Gravitational force drawing. Gravitational forces: definition, formula, types

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 the chemical composition of 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, arbitrary powers such as 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

Technically speaking, G = 6.672 x 10 –11 Nm 2 kg –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. The force of attraction cannot come slowly through mutation 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 existence. 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. Black holes with a mass of billions of suns are believed to exist at the centers of galaxies, including our galaxy, the 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.

The dilation of time by gravity near the event horizon is the basis of the new cosmological model created by creation physicist Dr. Russell Humphries, which he discusses 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”.

We all went through the law of universal gravitation in school. But what do we really know about gravity, apart from the information put into our heads by school teachers? Let's refresh our knowledge...

Fact one: Newton did not discover the law of universal gravitation

Everyone knows the famous parable of the apple that fell on Newton's head. But the fact is that Newton did not discover the law of universal gravitation, since this law is simply absent in his book "Mathematical Principles of Natural Philosophy". In this work there is neither a formula nor a formulation, which everyone can see for himself. Moreover, the first mention of the gravitational constant appears only in the 19th century and, accordingly, the formula could not have appeared earlier. By the way, the coefficient G, which reduces the result of calculations by 600 billion times, has no physical meaning, and was introduced to hide contradictions.

Fact Two: Faking the Gravitational Attraction Experiment

It is believed that Cavendish was the first to demonstrate gravitational attraction in laboratory blanks, using a torsion balance - a horizontal rocker with weights at the ends suspended on a thin string. The rocker could turn on a thin wire. According to the official version, Cavendish brought a pair of 158 kg discs to the weights of the rocker from opposite sides and the rocker turned at a small angle. However, the methodology of the experiment was incorrect and the results were falsified, which was convincingly proven by the physicist Andrei Albertovich Grishaev. Cavendish spent a long time reworking and adjusting the installation so that the results fit Newton's average density of the earth. The methodology of the experiment itself provided for the movement of the blanks several times, and the reason for the rotation of the rocker was the microvibrations from the movement of the blanks, which were transmitted to the suspension.

This is confirmed by the fact that such a simple installation of the 18th century for educational purposes should have been, if not in every school, then at least in the physics departments of universities, in order to show students in practice the result of the law of universal gravitation. However, the Cavendish setting is not used in the curriculum, and schoolchildren and students take their word for it that two discs attract each other.

Fact three: The law of universal gravitation does not work during a solar eclipse

If we substitute reference data for the earth, moon and sun into the formula for the law of universal gravitation, then at the moment when the moon flies between the earth and the sun, for example, at the time of a solar eclipse, the force of attraction between the sun and the moon is more than 2 times higher than between Earth and Moon!

According to the formula, the moon would have to leave the orbit of the earth and begin to revolve around the sun.

Gravitational constant - 6.6725×10−11 m³/(kg s²).
The mass of the moon is 7.3477 × 1022 kg.
The mass of the Sun is 1.9891 × 1030 kg.
The mass of the Earth is 5.9737 × 1024 kg.
The distance between the Earth and the Moon = 380,000,000 m.
Distance between the Moon and the Sun = 149,000,000,000 m.

Earth and Moon:
6.6725×10-11 x 7.3477×1022 x 5.9737×1024 / 3800000002 = 2.028×1020 H
Moon and sun:
6.6725 x 10-11 x 7.3477 x 1022 x 1.9891 x 1030 / 1490000000002 = 4.39 x 1020 H

2.028×1020H<< 4,39×1020 H
The force of attraction between the earth and the moon<< Сила притяжения между Луной и Солнцем

These calculations can be criticized by the fact that the moon is an artificial hollow body and the reference density of this celestial body is most likely not determined correctly.

Indeed, experimental evidence suggests that the Moon is not a solid body, but a thin-walled shell. The authoritative journal Science describes the results of seismic sensors after the third stage of the Apollo 13 rocket hit the surface of the Moon: “The seismic call was detected for more than four hours. On Earth, if a rocket hit at an equivalent distance, the signal would only last a few minutes.”

Seismic vibrations that decay so slowly are typical of a hollow resonator, not a solid body.
But the Moon, among other things, does not show its attractive properties with respect to the Earth - the Earth-Moon pair does not move around a common center of mass, as it would be according to the law of universal gravitation, and the Earth's ellipsoidal orbit, contrary to this law, does not become zigzag.

Moreover, the parameters of the orbit of the Moon itself do not remain constant, the orbit "evolves" in scientific terminology, and it does this contrary to the law of universal gravitation.

Fact four: the absurdity of the theory of ebbs and flows

How is it, some will object, because even schoolchildren know about the ocean tides on Earth, which occur due to the attraction of water to the Sun and Moon.

According to the theory, the gravity of the Moon forms a tidal ellipsoid in the ocean, with two tidal humps, which, due to daily rotation, move along the surface of the Earth.

However, practice shows the absurdity of these theories. After all, according to them, a tidal hump 1 meter high in 6 hours should move through the Drake Strait from the Pacific to the Atlantic. Since water is incompressible, a mass of water would raise the level to a height of about 10 meters, which does not happen in practice. In practice, tidal phenomena occur autonomously in areas of 1000-2000 km.

Laplace was also amazed by the paradox: why in the seaports of France high water sets in sequentially, although, according to the concept of a tidal ellipsoid, it should come there simultaneously.

Fact Five: The Theory of Mass Gravity Doesn't Work

The principle of gravity measurements is simple - gravimeters measure the vertical components, and the deviation of the plumb line shows the horizontal components.

The first attempt to test the theory of mass gravitation was made by the British in the middle of the 18th century on the coast of the Indian Ocean, where, on the one hand, there is the world's highest stone ridge of the Himalayas, and on the other, an ocean bowl filled with much less massive water. But, alas, the plumb line does not deviate towards the Himalayas! Moreover, ultra-sensitive instruments - gravimeters - do not detect a difference in the gravity of a test body at the same height both over massive mountains and over less dense seas of a kilometer depth.

To save the accustomed theory, scientists came up with a support for it: they say the reason for this is “isostasis” - denser rocks are located under the seas, and loose rocks under the mountains, and their density is exactly the same as to adjust everything to the desired value.

It has also been empirically established that gravimeters in deep mines show that gravity does not decrease with depth. It continues to grow, being dependent only on the square of the distance to the center of the earth.

Fact six: gravity is not generated by matter or mass

According to the formula of the law of universal gravitation, Two masses, m1 and m2, whose dimensions can be neglected in comparison with the distances between them, are allegedly attracted to each other by a force directly proportional to the product of these masses and inversely proportional to the square of the distance between them. However, in fact, there is not a single evidence that the substance has a gravitational attraction effect. Practice shows that gravitation is not generated by matter or masses, it is independent of them, and massive bodies only obey gravity.

The independence of gravitation from matter is confirmed by the fact that, with the rarest exception, small bodies of the solar system have no gravitational attraction at all. With the exception of the Moon, more than six dozen satellites of the planets show no signs of their own gravity. This has been proven by both indirect and direct measurements, for example, since 2004, the Cassini probe in the vicinity of Saturn flies close to its satellites from time to time, but no changes in the speed of the probe have been recorded. With the help of the same Cassini, a geyser was discovered on Enceladus, the sixth largest satellite of Saturn.

What physical processes must take place on a cosmic piece of ice in order for steam jets to fly into space?
For the same reason, Titan, Saturn's largest moon, has a gaseous tail as a result of atmospheric sinking.

The satellites predicted by the theory of asteroids have not been found, despite their huge number. And in all reports of double, or paired asteroids, which allegedly revolve around a common center of mass, there was no evidence of the circulation of these pairs. Companions happened to be nearby, moving in quasi-synchronous orbits around the sun.

Attempts to put artificial satellites into orbit of asteroids ended in failure. Examples include the NEAR probe, which was driven to the Eros asteroid by the Americans, or the Hayabusa probe, which the Japanese sent to the Itokawa asteroid.

Fact seven: Saturn's asteroids do not obey the law of universal gravitation

At one time, Lagrange, trying to solve the three-body problem, obtained a stable solution for a particular case. He showed that the third body can move in the orbit of the second, all the time being in one of two points, one of which is ahead of the second body by 60 °, and the second is behind by the same amount.

However, two groups of asteroid companions, found behind and ahead in the orbit of Saturn, and which astronomers joyfully called the Trojans, went out of the predicted areas, and the confirmation of the law of universal gravitation turned into a puncture.

Fact eight: contradiction with the general theory of relativity

According to modern concepts, the speed of light is finite, as a result, we see distant objects not where they are located at the moment, but at the point where the light beam we saw started from. But how fast does gravity travel?

After analyzing the data accumulated by that time, Laplace found that "gravity" propagates faster than light by at least seven orders of magnitude! Modern measurements by receiving pulses from pulsars have pushed the speed of propagation of gravity even further - at least 10 orders of magnitude faster than the speed of light. Thus, experimental studies are in conflict with the general theory of relativity, on which official science still relies, despite its complete failure.

Fact Nine: Gravity Anomalies

There are natural gravity anomalies, which also do not find any intelligible explanation from official science. Here are some examples:

Fact ten: studies of the vibrational nature of antigravity

There are a large number of alternative studies with impressive results in the field of antigravity, which fundamentally refute the theoretical calculations of official science.

Some researchers analyze the vibrational nature of antigravity. This effect is clearly presented in modern experience, where drops hang in the air due to acoustic levitation. Here we see how, with the help of a sound of a certain frequency, it is possible to confidently hold drops of liquid in the air ...

But the effect at first glance is explained by the principle of the gyroscope, but even such a simple experiment for the most part contradicts gravity in its modern sense.

Few people know that Viktor Stepanovich Grebennikov, a Siberian entomologist who studied the effect of cavity structures in insects, described the phenomena of antigravity in insects in his book "My World". Scientists have long known that massive insects, such as the cockchafer, fly against the laws of gravity rather than because of them.

Moreover, based on his research, Grebennikov created an anti-gravity platform.

Viktor Stepanovich died under rather strange circumstances and his achievements were partially lost, however, some part of the prototype of the anti-gravity platform has been preserved and can be seen in the Grebennikov Museum in Novosibirsk.

Another practical application of anti-gravity can be observed in the city of Homestead in Florida, where there is a strange structure of coral monolithic blocks, which the people called the Coral Castle. It was built by a native of Latvia - Edward Lidskalnin in the first half of the 20th century. This man of thin build did not have any tools, did not even have a car and no equipment at all.

It was not used at all by electricity, also due to its absence, and nevertheless somehow descended to the ocean, where it carved multi-ton stone blocks and somehow delivered them to its site, laying them out with perfect accuracy.

After Ed's death, scientists began to carefully study his creation. For the sake of the experiment, a powerful bulldozer was brought in, and an attempt was made to move one of the 30-ton blocks of the coral castle. The bulldozer roared, skidded, but did not move a huge stone.

A strange device was found inside the castle, which scientists called a direct current generator. It was a massive structure with many metal parts. 240 permanent bar magnets were built into the outside of the device. But how Edward Leedskalnin actually made multi-ton blocks move is still a mystery.

The studies of John Searle are known, in whose hands unusual generators came to life, rotated and generated energy; disks with a diameter of half a meter to 10 meters rose into the air and made controlled flights from London to Cornwall and back.

The professor's experiments were repeated in Russia, the USA and Taiwan. In Russia, for example, in 1999, under No. 99122275/09, an application for a patent "device for generating mechanical energy" was registered. Vladimir Vitalievich Roshchin and Sergey Mikhailovich Godin, in fact, reproduced the SEG (Searl Effect Generator) and conducted a series of studies with it. The result was a statement: you can get 7 kW of electricity without spending; the rotating generator lost up to 40% in weight.

Searle's first lab equipment was taken to an unknown destination while he himself was in prison. The installation of Godin and Roshchin simply disappeared; all publications about her, with the exception of the application for an invention, disappeared.

Also known is the Hutchison Effect, named after the Canadian engineer-inventor. The effect is manifested in the levitation of heavy objects, the alloy of dissimilar materials (for example, metal + wood), the anomalous heating of metals in the absence of burning substances near them. Here is a video of these effects:

Whatever gravity really is, it should be recognized that official science is completely incapable of clearly explaining the nature of this phenomenon..

Yaroslav Yargin

First, imagine the Earth as a non-moving ball (Fig. 3.1, a). The gravitational force F between the Earth (mass M) and an object (mass m) is determined by the formula: F=Gmm/r2

where r is the radius of the Earth. The constant G is known as universal gravitational constant and extremely small. When r is constant, the force F is const. m. The attraction of a body of mass m by the Earth determines the weight of this body: W = mg comparison of the equations gives: g = const = GM/r 2 .

The attraction of a body of mass m by the Earth causes it to fall "down" with an acceleration g, which is constant at all points A, B, C and everywhere on the earth's surface (Fig. 3.1.6).

The free body force diagram also shows that there is a force acting on the Earth from the side of a body of mass m, which is directed opposite to the force acting on the body from the Earth. However, the mass M of the Earth is so large that the "upward" acceleration a "of the Earth, calculated by the formula F \u003d Ma", is insignificant and can be neglected. The earth has a shape other than spherical: the radius at the pole r p is less than the radius at the equator r e. This means that the force of attraction of a body with mass m at the pole F p \u003d GMm / r 2 p is greater than at the equator F e = GMm/r e . Therefore, the acceleration of free fall g p at the pole is greater than the acceleration of free fall g e at the equator. The acceleration g changes with latitude in accordance with the change in the radius of the Earth.

As you know, the Earth is in constant motion. It rotates around its axis, making one revolution every day, and moves in orbit around the Sun with a revolution of one year. Taking for simplicity the Earth as a homogeneous ball, let's consider the motion of bodies of mass m on the pole A and on the equator C (Fig. 3.2). In one day, the body at point A rotates 360 °, remaining in place, while the body located at point C covers a distance of 2lg. In order for the body located at point C to move in a circular orbit, some kind of force is needed. This is a centripetal force, which is determined by the formula mv 2 /r, where v is the speed of the body in orbit. The force of gravitational attraction acting on a body located at point C, F = GMm/r must:

a) ensure the movement of the body in a circle;

b) attract the body to the Earth.

Thus, F = (mv 2 /r) + mg at the equator, and F = mg at the pole. This means that g changes with latitude as the radius of the orbit changes from r at C to zero at A.

It is interesting to imagine what would happen if the speed of the Earth's rotation increased so much that the centripetal force acting on the body at the equator would become equal to the force of attraction, i.e. mv 2 / r = F = GMm / r 2 . The total gravitational force would be used solely to keep the body at point C in a circular orbit, and there would be no force left on the surface of the Earth. Any further increase in the speed of the Earth's rotation would allow the body to "float away" into space. At the same time, if a spacecraft with astronauts on board is launched to a height R above the center of the Earth with a speed v, such that the equality mv*/R=F = GMm/R 2 is satisfied, then this spacecraft will rotate around the Earth in conditions of weightlessness.

Precise measurements of the free fall acceleration g show that g varies with latitude, as shown in Table 3.1. It follows from this that the weight of a certain body changes over the surface of the Earth from a maximum at a latitude of 90 ° to a minimum at a latitude of 0 °.

At this level of training, small changes in acceleration g are usually neglected and an average value of 9.81 m-s 2 is used. To simplify calculations, the acceleration g is often taken as the nearest integer, i.e. 10 ms - 2, and, thus, the force of attraction acting from the Earth on a body of mass 1 kg, i.e. weight, taken as 10 N. Most examination boards for examinees suggest using g \u003d 10 m-s - 2 or 10 N-kg -1 in order to simplify calculations.

« Physics - Grade 10 "

Why does the moon move around the earth?
What happens if the moon stops?
Why do the planets revolve around the sun?

In Chapter 1, it was discussed in detail that the globe imparts the same acceleration to all bodies near the surface of the Earth - the acceleration of free fall. But if the globe imparts acceleration to the body, then, according to Newton's second law, it acts on the body with some force. The force with which the earth acts on the body is called gravity. First, let's find this force, and then consider the force of universal gravitation.

Modulo acceleration is determined from Newton's second law:

In the general case, it depends on the force acting on the body and its mass. Since the acceleration of free fall does not depend on the mass, it is clear that the force of gravity must be proportional to the mass:

The physical quantity is the free fall acceleration, it is constant for all bodies.

Based on the formula F = mg, you can specify a simple and practically convenient method for measuring the masses of bodies by comparing the mass of a given body with the standard unit of mass. The ratio of the masses of two bodies is equal to the ratio of the forces of gravity acting on the bodies:

This means that the masses of bodies are the same if the forces of gravity acting on them are the same.

This is the basis for the determination of masses by weighing on a spring or balance scale. By ensuring that the force of pressure of the body on the scales, equal to the force of gravity applied to the body, is balanced by the force of pressure of the weights on the other scales, equal to the force of gravity applied to the weights, we thereby determine the mass of the body.

The force of gravity acting on a given body near the Earth can be considered constant only at a certain latitude near the Earth's surface. If the body is lifted or moved to a place with a different latitude, then the acceleration of free fall, and hence the force of gravity, will change.

The force of gravity.

Newton was the first to rigorously prove that the reason that causes the fall of a stone to the Earth, the movement of the Moon around the Earth and the planets around the Sun, is the same. This gravitational force acting between any bodies of the Universe.

Newton came to the conclusion that if it were not for air resistance, then the trajectory of a stone thrown from a high mountain (Fig. 3.1) with a certain speed could become such that it would never reach the Earth's surface at all, but would move around it like how the planets describe their orbits in the sky.

Newton found this reason and was able to accurately express it in the form of one formula - the law of universal gravitation.

Since the force of universal gravitation imparts the same acceleration to all bodies, regardless of their mass, it must be proportional to the mass of the body on which it acts:

“Gravity exists for all bodies in general and is proportional to the mass of each of them ... all planets gravitate towards each other ...” I. Newton

But since, for example, the Earth acts on the Moon with a force proportional to the mass of the Moon, then the Moon, according to Newton's third law, must act on the Earth with the same force. Moreover, this force must be proportional to the mass of the Earth. If the gravitational force is truly universal, then from the side of a given body any other body must be acted upon by a force proportional to the mass of this other body. Consequently, the force of universal gravitation must be proportional to the product of the masses of the interacting bodies. From this follows the formulation of the law of universal gravitation.

Law of gravity:

The force of mutual attraction of two bodies is directly proportional to the product of the masses of these bodies and inversely proportional to the square of the distance between them:

The proportionality factor G is called gravitational constant.

The gravitational constant is numerically equal to the force of attraction between two material points with a mass of 1 kg each, if the distance between them is 1 m. After all, with masses m 1 \u003d m 2 \u003d 1 kg and a distance r \u003d 1 m, we get G \u003d F (numerically).

It must be kept in mind that the law of universal gravitation (3.4) as a universal law is valid for material points. In this case, the forces of gravitational interaction are directed along the line connecting these points (Fig. 3.2, a).

It can be shown that homogeneous bodies having the shape of a ball (even if they cannot be considered material points, Fig. 3.2, b) also interact with the force defined by formula (3.4). In this case, r is the distance between the centers of the balls. The forces of mutual attraction lie on a straight line passing through the centers of the balls. Such forces are called central. The bodies whose fall to the Earth we usually consider are much smaller than the Earth's radius (R ≈ 6400 km).

Such bodies, regardless of their shape, can be considered as material points and the force of their attraction to the Earth can be determined using the law (3.4), bearing in mind that r is the distance from the given body to the center of the Earth.

A stone thrown to the Earth will deviate under the action of gravity from a straight path and, having described a curved trajectory, will finally fall to the Earth. If you throw it with more speed, it will fall further.” I. Newton

Definition of the gravitational constant.

Now let's find out how you can find the gravitational constant. First of all, note that G has a specific name. This is due to the fact that the units (and, accordingly, the names) of all quantities included in the law of universal gravitation have already been established earlier. The law of gravitation gives a new connection between known quantities with certain names of units. That is why the coefficient turns out to be a named value. Using the formula of the law of universal gravitation, it is easy to find the name of the unit of gravitational constant in SI: N m 2 / kg 2 \u003d m 3 / (kg s 2).

To quantify G, it is necessary to independently determine all the quantities included in the law of universal gravitation: both masses, force and distance between bodies.

The difficulty lies in the fact that the gravitational forces between bodies of small masses are extremely small. It is for this reason that we do not notice the attraction of our body to surrounding objects and the mutual attraction of objects to each other, although gravitational forces are the most universal of all forces in nature. Two people weighing 60 kg at a distance of 1 m from each other are attracted with a force of only about 10 -9 N. Therefore, to measure the gravitational constant, rather subtle experiments are needed.

The gravitational constant was first measured by the English physicist G. Cavendish in 1798 using a device called a torsion balance. The scheme of the torsion balance is shown in Figure 3.3. A light rocker with two identical weights at the ends is suspended on a thin elastic thread. Two heavy balls are motionlessly fixed nearby. Gravitational forces act between weights and motionless balls. Under the influence of these forces, the rocker turns and twists the thread until the resulting elastic force becomes equal to the gravitational force. The angle of twist can be used to determine the force of attraction. To do this, you only need to know the elastic properties of the thread. The masses of bodies are known, and the distance between the centers of interacting bodies can be directly measured.

From these experiments, the following value for the gravitational constant was obtained:

G \u003d 6.67 10 -11 N m 2 / kg 2.

Only in the case when bodies of enormous masses interact (or at least the mass of one of the bodies is very large), the gravitational force reaches a large value. For example, the Earth and the Moon are attracted to each other with a force F ≈ 2 10 20 N.

Dependence of free fall acceleration of bodies on geographic latitude.

One of the reasons for the increase in the acceleration of free fall when moving the point where the body is located from the equator to the poles is that the globe is somewhat flattened at the poles and the distance from the center of the Earth to its surface at the poles is less than at the equator. Another reason is the rotation of the Earth.

Equality of inertial and gravitational masses.

The most striking property of gravitational forces is that they impart the same acceleration to all bodies, regardless of their masses. What would you say about a football player whose kick would equally accelerate an ordinary leather ball and a two-pound weight? Everyone will say that it is impossible. But the Earth is just such an “extraordinary football player”, with the only difference that its effect on bodies does not have the character of a short-term impact, but continues continuously for billions of years.

In Newton's theory, mass is the source of the gravitational field. We are in the Earth's gravitational field. At the same time, we are also sources of the gravitational field, but due to the fact that our mass is significantly less than the mass of the Earth, our field is much weaker and the surrounding objects do not react to it.

The unusual property of gravitational forces, as we have already said, is explained by the fact that these forces are proportional to the masses of both interacting bodies. The mass of the body, which is included in Newton's second law, determines the inertial properties of the body, i.e., its ability to acquire a certain acceleration under the action of a given force. This inertial mass m and.

It would seem, what relation can it have to the ability of bodies to attract each other? The mass that determines the ability of bodies to attract each other is the gravitational mass m r .

It does not follow at all from Newtonian mechanics that the inertial and gravitational masses are the same, i.e. that

m and = m r . (3.5)

Equality (3.5) is a direct consequence of experience. It means that one can simply speak of the mass of a body as a quantitative measure of both its inertial and gravitational properties.

The gravitational force is the foundation on which the universe rests. Thanks to gravity, the Sun does not explode, the atmosphere does not escape into space, people and animals move freely on the surface, and plants bear fruit.

Celestial mechanics and the theory of relativity

The law of universal gravitation is studied in grades 8-9 of high school. Diligent students know about the famous apple that fell on the head of the great Isaac Newton and the discoveries that followed. In fact, to give a clear definition of gravity is much more difficult. Modern scientists continue discussions on how bodies interact in outer space and whether antigravity exists. It is extremely difficult to study this phenomenon in terrestrial laboratories, therefore, there are several basic theories of gravity:

Newtonian gravity

In 1687, Newton laid the foundations for celestial mechanics, which studies the motion of bodies in empty space. He calculated the gravitational pull of the moon on the earth. According to the formula, this force directly depends on their mass and the distance between objects.

F = (G m1 m2)/r2
Gravitational constant G=6.67*10-11

The equation is not entirely relevant when a strong gravitational field or the attraction of more than two objects is being analyzed.

Einstein's theory of gravity

In the course of various experiments, scientists came to the conclusion that there are some errors in Newton's formula. The basis of celestial mechanics is a long-range force that works instantly regardless of the distance, which does not correspond to the theory of relativity.

According to A. Einstein's theory developed at the beginning of the 20th century, information does not propagate faster than the speed of light in vacuum, so gravitational effects arise as a result of space-time deformation. The greater the mass of an object, the greater the curvature into which lighter objects roll.

quantum gravity

A very controversial and not fully formed theory that explains the interaction of bodies as an exchange of special particles - gravitons.

At the beginning of the 21st century, scientists managed to conduct several significant experiments, including with the help of the Hadron Collider, and develop the theory of loop quantum gravity and string theory.

Universe without gravity

Fantasy novels often describe various gravitational distortions, anti-gravity chambers, and spaceships with an artificial gravitational field. Readers sometimes do not even think about how unrealistic the plots of books are and what will happen if gravity decreases / increases or completely disappears.

Man is adapted to earth's gravity, so in other conditions he will have to change dramatically. Weightlessness leads to muscle atrophy, a reduction in the number of red blood cells and a disruption in the work of all vital systems of the body, and with an increase in the gravitational field, people simply cannot move.
Air and water, plants and animals, houses and cars will fly into outer space. Even if people manage to stay, they will quickly die without oxygen and food. Low gravity on the Moon is the main reason for the absence of an atmosphere on it, and, accordingly, life.
Our planet will fall apart as the pressure in the very center of the Earth disappears, all existing volcanoes erupt and the tectonic plates begin to diverge.
Stars will explode due to the intense pressure and chaotic collision of particles in the core.
The universe will turn into a formless stew of atoms and molecules that are unable to combine to create something more.

Fortunately for mankind, the shutdown of gravity and the terrible events that will follow will never happen. The dark scenario simply demonstrates how important gravity is. She is much weaker than electromagnetism, strong or weak interactions, but in fact, without it, our world will cease to exist.