Gravity: formula, definition. The law of universal gravitation. Gravity. Gravity acceleration Law of gravity drawing

Obi-Wan Kenobi said that strength holds the galaxy together. The same can be said about gravity. Fact: Gravity allows us to walk on the Earth, the Earth to revolve around the Sun, and the Sun to move around the supermassive black hole at the center of our galaxy. How to understand gravity? This is discussed in our article.

Let us say right away that you will not find here a uniquely correct answer to the question “What is gravity.” Because it simply doesn't exist! Gravity is one of the most mysterious phenomena, over which scientists are puzzling and still cannot fully explain its nature.

There are many hypotheses and opinions. There are more than a dozen theories of gravity, alternative and classical. We will look at the most interesting, relevant and modern ones.

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Gravity is a physical fundamental interaction

There are 4 fundamental interactions in physics. Thanks to them, the world is exactly what it is. Gravity is one of these interactions.

Fundamental interactions:

gravity;
electromagnetism;
strong interaction;
weak interaction.

Gravity is the weakest of the four fundamental forces.

Currently, the current theory describing gravity is GTR (general relativity). It was proposed by Albert Einstein in 1915-1916.

However, we know that it is too early to talk about the ultimate truth. After all, several centuries before the appearance of general relativity in physics, Newton’s theory dominated to describe gravity, which was significantly expanded.

Within the framework of general relativity, it is currently impossible to explain and describe all issues related to gravity.

Before Newton, it was widely believed that gravity on earth and gravity in heaven were different things. It was believed that the planets move according to their own ideal laws, different from those on Earth.

Newton discovered the law of universal gravitation in 1667. Of course, this law existed even during the time of dinosaurs and much earlier.

Ancient philosophers thought about the existence of gravity. Galileo experimentally calculated the acceleration of gravity on Earth, discovering that it is the same for bodies of any mass. Kepler studied the laws of motion of celestial bodies.

Newton managed to formulate and generalize the results of his observations. Here's what he got:

Two bodies attract each other with a force called gravitational force or gravity.

Formula for the force of attraction between bodies:

G is the gravitational constant, m is the mass of bodies, r is the distance between the centers of mass of bodies.

What is the physical meaning of the gravitational constant? It is equal to the force with which bodies with masses of 1 kilogram each act on each other, being at a distance of 1 meter from each other.

According to Newton's theory, every object creates a gravitational field. The accuracy of Newton's law has been tested at distances less than one centimeter. Of course, for small masses these forces are insignificant and can be neglected.

Newton's formula is applicable both for calculating the force of attraction of planets to the sun and for small objects. We simply do not notice the force with which, say, the balls on a billiard table are attracted. Nevertheless, this force exists and can be calculated.

The force of attraction acts between any bodies in the Universe. Its effect extends to any distance.

Newton's law of universal gravitation does not explain the nature of the force of gravity, but establishes quantitative laws. Newton's theory does not contradict GTR. It is quite sufficient for solving practical problems on an Earth scale and for calculating the motion of celestial bodies.

Gravity in general relativity

Despite the fact that Newton's theory is quite applicable in practice, it has a number of disadvantages. The law of universal gravitation is a mathematical description, but does not provide insight into the fundamental physical nature of things.

According to Newton, the force of gravity acts at any distance. And it works instantly. Considering that the fastest speed in the world is the speed of light, there is a discrepancy. How can gravity act instantly at any distance, when it takes light not an instant, but several seconds or even years to overcome them?

Within the framework of general relativity, gravity is considered not as a force that acts on bodies, but as a curvature of space and time under the influence of mass. Thus, gravity is not a force interaction.

What is the effect of gravity? Let's try to describe it using an analogy.

Let's imagine space in the form of an elastic sheet. If you place a light tennis ball on it, the surface will remain level. But if you place a heavy weight next to the ball, it will press a hole on the surface, and the ball will begin to roll towards the large, heavy weight. This is “gravity”.

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Discovery of gravitational waves

Gravitational waves were predicted by Albert Einstein back in 1916, but they were discovered only a hundred years later, in 2015.

What are gravitational waves? Let's draw an analogy again. If you throw a stone into calm water, circles will appear on the surface of the water from where it falls. Gravitational waves are the same ripples, disturbances. Just not on the water, but in world space-time.

Instead of water there is space-time, and instead of a stone, say, a black hole. Any accelerated movement of mass generates a gravitational wave. If the bodies are in a state of free fall, when a gravitational wave passes, the distance between them will change.

Since gravity is a very weak force, detecting gravitational waves has been associated with great technical difficulties. Modern technologies have made it possible to detect a burst of gravitational waves only from supermassive sources.

A suitable event for detecting a gravitational wave is the merger of black holes. Unfortunately or fortunately, this happens quite rarely. Nevertheless, scientists managed to register a wave that literally rolled across the space of the Universe.

To record gravitational waves, a detector with a diameter of 4 kilometers was built. During the passage of the wave, vibrations of mirrors on suspensions in a vacuum and the interference of light reflected from them were recorded.

Gravitational waves confirmed the validity of general relativity.

Gravity and elementary particles

In the standard model, certain elementary particles are responsible for each interaction. We can say that particles are carriers of interactions.

The graviton, a hypothetical massless particle with energy, is responsible for gravity. By the way, in our separate material, read more about the Higgs boson, which has caused a lot of noise, and other elementary particles.

Finally, here are some interesting facts about gravity.

10 facts about gravity

To overcome the force of Earth's gravity, a body must have a speed of 7.91 km/s. This is the first escape velocity. It is enough for a body (for example, a space probe) to move in orbit around the planet.
To escape the Earth's gravitational field, the spacecraft must have a speed of at least 11.2 km/s. This is the second escape velocity.
The objects with the strongest gravity are black holes. Their gravity is so strong that they even attract light (photons).
You will not find the force of gravity in any equation of quantum mechanics. The fact is that when you try to include gravity in the equations, they lose their relevance. This is one of the most important problems of modern physics.
The word gravity comes from the Latin “gravis”, which means “heavy”.
The more massive the object, the stronger the gravity. If a person who weighs 60 kilograms on Earth weighs himself on Jupiter, the scales will show 142 kilograms.
NASA scientists are trying to develop a gravity beam that will allow objects to be moved without contact, overcoming the force of gravity.
Astronauts in orbit also experience gravity. More precisely, microgravity. They seem to fall endlessly along with the ship they are in.
Gravity always attracts and never repels.
The black hole, the size of a tennis ball, attracts objects with the same force as our planet.

Now you know the definition of gravity and can tell what formula is used to calculate the force of attraction. If the granite of science is pressing you to the ground stronger than gravity, contact our student service. We will help you study easily under the heaviest loads!

Between any bodies in nature there is a force of mutual attraction called force of universal gravity(or gravitational forces). was discovered by Isaac Newton in 1682. When he was still 23 years old, he suggested that the forces that keep the Moon in its orbit are of the same nature as the forces that make an apple fall to Earth.

Gravity (mg) is directed vertically strictly to the center of the earth; Depending on the distance to the surface of the globe, the acceleration of gravity is different. At the Earth's surface in mid-latitudes its value is about 9.8 m/s 2 . as you move away from the Earth's surface g decreases.

Body weight (weight strength) – is the force with which a body acts onhorizontal support or stretches the suspension. It is assumed that the body motionless relative to the support or suspension. Let the body lie on a horizontal table motionless relative to the Earth. Denoted by the letter R.

Body weight and gravity differ in nature: The weight of a body is a manifestation of the action of intermolecular forces, and the force of gravity is of gravitational nature.

If acceleration a = 0 , then the weight is equal to the force with which the body is attracted to the Earth, namely . [P] = N.

If the condition is different, then the weight changes:

if acceleration A not equal 0 , then the weight P = mg - ma (down) or P = mg + ma (up);
if the body falls freely or moves with free fall acceleration, i.e. a =g(Fig. 2), then the body weight is equal to 0 (P=0 ). The state of a body in which its weight is zero is called weightlessness.

IN weightlessness There are also astronauts. IN weightlessness For a moment, you too find yourself when you jump while playing basketball or dancing.

Home experiment: A plastic bottle with a hole at the bottom is filled with water. We release it from our hands from a certain height. While the bottle falls, water does not flow out of the hole.

Weight of a body moving with acceleration (in an elevator) A body in an elevator experiences overloads

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.

Not only the most mysterious of forces of nature, but also the most powerful.

Man on the path of progress

Historically it turned out that Human as it moves forward ways of progress mastered the increasingly powerful forces of nature. He started when he had nothing but a stick clutched in his fist and his own physical strength. But he was wise, and he brought the physical strength of animals into his service, making them domesticated. The horse sped up his run, the camel made the desert passable, the elephant made the swampy jungle. But the physical strength of even the strongest animals is immeasurably small compared to the forces of nature. Man was the first to subjugate the element of fire, but only in its most weakened versions. At first - for many centuries - he used only wood as fuel - a very low-energy type of fuel. Somewhat later, he learned to use this source of energy to use the energy of the wind, the man raised the white wing of the sail into the air - and the light ship flew like a bird across the waves. Sailboat on the waves. He exposed the windmill blades to the gusts of wind - and the heavy stones of the millstones began to spin, and the pestles of the grinders began to rattle. But it is clear to everyone that the energy of air jets is far from being concentrated. In addition, both the sail and the windmill were afraid of the blows of the wind: the storm tore the sails and sank the ships, the storm broke the wings and overturned the mills. Even later, man began to conquer flowing water. The wheel is not only the most primitive of devices capable of converting the energy of water into rotational motion, but also the least powerful in comparison with various types. Man walked ever forward along the ladder of progress and needed more and more energy. He began to use new types of fuel - already the transition to burning coal increased the energy intensity of a kilogram of fuel from 2500 kcal to 7000 kcal - almost three times. Then the time came for oil and gas. The energy content of each kilogram of fossil fuel has again increased by one and a half to two times. Steam engines replaced steam turbines; mill wheels were replaced by hydraulic turbines. Next, the man extended his hand to the fissioning uranium atom. However, the first use of a new type of energy had tragic consequences - the nuclear fire of Hiroshima in 1945 incinerated 70 thousand human hearts within a matter of minutes. In 1954, the world's first Soviet nuclear power plant came online, turning the power of uranium into the radiant force of electric current. And it should be noted that a kilogram of uranium contains two million times more energy than a kilogram of the best oil. This was a fundamentally new fire, which could be called physical, because it was physicists who studied the processes leading to the birth of such fabulous amounts of energy. Uranium is not the only nuclear fuel. A more powerful type of fuel is already being used - hydrogen isotopes. Unfortunately, man has not yet been able to subjugate the hydrogen-helium nuclear flame. He knows how to momentarily light his all-burning fire, igniting the reaction in the hydrogen bomb with a flash of uranium explosion. But scientists are also seeing a hydrogen reactor getting closer and closer, which will generate an electric current as a result of the fusion of nuclei of hydrogen isotopes into helium nuclei. Again, the amount of energy that a person can take from each kilogram of fuel will increase almost tenfold. But will this step be the last in the coming history of mankind’s power over the forces of nature? No! Ahead is mastering the gravitational form of energy. It is even more prudently packaged by nature than even the energy of hydrogen-helium fusion. Today this is the most concentrated form of energy that a person can even imagine. Nothing further is yet visible there, beyond the cutting edge of science. And although we can confidently say that power plants will work for humans, converting gravitational energy into electric current (and perhaps into a stream of gas escaping from the nozzle of a jet engine, or into the planned transformation of the ubiquitous atoms of silicon and oxygen into atoms of ultra-rare metals), We cannot yet say anything about the details of such a power plant (rocket engine, physical reactor).

The force of universal gravitation at the origins of the birth of Galaxies

The force of universal gravitation is at the origins of the birth of galaxies from prestellar matter, as Academician V.A. Ambartsumyan is convinced of. It extinguishes stars that have burned out their time, having used up the stellar fuel they were given at birth. Many physicists explain the existence of quasars by the intervention of universal gravity (more details:) Look around: here on Earth everything is largely controlled by this force. It is this that determines the layered structure of our planet - the alternation of lithosphere, hydrosphere and atmosphere. It is she who holds a thick layer of air gases, at the bottom of which and thanks to which we all exist. Without gravity, the Earth would immediately fall out of its orbit around the Sun, and the globe itself would fall apart, torn apart by centrifugal forces. It is difficult to find anything that would not be, to one degree or another, dependent on the force of universal gravity. Of course, the ancient philosophers, very observant people, could not help but notice that a stone thrown upward always comes back. Plato in the 4th century BC explained this by saying that all the substances of the Universe tend to where most of the similar substances are concentrated: a thrown stone falls to the ground or goes to the bottom, spilled water seeps into the nearest pond or into a river making its way to the sea , the smoke of the fire rushes towards its kindred clouds. Plato's student, Aristotle, clarified that all bodies have special properties of heaviness and lightness. Heavy bodies - stones, metals - rush to the center of the Universe, light bodies - fire, smoke, vapors - to the periphery. This hypothesis, which explains some phenomena associated with the force of universal gravity, has existed for more than 2 thousand years.

Scientists about the force of universal gravity

Probably the first to raise the question about force of universal gravity truly scientifically, there was a genius of the Renaissance - Leonardo da Vinci. Leonardo proclaimed that gravity is not unique to the Earth, that there are many centers of gravity. And he also expressed the idea that the force of gravity depends on the distance to the center of gravity. The works of Copernicus, Galileo, Kepler, Robert Hooke brought closer and closer to the idea of the law of universal gravitation, but in its final formulation this law is forever associated with the name of Isaac Newton.

Isaac Newton on the force of universal gravitation

born January 4, 1643. He graduated from Cambridge University, became a bachelor, then a master of science.

Isaac Newton. Everything that follows is an endless wealth of scientific work. But his main work is “Mathematical Principles of Natural Philosophy,” published in 1687 and usually called simply “Principles.” It is in them that the great is formulated. Probably everyone remembers him from high school.

All bodies attract each other with a force directly proportional to the product of the masses of these bodies and inversely proportional to the square of the distance between them...

Some of the provisions of this formulation were able to anticipate Newton's predecessors, but no one had ever succeeded in achieving it in its entirety. It took the genius of Newton to assemble these fragments into a single whole in order to extend the gravity of the Earth to the Moon, and the Sun to the entire planetary system. From the law of universal gravitation, Newton deduced all the laws of planetary motion previously discovered by Kepler. They turned out to be simply its consequences. Moreover, Newton showed that not only Kepler's laws, but also deviations from these laws (in the world of three or more bodies) are a consequence of universal gravity... This was a great triumph of science. It seemed that the main force of nature that moves the worlds had finally been discovered and mathematically described, a force that controls air molecules, apples, and the Sun. The step taken by Newton was gigantic, immeasurably huge. The first popularizer of the works of the brilliant scientist, the French writer François Marie Arouet, world-famous under the pseudonym Voltaire, said that Newton suddenly realized the existence of the law named after him when he looked at a falling apple. Newton himself never mentioned this apple. And it’s hardly worth wasting time today to refute this beautiful legend. And, apparently, Newton came to comprehend the great power of nature through logical reasoning. Probably, it was this that was included in the corresponding chapter of “Beginnings”.

The force of universal gravity affects the flight of the nucleus

Suppose that on a very high mountain, so high that its top is no longer in the atmosphere, we have installed a gigantic artillery piece. Its barrel was placed strictly parallel to the surface of the globe and fired. Having described the arc, the core falls to Earth . We increase the charge, improve the quality of the gunpowder, and in one way or another force the cannonball to move at a higher speed after the next shot. The arc described by the core becomes flatter. The core falls much further from the foot of our mountain. We also increase the charge and shoot. The core flies along such a flat trajectory that it descends parallel to the surface of the globe. The core can no longer fall to the Earth: at the same speed with which it decreases, the Earth escapes from under it. And, having described a ring around our planet, the core returns to the point of departure. The gun can be removed in the meantime. After all, the flight of the core around the globe will take over an hour. And then the core will quickly fly over the top of the mountain and set off on a new flight around the Earth. If, as we agreed, the core does not experience any air resistance, it will never be able to fall. For this, the core speed should be close to 8 km/sec. What if we increase the speed of the core's flight? It will first fly in an arc, flatter than the curvature of the earth's surface, and begin to move away from the Earth. At the same time, its speed will decrease under the influence of the Earth's gravity. And finally, turning around, it will begin to fall back to Earth, but will fly past it and close not a circle, but an ellipse. The core will move around the Earth in exactly the same way as the Earth moves around the Sun, namely along an ellipse, at one of the foci of which the center of our planet will be located. If you further increase the initial speed of the core, the ellipse will become more stretched. It is possible to stretch this ellipse so that the core will reach the lunar orbit or even much further. But until the initial speed of this core exceeds 11.2 km/sec, it will remain a satellite of the Earth. The core, which received a speed of over 11.2 km/sec when fired, will forever fly away from the Earth along a parabolic trajectory. If an ellipse is a closed curve, then a parabola is a curve that has two branches going to infinity. Moving along an ellipse, no matter how elongated it may be, we will inevitably systematically return to the starting point. Moving along a parabola, we will never return to the starting point. But, having left the Earth at this speed, the core will not yet be able to fly to infinity. The powerful gravity of the Sun will bend the trajectory of its flight, closing it around itself like the trajectory of a planet. The core will become the sister of the Earth, an independent tiny planet in our family of planets. In order to direct the core beyond the planetary system, to overcome solar gravity, it is necessary to give it a speed of over 16.7 km/sec, and direct it so that the speed of the Earth’s own motion is added to this speed. A speed of about 8 km/sec (this speed depends on the height of the mountain from which our cannon fires) is called circular speed, speeds from 8 to 11.2 km/sec are elliptical, from 11.2 to 16.7 km/sec are parabolic , and above this number - at liberating speeds. It should be added here that the given values of these velocities are valid only for the Earth. If we lived on Mars, the circular speed would be much more easily achievable for us - it is only about 3.6 km/sec, and the parabolic speed is only slightly higher than 5 km/sec. But sending the core into space from Jupiter would be much more difficult than from Earth: the circular speed on this planet is 42.2 km/sec, and the parabolic speed is even 61.8 km/sec! It would be most difficult for the inhabitants of the Sun to leave their world (if, of course, such could exist). The circular speed of this giant should be 437.6, and the breakaway speed - 618.8 km/sec! Thus, Newton, at the end of the 17th century, a hundred years before the first flight of the Montgolfier brothers’ hot air balloon, two hundred years before the first flights of the Wright brothers’ airplane, and almost a quarter of a millennium before the takeoff of the first liquid-propellant rockets, showed the way to the sky for satellites and spaceships.

The force of universal gravity is inherent in every sphere

By using law of universal gravitation unknown planets were discovered, cosmogonic hypotheses of the origin of the solar system were created. The main force of nature, which controls the stars, the planets, apples in the garden, and gas molecules in the atmosphere, has been discovered and mathematically described. But we do not know the mechanism of universal gravitation. Newtonian gravity does not explain, but clearly represents the modern state of planetary motion. We do not know what causes the interaction of all bodies in the Universe. And it cannot be said that Newton was not interested in this reason. For many years he pondered its possible mechanism. By the way, this is indeed an extremely mysterious power. A force that manifests itself through hundreds of millions of kilometers of space, devoid at first glance of any material formations with the help of which the transfer of interaction could be explained.

Newton's hypotheses

AND Newton resorted to hypothesis about the existence of a certain ether that supposedly fills the entire Universe. In 1675, he explained the attraction to the Earth by the fact that the ether, which fills the entire Universe, rushes in continuous streams to the center of the Earth, capturing all objects in this movement and creating the force of gravity. The same flow of ether rushes towards the Sun and, carrying planets and comets with it, ensures their elliptical trajectories... This was not a very convincing, although absolutely mathematically logical, hypothesis. But then, in 1679, Newton created a new hypothesis explaining the mechanism of gravity. This time he gives the ether the property of having different concentrations near the planets and far from them. The farther from the center of the planet, the supposedly denser the ether. And it has the property of squeezing out all material bodies from their denser layers into less dense ones. And all the bodies are squeezed out onto the surface of the Earth. In 1706, Newton sharply denied the very existence of the ether. In 1717, he again returned to the hypothesis of extruding ether. Newton's brilliant brain struggled to solve the great mystery and did not find it. This explains such sharp throwing from side to side. Newton liked to say:

I don't make hypotheses.

And although, as soon as we were able to verify, this is not entirely true, something else can be stated for sure: Newton knew how to clearly distinguish between indisputable things and unsteady and controversial hypotheses. And in “Principles” there is a formula for the great law, but there are no attempts to explain its mechanism. The great physicist bequeathed this riddle to the man of the future. He died in 1727. It has not been solved to this day. The discussion about the physical essence of Newton's law took two centuries. And perhaps this discussion would not concern the very essence of the law if it answered exactly all the questions asked of it. But the fact of the matter is that over time it turned out that this law is not universal. That there are cases when he cannot explain this or that phenomenon. Let's give examples.

The force of universal gravitation in Seeliger's calculations

The first of them is the Seeliger paradox. Considering the Universe to be infinite and uniformly filled with matter, Seeliger tried to calculate, according to Newton’s law, the force of universal gravitation created by the entire infinitely large mass of the infinite Universe at some point. This was not an easy task from the point of view of pure mathematics. Having overcome all the difficulties of the most complex transformations, Seeliger established that the desired force of universal gravitation is proportional to the radius of the Universe. And since this radius is equal to infinity, then the gravitational force must be infinitely large. However, in practice we do not observe this. This means that the law of universal gravitation does not apply to the entire Universe. However, other explanations for the paradox are possible. For example, we can assume that matter does not uniformly fill the entire Universe, but its density gradually decreases and, finally, somewhere very far away there is no matter at all. But to imagine such a picture means to admit the possibility of the existence of space without matter, which is generally absurd. We can assume that the force of universal gravity weakens faster than the square of the distance increases. But this calls into question the amazing harmony of Newton's law. No, and this explanation did not satisfy scientists. The paradox remained a paradox.

Observations of the movement of Mercury

Another fact, the actions of the force of universal gravitation, not explained by Newton's law, brought observations of the movement of Mercury- closest to the planet. Accurate calculations using Newton's law showed that perhelion - the point of the ellipse along which Mercury moves closest to the Sun - should shift by 531 arcseconds per 100 years. And astronomers have determined that this displacement is equal to 573 arcseconds. This excess - 42 arc seconds - also could not be explained by scientists, using only formulas arising from Newton's law. Explained the Seeliger paradox, the shift of the perihelion of Mercury, and many other paradoxical phenomena and inexplicable facts Albert Einstein, one of the greatest, if not the greatest physicist of all time. Among the annoying little things was the question of ethereal wind.

Albert Michelson's experiments

It seemed that this question did not directly concern the problem of gravitation. He related to optics, to light. More precisely, to determine its speed. The speed of light was first determined by a Danish astronomer Olaf Roemer, observing the eclipse of the satellites of Jupiter. This happened back in 1675. American physicist Albert Michelson at the end of the 18th century, he carried out a series of determinations of the speed of light under terrestrial conditions, using the apparatus he designed. In 1927, he gave the speed of light a value of 299796 + 4 km/sec - this was excellent accuracy for those times. But the point is different. In 1880, he decided to explore the ethereal wind. He wanted to finally establish the existence of that very ether, the presence of which they tried to explain both the transmission of gravitational interaction and the transmission of light waves. Michelson was probably the most remarkable experimentalist of his time. He had excellent equipment. And he was almost sure of success.

The essence of experience

Experience was intended this way. The Earth moves in its orbit at a speed of about 30 km/sec. Moves through the ether. This means that the speed of light from a source standing in front of the receiver relative to the movement of the Earth must be greater than from a source standing on the other side. In the first case, the speed of the etheric wind must be added to the speed of light; in the second case, the speed of light must decrease by this amount.

The movement of the Earth in its orbit around the Sun. Of course, the speed of the Earth's orbit around the Sun is only one ten-thousandth the speed of light. It is very difficult to detect such a small term, but it is not for nothing that Michelson was called the king of accuracy. He used a clever method to capture the “subtle” difference in the speed of light rays. He split the beam into two equal streams and directed them in mutually perpendicular directions: along the meridian and along the parallel. Having reflected from the mirrors, the rays returned. If a beam traveling along a parallel were influenced by the ethereal wind, when it was added to a meridional beam, interference fringes would appear, and the waves of the two beams would be out of phase. However, it was difficult for Michelson to measure the paths of both rays with such great accuracy so that they were absolutely identical. So he built the apparatus so that there were no interference fringes, and then rotated it 90 degrees. The meridional ray became latitudinal and vice versa. If there is an etheric wind, black and light stripes should appear under the eyepiece! But they were not there. Perhaps, when turning the apparatus, the scientist moved it. He set it up at noon and secured it. After all, in addition to the fact that it also rotates around an axis. And therefore, at different times of the day, the latitude beam occupies a different position relative to the oncoming ethereal wind. Now, when the device is strictly motionless, one can be convinced of the accuracy of the experiment. There were no interference fringes again. The experiment was carried out many times, and Michelson, and with him all the physicists of that time, were amazed. No ethereal wind was detected! The light moved in all directions at the same speed! No one has been able to explain this. Michelson repeated the experiment again and again, improved the equipment, and finally achieved almost incredible measurement accuracy, an order of magnitude greater than what was necessary for the success of the experiment. And again nothing!

Albert Einstein's experiments

The next big step in knowledge of the force of universal gravity did Albert Einstein. Albert Einstein was once asked:

- How did you come to your special theory of relativity? Under what circumstances did the brilliant idea strike you? The scientist replied: “I always imagined that this was the case.”

Maybe he didn’t want to be frank, maybe he wanted to get rid of his annoying interlocutor. But it is difficult to imagine that the concept of the connections between time, space and speed discovered by Einstein was innate. No, of course, first a guess flashed through, bright as lightning. Then its development began. No, there are no contradictions with known phenomena. And then those five pages, filled with formulas, appeared that were published in a physics journal. Pages that opened a new era in physics. Imagine a starship flying in space. Let us warn you right away: the starship is very unique, the kind you have never read about in science fiction stories. Its length is 300 thousand kilometers, and its speed is, let’s say, 240 thousand km/sec. And this spaceship flies past one of the intermediate platforms in space, without stopping at it. At full speed. One of its passengers is standing on the deck of the starship with a watch. And you and I, reader, are standing on a platform - its length must correspond to the size of the starship, i.e. 300 thousand kilometers, because otherwise it will not be able to land on it. And we also have a watch in our hands. We notice: at that moment, when the nose of the spaceship reached the rear edge of our platform, a lantern flashed on it, illuminating the space surrounding it. A second later, the beam of light reached the front edge of our platform. We have no doubt about this, because we know the speed of light, and we managed to accurately detect the corresponding moment on the clock. And on the spaceship... But the spaceship was also flying towards the beam of light. And we definitely saw that the light illuminated its stern at the moment when it was somewhere near the middle of the platform. We definitely saw that the beam of light did not travel 300 thousand kilometers from the bow to the stern of the ship. But the passengers on the deck of the starship are sure of something else. They are confident that their beam covered the entire distance from bow to stern of 300 thousand kilometers. After all, he spent a whole second on this. They also absolutely accurately detected this on their watch. And how could it be otherwise: after all, the speed of light does not depend on the speed of the source... How can this be? We see one thing from a stationary platform, and they see something else on the deck of a starship? What's the matter?

Einstein's theory of relativity

It should be noted right away: Einstein's theory of relativity at first glance, it absolutely contradicts our established understanding of the structure of the world. We can say that it also contradicts common sense, as we are accustomed to represent it. This has happened more than once in the history of science. But the discovery of the spherical shape of the Earth also contradicted common sense. How can people live on the opposite side and not fall into the abyss? For us, the sphericity of the Earth is an undoubted fact, and from the point of view of common sense, any other assumption is meaningless and wild. But step back from your time, imagine the first appearance of this idea, and it becomes clear how difficult it would be to accept. Well, would it be easier to admit that the Earth is not motionless, but flies along its trajectory tens of times faster than a cannonball? These were all failures of common sense. That's why modern physicists never refer to it. Now let's return to the special theory of relativity. The world first learned about it in 1905 from an article signed by a little-known name - Albert Einstein. And he was only 26 years old at that time. Einstein made a very simple and logical assumption from this paradox: from the point of view of an observer on the platform, less time has passed in a moving carriage than was measured by your wristwatch. In the carriage, the passage of time slowed down compared to time on the stationary platform. Absolutely amazing things logically flowed from this assumption. It turned out that a person going to work on a tram, compared to a pedestrian walking the same way, not only saves time due to speed, but it also goes slower for him. However, do not try to preserve eternal youth in this way: even if you become a carriage driver and spend a third of your life on a tram, in 30 years you will gain hardly more than a millionth of a second. For the gain in time to become noticeable, you need to move at a speed close to the speed of light. It turns out that an increase in the speed of bodies is reflected in their mass. The closer the speed of a body is to the speed of light, the greater its mass. When the speed of a body is equal to the speed of light, its mass is equal to infinity, i.e. it is greater than the mass of the Earth, the Sun, the Galaxy, our entire Universe... This is how much mass can be concentrated in a simple cobblestone, accelerating it to the speed of light! This imposes a limitation that does not allow any material body to develop a speed equal to the speed of light. After all, as the mass grows, it becomes more and more difficult to accelerate it. And an infinite mass cannot be moved from its place by any force. However, nature has made a very important exception to this law for a whole class of particles. For example, for photons. They can move at the speed of light. More precisely, they cannot move at any other speed. It is unthinkable to imagine a motionless photon. When stationary, it has no mass. Neutrinos also do not have a rest mass, and they are also condemned to eternal uncontrolled flight through space at the maximum speed possible in our Universe, without overtaking light or falling behind it. Isn’t it true that each of the consequences of the special theory of relativity that we have listed is surprising and paradoxical! And each, of course, contradicts “common sense”! But here’s what’s interesting: not in their specific form, but as a broad philosophical position, all these amazing consequences were predicted by the founders of dialectical materialism. What do these results indicate? About the connections that interconnect energy and mass, mass and speed, speed and time, the speed and length of a moving object... Einstein's discovery of interdependence, like cement (more details:), connecting together reinforcement, or foundation stones, connected together the seemingly before that, things and phenomena were independent of each other and created the basis on which, for the first time in the history of science, it became possible to build a harmonious building. This building is an idea of how our Universe works. But first, at least a few words about the general theory of relativity, also created by Albert Einstein.

Albert Einstein. This name - general theory of relativity - does not quite correspond to the content of the theory that will be discussed. It establishes the interdependence between space and matter. Apparently it would be more correct to call it space-time theory, or theory of gravity. But this name has become so intertwined with Einstein’s theory that even raising the question of replacing it now seems indecent to many scientists. The general theory of relativity established the interdependence between matter and the time and space that contain it. It turned out that space and time not only cannot be imagined as existing separately from matter, but their properties also depend on the matter filling them. Einstein published the general theory of relativity in 1916 and had been working on it since 1907. It is not realistic to try to present it in several pages without using mathematical formulas.

Starting point for reasoning

Therefore, we can only indicate starting point and provide some important conclusions. At the beginning of space travel, an unexpected catastrophe destroyed the library, film collection and other repositories of the mind and memory of people flying through space. And the nature of the native planet was forgotten in the change of centuries. Even the law of universal gravitation is forgotten, because the rocket flies in intergalactic space, where it is almost not felt. However, the ship's engines work great, and the energy supply in the batteries is practically unlimited. Most of the time the ship moves by inertia, and its inhabitants are accustomed to weightlessness. But sometimes they turn on the engines and slow down or speed up the movement of the ship. When the jet nozzles blaze into the void with a colorless flame and the ship moves at an accelerated pace, the inhabitants feel that their bodies are becoming weighty, they are forced to walk around the ship, and not fly along the corridors. And now the flight is close to completion. The ship flies up to one of the stars and falls into the orbit of the most suitable planet. The spaceships go outside, walk on the soil covered with fresh greenery, continuously experiencing the same feeling of heaviness, familiar from the time when the ship was moving at an accelerated pace. But the planet moves evenly. It can’t fly towards them with a constant acceleration of 9.8 m/sec2! And they have the first assumption that the gravitational field (gravitational force) and acceleration give the same effect, and perhaps have a common nature. None of our earthling contemporaries were on such a long flight, but many felt the phenomenon of “heaviness” and “lightening” of their body. Even an ordinary elevator, when it moves at an accelerated pace, creates this feeling. When going down, you feel a sudden loss of weight; when going up, on the contrary, the floor presses on your legs with greater force than usual. But one feeling does not prove anything. After all, sensations are trying to convince us that the Sun moves across the sky around the motionless Earth, that all the stars and planets are at the same distance from us, in the firmament, etc. Scientists have subjected sensations to experimental testing. Newton also thought about the strange identity of the two phenomena. He tried to give them numerical characteristics. Having measured gravitational and , he was convinced that their values were always strictly equal to each other. He made the pendulums of the pilot plant from all kinds of materials: silver, lead, glass, salt, wood, water, gold, sand, wheat. The result was the same. Equivalence principle, which we are talking about, lies at the basis of the general theory of relativity, although the modern interpretation of the theory no longer needs this principle. Skipping the mathematical conclusions that follow from this principle, let us move directly to some consequences of the general theory of relativity. The presence of large masses of matter greatly affects the surrounding space. It leads to such changes in it that can be defined as heterogeneity of space. These inhomogeneities direct the movement of any masses that find themselves near the attracting body. Usually they resort to this analogy. Imagine a canvas stretched tightly onto a frame parallel to the earth's surface. Place a heavy weight on it. This will be our large attracting mass. It will, of course, bend the canvas and end up in some kind of depression. Now roll the ball along this canvas so that part of its path lies next to the attracting mass. Depending on how the ball is launched, there are three possible options.

The ball will fly far enough from the depression created by the deflection of the canvas and will not change its movement.
The ball will touch the depression, and the lines of its movement will bend towards the attracting mass.
The ball will fall into this hole, will not be able to get out of it, and will make one or two revolutions around the gravitating mass.

Isn’t it true that the third option very beautifully models the capture by a star or planet of a foreign body carelessly flying into their field of attraction? And the second case is the bending of the trajectory of a body flying at a speed greater than the possible capture speed! The first case is similar to flying beyond the practical reach of the gravitational field. Yes, precisely practical, because theoretically the gravitational field is limitless. Of course, this is a very distant analogy, primarily because no one can really imagine the deflection of our three-dimensional space. Nobody knows what the physical meaning of this deflection, or curvature, as they often say, is. From the general theory of relativity it follows that any material body can move in a gravitational field only along curved lines. Only in particular, special cases does the curve turn into a straight line. A ray of light also obeys this rule. After all, it consists of photons that have a certain mass in flight. And the gravitational field exerts its influence on it, just like on a molecule, an asteroid or a planet. Another important conclusion is that the gravitational field also changes the passage of time. Near a large attracting mass, in the strong gravitational field it creates, the passage of time should be slower than far from it. You see, the general theory of relativity is fraught with paradoxical conclusions that can once again overturn our ideas of “common sense”!

Gravitational collapse

Let's talk about an amazing phenomenon that has a cosmic character - gravitational collapse (catastrophic compression). This phenomenon occurs in gigantic accumulations of matter, where gravitational forces reach such enormous magnitudes that no other forces existing in nature can resist them. Remember Newton's famous formula: the smaller the square of the distance between gravitating bodies, the greater the gravitational force. Thus, the denser a material formation becomes, the smaller its size, the more rapidly the forces of gravity increase, the more inevitable their destructive embrace. There is a cunning technique with which nature fights the seemingly limitless compression of matter. To do this, it stops the very passage of time in the sphere of action of supergiant gravitational forces, and the bound masses of matter seem to be turned off from our Universe, frozen in a strange lethargic sleep. The first of these “black holes” in space has probably already been discovered. According to the assumption of Soviet scientists O. Kh. Guseinov and A. Sh. Novruzova, it is Delta Gemini - a double star with one invisible component. The visible component has a mass of 1.8 solar, and its invisible “companion” should be four times more massive than the visible one, according to calculations. But there are no traces of it: it is impossible to see the most amazing creation of nature, the “black hole”. The Soviet scientist Professor K.P. Stanyukovich, as they say, “at the tip of his pen,” through purely theoretical constructions, showed that particles of “frozen matter” can be very diverse in size.

Its giant formations are possible, similar to quasars, continuously emitting as much energy as all 100 billion stars of our Galaxy emit.
Much more modest clumps, equal to only a few solar masses, are possible. Both objects can arise themselves from ordinary, non-sleeping matter.
And formations of a completely different class are possible, comparable in mass to elementary particles.

In order for them to arise, the matter that composes them must first be subjected to gigantic pressure and driven into the limits of the Schwarzschild sphere - a sphere where time stops completely for an external observer. And even if after this the pressure is removed, the particles for which time has stopped will continue to exist independently of our Universe.

Plankeons

The author of the hypothesis named such particles in honor of the famous German physicist Max Planck - plankeons. Plankeons are a completely special class of particles. They have, according to K. P. Stanyukovich, an extremely interesting property: they carry matter in an unchanged form, the way it was millions and billions of years ago. Looking inside the plankeon, we would be able to see matter as it was at the moment of the birth of our Universe. According to theoretical calculations, there are about 10 80 plankeons in the Universe, approximately one plankeon in a cube of space with a side of 10 centimeters. By the way, simultaneously with Stanyukovich and (independently from him), the hypothesis about plankeons was put forward by Academician M.A. Markov. Only Markov gave them another name - maximons. The special properties of plankeons can also be used to explain the sometimes paradoxical transformations of elementary particles. It is known that in the collision of two particles never form fragments, but other elementary particles arise. This is truly amazing: in the ordinary world, breaking a vase, we will never get whole cups or even rosettes. But suppose that in the depths of each elementary particle there is hidden a plankeon, one or more, and sometimes many plankeons. At the moment of collision of particles, the tightly tied “bag” of the plankeon opens slightly, some particles will “fall” into it, and in return those that we consider to have arisen during the collision will “pop out.” At the same time, the plankeon, like a prudent accountant , will provide all the "conservation laws" accepted in the world of elementary particles. Well, what does the mechanism of universal gravitation have to do with it? "Responsible" for gravitation, according to the hypothesis of K. P. Stanyukovich, are tiny particles, the so-called gravitons, continuously emitted by elementary particles. Gravitons are as much smaller than the latter as a speck of dust dancing in a sunbeam is smaller than the globe. The emission of gravitons obeys a number of laws. In particular, they fly more easily into that area of space. Which contains fewer gravitons. This means that if there are two celestial bodies in space, both will emit gravitons predominantly “outward”, in directions opposite to each other. This creates an impulse that causes the bodies to come closer and attract each other. Leaving their elementary particles, gravitons take part of the mass with them. No matter how small they are, the loss of mass cannot but be noticeable over time. But this time is unimaginably huge. It will take about 100 billion years for all the matter in the Universe to turn into a gravitational field.

Gravitational field. But is that all? According to K.P. Stanyukovich, about 95 percent of the mass of matter is hidden in plankeons of various sizes and is in a state of lethargic sleep, but over time the plankeons open up, and the amount of “normal” matter increases.

Why does a stone released from your hands fall to Earth? Because he is attracted by the Earth, each of you will say. In fact, the stone falls to the Earth with the acceleration of gravity. Consequently, a force directed towards the Earth acts on the stone from the side of the Earth. According to Newton's third law, the stone acts on the Earth with the same magnitude force directed towards the stone. In other words, forces of mutual attraction act between the Earth and the stone.

Newton was the first to first guess and then strictly prove that the reason that causes a stone to fall to the Earth, the movement of the Moon around the Earth and the planets around the Sun is the same. This is the force of gravity acting between any bodies in the Universe. Here is the course of his reasoning, given in Newton’s main work, “The Mathematical Principles of Natural Philosophy”:

“A stone thrown horizontally will deviate under the influence of gravity from a straight path and, having described a curved trajectory, will finally fall to the Earth. If you throw it at a higher speed, it will fall further” (Fig. 1).

Continuing these arguments, Newton comes to the conclusion that if it were not for air resistance, then the trajectory of a stone thrown from a high mountain at a certain speed could become such that it would never reach the surface of the Earth at all, but would move around it “like “how the planets describe their orbits in celestial space.”

Now we have become so familiar with the movement of satellites around the Earth that there is no need to explain Newton’s thought in more detail.

So, according to Newton, the movement of the Moon around the Earth or the planets around the Sun is also a free fall, but only a fall that lasts, without stopping, for billions of years. The reason for such a “fall” (whether we are really talking about the fall of an ordinary stone to the Earth or the movement of planets in their orbits) is the force of universal gravity. What does this force depend on?

Dependence of gravitational force on the mass of bodies

Galileo proved that during free fall the Earth imparts the same acceleration to all bodies in a given place, regardless of their mass. But according to Newton's second law, acceleration is inversely proportional to mass. How can we explain that the acceleration imparted to a body by the force of gravity of the Earth is the same for all bodies? This is possible only if the force of gravity towards the Earth is directly proportional to the mass of the body. In this case, increasing the mass m, for example, by doubling will lead to an increase in the force modulus F also doubled, and the acceleration, which is equal to \(a = \frac (F)(m)\), will remain unchanged. Generalizing this conclusion for gravitational forces between any bodies, we conclude that the force of universal gravity is directly proportional to the mass of the body on which this force acts.

But at least two bodies are involved in mutual attraction. Each of them, according to Newton’s third law, is acted upon by gravitational forces of equal magnitude. Therefore, each of these forces must be proportional to both the mass of one body and the mass of the other body. Therefore, the force of universal gravity between two bodies is directly proportional to the product of their masses:

\(F \sim m_1 \cdot m_2\)

Dependence of gravitational force on the distance between bodies

It is well known from experience that the acceleration of gravity is 9.8 m/s 2 and it is the same for bodies falling from a height of 1, 10 and 100 m, i.e. it does not depend on the distance between the body and the Earth. This seems to mean that force does not depend on distance. But Newton believed that distances should be counted not from the surface, but from the center of the Earth. But the radius of the Earth is 6400 km. It is clear that several tens, hundreds or even thousands of meters above the Earth’s surface cannot noticeably change the value of the acceleration of gravity.

To find out how the distance between bodies affects the strength of their mutual attraction, it would be necessary to find out what the acceleration of bodies distant from the Earth at sufficiently large distances is. However, it is difficult to observe and study the free fall of a body from a height of thousands of kilometers above the Earth. But nature itself came to the rescue here and made it possible to determine the acceleration of a body moving in a circle around the Earth and therefore possessing centripetal acceleration, caused, of course, by the same force of attraction to the Earth. Such a body is the Earth’s natural satellite – the Moon. If the force of attraction between the Earth and the Moon did not depend on the distance between them, then the centripetal acceleration of the Moon would be the same as the acceleration of a body freely falling near the surface of the Earth. In reality, the centripetal acceleration of the Moon is 0.0027 m/s 2 .

Let's prove it. The rotation of the Moon around the Earth occurs under the influence of the gravitational force between them. Approximately, the orbit of the Moon can be considered a circle. Consequently, the Earth imparts centripetal acceleration to the Moon. It is calculated using the formula \(a = \frac (4 \pi^2 \cdot R)(T^2)\), where R– radius of the lunar orbit, equal to approximately 60 Earth radii, T≈ 27 days 7 hours 43 minutes ≈ 2.4∙10 6 s – the period of the Moon’s revolution around the Earth. Considering that the radius of the Earth R z ≈ 6.4∙10 6 m, we find that the centripetal acceleration of the Moon is equal to:

\(a = \frac (4 \pi^2 \cdot 60 \cdot 6.4 \cdot 10^6)((2.4 \cdot 10^6)^2) \approx 0.0027\) m/s 2.

The found acceleration value is less than the acceleration of free fall of bodies at the Earth's surface (9.8 m/s 2) by approximately 3600 = 60 2 times.

Thus, an increase in the distance between the body and the Earth by 60 times led to a decrease in the acceleration imparted by gravity, and, consequently, the force of gravity itself by 60 2 times.

This leads to an important conclusion: the acceleration imparted to bodies by the force of gravity towards the Earth decreases in inverse proportion to the square of the distance to the center of the Earth

\(F \sim \frac (1)(R^2)\).

Law of Gravity

In 1667, Newton finally formulated the law of universal gravitation:

\(F = G \cdot \frac (m_1 \cdot m_2)(R^2).\quad (1)\)

The force of mutual attraction between 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.

Proportionality factor G called gravitational constant.

Law of Gravity valid only for bodies whose dimensions are negligible compared to the distance between them. In other words, it is only fair for material points. In this case, the forces of gravitational interaction are directed along the line connecting these points (Fig. 2). This kind of force is called central.

To find the gravitational force acting on a given body from the side of another, in the case when the sizes of the bodies cannot be neglected, proceed as follows. Both bodies are mentally divided into such small elements that each of them can be considered a point. By adding up the gravitational forces acting on each element of a given body from all elements of another body, we obtain the force acting on this element (Fig. 3). Having performed such an operation for each element of a given body and adding up the resulting forces, the total gravitational force acting on this body is found. This task is difficult.

There is, however, one practically important case when formula (1) is applicable to extended bodies. It can be proven that spherical bodies, the density of which depends only on the distances to their centers, when the distances between them are greater than the sum of their radii, are attracted with forces whose moduli are determined by formula (1). In this case R is the distance between the centers of the balls.

And finally, since the sizes of bodies falling on the Earth are much smaller than the sizes of the Earth, these bodies can be considered as point bodies. Then under R in formula (1) one should understand the distance from a given body to the center of the Earth.

Between all bodies there are forces of mutual attraction, depending on the bodies themselves (their masses) and on the distance between them.

Physical meaning of the gravitational constant

From formula (1) we find

\(G = F \cdot \frac (R^2)(m_1 \cdot m_2)\).

It follows that if the distance between bodies is numerically equal to unity ( R= 1 m) and the masses of interacting bodies are also equal to unity ( m 1 = m 2 = 1 kg), then the gravitational constant is numerically equal to the force modulus F. Thus ( physical meaning ),

the gravitational constant is numerically equal to the modulus of the gravitational force acting on a body of mass 1 kg from another body of the same mass at a distance between the bodies of 1 m.

In SI, the gravitational constant is expressed as

Cavendish experience

The value of the gravitational constant G can only be found experimentally. To do this, you need to measure the gravitational force modulus F, acting on the body by mass m 1 from the side of a body of mass m 2 at a known distance R between bodies.

The first measurements of the gravitational constant were made in the middle of the 18th century. Estimate, albeit very roughly, the value G at that time it was possible as a result of considering the attraction of a pendulum to a mountain, the mass of which was determined by geological methods.

Accurate measurements of the gravitational constant were first carried out in 1798 by the English physicist G. Cavendish using an instrument called a torsion balance. A torsion balance is shown schematically in Figure 4.

Cavendish secured two small lead balls (5 cm in diameter and mass m 1 = 775 g each) at opposite ends of a two-meter rod. The rod was suspended on a thin wire. For this wire, the elastic forces that arise in it when twisted at various angles were previously determined. Two large lead balls (20 cm in diameter and weighing m 2 = 49.5 kg) could be brought close to the small balls. The attractive forces from the large balls caused the small balls to move towards them, while the stretched wire twisted a little. The degree of twist was a measure of the force acting between the balls. The angle of twist of the wire (or rotation of the rod with small balls) turned out to be so small that it had to be measured using an optical tube. The result obtained by Cavendish differs by only 1% from the value of the gravitational constant accepted today:

G ≈ 6.67∙10 -11 (N∙m 2)/kg 2

Thus, the attractive forces of two bodies weighing 1 kg each, located at a distance of 1 m from each other, are equal in modules to only 6.67∙10 -11 N. This is a very small force. Only in the case when bodies of enormous mass interact (or at least the mass of one of the bodies is large) does the gravitational force become large. For example, the Earth attracts the Moon with a force F≈ 2∙10 20 N.

Gravitational forces are the “weakest” of all natural forces. This is due to the fact that the gravitational constant is small. But with large masses of cosmic bodies, the forces of universal gravity become very large. These forces keep all the planets near the Sun.

The meaning of the law of universal gravitation

The law of universal gravitation underlies celestial mechanics - the science of planetary motion. With the help of this law, the positions of celestial bodies in the firmament for many decades in advance are determined with great accuracy and their trajectories are calculated. The law of universal gravitation is also used in calculating the motion of artificial Earth satellites and interplanetary automatic vehicles.

Disturbances in the motion of planets. Planets do not move strictly according to Kepler's laws. Kepler's laws would be strictly observed for the motion of a given planet only in the case when this one planet revolved around the Sun. But there are many planets in the Solar System, they are all attracted both by the Sun and by each other. Therefore, disturbances in the motion of the planets arise. In the Solar System, disturbances are small because the attraction of a planet by the Sun is much stronger than the attraction of other planets. When calculating the apparent positions of the planets, disturbances must be taken into account. When launching artificial celestial bodies and when calculating their trajectories, an approximate theory of the motion of celestial bodies is used - perturbation theory.

Discovery of Neptune. One of the striking examples of the triumph of the law of universal gravitation is the discovery of the planet Neptune. In 1781, the English astronomer William Herschel discovered the planet Uranus. Its orbit was calculated and a table of the positions of this planet was compiled for many years to come. However, a check of this table, carried out in 1840, showed that its data diverges from reality.

Scientists have suggested that the deviation in the movement of Uranus is caused by the attraction of an unknown planet located even further from the Sun than Uranus. Knowing the deviations from the calculated trajectory (disturbances in the movement of Uranus), the Englishman Adams and the Frenchman Leverrier, using the law of universal gravitation, calculated the position of this planet in the sky. Adams finished his calculations early, but the observers to whom he reported his results were in no hurry to check. Meanwhile, Leverrier, having completed his calculations, indicated to the German astronomer Halle the place where to look for the unknown planet. On the very first evening, September 28, 1846, Halle, pointing the telescope at the indicated location, discovered a new planet. She was named Neptune.

In the same way, the planet Pluto was discovered on March 14, 1930. Both discoveries are said to have been made "at the tip of a pen."

Using the law of universal gravitation, you can calculate the mass of planets and their satellites; explain phenomena such as the ebb and flow of water in the oceans, and much more.

The forces of universal gravity are the most universal of all the forces of nature. They act between any bodies that have mass, and all bodies have mass. There are no barriers to the forces of gravity. They act through any body.

Literature

Kikoin I.K., Kikoin A.K. Physics: Textbook. for 9th grade. avg. school – M.: Education, 1992. – 191 p.
Physics: Mechanics. 10th grade: Textbook. for in-depth study of physics / M.M. Balashov, A.I. Gomonova, A.B. Dolitsky and others; Ed. G.Ya. Myakisheva. – M.: Bustard, 2002. – 496 p.