Level of gravity on earth. What is gravity in simple words

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

1. 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.
2. 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.
3. The objects with the strongest gravity are black holes. Their gravity is so strong that they even attract light (photons).
4. 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.
5. The word gravity comes from the Latin “gravis”, which means “heavy”.
6. 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.
7. NASA scientists are trying to develop a gravity beam that will allow objects to be moved without contact, overcoming the force of gravity.
8. Astronauts in orbit also experience gravity. More precisely, microgravity. They seem to fall endlessly along with the ship they are in.
9. Gravity always attracts and never repels.
10. 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!

To the question “What is force?” physics answers this way: “Force is a measure of the interaction of material bodies with each other or between bodies and other material objects - physical fields.” All forces in nature can be classified into four fundamental types of interactions: strong, weak, electromagnetic and gravitational. Our article talks about what gravitational forces are - a measure of the last and, perhaps, most widespread type of these interactions in nature.

Let's start with the gravity of the earth

Everyone alive knows that there is a force that attracts objects to the earth. It is commonly referred to as gravity, gravity, or gravity. Thanks to its presence, humans have the concepts of “up” and “down,” which determine the direction of movement or location of something relative to the earth’s surface. So in a particular case, on the surface of the earth or near it, gravitational forces manifest themselves, which attract objects with mass to each other, manifesting their effect at any distance, both small and very large, even by cosmic standards.

Gravity and Newton's third law

As is known, any force, if it is considered as a measure of the interaction of physical bodies, is always applied to one of them. So in the gravitational interaction of bodies with each other, each of them experiences such types of gravitational forces that are caused by the influence of each of them. If there are only two bodies (it is assumed that the action of all others can be neglected), then each of them, according to Newton’s third law, will attract the other body with the same force. So the Moon and the Earth attract each other, resulting in the ebb and flow of the Earth's seas.

Each planet in the solar system experiences several gravitational forces from the Sun and other planets. Of course, it is the gravitational force of the Sun that determines the shape and size of its orbit, but astronomers also take into account the influence of other celestial bodies in their calculations of the trajectories of their movement.

Which will fall to the ground faster from a height?

The main feature of this force is that all objects fall to the ground at the same speed, regardless of their mass. Once upon a time, right up to the 16th century, it was believed that everything was the other way around - heavier bodies should fall faster than lighter ones. To dispel this misconception, Galileo Galilei had to perform his famous experiment of simultaneously dropping two cannonballs of different weights from the leaning Tower of Pisa. Contrary to the expectations of witnesses to the experiment, both nuclei reached the surface at the same time. Today, every schoolchild knows that this happened due to the fact that gravity imparts to any body the same acceleration of free fall g = 9.81 m/s 2 regardless of the mass m of this body, and its value according to Newton’s second law is equal to F = mg.

Gravitational forces on the Moon and on other planets have different values ​​of this acceleration. However, the nature of the action of gravity on them is the same.

Gravity and body weight

If the first force is applied directly to the body itself, then the second to its support or suspension. In this situation, elastic forces always act on the bodies from the supports and suspensions. Gravitational forces applied to the same bodies act towards them.

Imagine a weight suspended above the ground by a spring. Two forces are applied to it: the elastic force of the stretched spring and the force of gravity. According to Newton's third law, the load acts on the spring with a force equal and opposite to the elastic force. This force will be its weight. A load weighing 1 kg has a weight equal to P = 1 kg ∙ 9.81 m/s 2 = 9.81 N (newton).

Gravitational forces: definition

The first quantitative theory of gravity, based on observations of planetary motion, was formulated by Isaac Newton in 1687 in his famous “Principles of Natural Philosophy.” He wrote that the gravitational forces that act on the Sun and planets depend on the amount of matter they contain. They spread over long distances and always decrease as the reciprocal of the square of the distance. How can we calculate these gravitational forces? The formula for the force F between two objects with masses m 1 and m 2 located at a distance r is:

• F=Gm 1 m 2 /r 2 ,
  where G is a constant of proportionality, a gravitational constant.

Physical mechanism of gravity

Newton was not completely satisfied with his theory, since it assumed interaction between attracting bodies at a distance. The great Englishman himself was sure that there must be some physical agent responsible for transferring the action of one body to another, which he quite clearly stated in one of his letters. But the time when the concept of a gravitational field that permeates all space was introduced came only four centuries later. Today, speaking about gravity, we can talk about the interaction of any (cosmic) body with the gravitational field of other bodies, the measure of which is the gravitational forces arising between each pair of bodies. The law of universal gravitation, formulated by Newton in the above form, remains true and is confirmed by many facts.

Gravity theory and astronomy

It was very successfully applied to solving problems of celestial mechanics during the 18th and early 19th centuries. For example, mathematicians D. Adams and W. Le Verrier, analyzing disturbances in the orbit of Uranus, suggested that it is subject to gravitational forces of interaction with an as yet unknown planet. They indicated its expected position, and soon Neptune was discovered there by astronomer I. Galle.

There was still one problem though. Le Verrier in 1845 calculated that the orbit of Mercury precesses by 35" per century, in contrast to the zero value of this precession obtained from Newton's theory. Subsequent measurements gave a more accurate value of 43". (The observed precession is actually 570"/century, but a careful calculation to subtract the influence from all other planets gives a value of 43".)

It was not until 1915 that Albert Einstein was able to explain this discrepancy within the framework of his theory of gravity. It turned out that the massive Sun, like any other massive body, bends space-time in its vicinity. These effects cause deviations in the orbits of planets, but on Mercury, as the smallest planet and closest to our star, they are most pronounced.

Inertial and gravitational masses

As noted above, Galileo was the first to observe that objects fall to the ground at the same speed, regardless of their mass. In Newton's formulas, the concept of mass comes from two different equations. His second law says that a force F applied to a body with mass m gives acceleration according to the equation F = ma.

However, the force of gravity F applied to a body satisfies the formula F = mg, where g depends on the other body interacting with the one in question (the earth usually when we talk about gravity). In both equations m is a coefficient of proportionality, but in the first case it is inertial mass, and in the second it is gravitational mass, and there is no obvious reason that they should be the same for any physical object.

However, all experiments show that this is indeed the case.

Einstein's theory of gravity

He took the fact of equality of inertial and gravitational masses as a starting point for his theory. He managed to construct the gravitational field equations, the famous Einstein equations, and with their help calculate the correct value for the precession of the orbit of Mercury. They also give a measured value for the deflection of light rays that pass near the Sun, and there is no doubt that they give the correct results for macroscopic gravity. Einstein's theory of gravity, or general theory of relativity (GR) as he called it, is one of the greatest triumphs of modern science.

Are gravitational forces acceleration?

If you cannot distinguish inertial mass from gravitational mass, then you cannot distinguish gravity from acceleration. The gravitational field experiment can instead be performed in an accelerating elevator in the absence of gravity. When an astronaut in a rocket accelerates away from the earth, he experiences a force of gravity that is several times greater than Earth's, with the vast majority of it coming from acceleration.

If no one can distinguish gravity from acceleration, then the former can always be reproduced by acceleration. A system in which acceleration replaces gravity is called inertial. Therefore, the Moon in low-Earth orbit can also be considered as an inertial system. However, this system will differ from point to point as the gravitational field changes. (In the example of the Moon, the gravitational field changes direction from one point to another.) The principle that one can always find an inertial system at any point in space and time at which physics obeys the laws in the absence of gravity is called the equivalence principle.

Gravity as a manifestation of the geometric properties of space-time

The fact that gravitational forces can be thought of as accelerations in inertial coordinate systems that differ from point to point means that gravity is a geometric concept.

We say that spacetime is curved. Consider a ball on a flat surface. It will rest or, if there is no friction, move uniformly in the absence of any forces acting on it. If the surface is curved, the ball will accelerate and move to the lowest point, taking the shortest path. Similarly, Einstein's theory states that four-dimensional space-time is curved, and a body moves in this curved space along a geodesic line that corresponds to the shortest path. Therefore, the gravitational field and the gravitational forces acting in it on physical bodies are geometric quantities that depend on the properties of space-time, which change most strongly near massive bodies.

Since ancient times, humanity 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 gravity is the reason for everything. What it is, and why this phenomenon is so important on the scale of the Universe, we will consider today.

Introductory part

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 theory of gravity was formulated by a genius whose hypotheses predetermined the development of physics for many centuries to come. Albert Einstein, one of the greatest minds of the last century, developed and continued (albeit in a completely different direction) this teaching.

For centuries, scientists have observed gravity and tried to understand and measure it. Finally, in the last few decades, even such a phenomenon as gravity has been put at the service of humanity (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 call this 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 situation is the other way around, Einstein's conclusions should be used.

Let’s make a reservation right away: at present, the very nature of gravity is not fully understood in principle. We still don’t fully understand what it is.

Theories of Newton and Einstein

According to the classical teaching of Isaac Newton, all bodies attract each other with a force directly proportional to their mass, inversely proportional to the square of the distance that lies between them. Einstein 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, Einstein’s classical equation does not even provide for the chance that space will continue to influence matter and the resulting magnetic field.

The law of gravity (universal gravitation) is best known, the mathematical expression of which belongs to Newton:

\[ F = γ \frac[-1.2](m_1 m_2)(r^2) \]

γ refers to 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 between elementary particles differ significantly in their strength.

The most powerful 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 “attached” 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 (you already know what it is) in the form of atoms and subatomic particles is the easiest type of interaction.

The gravitational field in this case is so weak that it is difficult to imagine. Oddly enough, it is they who “monitor” the movement of celestial bodies, whose mass is sometimes impossible to imagine. All this is possible thanks 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. Thus, the Earth’s gravity holds even the Moon in its field, and a similar force from Jupiter easily supports the orbits of several satellites at once, the mass of each of which is quite comparable to that of the Earth!
• In addition, it always provides attraction between objects, and with distance this force weakens at a small speed.

The formation of a more or less coherent theory of gravity occurred relatively recently, and precisely based on the results of centuries-old observations of the movement 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 probable interactions. Galileo and Kepler, two outstanding astronomers of that time, helped prepare the ground 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 mathematically. 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 spaceship is not affected by the gravity of some massive object.

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

Thus, gravitational forces are proportional to the mass of objects. They can be expressed numerically by obtaining the product of the masses of both bodies under consideration. This force strictly obeys the inverse relationship to the square of the distance between objects. All other interactions depend completely differently on the distances between two bodies.

Mass as the cornerstone of the theory

The mass of objects has become a special point of contention around which Einstein's entire modern theory of gravity and relativity is built. If you remember the Second, 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 exposed to an external force, it is the mass that determines how large this acceleration will be. Let's look at a more understandable example. Imagine a scooter and a bus: if you apply exactly the same force to them, they will reach different speeds in different times. The theory of gravity explains all this.

What is the relationship between mass and gravity?

If we talk about gravity, then mass in this phenomenon plays a role completely opposite to the one 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 look at the force with which 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 gravity is directly proportional to the mass of the body.

If we consider Newton's Third Law, we can see that it says exactly the same thing. The force of gravity, which acts on two bodies located at equal distances 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 summarize 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 that in the same gravitational field the acceleration of completely different objects will be equal. Let's assume that we have two bodies. Let's assign mass z to one of them, and mass Z to the other. Both objects are dropped to the ground, where they fall freely.

How is the ratio of attractive forces determined? It is shown by the simplest mathematical formula - z/Z. But the acceleration they receive as a result of the force of gravity will be absolutely 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 equal acceleration of different bodies in a gravitational field has been discovered for a relatively long time. These phenomena received the following name: “The principle of equivalence.” This term once again emphasizes that acceleration and inertia are often equivalent (to a certain extent, of course).

About the importance of the G value

From the school physics course, we remember that the acceleration of gravity on the surface of our planet (Earth’s gravity) is equal to 10 m/sec.² (9.8, of course, but this value is used for simplicity of calculations). Thus, if you do not take into account air resistance (at a significant height with a short fall distance), you will get the effect when the body acquires an acceleration increment of 10 m/sec. every second. So, a book that fell 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.

The acceleration of gravity in the physical literature is denoted by the letter “g”. Since the shape of the Earth is to a certain extent more reminiscent of a tangerine than a sphere, the value of this quantity is not the same in all its regions. So, the acceleration is higher at the poles, and at the tops of high mountains it becomes less.

Even in the mining industry, gravity plays an important role. The physics of this phenomenon can sometimes save a lot of time. Thus, geologists are especially interested in the perfectly accurate determination of g, since this allows them to explore and locate mineral deposits with exceptional accuracy. By the way, what does the gravitation formula look like, in which the quantity we considered plays an important role? Here she is:

Note! In this case, the gravitation formula means by G the “gravitational constant”, the meaning 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 humanity owes the modern understanding of the very nature of the space-time continuum.

Theory of relativity, works of Albert Einstein

In the time of Isaac Newton, it was believed that reference points can be represented in the form of some kind of rigid “rods”, with the help of which the position of a body in a spatial coordinate system is established. At the same time, it was assumed that all observers who mark these coordinates will be in the same 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 the boundaries of our planet there are no deviations in this rule.

Einstein proved that the accuracy of the measurement would really matter if a hypothetical clock moved significantly 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? whose speed is the same or greater, events can occur at different times.

But how does gravity relate to the theory of relativity? Let's look at this question in detail.

The connection between the theory of relativity and gravitational forces

In recent years, a huge number of discoveries have been made in the field of subatomic particles. The conviction is growing stronger that we are about to find the final particle, beyond which our world cannot fragment. The more insistent becomes the need to find out exactly how the smallest “building blocks” of our universe are influenced 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 “incompetence” of Newton’s classical mechanics in the area under consideration, researchers focused on a complete rethinking of the previously obtained data. Gravity itself has undergone a major revision. What is it at the subatomic particle level? Does it have any significance in this amazing multidimensional world?

A simple solution?

At first, many assumed that the discrepancy between Newton's gravitation and the theory of relativity could be explained quite simply by drawing analogies from the field of electrodynamics. One could assume that the gravitational field propagates like a magnetic field, after which it can be declared a “mediator” in the interactions of celestial bodies, explaining many of the inconsistencies between the old and new theories. The fact is that then the relative speeds of propagation of the forces in question would be significantly 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 precisely such views, but 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 precisely the generally accepted source of the emergence of powerful gravitational fields.

High speeds greatly affect the masses of bodies, and this is in no way similar to the interaction of speed and charge. The higher the speed, the greater the body mass. The problem is that the latter value would automatically become infinite if moving at the speed of light or faster. Therefore, Einstein concluded that there is not a gravitational field, but a tensor field, to describe 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 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...

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

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

The law of universal gravitation is one of the applications of the inverse square law, which is also found in the study of radiation (see, for example, Light Pressure), and is a direct consequence of the quadratic increase in the area of ​​the sphere with increasing radius, which leads to a quadratic decrease in the contribution of any unit area to area of ​​the entire sphere.

The gravitational field, like the gravity field, is potential. This means that you can introduce the potential energy of gravitational attraction of a pair of bodies, and this energy will not change after moving the bodies along a closed loop. The potentiality of the gravitational field entails the law of conservation of the sum of kinetic and potential energy and, when studying the motion of bodies in a gravitational field, often significantly simplifies the solution. Within the framework of Newtonian mechanics, gravitational interaction is long-range. This means that no matter how a massive body moves, at any point in space the gravitational potential depends only on the position of the body at a given moment in time.

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

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

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

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

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

Celestial mechanics and some of its tasks

The simplest problem of celestial mechanics is the gravitational interaction of two point or spherical bodies in empty space. This problem within the framework of classical mechanics is solved analytically in a closed form; the result of its solution is often formulated in the form of Kepler's three laws.

As the number of interacting bodies increases, the task becomes dramatically more complicated. Thus, the already famous three-body problem (that is, the motion of three bodies with non-zero masses) cannot be solved analytically in a general form. With a numerical solution, instability of the solutions relative to the initial conditions occurs quite quickly. When applied to the Solar System, this instability does not allow us to accurately predict the motion of planets on scales exceeding a hundred million years.

In some special cases, it is possible to find an approximate solution. The most important is the case when the mass of one body is significantly greater than the mass of other bodies (examples: the Solar system and the dynamics of the rings of Saturn). In this case, as a first approximation, we can assume that light bodies do not interact with each other and move along Keplerian trajectories around the massive body. The interactions between them can be taken into account within the framework of perturbation theory and averaged over time. In this case, non-trivial phenomena may arise, such as resonances, attractors, chaos, etc. A clear example of such phenomena is the complex structure of the rings of Saturn.

Despite attempts to accurately describe the behavior of a system of a large number of attracting bodies of approximately the same mass, this cannot be done due to the phenomenon of dynamic chaos.

Strong gravitational fields

In strong gravitational fields, as well as when moving in a gravitational field at relativistic speeds, the effects of the general theory of relativity (GTR) begin to appear:

• changing the geometry of space-time;
  • as a consequence, the deviation of the law of gravity from Newtonian;
  • and in extreme cases - the emergence of black holes;
• delay of potentials associated with the finite speed of propagation of gravitational disturbances;
  • as a consequence, the appearance of gravitational waves;
• nonlinearity effects: gravity tends to interact with itself, so the principle of superposition in strong fields no longer holds.

Gravitational radiation

One of the important predictions of general relativity is gravitational radiation, the presence of which has not yet been confirmed by direct observations. However, there is significant indirect evidence in favor of its existence, namely: energy losses in close binary systems containing compact gravitating objects (such as neutron stars or black holes), in particular, in the famous PSR B1913+16 system (Hulse-Taylor pulsar) - are in good agreement with the general relativity model, in which this energy is carried away precisely by gravitational radiation.

Gravitational radiation can only be generated by systems with variable quadrupole or higher multipole moments, this fact suggests that the gravitational radiation of most natural sources is directional, which significantly complicates its detection. Gravity power n-field source is proportional if the multipole is of electric type, and - if the multipole is magnetic type, where v is the characteristic speed of movement of sources in the radiating system, and c- speed of light. Thus, the dominant moment will be the quadrupole moment of the electric type, and the power of the corresponding radiation is equal to:

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

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

Subtle effects of gravity

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

In addition to the classical effects of gravitational attraction and time dilation, the general theory of relativity predicts the existence of other manifestations of gravity, which under terrestrial conditions are very weak and their detection and experimental verification are therefore very difficult. Until recently, overcoming these difficulties seemed beyond the capabilities of experimenters.

Among them, in particular, we can name the entrainment of inertial frames of reference (or the Lense-Thirring effect) and the gravitomagnetic field. In 2005, NASA's robotic Gravity Probe B conducted an unprecedented precision experiment to measure these effects near Earth. Processing of the obtained data was carried out until May 2011 and confirmed the existence and magnitude of the effects of geodetic precession and drag of inertial reference systems, although with an accuracy somewhat less than originally assumed.

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

Classical theories of gravity

See also: Theories of gravity

Due to the fact that quantum effects of gravity are extremely small even under the most extreme experimental and observational conditions, there are still no reliable observations of them. Theoretical estimates show that in the vast majority of cases one can limit oneself to the classical description of gravitational interaction.

There is a modern canonical classical theory of gravity - the general theory of relativity, and many clarifying hypotheses and theories of varying degrees of development, competing with each other. All of these theories make very similar predictions within the approximation in which experimental tests are currently carried out. The following are several basic, most well-developed or known theories of gravity.

General theory of relativity

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

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

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

However, general relativity has been confirmed experimentally until very recently (2012). In addition, many alternative approaches to Einstein's, but standard for modern physics, approaches to the formulation of the theory of gravity lead to a result coinciding with general relativity in the low-energy approximation, which is the only one now accessible to experimental verification.

Einstein-Cartan theory

A similar division of equations into two classes also occurs in the RTG, where the second tensor equation is introduced to take into account the connection between non-Euclidean space and Minkowski space. Thanks to the presence of a dimensionless parameter in the Jordan-Brans-Dicke theory, it becomes possible to choose it so that the results of the theory coincide with the results of gravitational experiments. Moreover, as the parameter tends to infinity, the predictions of the theory become closer and closer to general relativity, so it is impossible to refute the Jordan-Brans-Dicke theory by any experiment confirming the general theory of relativity.

Quantum theory of gravity

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

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

String theory

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

Loop quantum gravity

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

Main article: Causal dynamic triangulation

In it, the space-time manifold is constructed from elementary Euclidean simplexes (triangle, tetrahedron, pentachore) of dimensions on the order of Planckian ones, taking into account the principle of causality. The four-dimensionality and pseudo-Euclidean nature of space-time on macroscopic scales are not postulated in it, but are a consequence of the theory.

see also

Notes

Literature

• Vizgin V. P. Relativistic theory of gravity (origins and formation, 1900-1915). - M.: Nauka, 1981. - 352c.
• Vizgin V. P. Unified theories in the 1st third of the twentieth century. - M.: Nauka, 1985. - 304c.
• Ivanenko D. D., Sardanashvili G. A. Gravity. 3rd ed. - M.: URSS, 2008. - 200 p.
• Misner C., Thorne K., Wheeler J. Gravity. - M.: Mir, 1977.
• Thorne K. Black holes and folds of time. Einstein's bold legacy. - M.: State Publishing House of Physical and Mathematical Literature, 2009.

Links

• The law of universal gravitation or “Why doesn’t the Moon fall to Earth?” - Just about difficult things
• Problems with Gravity (BBC documentary, video)
• Earth and Gravity; Relativistic theory of gravity (TV show Gordon “Dialogues”, video)

Theories of gravity
Standard theories of gravity

The most important phenomenon constantly studied by physicists is movement. 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 common 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 far and wide.

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

Perhaps the study of gravity became 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 the gravitation of bodies became interested in ancient Greece.

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

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

Movement task

Let's conduct a thought experiment. Let's take a small ball in our left hand. Let's take the same one on the right. Let's release the right ball and it will begin 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 should 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 what has potential energy, where is it recorded in it?

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

Newton's gravity

In 1666, the greatest English physicist and mechanic I. Newton discovered a law that can quantitatively calculate the force due to which all matter in the Universe tends to each other. This phenomenon is called universal gravity. When you are asked: “Formulate the law of universal gravitation,” your answer should sound like this:

The force of gravitational interaction contributing to the attraction of two bodies is located in direct proportion to the masses of these bodies and in inverse proportion 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 of 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 thing is that the distance between their centers r1+r2 is different from zero. 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 – force of attraction,
• – masses,
• r – distance,
• G – gravitational constant equal to 6.67·10−11 m³/(kg·s²).

What is weight, if we just looked at the force of gravity?

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 relation should be perceived 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 it is not surprising that we personally we feel the Sun's gravity much weaker than the Earth's. Although the massive Sun has a large mass, it is very far from us. is also far from the Sun, but it is attracted to it, since it has a large mass. How to find the gravitational force of two bodies, namely, how to calculate the gravitational force of the Sun, 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 acceleration of free fall of the Earth (9.81 m/s 2).

Important! There are not two, three, ten types of attractive forces. Gravity is the only force that gives a quantitative characteristic of attraction. Weight (P = mg) and gravitational force are the same thing.

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

Thus, since F = mg:

.

The masses m are reduced, and the expression for the acceleration of free fall remains:

As we can see, the acceleration of gravity is truly a constant value, since its formula includes constant quantities - 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 gravity is equal to 9.81 m/s 2.

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

Let's return to the attraction of the Earth and the Sun. Let's try to prove with an example that the globe attracts you and me more strongly 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 Earth:

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

The force of gravitational attraction between man and the Sun:

As we 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 attracts our planet more than a billion billion times stronger than the planet attracts you and me.

First escape velocity

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

True, he imagined it a little differently, in his understanding it was not a vertically standing rocket aimed at the sky, but a body that horizontally made a jump from the top of a mountain. This 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 the air there is so thin, the air particles are no longer as tied to gravity as those that “fell” to the surface.

Let's try to find out what escape velocity is.

The first escape velocity v1 is the speed 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 value for our planet.

Let's write down Newton's second law for a body that rotates around a 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, a body is subject to centrifugal acceleration, thus:

.

The masses are reduced, we get:

,

This speed is called the first escape velocity:

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

First escape velocity

Second escape velocity

However, even having accelerated the body to the first escape velocity, we will not be able to completely break its gravitational connection with the Earth. This is why we need a second escape velocity. When this speed is reached the body leaves the planet's gravitational field and all possible closed orbits.

Important! It is often mistakenly believed that in order to get to the Moon, astronauts had to reach the second escape 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, let's pose the problem a little differently. Let's say a body flies from infinity to a planet. Question: what speed will be reached on the surface upon landing (without taking into account the atmosphere, of course)? This is exactly the speed the body will need to leave the planet.

The law of universal gravitation. Physics 9th grade

Law of Universal Gravitation.

Conclusion

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