Discovery and application of the law of universal gravitation. Discovery of the planets using the law of universal gravitation. Disturbances in the motion of the planets

02.11.2019

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

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

LESSON OBJECTIVES:

to 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;
to consolidate the studied topic in solving qualitative and computational problems.

EQUIPMENT: projection equipment, TV, video recorder, video films “About universal gravitation”, “About the force that rules the worlds”.

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

What branch of physics is called mechanics?

What do we call cinematics? (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 is the question of dynamics? Why, for what reason, one way or another, do bodies move? Why is there an acceleration?

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

List the basic physical quantities of dynamics? (Mass, force.)

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

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

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

When is the body moving with acceleration?

Formulate Newton's third 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 to study the topic of the lesson.

(On the board or screen, questions and a drawing.)

Today we have to answer the questions:

Why is there a fall of bodies on Earth?
why planets move around the sun?
why does the moon move around the earth?
how to explain the existence of ebbs and flows of the seas and oceans on Earth?

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

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

But 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 operate forces of gravity, generalized into law.

TOPIC. THE LAW OF UNIVERSAL GRAVITATION.

During the lesson, we will use the 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 make short presentations.

Message 1. According to the legend, the discovery of the law of universal gravitation is “to blame” for the apple, the fall of which from the tree was observed by Newton. There is evidence from a contemporary of Newton, his biographer, on this score:

“After dinner... 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 the fall of an apple. Why does an 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 in the same way as the Earth pulls the apple. There must therefore be a force, like that which we call gravity, extending throughout the universe.”

These thoughts occupied Newton already in 1665-1666, when he, a novice scientist, was in his village house, where he left Cambridge in connection with the plague epidemic that swept the big cities of England.

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

Thank you for message. We cannot trace in detail the course of Newton's thoughts, but nevertheless we will try to reproduce them in general terms.

TEXT ON 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 the consequences, which are verified again in practice.

What data of practice were known to Isaac Newton, what was discovered in science by 1667?

Message 2. Thousands of years ago, it was noticed that by the location of the heavenly bodies it is possible to predict river floods, and hence crops, to draw up 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.

Thus was born the science of astronomy. 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 hypotheses have been put forward 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, the Sun, Mars, Jupiter, Saturn revolve.

The development of trade between the West and the East in the 15th century made increased demands on navigation, gave impetus to the 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 Copernicus, the sun is at the center of the world. Five planets known by that time and the Earth, which is also a planet, revolve around the Sun, and is no different from other planets. Copernicus argued that the rotation of the Earth around the Sun is completed in a year, and the rotation of the Earth around its axis occurs in a day.

The ideas of Nicolaus Copernicus were further 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 say?

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

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

The planets move at a variable speed.

The squares of the periods of revolution of the planets around the Sun are related as the cubes of their semi-major axes.

These laws are the result of mathematical generalization of astronomical observational data. But it was completely incomprehensible why the planets move 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 affected by the gravitational force 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 an attraction between the planets and the Sun. The force of gravity is inversely proportional to the square of the distance between the bodies.

But the question immediately arises: is this law only valid for the gravitation of the planets and the Sun, or does the attraction of bodies to the Earth obey 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 side of the Earth, imparting centripetal acceleration to the Moon.

The centripetal acceleration of the Moon during its movement around the Earth can be calculated by the formula: , where v is the speed of the Moon during its orbit, R is the radius of the orbit. The calculation gives a\u003d 0.0027 m / s 2.

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

Acceleration of falling bodies to the Earth g = 9.81 m/s 2 . Acceleration during the movement of the moon around the earth a\u003d 0.0027 m / s 2.

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

From this follows the conclusion that the force which acts on the moon is the same force which we call the force of gravity.

This force decreases inversely with 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 grandiose. Newton concludes that not only bodies gravitate to the Earth, planets to the Sun, but all bodies in nature are attracted to each other with forces that obey the inverse square law, that is, gravitation, gravity is a worldwide, universal phenomenon.

Gravitational forces are fundamental forces.

Just think about it: universal gravitation. Worldwide!

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

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

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

Galileo found 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 force of gravity is proportional to the mass of the body on which it acts.

Let there be two attracting balls with masses m 1 and m 2 . The force of gravity acts on the first from the second. But also on the second 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 gravitational force is proportional to the masses of the interacting bodies.

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

G is the constant of universal gravitation, the gravitational constant.

Why does the ball fall on the table (the ball interacts with the Earth), and two balls lying on the table do not attract each other noticeably?

Let us 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 are attracted, located at a distance of 1 m from each other. 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 are attracted to each other with very little force. She is invisible to the naked eye.

Fragment of the film "On universal gravitation". (On the Cavendish experiment.)

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 the data of practice by means of mathematical processing (which was known before him in science), derived the law of universal gravitation, and obtained consequences from it.

Universal gravitation is universal:

On the basis of Newton's theory of gravitation, it was possible to describe the movement of natural and artificial bodies in the solar system, to calculate the orbits of planets and comets.
Based on this theory, the existence of the planets was predicted: Uranus, Neptune, Pluto and the satellite of 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, their masses are determined.
The onset of the tides of the seas and oceans is predicted.
Flight trajectories of shells and missiles are being determined, deposits of heavy ores are being explored.

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

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

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

THE LAW OF UNIVERSAL GRAVITY

1. Four balls have the same masses but different sizes. Which pair of balls will attract with more 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 with increasing distance between them?

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 of two bodies with 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 will happen to the force of the gravitational interaction of two bodies if the distance between them is increased by 3 times?

7. What will happen to the force of interaction of two bodies if the mass of one of them and the distance between them are doubled?

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

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

10. 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? How is the speed directed?

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

PROBLEM SOLVING WORKSHOP

Calculate the gravitational pull of the moon on the earth. The mass of the Moon is approximately equal to 7·10 22 kg, the mass of the Earth is 6·10 24 kg. The distance between the Moon and the Earth is assumed 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. Find the speed of the Earth in orbit if the mass of the Sun is 2 10 30 kg.
Two ships weighing 50,000 tons each are in the roadstead at a distance of 1 km from one another. What is the force of attraction between them?

SOLVE YOURSELF

With what force are two bodies of mass 20 tons attracted to each other if the distance between their centers of mass is 10 m?
What is the force exerted by the Moon on a 1 kg weight on the surface of 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 at a distance of 0.1 m from each other and are attracted 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.

REFERENCES:

Vorontsov-Velyaminov B.A. Astronomy. – M.: Enlightenment, 1994.
Gontaruk T.I. I know 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 work. 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.: Enlightenment, 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.

The law of universal gravitation underlies celestial mechanics - the science of planetary motion. With the help of this law, the positions of celestial bodies in the firmament for many decades to come are determined with great accuracy and their trajectories are calculated. The law of universal gravitation is also used in calculations of the motion of artificial earth satellites and interplanetary automatic vehicles.
Disturbances in the motion of the 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 if this planet alone revolved around the Sun. But there are many planets in the solar system, all of them are attracted by both the Sun and each other. Therefore, there are disturbances in the motion of the planets. In the solar system, perturbations are small, because the attraction of the planet by the Sun is much stronger than the attraction of other planets.
When calculating the apparent position of the planets, perturbations must be taken into account. When launching artificial celestial bodies and when calculating their trajectories, they use an approximate theory of the motion of celestial bodies - the theory of perturbations.
Discovery of Neptune
One of the clearest 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 differ from reality.
Scientists have suggested that the deviation in the motion 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 completed the calculations earlier, but the observers to whom he reported his results were in no hurry to verify. Meanwhile, Leverrier, having completed his calculations, indicated to the German astronomer Halle the place where to look for an unknown planet. On the very first evening, September 28, 1846, Halle, pointing the telescope to the indicated place, discovered a new planet. They named her Neptune.
In the same way, on March 14, 1930, the planet Pluto was discovered. Both discoveries are said to have been made "at the tip of a pen".
In § 3.2, we said that Newton discovered the law of universal gravitation using the laws of planetary motion - Kepler's laws. The correctness of the law of universal gravitation discovered by Newton is also 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 the planets and their satellites; explain phenomena such as the ebb and flow of water in the oceans, and much more.
There is no gravitational "shadow"
The forces of universal gravitation 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. Screens made of special substances impervious to gravity (like "kevorite" from H. G. Wells' novel "The First Men on the Moon") can only exist in the imagination of science fiction writers.
The rapid development of mechanics began after the discovery of the law of universal gravitation. It became clear that the same laws operate on Earth and in outer space.

Genius

Sir Isaac Newton is an English scientist. At one time, he devoted much 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, the light theory. He also made many 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 far back in time. Its classical form is a law that describes the interaction of a gravitational type that does not go beyond the framework of mechanics.

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

F = G, where by the symbol G we denote 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's take a closer look at its general characteristics.

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

A body with spherical symmetry forms a field outside of itself, similar to that created by a material point of the same mass located in 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. Accounting for the distortion that other massive bodies create is taken into account using the provisions of the perturbation theory.

Analyzing Accuracy

After Newton discovered the law of universal gravitation, it had to be tested and proved many times over. For this, a number of calculations and observations were made. Having come to agreement with its provisions and proceeding from the accuracy of its indicator, the experimental form of estimation serves as a clear confirmation of GR. Measurement of the quadrupole interactions of a body that rotates, but its antennas remain stationary, show 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 be established and take a single form, without any modifications. In 2007, this dogma was rechecked at a distance less than a centimeter (55 microns-9.59 mm). Taking into account the experimental errors, the scientists examined the distance range and found no obvious deviations in this law.

Observation of the Moon's orbit with respect to the Earth also confirmed its validity.

Euclidean space

Newton's classical theory of gravity is related to Euclidean space. The actual equality with a sufficiently high accuracy (10 -9) of the distance measures 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 in matter, the area of a spherical surface is exactly proportional to the square of its radius.

Data from history

Consider a brief summary of the 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 visited reflections on it. Kepler put forward the assumption that the gravitational force is inversely proportional to the distance from the star of the Sun and has distribution only in the ecliptic planes; according to Descartes, it was a consequence of the activity of vortices in the thickness of the ether. There was a series of guesses that contained a reflection of the correct guesses about the dependence on distance.

A letter from Newton to Halley contained information that Hooke, Wren and Buyo Ismael were the predecessors of Sir Isaac himself. However, no one before him managed to clearly, with the help of 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 testifies to the presence of a central force;
the attractive force 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 set it apart from previous hypotheses. Newton was engaged not only in the publication of the proposed formula of the phenomenon under consideration, but also proposed a model of a mathematical type in a holistic form:

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

This triad was able to investigate even the most complex movements of celestial objects to a fairly accurate extent, thus creating the basis for celestial mechanics. Up to the beginning of Einstein's activity in this model, the presence of a fundamental set of corrections was not required. Only mathematical apparatus had to be significantly improved.

Object for discussion

The discovered and proven law became, throughout the eighteenth century, a well-known subject of active controversy and scrupulous scrutiny. However, the century ended with a general agreement with his postulates and statements. Using the calculations of the law, it was possible to accurately determine the paths of the movement of bodies in heaven. A direct check was made in 1798. He did this using a torsion-type balance with great sensitivity. In the history of the discovery of the universal law of gravitation, a special place must be given to the interpretations introduced by Poisson. He developed the concept of the potential of gravity 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.

There were many difficulties in Newton's theory. The main one could be considered the inexplicability of long-range action. There was no exact answer to the question of how attractive forces are sent through vacuum space at infinite speed.

"Evolution" of the law

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

The potential of the 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 shift of the perihelion.
The indicator of the speed of movement in this group of systems is insignificant in comparison with the speed of light.

The proof that in a weak stationary field of gravitation GR 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 adequately describe the processes of the gravitational type on the quantum scale. An attempt to create a quantum gravitational theory is one of the most important tasks of contemporary physics.

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

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

Delusion

In the school curriculum, the answer to a 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 head of a scientist. However, this is a widespread misconception, and in fact, everything was able to do without a similar case of a 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 burst of momentary insight. As it was written above, it was developed for a long time and was presented for the first time in the works on the "Principles of Mathematics", which appeared on public display in 1687.