Universal gravity in brief. The law and force of universal gravitation

The law of universal gravitation was discovered by Newton in 1687 while studying the motion of the moon's satellite around the Earth. The English physicist clearly formulated a postulate characterizing the forces of attraction. In addition, by analyzing Kepler's laws, Newton calculated that gravitational forces must exist not only on our planet, but also in space.

Background

The law of universal gravitation was not born spontaneously. Since ancient times, people have studied the sky, mainly to compile agricultural calendars, calculate important dates, and religious holidays. Observations indicated that in the center of the “world” there is a Luminary (Sun), around which celestial bodies rotate in orbits. Subsequently, the dogmas of the church did not allow this to be considered, and people lost the knowledge accumulated over thousands of years.

In the 16th century, before the invention of telescopes, a galaxy of astronomers appeared who looked at the sky in a scientific way, discarding the prohibitions of the church. T. Brahe, having been observing space for many years, systematized the movements of the planets with special care. These highly accurate data helped I. Kepler subsequently discover his three laws.

By the time Isaac Newton discovered the law of gravitation (1667), the heliocentric system of the world of N. Copernicus was finally established in astronomy. According to it, each of the planets of the system rotates around the Sun in orbits that, with an approximation sufficient for many calculations, can be considered circular. At the beginning of the 17th century. I. Kepler, analyzing the works of T. Brahe, established kinematic laws characterizing the movements of the planets. The discovery became the foundation for elucidating the dynamics of planetary motion, that is, the forces that determine exactly this type of their motion.

Description of interaction

Unlike short-period weak and strong interactions, gravity and electromagnetic fields have long-range properties: their influence manifests itself over enormous distances. Mechanical phenomena in the macrocosm are affected by two forces: electromagnetic and gravitational. The influence of planets on satellites, the flight of an thrown or launched object, the floating of a body in a liquid - in each of these phenomena gravitational forces act. These objects are attracted by the planet and gravitate towards it, hence the name “law of universal gravitation”.

It has been proven that there is certainly a force of mutual attraction between physical bodies. Phenomena such as the fall of objects to the Earth, the rotation of the Moon and planets around the Sun, occurring under the influence of the forces of universal gravity, are called gravitational.

Law of universal gravitation: formula

Universal gravity is formulated as follows: any two material objects are attracted to each other with a certain force. The magnitude of this force is directly proportional to the product of the masses of these objects and inversely proportional to the square of the distance between them:

In the formula, m1 and m2 are the masses of the material objects being studied; r is the distance determined between the centers of mass of the calculated objects; G is a constant gravitational quantity expressing the force with which the mutual attraction of two objects weighing 1 kg each, located at a distance of 1 m, occurs.

What does the force of attraction depend on?

The law of gravity works differently depending on the region. Since the force of gravity depends on the values ​​of latitude in a certain area, similarly, the acceleration of gravity has different values ​​in different places. The force of gravity and, accordingly, the acceleration of free fall have a maximum value at the poles of the Earth - the force of gravity at these points is equal to the force of attraction. The minimum values ​​will be at the equator.

The globe is slightly flattened, its polar radius is approximately 21.5 km less than the equatorial radius. However, this dependence is less significant compared to the daily rotation of the Earth. Calculations show that due to the oblateness of the Earth at the equator, the magnitude of the acceleration due to gravity is slightly less than its value at the pole by 0.18%, and after daily rotation - by 0.34%.

However, in the same place on Earth, the angle between the direction vectors is small, so the discrepancy between the force of attraction and the force of gravity is insignificant, and it can be neglected in calculations. That is, we can assume that the modules of these forces are the same - the acceleration of gravity near the Earth’s surface is the same everywhere and is approximately 9.8 m/s².

Conclusion

Isaac Newton was a scientist who made a scientific revolution, completely rebuilt the principles of dynamics and, on their basis, created a scientific picture of the world. His discovery influenced the development of science and the creation of material and spiritual culture. It fell to Newton's fate to revise the results of the idea of ​​the world. In the 17th century Scientists have completed the grandiose work of building the foundation of a new science - physics.

So, the movement of planets, for example the Moon around the Earth or the Earth around the Sun, is the same fall, but only a fall that lasts indefinitely (in any case, if we ignore the transition of energy into “non-mechanical” forms).

The conjecture about the unity of causes governing the movement of planets and the fall of earthly bodies was expressed by scientists long before Newton. Apparently, the first to clearly express this idea was the Greek philosopher Anaxagoras, a native of Asia Minor, who lived in Athens almost two thousand years ago. He said that the Moon, if it did not move, would fall to the Earth.

However, Anaxagoras’ brilliant guess, apparently, did not have any practical impact on the development of science. She was destined to be misunderstood by her contemporaries and forgotten by her descendants. Ancient and medieval thinkers, whose attention was attracted by the movement of the planets, were very far from the correct (and more often than not any) interpretation of the causes of this movement. After all, even the great Kepler, who, at the cost of enormous labor, was able to formulate the exact mathematical laws of planetary motion, believed that the cause of this motion was the rotation of the Sun.

According to Kepler's ideas, the Sun, rotating, constantly pushes the planets into rotation. True, it remained unclear why the time of revolution of the planets around the Sun differs from the period of revolution of the Sun around its own axis. Kepler wrote about this: “if the planets did not have natural resistance, then it would be impossible to give reasons why they should not follow exactly the rotation of the Sun. But although in reality all the planets move in the same direction in which the rotation of the Sun occurs, the speed of their movement is not the same. The fact is that they mix, in certain proportions, the inertia of their own mass with the speed of their movement.”

Kepler failed to understand that the coincidence of the directions of motion of the planets around the Sun with the direction of rotation of the Sun around its axis is not associated with the laws of planetary motion, but with the origin of our solar system. An artificial planet can be launched both in the direction of rotation of the Sun and against this rotation.

Robert Hooke came much closer than Kepler to the discovery of the law of attraction of bodies. Here are his actual words from a work entitled An Attempt to Study the Motion of the Earth, published in 1674: “I will develop a theory which is in every respect consistent with the generally accepted rules of mechanics. This theory is based on three assumptions: firstly, that all celestial bodies, without exception, have a gravity directed towards their center, due to which they attract not only their own parts, but also all celestial bodies within their sphere of action. According to the second assumption, all bodies moving in a rectilinear and uniform manner will move in a straight line until they are deflected by some force and begin to describe trajectories in a circle, an ellipse, or some other less simple curve. According to the third assumption, the forces of attraction act the more strongly, the closer to them the bodies on which they act are located. I have not yet been able to establish by experience what the different degrees of attraction are. But if we develop this idea further, astronomers will be able to determine the law according to which all celestial bodies move.”

Truly, one can only be amazed that Hooke himself did not want to engage in the development of these ideas, citing being busy with other work. But a scientist appeared who made a breakthrough in this area

The history of Newton's discovery of the law of universal gravitation is quite well known. For the first time, the idea that the nature of the forces that make a stone fall and determine the movement of celestial bodies is one and the same arose with Newton the student, that the first calculations did not give the correct results, since the data available at that time on the distance from the Earth to the Moon were inaccurate, that 16 years later new, corrected information about this distance appeared. To explain the laws of planetary motion, Newton applied the laws of dynamics he created and the law of universal gravitation that he himself established.

He named the Galilean principle of inertia as the first law of dynamics, including it in the system of basic laws-postulates of his theory.

At the same time, Newton had to eliminate the mistake of Galileo, who believed that uniform motion in a circle was motion by inertia. Newton pointed out (and this is the second law of dynamics) that the only way to change the motion of a body - the value or direction of the velocity - is to act on it with some force. In this case, the acceleration with which a body moves under the influence of a force is inversely proportional to the mass of the body.

According to Newton's third law of dynamics, “to every action there is always an equal and opposite reaction.”

Consistently applying the principles - the laws of dynamics, he first calculated the centripetal acceleration of the Moon as it moves in orbit around the Earth, and then was able to show that the ratio of this acceleration to the acceleration of free fall of bodies at the Earth's surface is equal to the ratio of the squares of the radii of the Earth and the lunar orbit. From this Newton concluded that the nature of gravity and the force that holds the Moon in orbit are the same. In other words, according to his conclusions, the Earth and the Moon are attracted to each other with a force inversely proportional to the square of the distance between their centers Fg ≈ 1∕r2.

Newton was able to show that the only explanation for the independence of the acceleration of free fall of bodies from their mass is the proportionality of the force of gravity to the mass.

Summarizing the findings, Newton wrote: “there can be no doubt that the nature of gravity on other planets is the same as on Earth. In fact, let us imagine that the earth's bodies are raised to the orbit of the Moon and sent together with the Moon, also devoid of any movement, to fall to the Earth. Based on what has already been proven (meaning the experiments of Galileo), there is no doubt that at the same times they will pass through the same spaces as the Moon, for their masses are related to the mass of the Moon in the same way as their weights are to its weight.” So Newton discovered and then formulated the law of universal gravitation, which is rightfully the property of science.

2. Properties of gravitational forces.

One of the most remarkable properties of the forces of universal gravitation, or, as they are often called, gravitational forces, is reflected in the very name given by Newton: universal. These forces, so to speak, are “the most universal” among all the forces of nature. Everything that has mass - and mass is inherent in any form, any kind of matter - must experience gravitational influences. Even light is no exception. If we visualize gravitational forces with the help of strings that stretch from one body to another, then an innumerable number of such strings would have to permeate space anywhere. At the same time, it is worth noting that it is impossible to break such a thread and protect yourself from gravitational forces. There are no barriers to universal gravity; their radius of action is unlimited (r = ∞). Gravitational forces are long-range forces. This is the “official name” of these forces in physics. Due to long-range action, gravity connects all bodies of the Universe.

The relative slowness of the decrease of forces with distance at each step is manifested in our earthly conditions: after all, all bodies do not change their weight when transferred from one height to another (or, to be more precise, they change, but extremely insignificantly), precisely because with a relatively small change in distance - in this case from the center of the Earth - gravitational forces practically do not change.

By the way, it is for this reason that the law of measuring gravitational forces with distance was discovered “in the sky.” All the necessary data was drawn from astronomy. One should not, however, think that a decrease in gravity with height cannot be detected under terrestrial conditions. So, for example, a pendulum clock with an oscillation period of one second will fall behind a day by almost three seconds if it is raised from the basement to the top floor of Moscow University (200 meters) - and this is only due to a decrease in gravity.

The altitudes at which artificial satellites move are already comparable to the radius of the Earth, so to calculate their trajectory, taking into account the change in the force of gravity with distance is absolutely necessary.

Gravitational forces have another very interesting and unusual property, which will be discussed now.

For many centuries, medieval science accepted as an unshakable dogma Aristotle's statement that a body falls the faster the greater its weight. Even everyday experience confirms this: it is known that a piece of fluff falls slower than a stone. However, as Galileo was able to show for the first time, the whole point here is that air resistance, coming into play, radically distorts the picture that would be if only earthly gravity acted on all bodies. There is a remarkable experiment with the so-called Newton tube, which makes it possible to very easily evaluate the role of air resistance. Here is a short description of this experience. Imagine an ordinary glass tube (so that you can see what is happening inside) in which various objects are placed: pellets, pieces of cork, feathers or fluffs, etc. If you turn the tube over so that all this can fall, then the pellet will flash faster , followed by pieces of cork and, finally, the fluff will gradually fall. But let’s try to monitor the fall of the same objects when the air is pumped out of the tube. The fluff, having lost its former slowness, rushes along, keeping pace with the pellet and the cork. This means that its movement was delayed by air resistance, which had a lesser effect on the movement of the plug and even less on the movement of the pellet. Consequently, if it were not for air resistance, if only the forces of universal gravity acted on bodies - in a particular case, gravity - then all bodies would fall exactly the same, accelerating at the same pace.

But “there is nothing new under the sun.” Two thousand years ago, Lucretius Carus wrote in his famous poem “On the Nature of Things”:

everything that falls in rare air,

Should fall faster according to its own weight

Only because water or air is a subtle essence

I am not able to put obstacles in the way of things that are the same,

But it is more likely to yield to those with greater severity.

On the contrary, I am never capable of anything anywhere

The thing holds the emptiness and appears as some kind of support,

By nature, constantly giving in to everything.

Therefore, everything, rushing through the void without obstacles,

Have the same speed despite the difference in weight.

Of course, these wonderful words were a great guess. To turn this guess into a reliably established law, it took many experiments, starting with the famous experiments of Galileo, who studied the fall of balls of the same size, but made of different materials (marble, wood, lead, etc.) from the famous leaning Leaning Tower of Pisa, and ending with the most sophisticated modern measurements of the influence of gravity on light. And all this variety of experimental data persistently strengthens us in the belief that gravitational forces impart equal acceleration to all bodies; in particular, the acceleration of free fall caused by gravity is the same for all bodies and does not depend on the composition, structure, or mass of the bodies themselves.

This seemingly simple law expresses perhaps the most remarkable feature of gravitational forces. There are literally no other forces that accelerate all bodies equally, regardless of their mass.

So, this property of the forces of universal gravity can be compressed into one short statement: the gravitational force is proportional to the mass of bodies. Let us emphasize that here we are talking about the very mass that acts as a measure of inertia in Newton’s laws. It is even called inert mass.

The four words “gravitational force is proportional to mass” contain a surprisingly deep meaning. Large and small bodies, hot and cold, of very different chemical compositions, of any structure - they all experience the same gravitational interaction if their masses are equal.

Or maybe this law is really simple? After all, Galileo, for example, considered it almost self-evident. Here is his reasoning. Let two bodies of different weights fall. According to Aristotle, a heavy body should fall faster even in vacuum. Now let's connect the bodies. Then, on the one hand, the bodies should fall faster, since the total weight has increased. But, on the other hand, adding a part to a heavy body that falls more slowly should slow down this body. There is a contradiction that can be eliminated only if we assume that all bodies under the influence of gravity alone fall with the same acceleration. It's like everything is consistent! However, let us think again about the above reasoning. It is based on the common method of proof “by contradiction”: by assuming that a heavier body falls faster than a lighter one, we have arrived at a contradiction. And from the very beginning there was an assumption that the acceleration of free fall is determined by weight and only weight. (Strictly speaking, not by weight, but by mass.)

But this is not at all obvious in advance (i.e., before the experiment). What if this acceleration was determined by the volume of the bodies? Or temperature? Let's imagine that there is a gravitational charge, similar to an electric charge and, like the latter, completely unrelated directly to mass. The comparison with electric charge is very useful. Here are two specks of dust between the charged plates of a capacitor. Let these dust grains have equal charges, and the masses are in the ratio 1 to 2. Then the accelerations should differ by a factor of two: the forces determined by the charges are equal, and with equal forces, a body with twice the mass accelerates half as much. If you connect dust particles, then, obviously, the acceleration will have a new, intermediate value. No speculative approach without an experimental study of electrical forces can give anything here. The picture would be exactly the same if the gravitational charge were not associated with mass. But only experience can answer the question of whether such a connection exists. And we now understand that it was the experiments that proved the identical acceleration due to gravity for all bodies that essentially showed that the gravitational charge (gravitational or heavy mass) is equal to the inertial mass.

Experience and only experience can serve both as a basis for physical laws and as a criterion for their validity. Let us at least recall the record-breaking precision experiments conducted under the leadership of V.B. Braginsky at Moscow State University. These experiments, in which an accuracy of about 10-12 was obtained, once again confirmed the equality of heavy and inert mass.

It is on experience, on the wide testing of nature - from the modest scale of a small laboratory of a scientist to the grandiose cosmic scale - that the law of universal gravitation is based, which (to summarize everything said above) says:

The force of mutual attraction of any two bodies whose dimensions are much smaller than the distance between them is proportional to the product of the masses of these bodies and inversely proportional to the square of the distance between these bodies.

The proportionality coefficient is called the gravitational constant. If we measure length in meters, time in seconds, and mass in kilograms, the gravitational force will always be equal to 6.673*10-11, and its dimension will be m3/kg*s2 or N*m2/kg2, respectively.

G=6.673*10-11 N*m2/kg2

3. Gravitational waves.

Newton's law of universal gravitation does not say anything about the time of transmission of gravitational interaction. It is implicitly assumed that it occurs instantly, no matter how large the distances between the interacting bodies are. This view is generally typical of supporters of action at a distance. But from Einstein’s “special theory of relativity” it follows that gravity is transmitted from one body to another at the same speed as the light signal. If some body moves from its place, then the curvature of space and time caused by it does not change instantly. First, this will affect the immediate vicinity of the body, then the change will affect more and more distant areas, and, finally, a new distribution of curvature will be established throughout space, corresponding to the changed position of the body.

And here we come to the problem that has caused and continues to cause the greatest number of disputes and disagreements - the problem of gravitational radiation.

Can gravity exist if there is no mass creating it? According to Newton's law, definitely not. It makes no sense to even raise such a question there. However, as soon as we agreed that gravitational signals are transmitted, although at a very high, but still not infinite speed, everything changes radically. Indeed, imagine that at first the mass causing gravity, for example a ball, was at rest. All bodies around the ball will be affected by ordinary Newtonian forces. Now let’s remove the ball from its original place with great speed. At first, the surrounding bodies will not feel this. After all, gravitational forces do not change instantly. It takes time for changes in the curvature of space to spread in all directions. This means that the surrounding bodies will experience the same influence of the ball for some time, when the ball itself is no longer there (at least, in the same place).

It turns out that the curvatures of space acquire a certain independence, that it is possible to tear a body out of the area of ​​space where it caused the curvatures, and in such a way that these curvatures themselves, at least over large distances, will remain and develop according to their internal laws. Here is gravity without gravitating mass! We can go further. If you make the ball oscillate, then, as it turns out from Einstein’s theory, a kind of ripple is superimposed on the Newtonian picture of gravity - gravitational waves. To better imagine these waves, you need to use a model - a rubber film. If you not only press your finger on this film, but simultaneously make oscillatory movements with it, then these vibrations will begin to be transmitted along the stretched film in all directions. This is an analogue of gravitational waves. The further away from the source, the weaker such waves are.

And now at some point we will stop putting pressure on the film. The waves won't go away. They will exist independently, scattering further and further across the film, causing geometry to bend along the way.

In exactly the same way, waves of space curvature - gravitational waves - can exist independently. Many researchers draw this conclusion from Einstein’s theory.

Of course, all these effects are very weak. For example, the energy released when one match burns is many times greater than the energy of gravitational waves emitted by our entire solar system during the same time. But what is important here is not the quantitative, but the principled side of the matter.

Proponents of gravitational waves - and they seem to be in the majority now - predict another amazing phenomenon; the transformation of gravity into particles such as electrons and positrons (they must be born in pairs), protons, antitrons, etc. (Ivanenko, Wheeler, etc.).

It should look something like this. A wave of gravity reached a certain area of ​​space. At a certain moment, this gravity sharply, abruptly, decreases and at the same time, say, an electron-positron pair appears there. The same can be described as an abrupt decrease in the curvature of space with the simultaneous birth of a pair.

There are many attempts to translate this into quantum mechanical language. Particles are introduced into consideration - gravitons, which are compared to the non-quantum image of a gravitational wave. In the physical literature, the term “transmutation of gravitons into other particles” is in circulation, and these transmutations - mutual transformations - are possible between gravitons and, in principle, any other particles. After all, there are no particles that are insensitive to gravity.

Even though such transformations are unlikely, that is, they happen extremely rarely, on a cosmic scale they can turn out to be fundamental.

4. Curvature of space-time by gravity,

"Eddington's Parable"

A parable by the English physicist Eddington from the book “Space, Time and Gravity” (retelling):

“In an ocean that has only two dimensions, there once lived a breed of flat fish. It was observed that the fish generally swam in straight lines as long as they did not encounter obvious obstacles in their path. This behavior seemed quite natural. But there was a mysterious area in the ocean; when the fish fell into it, they seemed enchanted; some sailed through this area but changed the direction of their movement, others endlessly circled around this area. One fish (almost Descartes) proposed a theory of vortices; she said that in this area there are whirlpools that make everything that gets into them spin. Over time, a much more advanced theory was proposed (Newton's theory); they said that all fish are attracted to a very large fish - the sun fish, dormant in the middle of the region - and this explained the deviation of their paths. At first this theory seemed perhaps a little strange; but it was confirmed with amazing accuracy by a wide variety of observations. All fish have been found to have this attractive property, proportionate to their size; the law of attraction (analogous to the law of universal gravitation) was extremely simple, but despite this, it explained all movements with such precision that the accuracy of scientific research had never reached before. True, some fish, grumbling, declared that they did not understand how such an action at a distance was possible; but everyone agreed that this action was carried out by the ocean, and that it would be easier to understand when the nature of water was better studied. Therefore, almost every fish that wanted to explain gravity began by suggesting some mechanism by which it spread through water.

But there was a fish who looked at things differently. She noticed the fact that the big fish and the small ones always moved along the same paths, although it might seem that it would take a lot of force to deflect the big fish from its path. (The sunfish imparted equal accelerations to all bodies.) Therefore, instead of trying, she began to study in detail the paths of movement of fish and thus came to an astonishing solution to the problem. There was a high place in the world where the sunfish lay. The fish could not directly notice this because they were two-dimensional; but when the fish in its movement fell on the slope of this elevation, then although it tried to swim in a straight line, it involuntarily turned a little to the side. This was the secret of the mysterious attraction or curvature of paths that occurred in the mysterious area. »

This parable shows how the curvature of the world in which we live can give the illusion of gravity, and we see that an effect like gravity is the only way such curvature can manifest itself.

Briefly, this can be formulated as follows. Since gravity bends the paths of all bodies in the same way, we can think of gravity as the curvature of space-time.

5. Gravity on Earth.

If you think about the role that gravitational forces play in the life of our planet, entire oceans open up. And not only oceans of phenomena, but also oceans in the literal sense of the word. Oceans of water. Air ocean. Without gravity they would not exist.

A wave in the sea, the movement of every drop of water in the rivers that feed this sea, all currents, all winds, clouds, the entire climate of the planet are determined by the play of two main factors: solar activity and gravity.

Gravity not only holds people, animals, water and air on Earth, but also compresses them. This compression at the Earth's surface is not so great, but its role is important.

The ship is sailing on the sea. What prevents him from drowning is known to everyone. This is the famous buoyant force of Archimedes. But it appears only because water is compressed by gravity with a force that increases with increasing depth. Inside a spacecraft in flight, there is no buoyant force, and there is no weight either. The globe itself is compressed by gravitational forces to colossal pressures. At the center of the Earth, the pressure appears to exceed 3 million atmospheres.

Under the influence of long-acting pressure forces under these conditions, all substances that we are accustomed to consider solid behave like pitch or resin. Heavy materials sink to the bottom (if you can call the center of the Earth that way), and light materials float to the surface. This process has been going on for billions of years. It has not ended, as follows from Schmidt’s theory, even now. The concentration of heavy elements in the region of the Earth's center is slowly increasing.

Well, how does the attraction of the Sun and the closest celestial body of the Moon manifest itself on Earth? Only residents of the ocean coasts can observe this attraction without special instruments.

The sun acts in almost the same way on everything on and inside the Earth. The force with which the Sun attracts a person at noon, when he is closest to the Sun, is almost the same as the force acting on him at midnight. After all, the distance from the Earth to the Sun is ten thousand times greater than the Earth’s diameter, and an increase in the distance by one ten-thousandth when the Earth rotates half a turn around its axis practically does not change the force of gravity. Therefore, the Sun imparts almost identical accelerations to all parts of the globe and all bodies on its surface. Almost, but still not quite the same. Because of this difference, the ebb and flow of the ocean occurs.

On the section of the earth's surface facing the Sun, the force of gravity is somewhat greater than that necessary for the movement of this section along an elliptical orbit, and on the opposite side of the Earth it is somewhat less. As a result, according to Newton's laws of mechanics, the water in the ocean bulges slightly in the direction facing the Sun, and on the opposite side it recedes from the Earth's surface. Tidal forces, as they say, arise, stretching the globe and giving, roughly speaking, the surface of the oceans the shape of an ellipsoid.

The smaller the distances between interacting bodies, the greater the tidal forces. This is why the Moon has a greater influence on the shape of the world's oceans than the Sun. More precisely, tidal influence is determined by the ratio of the mass of a body to the cube of its distance from the Earth; this ratio for the Moon is approximately twice that for the Sun.

If there were no cohesion between the parts of the globe, then tidal forces would tear it apart.

Perhaps this happened to one of Saturn's satellites when it came close to this large planet. That fragmented ring that makes Saturn such a remarkable planet may be debris from the satellite.

So, the surface of the world's oceans is like an ellipsoid, the major axis of which faces the Moon. The earth rotates around its axis. Therefore, a tidal wave moves along the surface of the ocean towards the direction of rotation of the Earth. When it approaches the shore, the tide begins. In some places the water level rises to 18 meters. Then the tidal wave goes away and the tide begins to ebb. The water level in the ocean fluctuates, on average, with a period of 12 hours. 25min. (half a lunar day).

This simple picture is greatly distorted by the simultaneous tidal action of the Sun, water friction, continental resistance, the complexity of the configuration of ocean shores and bottom in coastal zones, and some other particular effects.

It is important that the tidal wave slows down the Earth's rotation.

True, the effect is very small. Over 100 years, the day increases by a thousandth of a second. But, acting for billions of years, the braking forces will lead to the fact that the Earth will always be turned to the Moon with one side, and the Earth’s day will become equal to the lunar month. This has already happened to Luna. The Moon is slowed down so much that it always faces the Earth with one side. To “look” at the far side of the Moon, it was necessary to send a spacecraft around it.

Law of Gravity

Gravity (universal gravitation, gravitation)(from Latin 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 imparts the same acceleration to all bodies without exception, regardless of their mass. Mainly gravity plays a decisive role on a cosmic scale. Term gravity also used as the name of the branch of physics that studies gravitational interaction. The most successful modern physical theory in classical physics that describes gravity is the general theory of relativity; the quantum theory of gravitational interaction has not yet been constructed.

Gravitational interaction

Gravitational interaction is one of the four fundamental interactions in our world. Within the framework of classical mechanics, gravitational interaction is described law of universal gravitation 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 - that is

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, 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 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 area of ​​the entire sphere.

The simplest problem 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 the form of Kepler's three laws.

As the number of interacting bodies increases, the task becomes dramatically more complicated. Thus, 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, instability of the solutions relative to the initial conditions occurs quite quickly. When applied to the Solar System, this instability makes it impossible to predict the motion of planets on scales larger than a hundred million years.

In some special cases, it is possible to find an approximate solution. The most important case is when the mass of one body is significantly greater than the mass of other bodies (examples: the solar system and the dynamics of the rings of Saturn). In this case, as a first approximation, we can assume that light bodies do not interact with each other and move along Keplerian trajectories around the massive body. The interactions between them can be taken into account within the framework of perturbation theory, and averaged over time. In this case, non-trivial phenomena may arise, such as resonances, attractors, chaos, etc. A clear example of such phenomena is the 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 Newton's;
• delay of potentials associated with the finite speed of propagation of gravitational disturbances; the appearance of gravitational waves;
• nonlinearity effects: gravitational waves tend to interact with each other, so the principle of superposition of waves in strong fields no longer holds true;
• changing 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: energy losses in the binary system with the pulsar PSR B1913+16 - the Hulse-Taylor pulsar - are in good agreement with a 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 significantly complicates its detection. Gravity power l-field source is proportional (v / c) 2l + 2 , if the multipole is of electric type, and (v / c) 2l + 4 - if the multipole is of magnetic type, where v is the characteristic speed of movement of sources in the radiating system, and c- 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 Q ij- quadrupole moment tensor of the mass distribution of the radiating system. Constant (1/W) allows us to estimate the order of magnitude of the radiation power.

From 1969 (Weber's experiments) 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 under terrestrial conditions are very weak and their detection and experimental verification are therefore very difficult. Until recently, overcoming these difficulties seemed beyond the capabilities of experimenters.

Among them, in particular, we can name the entrainment of inertial frames of reference (or the Lense-Thirring effect) and the gravitomagnetic field. In 2005, NASA's unmanned Gravity Probe B conducted an unprecedented precision experiment to measure these effects near Earth, but its 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 constructed. However, at low energies, in the spirit of quantum field theory, gravitational interaction can be represented as an exchange of gravitons - gauge bosons with spin 2.

Standard theories of gravity

Due to the fact that 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 one can limit oneself to the classical description of gravitational interaction.

There is a modern canonical classical theory of gravity - general theory of relativity, and many hypotheses and theories of varying degrees of development that clarify it, competing with each other (see the article Alternative theories of gravity). All of these theories make very similar predictions within the approximation in which experimental tests are currently carried out. The following are several basic, 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 flat Minkowski space, in which the laws of conservation of energy-momentum and angular momentum are unambiguously satisfied. Then the motion of bodies in Minkowski space is equivalent to the motion of these bodies in effective Riemannian space.

• In tensor equations to determine the metric, the graviton mass should be taken into account, and gauge conditions associated with the Minkowski space metric should be used. This does not allow the gravitational field to be destroyed even locally by choosing some suitable reference frame.

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, stationary and Euclidean.

On the other hand, there are no less convincing arguments by opponents of RTG, which boil down to the following points:

A similar thing occurs in RTG, where the second tensor equation is introduced to take into account the connection between non-Euclidean space and 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.

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. - 200 p.

see also

• Gravimeter

Links

• The law of universal gravitation or “Why doesn’t the Moon fall to Earth?” - Just about the complex

The 16th - 17th centuries are rightfully called by many one of the most glorious periods in the world. It was at this time that the foundations were largely laid, without which the further development of this science would have been simply unthinkable. Copernicus, Galileo, Kepler did a great job to establish physics as a science that can answer almost any question. Standing apart in a whole series of discoveries is the law of universal gravitation, the final formulation of which belongs to the outstanding English scientist Isaac Newton.

The main significance of this scientist’s work lay not in his discovery of the force of universal gravitation - both Galileo and Kepler spoke about the presence of this quantity even before Newton, but in the fact that he was the first to prove that the same forces act both on Earth and in outer space. the same forces of interaction between bodies.

Newton confirmed in practice and theoretically substantiated the fact that absolutely all bodies in the Universe, including those located on Earth, interact with each other. This interaction is called gravitational, while the process of universal gravitation itself is called gravitation.
This interaction occurs between bodies because there is a special, different type of matter, which in science is called a gravitational field. This field exists and operates around absolutely any object, and there is no protection from it, since it has the unique ability to penetrate any materials.

The force of universal gravitation, the definition and formulation of which was given, is directly dependent on the product of the masses of interacting bodies, and inversely dependent on the square of the distance between these objects. According to Newton’s opinion, irrefutably confirmed by practical research, the force of universal gravity is found according to the following formula:

In it, of particular importance is the gravitational constant G, which is approximately equal to 6.67*10-11(N*m2)/kg2.

The force of universal gravity with which bodies are attracted to the Earth is a special case of Newton's law and is called gravity. In this case, the gravitational constant and the mass of the Earth itself can be neglected, so the formula for finding the force of gravity will look like this:

Here g is nothing more than an acceleration whose numerical value is approximately equal to 9.8 m/s2.

Newton's law explains not only the processes occurring directly on Earth, it answers many questions related to the structure of the entire solar system. In particular, the force of universal gravitation has a decisive influence on the movement of planets in their orbits. A theoretical description of this movement was given by Kepler, but its justification became possible only after Newton formulated his famous law.

Newton himself connected the phenomena of terrestrial and extraterrestrial gravity using a simple example: when fired, it does not fly straight, but along an arcuate trajectory. Moreover, with an increase in the charge of gunpowder and the mass of the core, the latter will fly further and further. Finally, if we assume that it is possible to get so much gunpowder and construct such a cannon so that the cannonball flies around the globe, then, having made this movement, it will not stop, but will continue its circular (ellipsoidal) movement, turning into an artificial one. As a consequence, the force of the universal gravity is the same in nature both on Earth and in outer space.

Essay

Topic: Law of universal gravitation

Introduction

2 Law of Gravity

2.1 Discovery of Isaac Newton

2.2 Movement of bodies under the influence of gravity

3 AES - Artificial Earth satellites

Conclusion

Bibliography

Introduction

A person, studying phenomena, comprehends their essence and discovers the laws of nature. Thus, a body raised above the Earth and left to its own devices will begin to fall. It changes its speed, therefore, the force of gravity acts on it. This phenomenon is observed everywhere on our planet: the Earth attracts all bodies, including you and me. Is it only the Earth that has the property of acting on all bodies with a force of gravity?

Almost everything in the solar system revolves around the sun. Some planets have satellites, but while they make their way around the planet, they also move around the Sun with it. The Sun has a mass that exceeds the mass of the entire other population of the Solar System by 750 times. Thanks to this, the Sun causes the planets and everything else to move in orbits around it. On a cosmic scale, mass is the main characteristic of bodies, because all celestial bodies obey the law of universal gravitation.

Based on the laws of planetary motion established by I. Kepler, the great English scientist Isaac Newton (1643-1727), who was still recognized by no one at that time, discovered the law of universal gravitation, with the help of which it was possible to calculate with great accuracy for that time the movement of the Moon, planets and comets, explain the ebb and flow of the ocean.

Man uses these laws not only for a deeper knowledge of nature (for example, to determine the masses of celestial bodies), but also for solving practical problems (cosmonautics, astrodynamics).

Purpose of the work: to study the law of universal gravitation, show its practical significance, and reveal the concept of interaction of bodies using the example of this law.

The work consists of an introduction, main part, conclusion and list of references.

1 Laws of planetary motion - Kepler's laws

To fully appreciate the brilliance of the discovery of the Law of Universal Gravitation, let us return to its background. There is a legend that while walking through the apple orchard on his parents' estate, Newton saw the moon in the daytime sky, and right before his eyes an apple came off a branch and fell to the ground. Since Newton was working on the laws of motion at that very time, he already knew that the apple fell under the influence of the Earth's gravitational field. He also knew that the Moon does not just hang in the sky, but rotates in orbit around the Earth, and, therefore, it is affected by some kind of force that keeps it from breaking out of orbit and flying in a straight line away, into open space. Then it occurred to him that perhaps it was the same force that made both the apple fall to the ground and the Moon remain in Earth orbit - the gravitational force that exists between all bodies.

So, when Newton's great predecessors studied the uniformly accelerated motion of bodies falling on the surface of the Earth, they were sure that they were observing a phenomenon of a purely terrestrial nature - existing only close to the surface of our planet. When other scientists, studying the movement of celestial bodies, believed that in the celestial spheres there were completely different laws of movement than the laws governing movement here on Earth.

The very idea of ​​the universal force of gravity was repeatedly expressed earlier: Epicurus, Gassendi, Kepler, Borelli, Descartes, Roberval, Huygens and others thought about it. Descartes considered it the result of vortices in the ether. The history of science shows that almost all arguments concerning the movement of celestial bodies, before Newton, boiled down mainly to the fact that celestial bodies, being perfect, move in circular orbits due to their perfection, since a circle is an ideal geometric figure.

Thus, in modern terms, it was believed that there are two types of gravity, and this idea was firmly entrenched in the minds of people of that time. Everyone believed that there is earthly gravity, acting on the imperfect Earth, and there is celestial gravity, acting on the perfect heavens. The study of the movement of planets and the structure of the solar system ultimately led to the creation of the theory of gravity - the discovery of the law of universal gravitation.

The first attempt to create a model of the Universe was made by Ptolemy (~140). At the center of the universe, Ptolemy placed the Earth, around which planets and stars moved in large and small circles, like in a round dance. The geocentric system of Ptolemy lasted for more than 14 centuries and was only replaced by the heliocentric system of Copernicus in the middle of the 16th century.

At the beginning of the 17th century, based on the Copernican system, the German astronomer I. Kepler formulated three empirical laws of motion of the planets of the Solar system, using the results of observations of the motion of the planets of the Danish astronomer T. Brahe.

Kepler's First Law (1609): “All planets move in elliptical orbits, at one of the foci of which is the Sun.”

The elongation of the ellipse depends on the speed of the planet; on the distance at which the planet is located from the center of the ellipse. A change in the speed of a celestial body leads to the transformation of an elliptical orbit into a hyperbolic one, moving along which one can leave the solar system.

In Fig. Figure 1 shows the elliptical orbit of a planet whose mass is much less than the mass of the Sun. The sun is at one of the ellipse's foci. The point P of the trajectory closest to the Sun is called perihelion, point A, the farthest from the Sun, is called aphelion. The distance between aphelion and perihelion is the major axis of the ellipse.

Figure 1 - Elliptical orbit of a planet with mass

m <