The meaning of the law of universal gravitation. The history of the discovery of the law of universal gravitation - description, features and interesting facts The history of the discovery of the law of universal gravitation

Limits of applicability of the law

The law of universal gravitation is applicable only for material points, i.e. for bodies whose dimensions are significantly smaller than the distance between them; spherical bodies; for a ball of large radius interacting with bodies whose dimensions are significantly smaller than the dimensions of the ball.

But the law is not applicable, for example, to the interaction of an infinite rod and a ball. In this case, the force of gravity is inversely proportional only to the distance, and not to the square of the distance. And the force of attraction between a body and an infinite plane does not depend on distance at all.

Gravity

A special case of gravitational forces is the force of attraction of bodies towards the Earth. This force is called gravity. In this case, the law of universal gravitation has the form:

F t = G ∙mM/(R+h) 2

where m is body weight (kg),

M – mass of the Earth (kg),

R – radius of the Earth (m),

h – height above the surface (m).

But the force of gravity is F t = mg, hence mg = G mM/(R+h) 2, and the acceleration of gravity g = G ∙M/(R+h) 2.

On the Earth's surface (h = 0) g = G M/R 2 (9.8 m/s 2).

The acceleration of free fall depends

From the height above the Earth's surface;

From the latitude of the area (the Earth is a non-inertial reference system);

From the density of rocks of the earth's crust;

From the shape of the Earth (flattened at the poles).

In the above formula for g, the last three dependencies are not taken into account. At the same time, we emphasize once again that the acceleration of gravity does not depend on the mass of the body.

Application of the law in the discovery of new planets

When the planet Uranus was discovered, its orbit was calculated based on the law of universal gravitation. But the true orbit of the planet did not coincide with the calculated one. It was assumed that the orbital disturbance was caused by the presence of another planet located beyond Uranus, which, with its gravitational force, changes its orbit. To find a new planet, it was necessary to solve a system of 12 differential equations with 10 unknowns. This task was completed by the English student Adams; he sent the solution to the English Academy of Sciences. But there they did not pay attention to his work. And the French mathematician Le Verrier, having solved the problem, sent the result to the Italian astronomer Galle. And he, on the very first evening, pointing his pipe at the indicated point, discovered a new planet. She was given the name Neptune. In the same way, in the 30s of the twentieth century, the 9th planet of the solar system, Pluto, was discovered.

When asked what the nature of gravitational forces is, Newton answered: “I don’t know, but I don’t want to invent hypotheses.”

V. Questions to reinforce new material.

Review questions on the screen

How is the law of universal gravitation formulated?

What is the formula for the law of universal gravitation for material points?

What is the gravitational constant called? What is its physical meaning? What is the SI value?

What is the gravitational field?

Does the force of gravity depend on the properties of the medium in which the bodies are located?

Does the acceleration of free fall of a body depend on its mass?

Is the force of gravity the same at different points on the globe?

Explain the effect of the Earth's rotation around its axis on the acceleration of gravity.

How does the acceleration of gravity change with distance from the Earth's surface?

Why doesn't the Moon fall to Earth? ( The Moon revolves around the Earth, held by gravity. The Moon does not fall to the Earth because, having an initial speed, it moves by inertia. If the gravitational force of the Moon towards the Earth ceases, the Moon will rush in a straight line into the abyss of outer space. If the inertial movement had stopped, the Moon would have fallen to the Earth. The fall would have lasted four days, twelve hours, fifty-four minutes, seven seconds. This is what Newton calculated.)

VI. Solving problems on the topic of the lesson

Problem 1

At what distance is the force of attraction between two balls of mass 1 g equal to 6.7 10 -17 N?

(Answer: R = 1m.)

Problem 2

To what height did the spacecraft rise from the Earth's surface if the instruments noted a decrease in the acceleration of gravity to 4.9 m/s 2?

(Answer: h = 2600 km.)

Problem 3

The gravitational force between two balls is 0.0001N. What is the mass of one of the balls if the distance between their centers is 1 m, and the mass of the other ball is 100 kg?

(Answer: approximately 15 tons.)

Summing up the lesson. Reflection.

Homework

1. Learn §15, 16;

2. Complete exercise 16 (1, 2);

3. For those interested: §17.

4. Answer the microtest question:

A space rocket is moving away from the Earth. How will the gravitational force acting on the rocket from the Earth change when the distance to the center of the Earth increases by 3 times?

A) will increase 3 times; B) will decrease by 3 times;

B) will decrease by 9 times; D) will not change.

Applications: presentation in PowerPoint.

Literature:

Ivanova L.A. "Activation of cognitive activity of students when studying physics", "Prosveshchenie", Moscow 1982
Gomulina N.N. "Open Physics 2.0." and “Open Astronomy” – a new step. Computer at school: No. 3/ 2000. – P. 8 – 11.
Gomulina N.N. Educational interactive computer courses and simulation programs in physics // Physics at school. M.: No. 8 / 2000. – P. 69 – 74.
Gomulina N.N. “Application of new information and telecommunication technologies in school physics and astronomy education. dis. Research 2002
Povzner A.A., Sidorenko F.A. Graphic support for physics lectures. // XIII International Conference “Information Technologies in Education, ITO-2003” // Collection of works, part IV, – Moscow – Education – 2003 – p. 72-73.
Starodubtsev V.A., Chernov I.P. Development and practical use of multimedia tools in lectures//Physical education in universities - 2002. - Volume 8. - No. 1. p. 86-91.
http//www.polymedia.ru.
Ospennikova E.V., Khudyakova A.V. Working with computer models in school physical workshop classes // Modern physical workshop: Abstracts of reports. 8th Commonwealth Conference. – M.: 2004. - pp. 246-247.
Gomullina N.N. Review of new multimedia educational publications in physics, Questions of Internet Education, No. 20, 2004.
Physicus, Heureka-Klett Softwareverlag GmbH-Mediahouse, 2003
Physics. Basic school grades 7-9: part I, YDP Interactive Publishing – Education – MEDIA, 2003
Physics 7-11, Physikon, 2003

THE MEANING OF THE LAW OF GRAVITY

The law of universal gravitation underlies celestial mechanics- science of planetary motion.

With the help of this law, the positions of celestial bodies in the firmament for many decades in advance are determined with great accuracy and their trajectories are calculated.

The law of universal gravitation is also used in calculating the motion of artificial Earth satellites and interplanetary automatic vehicles.

Disturbances in the motion of planets

Planets do not move strictly according to Kepler's laws. Kepler's laws would be strictly observed for the motion of a given planet only in the case when this one planet revolved around the Sun. But there are many planets in the Solar System, they are all attracted both by the Sun and by each other. Therefore, disturbances in the motion of the planets arise. In the Solar System, disturbances are small because the attraction of a planet by the Sun is much stronger than the attraction of other planets.

When calculating the apparent positions of the planets, disturbances must be taken into account. When launching artificial celestial bodies and when calculating their trajectories, an approximate theory of the motion of celestial bodies is used - perturbation theory.

Discovery of Neptune

One of the striking examples of the triumph of the law of universal gravitation is the discovery of the planet Neptune. In 1781, the English astronomer William Herschel discovered the planet Uranus.

Its orbit was calculated and a table of the positions of this planet was compiled for many years to come. However, a check of this table, carried out in 1840, showed that its data diverges from reality.

Adams finished his calculations early, but the observers to whom he reported his results were in no hurry to check. Meanwhile, Leverrier, having completed his calculations, indicated to the German astronomer Halle the place where to look for the unknown planet.

Both discoveries are said to have been made "at the tip of a pen."

The correctness of the law of universal gravitation discovered by Newton is confirmed by the fact that with the help of this law and Newton’s second law one can derive Kepler’s laws. We will not present this conclusion.

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

The presented materials can be used when conducting a lesson, conference or workshop on solving problems on the topic “The Law of Universal Gravitation”.

LESSON PURPOSE: to show the universal nature of the law of universal gravitation.

LESSON OBJECTIVES:

study the law of universal gravitation and the limits of its application;
consider the history of the discovery of the law;
show the cause-and-effect relationships of Kepler's laws and the law of universal gravitation;
show the practical significance of the law;
consolidate the studied topic when solving qualitative and calculation problems.

EQUIPMENT: projection equipment, TV, VCR, video films “On Universal Gravitation”, “On the Force that Rules the Worlds”.

Let's start the lesson by reviewing the basic concepts of the mechanics course.

What branch of physics is called mechanics?

What do we call kinematics? (A section of mechanics that describes the geometric properties of motion without taking into account the masses of bodies and acting forces.) What types of motion do you know?

What question does dynamics solve? Why, for what reason, one way or another, do bodies move? Why does acceleration occur?

List the main physical quantities of kinematics? (Movement, speed, acceleration.)

List the main physical quantities of dynamics? (Mass, strength.)

What is body weight? (A physical quantity that quantitatively characterizes the properties of bodies that acquire different speeds during interaction, that is, characterizing the inert properties of the body.)

What physical quantity is called force? (Force is a physical quantity that quantitatively characterizes the external influence on a body, as a result of which it acquires acceleration.)

When does a body move uniformly and in a straight line?

In what case does a body move with acceleration?

Formulate Newton's III law - the law of interaction. (Bodies act on each other with forces equal in magnitude and opposite in direction.)

We repeated the basic concepts and main laws of mechanics that will help us study the topic of the lesson.

(There are questions and a drawing on the board or screen.)

Today we have to answer the questions:

Why are bodies falling on Earth?
why do planets move around the sun?
why does the moon move around the earth?
How can we explain the existence of ebbs and flows of seas and oceans on Earth?

According to Newton's II law, a body moves with acceleration only under the influence of force. Force and acceleration are directed in the same direction.

EXPERIENCE. Raise the ball to a height and release it. The body falls down. We know that the Earth attracts it to itself, that is, the force of gravity acts on the ball.

Is it only the Earth that has the ability to act on all bodies with a force called gravity?

Isaac Newton

In 1667, the English physicist Isaac Newton suggested that in general forces of mutual attraction act between all bodies.

They are now called the forces of universal gravitation or gravitational forces.

So: between the body and the Earth, between the planets and the Sun, between the Moon and the Earth act universal gravitational forces, generalized into law.

SUBJECT. LAW OF UNIVERSAL GRAVITY.

During the lesson we will use knowledge of the history of physics, astronomy, mathematics, the laws of philosophy and information from popular science literature.

Let's get acquainted with the history of the discovery of the law of universal gravitation. Several students will give short presentations.

Message 1. If you believe the legend, then the discovery of the law of universal gravitation is “to blame” for the apple that Newton observed falling from the tree. There is evidence from Newton’s contemporary, his biographer, on this matter:

“After lunch... we went into the garden and drank tea under the shade of several apple trees. Sir Isaac told me that this was exactly the situation he was in when the idea of gravity first occurred to him. It was caused by a falling apple. Why does the apple always fall vertically, he thought to himself. There must be an attractive force of matter, concentrated in the center of the Earth, proportional to its quantity. Therefore, the apple attracts the Earth just as the Earth attracts the apple. There must, therefore, be a force similar to that which we call gravity, extending throughout the entire Universe.”

These thoughts occupied Newton already in 1665-1666, when he, an aspiring scientist, was in his country house, where he had left Cambridge due to the plague epidemic that had swept through the large cities of England.

This great discovery was published 20 years later (1687). Not everything agreed with Newton’s guesses and calculations, and being a man of the highest demands on himself, he could not publish results that were not completed. (Biography of I. Newton.) (Appendix No. 1.)

Thank you for message. We cannot trace Newton's train of thought in detail, but we will still try to reproduce them in general terms.

TEXT ON THE BOARD OR SCREEN. Newton used the scientific method in his work:

from practice data,
through their mathematical processing,
to the general law, and from it
to consequences, which are verified again in practice.

What data practices were known to Isaac Newton that were discovered in science by 1667?

Message 2. Thousands of years ago it was noticed that by the location of celestial bodies one can predict river floods, and therefore harvests, and make calendars. By the stars - find the right path for sea ships. People have learned to calculate the timing of eclipses of the Sun and Moon.

This is how the science of astronomy was born. Its name comes from two Greek words: “astron”, which means star, and “nomos”, which in Russian means law. That is, the science of stellar laws.

Various assumptions have been made to explain the motion of the planets. The famous Greek astronomer Ptolemy in the 2nd century BC believed that the center of the Universe is the Earth, around which the Moon, Mercury, Venus, Sun, Mars, Jupiter, and Saturn revolve.

The development of trade between the West and the East in the 15th century placed increased demands on navigation and gave impetus to further study of the movement of celestial bodies and astronomy.

In 1515, the great Polish scientist Nicolaus Copernicus (1473 - 1543), a very brave man, refuted the doctrine of the immobility of the Earth. According to the teachings of Copernicus, the Sun is at the center of the world. There are five known planets around the Sun and the Earth, which is also a planet and is no different from other planets. Copernicus argued that the Earth rotates around the Sun in a year, and the Earth rotates around its axis in a day.

The ideas of Nicolaus Copernicus continued to be developed by the Italian thinker Giordano Bruno, the great scientist Galileo Galilei, the Danish astronomer Tycho Brahe, and the German astronomer Johannes Kepler. The first guesses were made that not only the Earth attracts bodies to itself, but the Sun also attracts planets to itself.

The first quantitative laws that opened the way to the idea of universal gravitation were the laws of Johannes Kepler. What do Kepler's findings indicate?

Message 3. Johannes Kepler, an outstanding German scientist, one of the creators of celestial mechanics, for 25 years, under conditions of severe need and adversity, summarized the data of astronomical observations of the movements of the planets. Three laws that tell us how the planets move were obtained by him.

According to Kepler's first law, planets move along closed curves called ellipses, with the Sun at one of the foci. (A sample design of material for projection onto the screen is presented in the Appendix.) (Appendix No. 2.)

Planets move at varying speeds.

The squares of the periods of revolution of the planets around the Sun are related to the cubes of their semimajor axes.

These laws are the result of a mathematical generalization of astronomical observation data. But it was completely unclear why the planets moved so “smartly”. Kepler's laws had to be explained, that is, deduced from some other, more general law.

Newton solved this difficult problem. He proved that if the planets move around the Sun in accordance with Kepler's laws, then they must be acted upon by the force of gravity from the Sun.

The force of gravity is inversely proportional to the square of the distance between the planet and the Sun.

Thank you for your performance. Newton proved that there is attraction between the planets and the Sun. The force of gravity is inversely proportional to the square of the distance between bodies.

But the question immediately arises: is this law valid only for the gravitation of planets and the Sun, or is the attraction of bodies to the Earth also subject to it?

Message 4. The Moon moves around the Earth in an approximately circular orbit. This means that a force acts on the Moon from the Earth, imparting centripetal acceleration to the Moon.

The centripetal acceleration of the Moon as it moves around the Earth can be calculated using the formula: , where v is the speed of the Moon as it moves in its orbit, R is the radius of the orbit. The calculation gives A= 0.0027 m/s 2 .

This acceleration is caused by the force of interaction between the Earth and the Moon. What kind of power is this? Newton concluded that this force obeys the same law as the attraction of the planets to the Sun.

Acceleration of falling bodies to Earth g = 9.81 m/s 2 . Acceleration as the Moon moves around the Earth A= 0.0027 m/s 2 .

Newton knew that the distance from the center of the Earth to the orbit of the Moon is about 60 times the radius of the Earth. Based on this, Newton decided that the ratio of accelerations, and therefore the corresponding forces, is equal to: , where r is the radius of the Earth.

From this it follows that the force that acts on the Moon is the same one that we call gravity.

This force decreases in inverse proportion to the square of the distance from the center of the Earth, that is, where r is the distance from the center of the Earth.

Thank you for message. Newton's next step is even more monumental. Newton concludes that not only bodies gravitate towards the Earth, planets towards the Sun, but also all bodies in nature are attracted to each other with forces that obey the inverse square law, that is, gravitation is a universal, universal phenomenon.

Gravitational forces are fundamental forces.

Just think: universal gravity. Worldwide!

What a majestic word! Everything, all bodies in the Universe are connected by some kind of threads. Where does this all-pervasive, limitless action of bodies on each other come from? How do bodies feel each other at gigantic distances through emptiness?

Does the force of universal gravity depend only on the distance between bodies?

Gravity, like any force, obeys Newton's II law. F= ma.

Galileo established that the force of gravity F heavy = mg. The force of gravity is proportional to the mass of the body on which it acts.

But gravity is a special case of gravity. Therefore, we can assume that the gravitational force is proportional to the mass of the body on which it acts.

Let there be two attracting balls of masses m 1 and m 2. The force of gravity acts on the first from the side of the second. But also on the second from the side of the first.

According to Newton's third law

If you increase the mass of the first body, then the force acting on it will increase.

So. The force of gravity is proportional to the masses of interacting bodies.

The law of universal gravitation was formulated in its final form by Newton in 1687 in his work “Mathematical Principles of Natural Philosophy”: “ All bodies attract each other with a force directly proportional to the product of the masses and inversely proportional to the square of the distance between them.” The force is directed along a straight line connecting material points.

G – constant of universal gravitation, gravitational constant.

Why does the ball fall on the table (the ball interacts with the Earth), but two balls lying on the table are not attracted to each other in any noticeable way?

Let's find out the meaning and units of measurement of the gravitational constant.

The gravitational constant is numerically equal to the force with which two bodies with a mass of 1 kg each, located at a distance of 1 m from each other, are attracted. The magnitude of this force is 6.67 10 –11 N.

; ;

In 1798, the numerical value of the gravitational constant was first determined by the English scientist Henry Cavendish using a torsion balance.

G is very small, so two bodies on Earth attract each other with very little force. It is invisible to the visible eye.

Fragment of the film “On Universal Gravitation.” (About Cavendish's experience.)

Limits of applicability of the law:

for material points (bodies whose dimensions can be neglected compared to the distance at which the bodies interact);
for spherical bodies.

If the bodies are not material points, then the laws are fulfilled, but the calculations become more complicated.

From the law of universal gravitation it follows that all bodies have the property of being attracted to each other - the property of gravitation (gravity).

From Newton's II law we know that mass is a measure of the inertia of bodies. Now we can say that mass is a measure of two universal properties of bodies - inertia and gravitation (gravity).

Let's return to the concept of the scientific method: Newton generalized these practices through mathematical processing (what was known before him in science), derived the law of universal gravitation, and obtained consequences from it.

Universal gravity is universal:

Based on Newton's theory of gravity, it was possible to describe the movement of natural and artificial bodies in the solar system and calculate the orbits of planets and comets.
Based on this theory, the existence of planets was predicted: Uranus, Neptune, Pluto and the satellite Sirius. (Appendix No. 3.)
In astronomy, the law of universal gravitation is fundamental, on the basis of which the parameters of the movement of space objects are calculated and their masses are determined.
The onset of the ebb and flow of the seas and oceans is predicted.
The flight trajectories of projectiles and missiles are determined, and heavy ore deposits are explored.

Newton's discovery of the law of universal gravitation is an example of solving the main problem of mechanics (to determine the position of a body at any moment in time).

Fragment of the video film “About the power that rules the worlds.”

You will see how the law of universal gravitation is used in practice to explain natural phenomena.

LAW OF GRAVITY

1. Four balls have the same masses, but different sizes. Which pair of balls will attract with greater force?

2. What attracts to itself with greater force: the Earth - the Moon or the Moon - the Earth?

3. How will the force of interaction between bodies change as the distance between them increases?

4. Where will the body be attracted to the Earth with greater force: on its surface or at the bottom of the well?

5. How will the force of interaction between two bodies of masses m and m change if the mass of one of them is increased by 2 times, and the mass of the other is reduced by 2 times, without changing the distance between them?

6. What happens to the force of gravitational interaction between two bodies if the distance between them is increased by 3 times?

7. What happens to the force of interaction between two bodies if the mass of one of them and the distance between them is doubled?

8. Why don’t we notice the attraction of surrounding bodies to each other, although the attraction of these bodies to the Earth is easy to observe?

9. Why does a button, coming off a coat, fall to the ground, because it is much closer to the person and is attracted to him?

10. The planets move in their orbits around the Sun. Where is the gravitational force acting on the planets from the Sun directed? Where is the planet's acceleration directed at any point in its orbit? What is the direction of the speed?

11. What explains the presence and frequency of sea tides on Earth?

PRACTICUM ON PROBLEM SOLVING

Calculate the force of gravity of the Moon on the Earth. The mass of the Moon is approximately 7·10 22 kg, the mass of the Earth is 6·10 24 kg. The distance between the Moon and the Earth is considered to be 384,000 km.
The Earth moves around the Sun in an orbit that can be considered circular, with a radius of 150 million km.
Two ships weighing 50,000 tons each are standing in a roadstead at a distance of 1 km from one another. What is the force of attraction between them?

DECIDE YOURSELF

With what force are two bodies weighing 20 tons attracted to each other if the distance between their centers of mass is 10 m?
With what force is a 1 kg weight located on the surface of the Moon attracted by the Moon? The mass of the Moon is 7.3 10 22 kg, and its radius is 1.7 10 8 cm?
At what distance will the force of attraction between two bodies weighing 1 ton each be equal to 6.67 10 -9 N.
Two identical balls are 0.1 m apart and attract each other with a force of 6.67 × 10 -15 N. What is the mass of each ball?
The masses of the Earth and the planet Pluto are almost the same, and their distances to the Sun are approximately 1:40. Find the ratio of their gravitational forces to the Sun.

LIST OF REFERENCES:

Vorontsov-Velyaminov B.A. Astronomy. – M.: Education, 1994.
Gontaruk T.I. I'm exploring the world. Space. – M.: AST, 1995.
Gromov S.V. Physics - 9. M.: Education, 2002.
Gromov S.V. Physics – 9. Mechanics. M.: Education, 1997.
Kirin L.A., Dick Yu.I. Physics – 10. collection of assignments and independent works. M.: ILEKSA, 2005.
Klimishin I.A. Elementary astronomy. – M.: Nauka, 1991.
Kochnev S.A. 300 questions and answers about the Earth and the Universe. – Yaroslavl: “Academy of Development”, 1997.
Levitan E.P. Astronomy. – M.: Education, 1999.
Myakishev G.Ya., Bukhovtsev B.B., Sotsky N.N. Physics - 10. M.: Education, 2003.
Subbotin G.P. Collection of problems in astronomy. – M.: “Aquarium”, 1997.
Encyclopedia for children. Volume 8. Astronomy. – M.: “Avanta +”, 1997.
Encyclopedia for children. Additional volume.
Cosmonautics. – M.: “Avanta +”, 2004.

Yurkina G.A. (compiler). From school to the universe.

M.: “Young Guard”, 1976.

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

In the same way, on March 14, 1930, the planet Pluto was discovered. The discovery of Neptune, made, as Engels put it, “at the tip of a pen,” is the most convincing proof of the validity of Newton’s law of universal gravitation.

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

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

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This article will focus on the history of the discovery of the law of universal gravitation. Here we will get acquainted with biographical information from the life of the scientist who discovered this physical dogma, consider its main provisions, the relationship with quantum gravity, the course of development and much more.

Genius

Sir Isaac Newton is a scientist originally from England. At one time, he devoted a lot of attention and effort to such sciences as physics and mathematics, and also brought a lot of new things to mechanics and astronomy. He is rightfully considered one of the first founders of physics in its classical model. He is the author of the fundamental work “Mathematical Principles of Natural Philosophy,” where he presented information about the three laws of mechanics and the law of universal gravitation. Isaac Newton laid the foundations of classical mechanics with these works. He also developed an integral type, light theory. He also made major contributions to physical optics and developed many other theories in physics and mathematics.

Law

The law of universal gravitation and the history of its discovery go back to the distant past. Its classical form is a law that describes gravitational-type interactions that do not go beyond the framework of mechanics.

Its essence was that the indicator of the force F of gravitational thrust arising between 2 bodies or points of matter m1 and m2, separated from each other by a certain distance r, maintains proportionality in relation to both indicators of mass and is inversely proportional to the square of the distance between the bodies:

F = G, where the symbol G denotes the gravitational constant equal to 6.67408(31).10 -11 m 3 /kgf 2.

Newton's gravity

Before considering the history of the discovery of the law of universal gravitation, let us familiarize ourselves in more detail with its general characteristics.

In the theory created by Newton, all bodies with large mass should generate a special field around themselves that attracts other objects to itself. It's called a gravitational field, and it has potential.

A body with spherical symmetry forms a field outside itself, similar to that created by a material point of the same mass located at the center of the body.

The direction of the trajectory of such a point in the gravitational field created by a body with a much larger mass obeys. Objects of the universe, such as, for example, a planet or a comet, also obey it, moving along an ellipse or hyperbola. The distortion that other massive bodies create is taken into account using the provisions of perturbation theory.

Analyzing accuracy

After Newton discovered the law of universal gravitation, it had to be tested and proven many times. For this purpose, a series of calculations and observations were made. Having come to agreement with its provisions and based on the accuracy of its indicator, the experimental form of evaluation serves as a clear confirmation of general relativity. Measuring the quadrupole interactions of a body that rotates, but its antennas remain stationary, shows us that the process of increasing δ depends on the potential r -(1+δ), at a distance of several meters and is in the limit (2.1±6.2) .10 -3 . A number of other practical confirmations allowed this law to establish itself and take a single form, without modifications. In 2007, this dogma was rechecked at a distance of less than a centimeter (55 microns-9.59 mm). Taking into account the errors of the experiment, scientists examined the distance range and found no obvious deviations in this law.

Observation of the Moon's orbit in relation to the Earth also confirmed its validity.

Euclidean space

Newton's classical theory of gravity is associated with Euclidean space. The actual equality with a fairly high accuracy (10 -9) of the indicators of the distance measure in the denominator of the equality discussed above shows us the Euclidean basis of the space of Newtonian mechanics, with a three-dimensional physical form. At such a point of matter, the area of the spherical surface has exact proportionality with respect to the square of its radius.

Data from history

Let us consider a brief history of the discovery of the law of universal gravitation.

Ideas were put forward by other scientists who lived before Newton. Epicurus, Kepler, Descartes, Roberval, Gassendi, Huygens and others thought about it. Kepler hypothesized that the force of gravity is inversely proportional to the distance from the Sun and extends only in the ecliptic planes; according to Descartes, it was a consequence of the activity of vortices in the thickness of the ether. There were a number of guesses that reflected the correct guesses about the dependence on distance.

A letter from Newton to Halley contained information that the predecessors of Sir Isaac himself were Hooke, Wren and Buyot Ismael. However, before him, no one had been able to clearly, using mathematical methods, connect the law of gravity and planetary motion.

The history of the discovery of the law of universal gravitation is closely connected with the work “Mathematical Principles of Natural Philosophy” (1687). In this work, Newton was able to derive the law in question thanks to Kepler's empirical law, which was already known by that time. He shows us that:

the form of movement of any visible planet indicates the presence of a central force;
the force of attraction of the central type forms elliptical or hyperbolic orbits.

About Newton's theory

An examination of the brief history of the discovery of the law of universal gravitation can also point us to a number of differences that distinguished it from previous hypotheses. Newton not only published the proposed formula for the phenomenon under consideration, but also proposed a mathematical model in its entirety:

position on the law of gravity;
provision on the law of motion;
systematics of methods of mathematical research.

This triad could fairly accurately study even the most complex movements of celestial objects, thus creating the basis for celestial mechanics. Until Einstein began his work, this model did not require a fundamental set of corrections. Only the mathematical apparatus had to be significantly improved.

Object for discussion

The discovered and proven law throughout the eighteenth century became a well-known subject of active debate and scrupulous verification. However, the century ended with general agreement with his postulates and statements. Using the calculations of the law, it was possible to accurately determine the paths of movement of bodies in the heavens. Direct verification was carried out in 1798. He did this using a torsion type balance with great sensitivity. In the history of the discovery of the universal law of gravity, it is necessary to give a special place to the interpretations introduced by Poisson. He developed the concept of gravitational potential and the Poisson equation, with which it was possible to calculate this potential. This type of model made it possible to study the gravitational field in the presence of an arbitrary distribution of matter.

Newton's theory had many difficulties. The main one could be considered the inexplicability of long-range action. It was impossible to accurately answer the question of how gravitational forces are sent through vacuum space at infinite speed.

"Evolution" of the law

Over the next two hundred years, and even more, many physicists attempted to propose various ways to improve Newton's theory. These efforts ended in triumph in 1915, namely the creation of the General Theory of Relativity, which was created by Einstein. He was able to overcome the whole range of difficulties. In accordance with the correspondence principle, Newton's theory turned out to be an approximation to the beginning of work on the theory in a more general form, which can be applied under certain conditions:

The potential of gravitational nature cannot be too large in the systems under study. The solar system is an example of compliance with all the rules for the movement of celestial bodies. The relativistic phenomenon finds itself in a noticeable manifestation of the perihelion shift.
The speed of movement in this group of systems is insignificant in comparison with the speed of light.

Proof that in a weak stationary gravitational field, general relativity calculations take the form of Newtonian ones is the presence of a scalar gravitational potential in a stationary field with weakly expressed force characteristics, which is able to satisfy the conditions of the Poisson equation.

Quantum scale

However, in history, neither the scientific discovery of the law of universal gravitation, nor the General Theory of Relativity could serve as the final gravitational theory, since both do not satisfactorily describe gravitational-type processes on the quantum scale. An attempt to create a quantum gravitational theory is one of the most important tasks in modern physics.

From the point of view of quantum gravity, interaction between objects is created through the exchange of virtual gravitons. In accordance with the uncertainty principle, the energy potential of virtual gravitons is inversely proportional to the period of time in which it existed, from the point of emission by one object to the moment in time at which it was absorbed by another point.

In view of this, it turns out that on a small distance scale the interaction of bodies entails the exchange of virtual-type gravitons. Thanks to these considerations, it is possible to conclude a statement about Newton’s law of potential and its dependence in accordance with the inverse proportionality index with respect to distance. The analogy between Coulomb's and Newton's laws is explained by the fact that the weight of gravitons is zero. The weight of photons has the same meaning.

Misconception

In the school curriculum, the answer to the question from history, how Newton discovered the law of universal gravitation, is the story of a falling apple fruit. According to this legend, it fell on the scientist’s head. However, this is a widespread misconception, and in reality everything was possible without such a case of possible head injury. Newton himself sometimes confirmed this myth, but in reality the law was not a spontaneous discovery and did not come in a fit of momentary insight. As was written above, it was developed over a long time and was first presented in the works on the “Mathematical Principles”, which were released to the public in 1687.