Gravity is the most powerful force in the Universe, one of the four fundamental foundations of the universe, which determines its structure. Once, thanks to her, planets, stars and entire galaxies arose. Today, it keeps the Earth in orbit in its never-ending journey around the Sun.

Attraction is of great importance for everyday life of a person. Thanks to this invisible force, the oceans of our world pulsate, rivers flow, raindrops fall to the ground. Since childhood, we feel the weight of our body and surrounding objects. The influence of gravity on our economic activity is also enormous.

The first theory of gravity was created by Isaac Newton at the end of the 17th century. His law of universal gravitation describes this interaction within the framework of classical mechanics. This phenomenon was described more widely by Einstein in his general theory of relativity, which was published at the beginning of the last century. The processes occurring with the force of gravity at the level of elementary particles should be explained by the quantum theory of gravity, but it has yet to be created.

Today we know much more about the nature of gravity than in Newton's time, but despite centuries of study, it still remains a real stumbling block in modern physics. There are many white spots in the existing theory of gravity, and we still do not understand exactly what generates it, and how this interaction is transferred. And, of course, we are very far from being able to control the force of gravity, so that antigravity or levitation will exist only on the pages of science fiction novels for a long time to come.

What fell on Newton's head?

People have thought about the nature of the force that attracts objects to the earth at all times, but it was only in the 17th century that Isaac Newton managed to lift the veil of secrecy. The basis for his breakthrough was laid by the works of Kepler and Galileo, brilliant scientists who studied the movements of celestial bodies.

A century and a half before Newton's Law of Universal Gravitation, the Polish astronomer Copernicus believed that attraction is "... nothing more than a natural desire that the father of the Universe bestowed on all particles, namely, to unite into one common whole, forming spherical bodies." Descartes, on the other hand, considered attraction to be the result of perturbations in the world ether. The Greek philosopher and scientist Aristotle was sure that mass affects the speed of falling bodies. And only Galileo Galilei at the end of the 16th century proved that this is not true: if there is no air resistance, all objects accelerate equally.

Contrary to the popular legend about the head and the apple, Newton went to understand the nature of gravity for more than twenty years. His law of gravity is one of the most significant scientific discoveries of all time. It is universal and allows you to calculate the trajectories of celestial bodies and accurately describes the behavior of objects around us. The classical theory of gravitation laid the foundations of celestial mechanics. Newton's three laws gave scientists the opportunity to discover new planets literally "on the tip of a pen", in the end, thanks to them, a person was able to overcome the earth's gravity and fly into space. They summed up a strict scientific basis for the philosophical concept of the material unity of the universe, in which all natural phenomena are interconnected and controlled by common physical rules.

Newton not only published a formula that allows you to calculate what the force that attracts bodies to each other is, he created a holistic model, which also included mathematical analysis. These theoretical conclusions have been repeatedly confirmed in practice, including with the help of the most modern methods.

In Newtonian theory, any material object generates an attraction field, which is called gravitational. Moreover, the force is proportional to the mass of both bodies and inversely proportional to the distance between them:

F = (G m1 m2)/r2

G is the gravitational constant, which is equal to 6.67 × 10−11 m³ / (kg s²). Henry Cavendish was the first to calculate it in 1798.

In everyday life and applied disciplines, the force with which the earth pulls on a body is spoken of as its weight. The attraction between any two material objects in the universe is what gravity is in simple terms.

The force of attraction is the weakest of the four fundamental interactions of physics, but due to its features, it is able to regulate the movement of star systems and galaxies:

• Attraction works at any distance, this is the main difference between gravity and strong and weak nuclear interaction. With increasing distance, its effect decreases, but it never becomes equal to zero, so we can say that even two atoms located at different ends of the galaxy exert mutual influence. It's just very small;
• Gravity is universal. The field of attraction is inherent in any material body. Scientists have not yet discovered an object on our planet or in space that would not participate in this type of interaction, so the role of gravity in the life of the Universe is enormous. In this, gravitation differs from electromagnetic interaction, whose influence on cosmic processes is minimal, since in nature most bodies are electrically neutral. Gravitational forces cannot be limited or shielded;
• Gravity acts not only on matter, but also on energy. For him, the chemical composition of objects does not matter, only their mass plays a role.

Using the Newtonian formula, the force of attraction can be easily calculated. For example, gravity on the Moon is several times less than on Earth, because our satellite has a relatively small mass. But it is enough for the formation of regular tides in the World Ocean. On Earth, the free fall acceleration is about 9.81 m/s2. Moreover, at the poles it is somewhat larger than at the equator.

Despite the great importance for the further development of science, Newton's laws had a number of weak points that haunted researchers. It was not clear how gravity works through absolutely empty space over vast distances, and at an incomprehensible speed. In addition, data gradually began to accumulate that contradicted Newton's laws: for example, the gravitational paradox or the displacement of Mercury's perihelion. It became obvious that the theory of universal gravitation needs to be improved. This honor fell to the brilliant German physicist Albert Einstein.

Attraction and relativity

Newton's refusal to discuss the nature of gravity ("I make no hypotheses") was an obvious weakness in his concept. Not surprisingly, many theories of gravity emerged in the years that followed.

Most of them belonged to the so-called hydrodynamic models, which tried to substantiate the emergence of gravity by the mechanical interaction of material objects with some intermediate substance that has certain properties. Researchers called it differently: "vacuum", "ether", "flow of gravitons", etc. In this case, the force of attraction between bodies arose as a result of a change in this substance, when it was absorbed by objects or screened flows. In reality, all such theories had one serious drawback: quite accurately predicting the dependence of the gravitational force on distance, they should have led to the deceleration of bodies that were moving relative to the “ether” or “graviton flow”.

Einstein approached this issue from a different angle. In his general theory of relativity (GR), gravity is seen not as an interaction of forces, but as a property of space-time itself. Any object that has mass causes it to bend, which causes attraction. In this case, gravity is a geometric effect, which is considered within the framework of non-Euclidean geometry.

Simply put, the space-time continuum affects matter, causing its movement. And that, in turn, affects the space, “indicating” to it how to bend.

The forces of attraction also act in the microcosm, but at the level of elementary particles, their influence, in comparison with the electrostatic interaction, is negligible. Physicists believe that the gravitational interaction was not inferior to the rest in the first moments (10 -43 seconds) after the Big Bang.

At present, the concept of gravity, proposed in the general theory of relativity, is the main working hypothesis accepted by the majority of the scientific community and confirmed by the results of numerous experiments.

Einstein in his work foresaw the amazing effects of gravitational forces, most of which have already been confirmed. For example, the ability of massive bodies to bend light rays and even slow down the passage of time. The latter phenomenon is necessarily taken into account in the operation of global satellite navigation systems, such as GLONASS and GPS, otherwise, after a few days, their error would be tens of kilometers.

In addition, a consequence of Einstein's theory are the so-called subtle effects of gravity, such as the gravimagnetic field and drag of inertial frames of reference (aka the Lense-Thirring effect). These manifestations of gravity are so weak that for a long time they could not be detected. Only in 2005, thanks to NASA's unique Gravity Probe B mission, the Lense-Thirring effect was confirmed.

Gravitational radiation or the most fundamental discovery of recent years

Gravitational waves are fluctuations in the geometric space-time structure that propagate at the speed of light. The existence of this phenomenon was also predicted by Einstein in general relativity, but due to the weakness of the gravitational force, its magnitude is very small, so it could not be detected for a long time. Only indirect evidence spoke in favor of the existence of radiation.

Such waves generate any material objects moving with asymmetric acceleration. Scientists describe them as "ripples of space-time." The most powerful sources of such radiation are colliding galaxies and collapsing systems consisting of two objects. A typical example of the latter case is the merger of black holes or neutron stars. In such processes, gravitational radiation can pass more than 50% of the total mass of the system.

Gravitational waves were first detected in 2015 by two LIGO observatories. Almost immediately, this event received the status of the largest discovery in physics in recent decades. In 2017, he was awarded the Nobel Prize. After that, scientists managed to detect gravitational radiation several more times.

Back in the 70s of the last century - long before experimental confirmation - scientists proposed using gravitational radiation for long-distance communication. Its undoubted advantage is its high ability to pass through any substance without being absorbed. But at present this is hardly possible, because there are huge difficulties in generating and receiving these waves. Yes, and we still do not have enough real knowledge about the nature of gravity.

Today, several installations similar to LIGO are operating in different countries of the world, and new ones are being built. It is likely that we will learn more about gravitational radiation in the near future.

Alternative theories of universal gravitation and the reasons for their creation

Currently, the dominant concept of gravity is general relativity. The entire existing array of experimental data and observations is consistent with it. At the same time, it has a large number of frankly weak points and controversial points, so attempts to create new models that explain the nature of gravity do not stop.

All theories of universal gravitation developed so far can be divided into several main groups:

• standard;
• alternative;
• quantum;
• unified field theory.

Attempts to create a new concept of universal gravitation were made as early as the 19th century. Various authors included in it the ether or the corpuscular theory of light. But the emergence of general relativity put an end to these researches. After its publication, the goal of scientists changed - now their efforts were aimed at improving the Einstein model, including new natural phenomena in it: the spin of particles, the expansion of the Universe, etc.

By the early 1980s, physicists had experimentally rejected all concepts except those that included general relativity as an integral part. At this time, "string theories" came into fashion, looking very promising. But experimental confirmation of these hypotheses has not been found. Over the past decades, science has reached significant heights and has accumulated a huge array of empirical data. Today, attempts to create alternative theories of gravity are inspired mainly by cosmological studies related to such concepts as "dark matter", "inflation", "dark energy".

One of the main tasks of modern physics is the unification of two fundamental directions: quantum theory and general relativity. Scientists seek to connect attraction with other types of interactions, thus creating a "theory of everything." This is exactly what quantum gravity does, the branch of physics that attempts to give a quantum description of the gravitational interaction. An offshoot of this direction is the theory of loop gravity.

Despite active and long-term efforts, this goal has not yet been achieved. And it's not even the complexity of this problem: it's just that quantum theory and general relativity are based on completely different paradigms. Quantum mechanics deals with physical systems operating against the background of ordinary space-time. And in the theory of relativity, space-time itself is a dynamic component that depends on the parameters of the classical systems that are in it.

Along with the scientific hypotheses of universal gravitation, there are theories that are very far from modern physics. Unfortunately, in recent years, such "opuses" have simply flooded the Internet and the shelves of bookstores. Some authors of such works generally inform the reader that gravity does not exist, and the laws of Newton and Einstein are inventions and hoaxes.

An example is the work of the "scientist" Nikolai Levashov, who claims that Newton did not discover the law of universal gravitation, and only the planets and our satellite the Moon have gravitational force in the solar system. The evidence given by this "Russian scientist" is rather strange. One of them is the flight of the American probe NEAR Shoemaker to the asteroid Eros, which took place in 2000. Levashov considers the lack of attraction between the probe and the celestial body to be evidence of the falsity of Newton's works and the conspiracy of physicists who hide the truth about gravity from people.

In fact, the spacecraft successfully completed its mission: first, it entered the asteroid's orbit, and then made a soft landing on its surface.

Artificial gravity and what it is for

There are two concepts associated with gravity that, despite their current theoretical status, are well known to the general public. These are anti-gravity and artificial gravity.

Antigravity is the process of countering the force of attraction, which can significantly reduce it or even replace it with repulsion. The mastery of such technology would lead to a real revolution in transportation, aviation, space exploration and radically change our whole life. But at present, the possibility of antigravity does not even have theoretical confirmation. Moreover, proceeding from general relativity, such a phenomenon is not feasible at all, since there can be no negative mass in our Universe. It is possible that in the future we will learn more about gravity and learn how to build aircraft based on this principle.

Artificial gravity is a man-made change in the existing force of gravity. Today, we do not really need such technology, but the situation will definitely change after the start of long-term space travel. And it has to do with our physiology. The human body, “accustomed” by millions of years of evolution to the constant gravity of the Earth, perceives the impact of reduced gravity extremely negatively. A long stay even in the conditions of lunar gravity (six times weaker than the earth) can lead to sad consequences. The illusion of attraction can be created using other physical forces, such as inertia. However, these options are complex and expensive. At the moment, artificial gravity does not even have theoretical justifications, it is obvious that its possible practical implementation is a matter of a very distant future.

Gravity is a concept known to everyone since school. It would seem that scientists should have thoroughly investigated this phenomenon! But gravity remains the deepest mystery to modern science. And this can be called an excellent example of how limited human knowledge about our vast and wonderful world is.

If you have any questions - leave them in the comments below the article. We or our visitors will be happy to answer them.

1. Obi-Wan Kenobi from Star Wars said that the Force “is all around us and penetrates us; it holds the galaxy together." He could well have said that about gravity. Its gravitational properties literally hold the galaxy together, and it "penetrates" us, physically pulling us towards Earth.

2. However, unlike the Force with its dark and light sides, gravity is not dual; it only attracts and never repels.

3. NASA is trying to develop a tractor beam that will be able to move physical objects, creating an attractive force that exceeds the force of gravity.

4. Roller coaster riders and astronauts on the Space Station experience microgravity—incorrectly called zero gravity—because they fall at the same speed as the ship they are in.

5. Anyone who weighs 60 kilograms on Earth would weigh 142 kilograms on Jupiter (if it were possible to stand on a gas giant). The greater mass of the planet means a greater force of attraction.

6. To leave the Earth's gravity well, any object must reach a speed of 11.2 kilometers per second - this is the escape velocity of our planet.

7. Gravity, oddly enough, is the weakest of the four fundamental forces of the universe. The other three are electromagnetism, the weak nuclear force that governs the decay of atoms; and the strong nuclear force, which holds the nuclei of atoms together.

8. A coin-sized magnet has enough electromagnetic force to overcome all of Earth's gravity and stick to a refrigerator.

9. The apple did not fall on Isaac Newton's head, but it made him wonder if the force that makes the apple fall affects the movement of the moon around the earth.

10. This same apple led to the emergence of the first law of inverse quadratic proportionality F = G * (mM) / r2 in science. This means that an object twice as far away exerts only a quarter of its former gravitational pull.

11. The law of inverse square proportionality also means that, technically, gravitational attraction has an unlimited range.

12. Another meaning of the word "gravity" - which means "something heavy or serious" - appeared earlier, and came from the Latin "gravis", which means "heavy".

13. The force of gravity accelerates all objects equally, regardless of weight. If you drop two balls of the same size but different weight from the roof, they will hit the ground at the same time. The greater inertia of a heavier object cancels out any additional speed it might have over a lighter one.

14. Einstein's general theory of relativity was the first theory to consider gravity as a curvature of space-time - the "fabric" that makes up the physical universe.

15. Any object that has mass bends the space-time around it. In 2011, NASA's Gravity Probe B experiment showed that the Earth is spinning the universe around itself like a wooden ball in molasses, exactly as Einstein predicted.

16. By bending space-time around it, a massive object sometimes redirects the rays of light that pass through it, just like a glass lens does. Gravitational lenses can easily magnify the apparent size of distant galaxies or smear their light into strange shapes.

17. The “three-body problem”, which describes all the possible patterns in which three objects can revolve around each other only under the influence of gravity, has occupied scientists for three hundred years. To date, only 16 of its solutions have been found - and 13 of them were obtained as recently as March of this year.

18. Although the other three fundamental forces get along well with quantum mechanics - the science of the ultra-small - gravity refuses to cooperate with it; quantum equations are violated by any attempt to include gravity in them. How to reconcile these two absolutely exact and completely opposite descriptions of the universe is one of the biggest problems of modern physics.

19. To better understand gravity, scientists are looking for gravitational waves - ripples in space-time that come from events like black hole collisions and star explosions.

20. Once they can detect gravitational waves, scientists will be able to look at the cosmos in a way they have never done before. “Every time we look at the universe in a new way,” says Louisiana Gravitational Wave Observatory physicist Amber Stuever, “it revolutionizes our understanding of it.”

Gravitational force is the force with which objects of a certain mass are attracted to each other, located at a certain distance from each other.

The English scientist Isaac Newton in 1867 discovered the law of universal gravitation. This is one of the fundamental laws of mechanics. The essence of this law is as follows:any two material particles are attracted to each other with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.

The force of attraction is the first force that a person felt. This is the force with which the Earth acts on all bodies located on its surface. And any person feels this force as his own weight.

Law of gravity

There is a legend that Newton discovered the law of universal gravitation quite by accident, walking in the evening in the garden of his parents. Creative people are constantly in search, and scientific discoveries are not instantaneous insight, but the fruit of long-term mental work. Sitting under an apple tree, Newton was thinking about another idea, and suddenly an apple fell on his head. It was clear to Newton that the apple fell as a result of the Earth's gravity. “But why doesn’t the moon fall to the Earth? he thought. “It means that some other force is acting on it, keeping it in orbit.” This is how the famous law of gravity.

Scientists who had previously studied the rotation of celestial bodies believed that celestial bodies obey some completely different laws. That is, it was assumed that there are completely different laws of attraction on the surface of the Earth and in space.

Newton combined these supposed kinds of gravity. Analyzing Kepler's laws describing the motion of the planets, he came to the conclusion that the force of attraction arises between any bodies. That is, both the apple that fell in the garden and the planets in space are affected by forces that obey the same law - the law of universal gravitation.

Newton found that Kepler's laws only work if there is an attractive force between the planets. And this force is directly proportional to the masses of the planets and inversely proportional to the square of the distance between them.

The force of attraction is calculated by the formula F=G m 1 m 2 / r 2

m 1 is the mass of the first body;

m2is the mass of the second body;

r is the distance between the bodies;

G is the coefficient of proportionality, which is called gravitational constant or gravitational constant.

Its value was determined experimentally. G\u003d 6.67 10 -11 Nm 2 / kg 2

If two material points with a mass equal to a unit of mass are at a distance equal to a unit of distance, then they are attracted with a force equal to G.

The forces of attraction are the gravitational forces. They are also called gravity. They are subject to the law of universal gravitation and appear everywhere, since all bodies have mass.

Gravity

The gravitational force near the surface of the Earth is the force with which all bodies are attracted to the Earth. They call her gravity. It is considered constant if the distance of the body from the Earth's surface is small compared to the radius of the Earth.

Since gravity, which is the gravitational force, depends on the mass and radius of the planet, it will be different on different planets. Since the radius of the Moon is less than the radius of the Earth, then the force of attraction on the Moon is less than on the Earth by 6 times. And on Jupiter, on the contrary, gravity is 2.4 times greater than gravity on Earth. But body weight remains constant, no matter where it is measured.

Many people confuse the meaning of weight and gravity, believing that gravity is always equal to weight. But it is not.

The force with which the body presses on the support or stretches the suspension, this is the weight. If the support or suspension is removed, the body will begin to fall with the acceleration of free fall under the action of gravity. The force of gravity is proportional to the mass of the body. It is calculated according to the formulaF= m g , Where m- body mass, g- acceleration of gravity.

Body weight can change, and sometimes disappear altogether. Imagine that we are in an elevator on the top floor. The elevator is worth it. At this moment, our weight P and the force of gravity F, with which the Earth pulls us, are equal. But as soon as the elevator began to move down with acceleration A , weight and gravity are no longer equal. According to Newton's second lawmg+ P = ma . P \u003d m g -ma.

It can be seen from the formula that our weight decreased as we moved down.

At the moment when the elevator picked up speed and began to move without acceleration, our weight is again equal to gravity. And when the elevator began to slow down its movement, acceleration A became negative and the weight increased. There is an overload.

And if the body moves down with the acceleration of free fall, then the weight will completely become equal to zero.

At a=g R=mg-ma= mg - mg=0

This is a state of weightlessness.

So, without exception, all material bodies in the Universe obey the law of universal gravitation. And the planets around the Sun, and all the bodies that are near the surface of the Earth.

The most important phenomenon constantly studied by physicists is motion. Electromagnetic phenomena, laws of mechanics, thermodynamic and quantum processes - all this is a wide range of fragments of the universe studied by physics. And all these processes come down, one way or another, to one thing - to.

In contact with

Everything in the universe moves. Gravity is a familiar phenomenon for all people since childhood, we were born in the gravitational field of our planet, this physical phenomenon is perceived by us at the deepest intuitive level and, it would seem, does not even require study.

But, alas, the question is why and How do all bodies attract each other?, remains to this day not fully disclosed, although it has been studied up and down.

In this article, we will consider what Newton's universal attraction is - the classical theory of gravity. However, before moving on to formulas and examples, let's talk about the essence of the problem of attraction and give it a definition.

Perhaps the study of gravity was the beginning of natural philosophy (the science of understanding the essence of things), perhaps natural philosophy gave rise to the question of the essence of gravity, but, one way or another, the question of gravity of bodies interested in ancient Greece.

Movement was understood as the essence of the sensual characteristics of the body, or rather, the body moved while the observer sees it. If we cannot measure, weigh, feel a phenomenon, does this mean that this phenomenon does not exist? Naturally, it doesn't. And since Aristotle understood this, reflections on the essence of gravity began.

As it turned out today, after many tens of centuries, gravity is the basis not only of the earth's attraction and the attraction of our planet to, but also the basis of the origin of the Universe and almost all existing elementary particles.

Movement task

Let's do a thought experiment. Take a small ball in your left hand. Let's take the same one on the right. Let's release the right ball, and it will start to fall down. The left one remains in the hand, it is still motionless.

Let's mentally stop the passage of time. The falling right ball "hangs" in the air, the left one still remains in the hand. The right ball is endowed with the “energy” of movement, the left one is not. But what is the deep, meaningful difference between them?

Where, in what part of the falling ball is it written that it must move? It has the same mass, the same volume. It has the same atoms, and they are no different from the atoms of a ball at rest. Ball has? Yes, this is the correct answer, but how does the ball know that it has potential energy, where is it recorded in it?

This is the task set by Aristotle, Newton and Albert Einstein. And all three brilliant thinkers partly solved this problem for themselves, but today there are a number of issues that need to be resolved.

Newtonian gravity

In 1666, the greatest English physicist and mechanic I. Newton discovered a law capable of quantitatively calculating the force due to which all matter in the universe tends to each other. This phenomenon is called universal gravitation. When asked: "Formulate the law of universal gravitation", your answer should sound like this:

The force of gravitational interaction, which contributes to the attraction of two bodies, is in direct proportion to the masses of these bodies and inversely proportional to the distance between them.

Important! Newton's law of attraction uses the term "distance". This term should be understood not as the distance between the surfaces of bodies, but as the distance between their centers of gravity. For example, if two balls with radii r1 and r2 lie on top of each other, then the distance between their surfaces is zero, but there is an attractive force. The point is that the distance between their centers r1+r2 is nonzero. On a cosmic scale, this clarification is not important, but for a satellite in orbit, this distance is equal to the height above the surface plus the radius of our planet. The distance between the Earth and the Moon is also measured as the distance between their centers, not their surfaces.

For the law of gravity, the formula is as follows:

,

• F is the force of attraction,
• - masses,
• r - distance,
• G is the gravitational constant, equal to 6.67 10−11 m³ / (kg s²).

What is weight, if we have just considered the force of attraction?

Force is a vector quantity, but in the law of universal gravitation it is traditionally written as a scalar. In a vector picture, the law will look like this:

.

But this does not mean that the force is inversely proportional to the cube of the distance between the centers. The ratio should be understood as a unit vector directed from one center to another:

.

Law of gravitational interaction

Weight and gravity

Having considered the law of gravity, one can understand that there is nothing surprising in the fact that we personally we feel the attraction of the sun is much weaker than the earth's. The massive Sun, although it has a large mass, is very far from us. also far from the Sun, but it is attracted to it, as it has a large mass. How to find the force of attraction of two bodies, namely, how to calculate the gravitational force of the Sun, the Earth and you and me - we will deal with this issue a little later.

As far as we know, the force of gravity is:

where m is our mass, and g is the free fall acceleration of the Earth (9.81 m/s 2).

Important! There are no two, three, ten kinds of forces of attraction. Gravity is the only force that quantifies attraction. Weight (P = mg) and gravitational force are one and the same.

If m is our mass, M is the mass of the globe, R is its radius, then the gravitational force acting on us is:

Thus, since F = mg:

.

The masses m cancel out, leaving the expression for the free fall acceleration:

As you can see, the acceleration of free fall is indeed a constant value, since its formula includes constant values ​​- the radius, the mass of the Earth and the gravitational constant. Substituting the values ​​of these constants, we will make sure that the acceleration of free fall is equal to 9.81 m / s 2.

At different latitudes, the radius of the planet is somewhat different, since the Earth is still not a perfect sphere. Because of this, the acceleration of free fall at different points on the globe is different.

Let's return to the attraction of the Earth and the Sun. Let's try to prove by example that the globe attracts us stronger than the Sun.

For convenience, let's take the mass of a person: m = 100 kg. Then:

• The distance between a person and the globe is equal to the radius of the planet: R = 6.4∙10 6 m.
• The mass of the Earth is: M ≈ 6∙10 24 kg.
• The mass of the Sun is: Mc ≈ 2∙10 30 kg.
• Distance between our planet and the Sun (between the Sun and man): r=15∙10 10 m.

Gravitational attraction between man and the Earth:

This result is fairly obvious from a simpler expression for the weight (P = mg).

The force of gravitational attraction between man and the Sun:

As you can see, our planet attracts us almost 2000 times stronger.

How to find the force of attraction between the Earth and the Sun? In the following way:

Now we see that the Sun pulls on our planet more than a billion billion times stronger than the planet pulls you and me.

first cosmic speed

After Isaac Newton discovered the law of universal gravitation, he became interested in how fast a body should be thrown so that it, having overcome the gravitational field, left the globe forever.

True, he imagined it a little differently, in his understanding it was not a vertically standing rocket directed into the sky, but a body that horizontally makes a jump from the top of a mountain. It was a logical illustration, because at the top of the mountain, the force of gravity is slightly less.

So, at the top of Everest, the acceleration of gravity will not be the usual 9.8 m / s 2, but almost m / s 2. It is for this reason that there is so rarefied, the air particles are no longer as attached to gravity as those that "fell" to the surface.

Let's try to find out what cosmic speed is.

The first cosmic velocity v1 is the velocity at which the body leaves the surface of the Earth (or another planet) and enters a circular orbit.

Let's try to find out the numerical value of this quantity for our planet.

Let's write Newton's second law for a body that revolves around the planet in a circular orbit:

,

where h is the height of the body above the surface, R is the radius of the Earth.

In orbit, centrifugal acceleration acts on the body, thus:

.

The masses are reduced, we get:

,

This speed is called the first cosmic speed:

As you can see, the space velocity is absolutely independent of the mass of the body. Thus, any object accelerated to a speed of 7.9 km / s will leave our planet and enter its orbit.

first cosmic speed

Second space velocity

However, even having accelerated the body to the first cosmic speed, we will not be able to completely break its gravitational connection with the Earth. For this, the second cosmic velocity is needed. Upon reaching this speed, the body leaves the gravitational field of the planet and all possible closed orbits.

Important! By mistake, it is often believed that in order to get to the Moon, astronauts had to reach the second cosmic velocity, because they first had to "disconnect" from the gravitational field of the planet. This is not so: the Earth-Moon pair are in the Earth's gravitational field. Their common center of gravity is inside the globe.

In order to find this speed, we set the problem a little differently. Suppose a body flies from infinity to a planet. Question: what speed will be achieved on the surface upon landing (without taking into account the atmosphere, of course)? It is this speed and it will take the body to leave the planet.

The law of universal gravitation. Physics Grade 9

The law of universal gravitation.

Conclusion

We have learned that although gravity is the main force in the universe, many of the reasons for this phenomenon are still a mystery. We learned what Newton's universal gravitational force is, learned how to calculate it for various bodies, and also studied some useful consequences that follow from such a phenomenon as the universal law of gravitation.

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

Introduction

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

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

scientific definition

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

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

Theories of Newton and Einstein

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

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

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

\[ F = γ \frac[-1.2](m_1 m_2)(r^2) \]

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

Interaction between elementary particles

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

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

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

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

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

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

Conclusions of Newton and some of his predecessors

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

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

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

Mass as the cornerstone of theory

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

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

What is the relationship between mass and attraction?

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

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

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

Features of acceleration of bodies in a gravitational field

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

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

What does the acceleration depend on in the described case?

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

On the importance of G

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

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

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

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

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

Theory of relativity, works of Albert Einstein

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

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

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

Relationship between relativity and gravitational forces

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

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

A simple solution?

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

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

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

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