Earth gravity speed. What is the law of universal gravitation: the formula of the great discovery. What determines the gravity of the planet

By what law are you going to hang me?
- And we hang everyone according to one law - the law of universal gravitation.

Law of gravity

The phenomenon of gravity is the law gravity. Two bodies act on each other with a force that is inversely proportional to the square of the distance between them and directly proportional to the product of their masses.

Mathematically, we can express this great law by the formula

Gravity acts over vast distances in the universe. But Newton argued that all objects are mutually attracted. Is it true that any two objects attract each other? Just imagine, it is known that the Earth attracts you sitting on a chair. But have you ever thought about the fact that a computer and a mouse attract each other? Or a pencil and pen on the table? In this case, we substitute the mass of the pen, the mass of the pencil into the formula, divide by the square of the distance between them, taking into account the gravitational constant, we obtain the force of their mutual attraction. But, it will come out so small (due to the small masses of the pen and pencil) that we do not feel its presence. Another thing is when it comes to the Earth and a chair, or the Sun and the Earth. The masses are significant, which means that we can already evaluate the effect of force.

Let's think about free fall acceleration. This is the operation of the law of attraction. Under the action of a force, the body changes speed the slower, the greater the mass. As a result, all bodies fall to the Earth with the same acceleration.

What is the cause of this invisible unique power? To date, the existence of a gravitational field is known and proven. You can learn more about the nature of the gravitational field in the additional material on the topic.

Think about what gravity is. Where is it from? What does it represent? After all, it cannot be that the planet looks at the Sun, sees how far it is removed, calculates the inverse square of the distance in accordance with this law?

Direction of gravity

There are two bodies, let's say body A and B. Body A attracts body B. The force with which body A acts begins on body B and is directed towards body A. That is, it "takes" body B and pulls it towards itself. Body B "does" the same thing with body A.

Every body is attracted by the Earth. The earth "takes" the body and pulls it towards its center. Therefore, this force will always be directed vertically downwards, and it is applied from the center of gravity of the body, it is called gravity.

The main thing to remember

Some methods of geological exploration, tide prediction and in Lately calculation of the movement of artificial satellites and interplanetary stations. Early calculation of the position of the planets.

Can we set up such an experiment ourselves, and not guess whether planets, objects are attracted?

Such a direct experience made Cavendish (Henry Cavendish (1731-1810) - English physicist and chemist) using the device shown in the figure. The idea was to hang a rod with two balls on a very thin quartz thread and then bring two large lead balls to the side of them. The attraction of the balls will twist the thread slightly - slightly, because the forces of attraction between ordinary objects are very weak. With the help of such an instrument, Cavendish was able to directly measure the force, distance and magnitude of both masses and, thus, determine gravitational constant G.

The unique discovery of the gravitational constant G, which characterizes the gravitational field in space, made it possible to determine the mass of the Earth, the Sun and other celestial bodies. Therefore, Cavendish called his experience "weighing the Earth."

Interestingly, the various laws of physics have some common features. Let's turn to the laws of electricity (Coulomb force). Electric forces are also inversely proportional to the square of the distance, but already between the charges, and the thought involuntarily arises that this pattern hides deep meaning. Until now, no one has been able to present gravity and electricity as two different manifestations of the same essence.

The force here also varies inversely with the square of the distance, but the difference in the magnitude of electric forces and gravitational forces is striking. In trying to establish the common nature of gravity and electricity, we find such a superiority of electric forces over gravitational forces that it is difficult to believe that both have the same source. How can you say that one is stronger than the other? After all, it all depends on what is the mass and what is the charge. Arguing about how strong gravity acts, you have no right to say: "Let's take a mass of such and such a size," because you choose it yourself. But if we take what Nature herself offers us (her own numbers and measures, which have nothing to do with our inches, years, our measures), then we can compare. We will take an elementary charged particle, such as, for example, an electron. Two elementary particles, two electrons, due to electric charge repel each other with a force inversely proportional to the square of the distance between them, and due to gravity attract each other again with a force inversely proportional to the square of the distance.

Question: What is the ratio of gravitational force to electrical force? Gravitation is related to electrical repulsion as one is to a number with 42 zeros. This is deeply puzzling. Where could such a huge number come from?

People are looking for this huge factor in other natural phenomena. They go through all sorts big numbers and if you need big number why not take, say, the ratio of the diameter of the Universe to the diameter of a proton - surprisingly, this is also a number with 42 zeros. And they say: maybe this coefficient is equal to the ratio of the diameter of the proton to the diameter of the universe? This is an interesting thought, but as the universe gradually expands, the constant of gravity must also change. Although this hypothesis has not yet been refuted, we do not have any evidence in its favor. On the contrary, some evidence suggests that the constant of gravity did not change in this way. This huge number remains a mystery to this day.

Einstein had to modify the laws of gravity in accordance with the principles of relativity. The first of these principles says that the distance x cannot be overcome instantly, while according to Newton's theory, forces act instantly. Einstein had to change Newton's laws. These changes, refinements are very small. One of them is this: since light has energy, energy is equivalent to mass, and all masses attract, light also attracts and, therefore, passing by the Sun, must be deflected. This is how it actually happens. The force of gravity is also slightly modified in Einstein's theory. But this very slight change in the law of gravity is just enough to explain some of the apparent irregularities in Mercury's motion.

Physical phenomena in the microcosm are subject to other laws than phenomena in the world of large scales. The question arises: how does gravity manifest itself in a world of small scales? The quantum theory of gravity will answer it. But there is no quantum theory of gravity yet. People have not yet been very successful in creating a theory of gravity that is fully consistent with quantum mechanical principles and with the uncertainty principle.

Don DeYoung

Gravity (or gravity) keeps us firmly on the ground and allows the earth to revolve around the sun. Thanks to this invisible force, rain falls to the ground, and the water level in the ocean rises and falls every day. Gravity keeps the earth in a spherical shape and also keeps our atmosphere from escaping into space. It would seem that this force of attraction, observed every day, should be well studied by scientists. But no! In many ways, gravity remains the deepest mystery to science. This mysterious power is a wonderful example of how limited modern scientific knowledge is.

What is gravity?

Isaac Newton was interested in this issue as early as 1686 and came to the conclusion that gravity is an attractive force that exists between all objects. He realized that the same force that causes the apple to fall to the ground is in its orbit. In fact, the force of gravity of the Earth causes the Moon to deviate from its straight path by about one millimeter every second during its rotation around the Earth (Figure 1). Newton's Universal Law of Gravity is one of the greatest scientific discoveries of all time.

Gravity is the "string" that keeps objects in orbit

Picture 1. An illustration of the moon's orbit not drawn to scale. In every second, the moon moves about 1 km. Over this distance, it deviates from the straight path by about 1 mm - this is due to the gravitational pull of the Earth (dashed line). The moon constantly seems to fall behind (or around) the earth, just as the planets around the sun also fall.

Gravity is one of the four fundamental forces of nature (Table 1). Note that of the four forces, this force is the weakest, and yet it is dominant relative to large space objects. As Newton showed, the attractive gravitational force between any two masses gets smaller and smaller as the distance between them gets larger and larger, but it never completely reaches zero (see The Design of Gravity).

Therefore, every particle in the entire universe actually attracts every other particle. Unlike the forces of the weak and strong nuclear forces, the force of attraction is long-range (Table 1). Magnetic and electrical interaction forces are also long-range forces, but gravity is unique in that it is both long-range and always attractive, meaning it can never run out (unlike electromagnetism, in which forces can either attract or repel).

Beginning with the great creationist scientist Michael Faraday in 1849, physicists have constantly searched for the hidden connection between the force of gravity and the force of the electromagnetic force. Currently, scientists are trying to combine all four fundamental forces into one equation or the so-called "Theory of Everything", but, without success! Gravity remains the most mysterious and least understood force.

Gravity cannot be shielded in any way. Whatever the composition of the barrier, it has no effect on the attraction between two separated objects. This means that in the laboratory it is impossible to create an anti-gravity chamber. The force of gravity does not depend on chemical composition objects, but depends on their mass, known to us as weight (the force of gravity on an object is equal to the weight of that object - the greater the mass, the greater the force or weight.) Blocks made of glass, lead, ice, or even styrofoam, and having the same mass , will experience (and exert) the same gravitational force. These data were obtained during experiments, and scientists still do not know how they can be theoretically explained.

Design in Gravity

The force F between two masses m 1 and m 2 located at a distance r can be written as the formula F = (G m 1 m 2) / r 2

Where G is the gravitational constant, first measured by Henry Cavendish in 1798.1

This equation shows that gravity decreases as the distance, r, between two objects gets larger, but never fully reaches zero.

The inverse-square nature of this equation is simply breathtaking. After all, there is no necessary reason why gravity should act in this way. In a disordered, random, and evolving universe, such arbitrary degrees, like r 1.97 or r 2.3 would seem more likely. However, accurate measurements showed an exact power to at least five decimal places, 2.00000. As one researcher said, this result seems "too precise".2 We can conclude that the force of attraction indicates an accurate, created design. In fact, if the degree were to deviate even slightly from 2, the orbits of the planets and the entire universe would become unstable.

Links and notes

1. Technically speaking, G = 6.672 x 10 –11 Nm 2 kg –2
2. Thompsen, D., "Very accurate about gravity", science news 118(1):13, 1980.

So what exactly is gravity? How is this force able to act in such a vast, empty outer space? And why does it even exist? Science has never been able to answer these basic questions about the laws of nature. Attractive power cannot come slowly through mutations or natural selection. It has been active since the very beginning of the existence of the universe. Like any other physical law, gravity is undoubtedly a wonderful evidence of a planned creation.

Some scientists have tried to explain gravity in terms of invisible particles, gravitons, that move between objects. Others talked about cosmic strings and gravitational waves. Recently, scientists with the help of a specially created laboratory LIGO (Eng. Laser Interferometer Gravitational-Wave Observatory) only managed to see the effect of gravitational waves. But the nature of these waves, how physically objects interact with each other at great distances, changing their shape, still remains a big question for everyone. We simply do not know the nature of the origin of the force of gravity and how it holds the stability of the entire universe.

Gravity and Scripture

Two passages from the Bible can help us understand the nature of gravity and physical science in general. The first passage, Colossians 1:17, explains that Christ “There is first of all, and everything is worth it to Him”. The Greek verb stands (συνισταω sunistao) means: to cling to, to be kept or held together. The Greek use of this word outside of the Bible means vessel containing water. The word used in the book of Colossians is in the perfect tense, which usually indicates a present ongoing state that has arisen from a completed past action. One of the physical mechanisms used in question is obviously the force of attraction, established by the Creator and unmistakably maintained today. Just imagine: if the force of gravity ceased to act for a moment, chaos would undoubtedly ensue. All celestial bodies, including the earth, moon, and stars, would no longer be held together. All that hour would be divided into separate, small parts.

The second Scripture, Hebrews 1:3, declares that Christ "holds all things with the word of his power." Word keeps (φερω pherō) again describes the maintenance or conservation of everything, including gravity. Word keeps used in this verse means much more than just holding a weight. It includes control over all ongoing movements and changes within the universe. This endless task is carried out through the almighty Word of the Lord, through which the universe itself came into being. Gravity, the "mysterious force" that remains poorly understood even after four hundred years of research, is one of the manifestations of this amazing divine care for the universe.

Distortions of time and space and black holes

Einstein's general theory of relativity considers gravity not as a force, but as a curvature of space itself near a massive object. Light, which traditionally follows straight lines, is predicted to bend as it travels through curved space. This was first demonstrated when astronomer Sir Arthur Eddington discovered a change in the apparent position of a star during a total eclipse in 1919, believing that light rays were bent by the sun's gravity.

General relativity also predicts that if a body is dense enough, its gravity will distort space so much that light cannot pass through it at all. Such a body absorbs light and everything else that its strong gravity has captured, and is called a Black Hole. Such a body can only be detected by its gravitational effects on other objects, by the strong curvature of light around it, and by the strong radiation emitted by matter that falls on it.

All matter inside a black hole is compressed at the center, which has infinite density. The "size" of the hole is determined by the event horizon, i.e. a boundary that surrounds the center of a black hole, and nothing (not even light) can escape from it. The radius of the hole is called the Schwarzschild radius, after the German astronomer Karl Schwarzschild (1873–1916), and is calculated as R S = 2GM/c 2 , where c is the speed of light in a vacuum. If the sun were to fall into a black hole, its Schwarzschild radius would be only 3 km.

There is solid evidence that once the nuclear fuel of a massive star runs out, it can no longer resist collapsing under its own enormous weight and falls into a black hole. It is believed that black holes with a mass of billions of suns exist at the centers of galaxies, including our galaxy, Milky Way. Many scientists believe that super-bright and very distant objects called quasars use the energy that is released when matter falls into a black hole.

According to the predictions of general relativity, gravity also distorts time. This has also been confirmed by very accurate atomic clocks, which run a few microseconds slower at sea level than in areas above sea level, where Earth's gravity is slightly weaker. Near the event horizon, this phenomenon is more noticeable. If we watch the clock of an astronaut who is approaching the event horizon, we will see that the clock is running slower. While in the event horizon, the clock will stop, but we will never be able to see it. Conversely, the astronaut will not notice that his clock is running slower, but he will see that our clock is running faster and faster.

The main danger to an astronaut near a black hole would be tidal forces, caused by gravity being stronger on parts of the body that are closer to the black hole than on parts further away from it. In terms of their power, the tidal forces near a black hole that has the mass of a star are stronger than any hurricane and easily tear into small pieces everything that comes across to them. However, while gravitational attraction decreases with the square of distance (1/r 2), tidal activity decreases with the cube of distance (1/r 3). Therefore, contrary to popular belief, the gravitational force (including tidal force) is weaker on the event horizons of large black holes than on small black holes. So tidal forces at the event horizon of a black hole in observable space would be less noticeable than the gentlest breeze.

Time dilation by gravity near the event horizon is the basis of a new cosmological model creationist physicist Dr. Russell Humphreys, whom he talks about in his book Starlight and Time. This model may help solve the problem of how we can see the light of distant stars in a young universe. In addition, today it is a scientific alternative to the non-biblical one, which is based on philosophical assumptions that go beyond the scope of science.

Note

Gravity, the "mysterious force" that, even after four hundred years of research, remains poorly understood...

Isaac Newton (1642–1727)

Photo: Wikipedia.org

Isaac Newton (1642–1727)

Isaac Newton published his discoveries about gravity and the motion of celestial bodies in 1687, in his famous work " Mathematical beginnings". Some readers quickly concluded that Newton's universe left no room for God, since everything can now be explained with equations. But Newton did not think so at all, as he said in the second edition of this famous work:

"Our most beautiful solar system, planets and comets can only be the result of the plan and domination of an intelligent and strong being."

Isaac Newton was not only a scientist. In addition to science, he devoted almost his entire life to the study of the Bible. His favorite Bible books were Daniel and Revelation, which describe God's plans for the future. In fact, Newton wrote more theological works than scientific ones.

Newton was respectful of other scientists such as Galileo Galilei. By the way, Newton was born in the same year that Galileo died, in 1642. Newton wrote in his letter: “If I saw further than others, it was because I stood on shoulders giants." Shortly before his death, probably reflecting on the mystery of gravity, Newton modestly wrote: “I don’t know how the world perceives me, but to myself I seem to be only a boy playing on the seashore, who amuses himself by looking for a pebble more colorful than others, or a beautiful shell, while a huge ocean of unexplored truth."

Newton is buried in Westminster Abbey. The Latin inscription on his tomb ends with the words: “Let mortals rejoice that such an ornament of the human race lived among them”.

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

So, Galileo argued that all bodies released from a certain height near the surface of the Earth will fall with the same acceleration g (if air resistance is neglected). The force causing this acceleration is called gravity. Let us apply Newton's second law to the force of gravity, considering as acceleration a acceleration of gravity g . Thus, the force of gravity acting on the body can be written as:

F g =mg

This force is directed downward towards the center of the Earth.

Because in SI system g = 9.8 , then the force of gravity acting on a body with a mass of 1 kg is.

We apply the formula of the law of universal gravitation to describe the force of gravity - the force of gravity between the earth and a body located on its surface. Then m 1 will be replaced by the mass of the Earth m 3 , and r - by the distance to the center of the Earth, i.e. to the Earth's radius r 3 . Thus we get:

Where m is the mass of a body located on the surface of the Earth. From this equality it follows that:

In other words, the acceleration of free fall on the surface of the earth g is determined by the values ​​m 3 and r 3 .

On the Moon, on other planets, or in outer space, the force of gravity acting on a body of the same mass will be different. For example, on the Moon the value g represents only one-sixth g on Earth, and a body of mass 1 kg is affected by a force of gravity equal to only 1.7 N.

Until the gravitational constant G was measured, the mass of the Earth remained unknown. And only after G was measured, using the ratio, it was possible to calculate the mass of the earth. This was first done by Henry Cavendish himself. Substituting in the formula the acceleration of free fall the value g=9.8m/s and the radius of the earth r z =6.3810 6 we obtain the following value of the mass of the Earth:

For the gravitational force acting on bodies near the surface of the Earth, one can simply use the expression mg. If it is necessary to calculate the force of attraction acting on a body located at some distance from the Earth, or the force caused by another celestial body (for example, the Moon or another planet), then the value of g should be used, calculated using the well-known formula, in which r 3 and m 3 must be replaced by the corresponding distance and mass, you can also directly use the formula of the law of universal gravitation. There are several methods for determining the acceleration due to gravity very accurately. One can find g simply by weighing a standard weight on a spring balance. Geological scales must be amazing - their spring changes tension when a load of less than a millionth of a gram is added. Excellent results are given by torsion quartz balances. Their device is, in principle, simple. A lever is welded to a horizontally stretched quartz filament, with the weight of which the filament is slightly twisted:

The pendulum is also used for the same purpose. Until recently, pendulum methods for measuring g were the only ones, and only in the 60s - 70s. They began to be replaced by more convenient and accurate weight methods. In any case, by measuring the period of oscillation of a mathematical pendulum, the formula can be used to find the value of g quite accurately. By measuring the value of g in different places on the same instrument, one can judge the relative changes in the force of gravity with an accuracy of parts per million.

The values ​​of the gravitational acceleration g at different points on the Earth are slightly different. From the formula g = Gm 3 it can be seen that the value of g must be smaller, for example, at the tops of mountains than at sea level, since the distance from the center of the Earth to the top of the mountain is somewhat greater. Indeed, this fact was established experimentally. However, the formula g=Gm 3 /r 3 2 does not give an exact value of g at all points, since the surface of the earth is not exactly spherical: not only do mountains and seas exist on its surface, but there is also a change in the radius of the Earth at the equator; in addition, the mass of the earth is not uniformly distributed; The rotation of the Earth also affects the change in g.

However, the properties of gravitational acceleration turned out to be more complicated than Galileo thought. Find out that the magnitude of the acceleration depends on the latitude at which it is measured:

The magnitude of the free fall acceleration also varies with height above the Earth's surface:

The gravitational acceleration vector is always directed vertically down, but along a plumb line at a given location on the Earth.

Thus, at the same latitude and at the same height above sea level, the acceleration of gravity should be the same. Accurate measurements show that very often there are deviations from this norm - gravity anomalies. The reason for the anomalies is the inhomogeneous mass distribution near the measurement site.

As already mentioned, the gravitational force from the side of a large body can be represented as the sum of the forces acting from the individual particles of a large body. The attraction of the pendulum by the Earth is the result of the action of all particles of the Earth on it. But it is clear that close particles make the greatest contribution to the total force - after all, attraction is inversely proportional to the square of the distance.

If heavy masses are concentrated near the place of measurement, g will be greater than the norm, otherwise g is less than the norm.

If, for example, g is measured on a mountain or on an airplane flying over the sea at the height of a mountain, then in the first case a large figure will be obtained. Also above the norm is the value of g on secluded oceanic islands. It is clear that in both cases the increase in g is explained by the concentration of additional masses at the place of measurement.

Not only the value of g, but also the direction of gravity can deviate from the norm. If you hang a load on a thread, then the elongated thread will show the vertical for this place. This vertical may deviate from the norm. The “normal” direction of the vertical is known to geologists from special maps, on which the “ideal” figure of the Earth is built according to the data on the values ​​of g.

Let's make an experiment with a plumb line at the foot of a large mountain. The weight of a plumb line is attracted by the Earth to its center and by the mountain - to the side. The plumb line must deviate under such conditions from the direction of the normal vertical. Since the mass of the Earth is much greater than the mass of the mountain, such deviations do not exceed a few arcseconds.

The “normal” vertical is determined by the stars, since for any geographic point it has been calculated at which place in the sky at a given moment of the day and year the vertical of the “ideal” figure of the Earth “rests”.

Plumb line deviations sometimes lead to strange results. For example, in Florence, the influence of the Apennines leads not to attraction, but to repulsion of the plumb line. There can be only one explanation: there are huge voids in the mountains.

A remarkable result is obtained by measuring the acceleration of gravity on the scale of continents and oceans. The continents are much heavier than the oceans, so it would seem that the g values ​​over the continents should be larger. Than over the oceans. In reality, the values ​​of g, along the same latitude over the oceans and continents, are on average the same.

Again, there is only one explanation: the continents rest on lighter rocks, and the oceans on heavier ones. Indeed, where direct exploration is possible, geologists establish that the oceans rest on heavy basalt rocks, and the continents on light granites.

But the following question immediately arises: why do heavy and light rocks exactly compensate for the difference in weights between continents and oceans? Such compensation cannot be a matter of chance; its causes must be rooted in the structure of the Earth's shell.

Geologists believe that the upper parts of the earth's crust seem to float on the underlying plastic, that is, easily deformable mass. The pressure at depths of about 100 km should be the same everywhere, just as the pressure at the bottom of a vessel with water, in which pieces of wood of different weights float, is the same. Therefore, a column of matter with an area of ​​1 m 2 from the surface to a depth of 100 km should have the same weight both under the ocean and under the continents.

This equalization of pressures (it is called isostasy) leads to the fact that over the oceans and continents along the same latitude line, the value of the acceleration of gravity g does not differ significantly. Local gravity anomalies serve geological exploration, the purpose of which is to find deposits of minerals underground, without digging holes, without digging mines.

Heavy ore must be sought in those places where g is greatest. On the contrary, deposits of light salt are detected by locally underestimated values ​​of g. You can measure g to the nearest millionth of 1 m/s 2 .

Reconnaissance methods using pendulums and ultra-precise scales are called gravitational. They are of great practical importance, in particular for the search for oil. The fact is that with gravity methods of exploration it is easy to detect underground salt domes, and very often it turns out that where there is salt, there is also oil. Moreover, oil lies in the depths, and salt is closer to the earth's surface. Oil was discovered by gravity exploration in Kazakhstan and elsewhere.

Instead of pulling the cart with a spring, it can be given acceleration by attaching a cord thrown over the pulley, from the opposite end of which a load is suspended. Then the force imparting acceleration will be due to weighing this cargo. The free fall acceleration is again imparted to the body by its weight.

In physics, weight is the official name for the force that is caused by the attraction of objects to the earth's surface - "the attraction of gravity." The fact that bodies are attracted toward the center of the earth makes this explanation reasonable.

However you define it, weight is a force. It is no different from any other force, except for two features: the weight is directed vertically and acts constantly, it cannot be eliminated.

In order to directly measure the weight of a body, we must use a spring balance calibrated in units of force. Since this is often inconvenient, we compare one weight with another using a balance scale, i.e. find the relation:

EARTH GRAVITY ACTING ON BODY X EARTH ATTRACTION AFFECTING THE STANDARD OF MASS

Suppose that the body X is attracted 3 times stronger than the mass standard. In this case, we say that the earth's gravity acting on body X is 30 newtons of force, which means that it is 3 times the earth's gravity acting on a kilogram of mass. The concepts of mass and weight are often confused, between which there is a significant difference. Mass is a property of the body itself (it is a measure of inertia or its "amount of matter"). Weight, on the other hand, is the force with which the body acts on the support or stretches the suspension (weight is numerically equal to the force of gravity if the support or suspension does not have acceleration).

If we use a spring scale to measure the weight of an object with very high accuracy, and then transfer the scales to another place, we will find that the weight of the object on the surface of the Earth varies somewhat from place to place. We know that far from the surface of the Earth, or in the depths of the globe, the weight should be much less.

Does the mass change? Scientists, reflecting on this issue, have long come to the conclusion that the mass should remain unchanged. Even at the center of the earth, where gravity, acting in all directions, should produce a net force of zero, the body would still have the same mass.

Thus, the mass, measured by the difficulty we encounter in trying to accelerate the movement of a small cart, is the same everywhere: on the surface of the Earth, in the center of the Earth, on the Moon. Weight estimated from the extension of the spring balance (and feel

in the muscles of the hand of a person holding a scale) will be much less on the Moon and almost zero at the center of the Earth. (fig.7)

How great is the earth's gravity acting on different masses? How to compare the weights of two objects? Let's take two identical pieces of lead, say, 1 kg each. The earth attracts each of them with the same force, equal to the weight of 10 N. If you combine both pieces of 2 kg, then the vertical forces simply add up: the Earth attracts 2 kg twice as much as 1 kg. We will get exactly the same doubled attraction if we fuse both pieces into one or place them one on top of the other. The gravitational pulls of any homogeneous material simply add up, and there is no absorption or shielding of one piece of matter by another.

For any homogeneous material, weight is proportional to mass. Therefore, we believe that the Earth is the source of the “gravity field” emanating from its center vertically and capable of attracting any piece of matter. The gravity field acts the same way on, say, every kilogram of lead. But what about the attractive forces acting on the same masses of different materials, for example, 1 kg of lead and 1 kg of aluminum? The meaning of this question depends on what is meant by equal masses. The simplest way to compare masses, which is used in scientific research and in commercial practice, is the use of a balance scale. They compare the forces that pull both loads. But given in this way the same masses of, say, lead and aluminum, we can assume that equal weights have equal masses. But in fact, here we are talking about two completely different types of mass - inertial and gravitational mass.

Quantity in the formula Represents an inertial mass. In experiments with trolleys, which are accelerated by a spring, the value acts as a characteristic of the "heaviness of the substance" showing how difficult it is to impart acceleration to the body under consideration. The quantitative characteristic is the ratio. This mass is a measure of inertia, the tendency of mechanical systems to resist a change of state. Mass is a property that must be the same near the surface of the Earth, and on the Moon, and in deep space, and in the center of the Earth. What is its connection with gravity and what actually happens when weighing?

Quite independently of the inertial mass, one can introduce the concept of gravitational mass as the amount of matter attracted by the Earth.

We believe that the Earth's gravitational field is the same for all objects in it, but we attribute to various

metam different masses, which are proportional to the attraction of these objects by the field. This is the gravitational mass. We say that different objects have different weights because they have different gravitational masses that are attracted by the gravitational field. Thus, gravitational masses are, by definition, proportional to the weights as well as the force of gravity. The gravitational mass determines with what force the body is attracted by the Earth. At the same time, gravity is mutual: if the Earth attracts a stone, then the stone also attracts the Earth. This means that the gravitational mass of a body also determines how strongly it attracts another body, the Earth. Thus, the gravitational mass measures the amount of matter on which the earth's gravity acts, or the amount of matter that causes gravitational attraction between bodies.

The gravitational attraction acts on two identical pieces of lead twice as much as on one. The gravitational masses of the lead pieces must be proportional to the inertial masses, since the masses of both are obviously proportional to the number of lead atoms. The same applies to pieces of any other material, say wax, but how does a piece of lead compare to a piece of wax? The answer to this question is given by a symbolic experiment on the study of the fall of bodies of various sizes from the top of the inclined Leaning Tower of Pisa, the one that, according to legend, was performed by Galileo. Drop two pieces of any material of any size. They fall with the same acceleration g. The force acting on a body and giving it acceleration6 is the attraction of the Earth applied to this body. The force of attraction of bodies by the Earth is proportional to the gravitational mass. But gravity imparts the same acceleration g to all bodies. Therefore, gravity, like weight, must be proportional to the inertial mass. Therefore, bodies of any shape contain the same proportions of both masses.

If we take 1 kg as a unit of both masses, then the gravitational and inertial masses will be the same for all bodies of any size from any material and in any place.

Here's how it's proven. Let us compare the kilogram standard made of platinum6 with a stone of unknown mass. Let's compare their inertial masses by moving each of the bodies in turn in a horizontal direction under the action of some force and measuring the acceleration. Assume that the mass of the stone is 5.31 kg. Earth's gravity is not involved in this comparison. Then we compare the gravitational masses of both bodies by measuring the gravitational attraction between each of them and some third body, most simply the Earth. This can be done by weighing both bodies. We will see that the gravitational mass of the stone is also 5.31 kg.

More than half a century before Newton proposed his law of universal gravitation, Johannes Kepler (1571-1630) discovered that “the intricate motion of the planets in the solar system could be described by three simple laws. Kepler's laws reinforced faith in the Copernican hypothesis that the planets revolve around the sun as well.

To assert at the beginning of the 17th century that the planets are around the Sun and not around the Earth was the greatest heresy. Giordano Bruno, who openly defended the Copernican system, was condemned as a heretic by the Holy Inquisition and burned at the stake. Even the great Gallileo, despite his close friendship with the Pope, was imprisoned, condemned by the Inquisition and forced to publicly renounce his views.

In those days, the teachings of Aristotle and Ptolemy were considered sacred and inviolable, saying that the orbits of the planets arise as a result of complex movements along a system of circles. So to describe the orbit of Mars, a dozen or so circles of various diameters were required. Johannes Kepler set the task of "proving" that Mars and the Earth must revolve around the Sun. He was trying to find an orbit of the simplest geometric shape, which would exactly match the numerous measurements of the planet's position. Years of tedious calculations passed before Kepler was able to formulate three simple laws that very accurately describe the motion of all planets:

First law: Each planet moves in an ellipse

one of the focuses of which is

Second law: Radius vector (the line connecting the Sun

and the planet) describes at equal intervals

time equal areas

Third law: The squares of the periods of the planets

proportional to the cubes of their means

distances from the sun:

R 1 3 /T 1 2 = R 2 3 /T 2 2

The significance of Kepler's works is enormous. He discovered the laws that Newton then connected with the law of universal gravitation. Of course, Kepler himself did not realize what his discoveries would lead to. "He was engaged in tedious hints of empirical rules, which in the future Newton was supposed to lead to a rational form." Kepler could not explain why the existence of elliptical orbits, but admired the fact that they exist.

On the basis of Kepler's third law, Newton concluded that the forces of attraction must decrease with increasing distance, and that attraction must change as (distance) -2. By discovering the law of universal gravitation, Newton transferred the simple idea of ​​the motion of the moon to the entire planetary system. He showed that attraction, according to the laws he derived, determines the movement of the planets in elliptical orbits, and the Sun should be in one of the foci of the ellipse. He was able to easily derive two other laws of Kepler, which also follow from his hypothesis of universal gravitation. These laws are valid if only the attraction of the Sun is taken into account. But one must also take into account the effect of other planets on a moving planet, although in solar system these attractions are small compared to the attraction of the Sun.

Kepler's second law follows from the arbitrary dependence of the force of attraction on distance, if this force acts along a straight line connecting the centers of the planet and the Sun. But Kepler's first and third laws are satisfied only by the law of inverse proportionality of the forces of attraction to the square of the distance.

To get Kepler's third law, Newton simply combined the laws of motion with the law of universal gravitation. For the case of circular orbits, one can argue as follows: let a planet with a mass equal to m moves with a speed v along a circle of radius R around the Sun, whose mass is equal to M. This movement can be carried out only if an external force acts on the planet F = mv 2 /R, which creates a centripetal acceleration v 2 /R. Suppose that the attraction between the Sun and the planet just creates the necessary force. Then:

GMm/r 2 = mv 2 /R

and the distance r between m and M is equal to the radius of the orbit R. But the speed

where T is the time it takes the planet to make one revolution. Then

To get Kepler's third law, you need to move all R and T to one side of the equation, and all other quantities to the other:

R 3 /T 2 \u003d GM / 4 2

If we now pass to another planet with a different orbital radius and period of revolution, then the new ratio will again be equal to GM/4 2 ; this value will be the same for all planets, since G is a universal constant, and the mass M is the same for all planets revolving around the Sun. Thus, the value of R 3 /T 2 will be the same for all planets in accordance with Kepler's third law. This calculation allows you to get the third law for elliptical orbits, but in this case R is the average value between the largest and smallest distance of the planet from the Sun.

Armed with powerful mathematical methods and guided by excellent intuition, Newton applied his theory to a large number of problems included in his PRINCIPLES concerning the features of the Moon, the Earth, other planets and their movement, as well as other celestial bodies: satellites, comets.

The moon experiences numerous perturbations that deviate it from a uniform circular motion. First of all, it moves along a Keplerian ellipse, in one of the focuses of which is the Earth, like any satellite. But this orbit experiences small variations due to the attraction of the Sun. At the new moon, the moon is closer to the sun than the full moon, which appears two weeks later; this cause changes the attraction, which leads to slowing down and speeding up the movement of the moon during the month. This effect increases when the Sun is closer in winter, so that annual variations in the speed of the Moon are also observed. In addition, changes in solar attraction change the ellipticity of the lunar orbit; the lunar orbit deviates up and down, the plane of the orbit slowly rotates. Thus, Newton showed that the noted irregularities in the motion of the Moon are caused by universal gravitation. He did not develop the problem of solar attraction in all details, the motion of the Moon remained a complex problem, which is being developed with increasing detail to this day.

Ocean tides have long remained a mystery, which, it would seem, could be explained by establishing their connection with the movement of the moon. However, people believed that such a connection could not really exist, and even Galileo ridiculed this idea. Newton showed that the ebb and flow of the tide is due to the uneven attraction of water in the ocean from the side of the moon. The center of the lunar orbit does not coincide with the center of the Earth. The Moon and Earth together revolve around their common center of mass. This center of mass is located at a distance of about 4800 km from the center of the Earth, only 1600 km from the Earth's surface. When the Earth pulls on the Moon, the Moon pulls on the Earth with an equal and opposite force, due to which the force Mv 2 /r arises, causing the Earth to move around a common center of mass with a period equal to one month. The part of the ocean closest to the Moon is attracted more strongly (it is closer), the water rises - and a tide arises. The part of the ocean located at a greater distance from the Moon is attracted weaker than the land, and in this part of the ocean a water hump also rises. Therefore, there are two high tides in 24 hours. The sun also causes tides, although not so strong, because a large distance from the sun smooths out the unevenness of attraction.

Newton revealed the nature of comets - these guests of the solar system, which have always aroused interest and even sacred horror. Newton showed that comets move in very elongated elliptical orbits, with the Sun at the water focus. Their movement is determined, like the movement of the planets, by gravity. But they have a very small magnitude, so that they can only be seen when they pass close to the Sun. The comet's elliptical orbit can be measured, and the time of its return to our region can be accurately predicted. Their regular return at predicted dates allows us to verify our observations and provides yet another confirmation of the law of universal gravitation.

In some cases, the comet experiences a strong gravitational perturbation, passing near large planets, and moves to a new orbit with a different period. That is why we know that comets have little mass: the planets affect their motion, and comets do not affect the motion of the planets, although they act on them with the same force.

Comets move so fast and come so rarely that even today scientists are waiting for the moment when modern means can be applied to the study of a large comet.

If you think about what role gravity forces play in the life of our planet, then whole oceans of phenomena open up, and even oceans in the literal sense of the word: oceans of water, oceans of air. Without gravity, they would not exist.

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 on the lookout for scientific discoveries- this is not an instant insight, but the fruit of a long 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 unit mass are at a distance equal to a unit of distance, then they attract 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 the force of gravity, which is gravitational force, depends on the mass and radius of the planet, then 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's 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.

To the question "What is power?" 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 attributed to 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, the most widespread type of these interactions in nature.

Let's start with the attraction of the earth

Everyone living knows that there is a force that pulls objects to the ground. It is commonly referred to as gravity, gravity, or terrestrial attraction. Due to its presence, a person has 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 action at any, both the smallest and very large, even by cosmic standards, distances.

Gravity and Newton's third law

As you know, 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 another body with the same force. Thus, 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 forces of attraction from the Sun and other planets at once. 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 their trajectories.

What 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, until the 16th century, it was believed that the opposite was true - heavier bodies should fall faster than light ones. To dispel this misconception, Galileo Galilei had to perform his famous experiment of simultaneously dropping two cannonballs of different weights from the inclined Leaning Tower of Pisa. Contrary to the expectations of the witnesses of the experiment, both nuclei reached the surface at the same time. Today, every schoolchild knows that this happened due to the fact that gravity gives any body the same free fall acceleration g = 9.81 m / s 2, regardless of the mass m of this body, and its value, according to Newton's second law, is F = mg.

Gravitational forces on the Moon and other planets are different meanings 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 side of supports and suspensions. Gravitational forces applied to the same bodies act towards them.

Imagine a weight suspended above the ground on a spring. Two forces are applied to it: the elastic force of a 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 strength will be its weight. For a load weighing 1 kg, the weight is P \u003d 1 kg ∙ 9.81 m / s 2 \u003d 9.81 N (newton).

Gravitational forces: definition

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

• F \u003d Gm 1 m 2 / r 2,
  where G is the constant of proportionality, the gravitational constant.

The physical mechanism of gravity

Newton was not completely satisfied with his theory, since it involved interaction between gravitating bodies at a distance. The great Englishman himself was convinced that there must be some physical agent responsible for transferring the action of one body to another, about which he spoke quite clearly in one of his letters. But the time when the concept of a gravitational field was introduced, which permeates all space, came only after four centuries. Today, speaking of 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 in celestial mechanics during the 18th and early XIX century. For example, mathematicians D. Adams and W. Le Verrier, analyzing the violations of the orbit of Uranus, suggested that gravitational forces of interaction with a still unknown planet act on it. They indicated its supposed position, and soon the astronomer I. Galle discovered Neptune there.

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

It was not until 1915 that Albert Einstein was able to explain this inconsistency in terms 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 the planets, but Mercury, as the smallest and closest planet to our star, they manifest themselves most strongly.

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 the force F applied to a body with mass m gives an 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 another body interacting with the one under consideration (of the earth, usually when we talk about gravity). In both equations, m is a proportionality factor, but in the first case it is inertial mass, and in the second it is gravitational, 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 was able to construct the equations of the gravitational field, the famous Einstein equations, and with their help calculate the correct value for the precession of Mercury's orbit. They also give a measured value for the deflection of light rays that pass near the Sun, and there is no doubt that the correct results for macroscopic gravity follow from them. Einstein's theory of gravity, or general relativity (GR) as he called it, is one of the greatest triumphs of modern science.

Gravitational forces are acceleration?

If you cannot distinguish between inertial mass and gravitational mass, then you cannot distinguish between gravity and acceleration. An experiment in a gravitational field can instead be performed in a rapidly moving elevator in the absence of gravity. When an astronaut in a rocket accelerates, moving away from the earth, he experiences a force of gravity that is several times greater than that of the earth, and the vast majority of it comes 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 near-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 Moon example, the gravitational field changes direction from one point to another.) The principle that one can always find an inertial frame at any point in space and time in which physics obeys the laws in the absence of gravity is called the principle of equivalence.

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

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

We say that space-time 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 the body moves in this curved space along a geodesic line, which 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.