case, Einstein's conclusions should be used.

Let's make a reservation right away: at present, the very nature of gravity itself has not been fully studied in principle. What it is, we still do not fully understand.

Theories of Newton and Einstein

According to the classical teaching of Isaac Newton, all bodies are attracted to each other with a force that is directly proportional to their mass, inversely proportional to the square of the distance that lies between them. Einstein, on the other hand, argued that gravity between objects manifests itself in the case of curvature of space and time (and the curvature of space is possible only if there is matter in it).

This idea was very deep, but modern research proves it to be somewhat inaccurate. Today it is believed that gravity in space only bends space: time can be slowed down and even stopped, but the reality of changing the shape of temporary matter has not been theoretically confirmed. Therefore, the classical Einstein equation does not even provide for a chance that space will continue to influence matter and the emerging magnetic field.

To a greater extent, the law of gravity (universal gravitation) is known, the mathematical expression of which belongs precisely to Newton:

\[ F = γ \frac[-1.2](m_1 m_2)(r^2) \]

Under γ is understood the gravitational constant (sometimes the symbol G is used), the value of which is 6.67545 × 10−11 m³ / (kg s²).

Interaction between elementary particles

The incredible complexity of the space around us is largely due to the infinite number of elementary particles. There are also various interactions between them at levels that we can only guess at. However, all types of interaction of elementary particles among themselves differ significantly in their strength.

The most powerful of all the forces known to us bind together the components of the atomic nucleus. To separate them, you need to spend a truly colossal amount of energy. As for electrons, they are “tied” to the nucleus only by ordinary ones. To stop it, sometimes the energy that appears as a result of the most ordinary chemical reaction is enough. Gravity (what it is, you already know) in the variant of atoms and subatomic particles is the easiest kind of interaction.

The gravitational field in this case is so weak that it is difficult to imagine. Oddly enough, but it is they who “follow” the movement of celestial bodies, whose mass is sometimes impossible to imagine. All this is possible due to two features of gravity, which are especially pronounced in the case of large physical bodies:

• Unlike atomic ones, it is more noticeable at a distance from the object. So, the Earth's gravity keeps even the Moon in its field, and the similar force of Jupiter easily supports the orbits of several satellites at once, the mass of each of which is quite comparable to the Earth's!
• In addition, it always provides attraction between objects, and with distance this force weakens at a low speed.

The formation of a more or less coherent theory of gravitation occurred relatively recently, and precisely on the basis of the results of centuries-old observations of the motion of planets and other celestial bodies. The task was greatly facilitated by the fact that they all move in a vacuum, where there are simply no other possible interactions. Galileo and Kepler, two outstanding astronomers of the time, helped pave the way for new discoveries with their most valuable observations.

But only the great Isaac Newton was able to create the first theory of gravity and express it in a mathematical representation. This was the first law of gravity, the mathematical representation of which is presented above.

Conclusions of Newton and some of his predecessors

Unlike other physical phenomena that exist in the world around us, gravity manifests itself always and everywhere. You need to understand that the term "zero gravity", which is often found in pseudo-scientific circles, is extremely incorrect: even weightlessness in space does not mean that a person or a spacecraft is not affected by the attraction of some massive object.

In addition, all material bodies have a certain mass, expressed in the form of a force that was applied to them, and an acceleration obtained due to this impact.

Thus, gravitational forces are proportional to the mass of objects. Numerically, they can be expressed by obtaining the product of the masses of both considered bodies. This force strictly obeys the inverse dependence on the square of the distance between objects. All other interactions depend quite differently on the distances between two bodies.

Mass as the cornerstone of theory

The mass of objects has become a particular point of contention around which Einstein's entire modern theory of gravity and relativity is built. If you remember the Second, then you probably know that mass is a mandatory characteristic of any physical material body. It shows how an object will behave if force is applied to it, regardless of its origin.

Since all bodies (according to Newton) accelerate when an external force acts on them, it is the mass that determines how large this acceleration will be. Let's look at a clearer example. Imagine a scooter and a bus: if you apply exactly the same force to them, they will reach different speeds in different times. All this is explained by the theory of gravity.

What is the relationship between mass and attraction?

If we talk about gravity, then the mass in this phenomenon plays a role completely opposite to that which it plays in relation to the force and acceleration of an object. It is she who is the primary source of attraction itself. If you take two bodies and see with what force they attract a third object, which is located at equal distances from the first two, then the ratio of all forces will be equal to the ratio of the masses of the first two objects. Thus, the force of attraction is directly proportional to the mass of the body.

If we consider Newton's Third Law, we can see that he says exactly the same thing. The force of gravity, which acts on two bodies located at an equal distance from the source of attraction, directly depends on the mass of these objects. In everyday life, we talk about the force with which a body is attracted to the surface of the planet as its weight.

Let's sum up some results. So, mass is closely related to acceleration. At the same time, it is she who determines the force with which gravity will act on the body.

Features of acceleration of bodies in a gravitational field

This amazing duality is the reason why, in the same gravitational field, the acceleration of completely different objects will be equal. Suppose we have two bodies. Let's assign a mass z to one of them, and Z to the other. Both objects are dropped to the ground, where they fall freely.

How is the ratio of forces of attraction determined? It is shown by the simplest mathematical formula - z / Z. That's just the acceleration they receive as a result of the force of gravity, will be exactly the same. Simply put, the acceleration that a body has in a gravitational field does not depend in any way on its properties.

What does the acceleration depend on in the described case?

It depends only (!) on the mass of objects that create this field, as well as on their spatial position. The dual role of mass and the equal acceleration of various bodies in a gravitational field have been discovered for a relatively long time. These phenomena have received the following name: "Principle of equivalence". This term once again emphasizes that acceleration and inertia are often equivalent (to a certain extent, of course).

On the importance of G

From the school physics course, we remember that the acceleration of free fall on the surface of our planet (Earth's gravity) is 10 m / s² (9.8 of course, but this value is used for ease of calculation). Thus, if air resistance is not taken into account (at a significant height with a small fall distance), then the effect will be obtained when the body acquires an acceleration increment of 10 m / s. every second. Thus, a book that has fallen from the second floor of a house will move at a speed of 30-40 m/sec by the end of its flight. Simply put, 10 m/s is the "speed" of gravity within the Earth.

Acceleration due to gravity in the physical literature is denoted by the letter "g". Since the shape of the Earth is to a certain extent more like a tangerine than a sphere, the value of this quantity is far from being the same in all its regions. So, at the poles, the acceleration is higher, and on the tops of high mountains it becomes less.

Even in the mining industry, gravity plays an important role. The physics of this phenomenon sometimes saves a lot of time. Thus, geologists are especially interested in the ideally accurate determination of g, since this allows exploration and finding of mineral deposits with exceptional accuracy. By the way, what does the gravity formula look like, in which the value we have considered plays an important role? There she is:

Note! In this case, the gravitational formula means by G the "gravitational constant", the value of which we have already given above.

At one time, Newton formulated the above principles. He perfectly understood both unity and universality, but he could not describe all aspects of this phenomenon. This honor fell to Albert Einstein, who was also able to explain the principle of equivalence. It is to him that mankind owes a modern understanding of the very nature of the space-time continuum.

Theory of relativity, works of Albert Einstein

At the time of Isaac Newton, it was believed that reference points can be represented as some kind of rigid "rods", with the help of which the position of the body in the spatial coordinate system is established. At the same time, it was assumed that all observers who mark these coordinates would be in a single time space. In those years, this provision was considered so obvious that no attempts were made to challenge or supplement it. And this is understandable, because within our planet there are no deviations in this rule.

Einstein proved that the accuracy of the measurement would be really significant if the hypothetical clock was moving much slower than the speed of light. Simply put, if one observer, moving slower than the speed of light, follows two events, then they will happen for him at the same time. Accordingly, for the second observer? the speed of which is the same or more, events can occur at different times.

But how is the force of gravity related to the theory of relativity? Let's explore this issue in detail.

Relationship between relativity and gravitational forces

In recent years, a huge number of discoveries in the field of subatomic particles have been made. The conviction is growing stronger that we are about to find the final particle, beyond which our world cannot be divided. The more insistent is the need to find out exactly how the smallest “bricks” of our universe are affected by those fundamental forces that were discovered in the last century, or even earlier. It is especially disappointing that the very nature of gravity has not yet been explained.

That is why, after Einstein, who established the “incapacity” of classical Newtonian mechanics in the area under consideration, researchers focused on a complete rethinking of the data obtained earlier. In many ways, gravity itself has undergone a revision. What is it at the level of subatomic particles? Does it have any meaning in this amazing multidimensional world?

A simple solution?

At first, many assumed that the discrepancy between Newton's gravity and the theory of relativity can be explained quite simply by drawing analogies from the field of electrodynamics. It could be assumed that the gravitational field propagates like a magnetic one, after which it can be declared a "mediator" in the interactions of celestial bodies, explaining many inconsistencies between the old and the new theory. The fact is that then the relative velocities of propagation of the forces under consideration would be much lower than the speed of light. So how are gravity and time related?

In principle, Einstein himself almost succeeded in constructing a relativistic theory based on just such views, only one circumstance prevented his intention. None of the scientists of that time had any information at all that could help determine the "speed" of gravity. But there was a lot of information related to the movements of large masses. As is known, they were just the generally recognized source of powerful gravitational fields.

High speeds strongly affect the masses of bodies, and this is not at all like the interaction of speed and charge. The higher the speed, the greater the mass of the body. The problem is that the last value would automatically become infinite in the case of movement at the speed of light or higher. Therefore, Einstein concluded that there is not a gravitational, but a tensor field, for the description of which many more variables should be used.

His followers came to the conclusion that gravity and time are practically unrelated. The fact is that this tensor field itself can act on space, but it is not able to influence time. However, the brilliant modern physicist Stephen Hawking has a different point of view. But that's a completely different story...

First, imagine the Earth as a non-moving ball (Fig. 3.1, a). The gravitational force F between the Earth (mass M) and an object (mass m) is determined by the formula: F=Gmm/r2

where r is the radius of the Earth. The constant G is known as universal gravitational constant and extremely small. When r is constant, the force F is const. m. The attraction of a body of mass m by the Earth determines the weight of this body: W = mg comparison of the equations gives: g = const = GM/r 2 .

The attraction of a body of mass m by the Earth causes it to fall "down" with an acceleration g, which is constant at all points A, B, C and everywhere on the earth's surface (Fig. 3.1.6).

The diagram of the forces of a free body also shows that there is a force acting on the Earth from the side of a body of mass m, which is directed opposite to the force acting on the body from the Earth. However, the mass M of the Earth is so large that the "upward" acceleration a "of the Earth, calculated by the formula F = Ma", is insignificant and can be neglected. The earth has a shape other than spherical: the radius at the pole r p is less than the radius at the equator r e. This means that the force of attraction of a body with mass m at the pole F p \u003d GMm / r 2 p is greater than at the equator F e = GMm/r e . Therefore, the acceleration of free fall g p at the pole is greater than the acceleration of free fall g e at the equator. The acceleration g changes with latitude in accordance with the change in the radius of the Earth.



As you know, the Earth is in constant motion. It rotates around its axis, making one revolution every day, and moves in orbit around the Sun with a revolution of one year. Taking for simplicity the Earth as a homogeneous ball, let's consider the motion of bodies of mass m on the pole A and on the equator C (Fig. 3.2). In one day, the body at point A rotates 360 °, remaining in place, while the body at point C covers a distance of 2lg. In order for the body located at point C to move in a circular orbit, some kind of force is needed. This is a centripetal force, which is determined by the formula mv 2 /r, where v is the speed of the body in orbit. The force of gravitational attraction acting on a body located at point C, F = GMm/r must:

a) ensure the movement of the body in a circle;

b) attract the body to the Earth.

Thus, F = (mv 2 /r) + mg at the equator, and F = mg at the pole. This means that g changes with latitude as the radius of the orbit changes from r at C to zero at A.

It is interesting to imagine what would happen if the speed of the Earth's rotation increased so much that the centripetal force acting on the body at the equator would become equal to the force of attraction, i.e. mv 2 / r = F = GMm / r 2 . The total gravitational force would be used solely to keep the body at point C in a circular orbit, and there would be no force left to act on the surface of the Earth. Any further increase in the speed of the Earth's rotation would allow the body to "float away" into space. At the same time, if a spacecraft with astronauts on board is launched to a height R above the center of the Earth with a speed v, such that the equality mv*/R=F = GMm/R 2 is satisfied, then this spacecraft will rotate around the Earth in conditions of weightlessness.

Accurate measurements of the free fall acceleration g show that g varies with latitude, as shown in Table 3.1. It follows from this that the weight of a certain body changes over the surface of the Earth from a maximum at a latitude of 90 ° to a minimum at a latitude of 0 °.



At this level of training, small changes in acceleration g are usually ignored and an average value of 9.81 m-s 2 is used. To simplify calculations, the acceleration g is often taken as the nearest integer, i.e. 10 ms - 2, and, thus, the force of attraction acting from the Earth on a body of mass 1 kg, i.e. weight, taken as 10 N. Most examination boards for examinees suggest using g \u003d 10 m-s - 2 or 10 N-kg -1 in order to simplify calculations.