Establishment Newton law universal gravity appeared the most important event in history physicists. Its significance is determined primarily by its versatility gravitational interaction. One of the central branches of astronomy—celestial mechanics—is based on the law of universal gravitation. We feel the force of gravity towards the Earth, but the attraction of small bodies to each other is imperceptible. It was necessary to experimentally prove the validity of the law of universal gravitation for ordinary bodies. This is exactly what G. Cavendish did, simultaneously determining the average density of the Earth.

where m 1 and m 2 are masses material points, R is the distance between them, a F- the strength of interaction between them. To early XIX century G was not introduced into the law of universal gravitation, since for all calculations in celestial mechanics it is enough to use constants GM, having kinematic dimension. Constant G appeared for the first time, apparently, only after the unification of units and the transition to a single metric system measures in late XVIII century. Numerical value G can be calculated through the average density of the Earth, which had to be determined experimentally. It is obvious that when known values density c and radius R of the Earth, as well as acceleration free fall g on its surface you can find G:

The experiment was originally proposed John Michell. It was he who designed the main part in the experimental installation - a torsion balance, but died in 1793 without ever getting any experience. After his death experimental setup moved on to Henry Cavendish. Cavendish modified the setup, conducted experiments and described them in Philosophical Transactions in 1798.

Installation

Torsion scales

The installation is a wooden rocker with small lead balls attached to its ends. It is suspended on a thread of silver-plated copper 1 m long. The balls are brought to the balls larger size weighing 159 kg, also made of lead. As a result of the action of gravitational forces, the rocker twists at a certain angle. The rigidity of the thread was such that the rocker made one oscillation every 15 minutes. The angle of rotation of the rocker arm was determined using a beam of light directed at a mirror on the rocker arm and reflected into a microscope. Knowing elastic properties threads, as well as the angle of rotation of the rocker arm, can be calculated gravitational constant.

To prevent convection currents, the installation was enclosed in a windproof chamber. The deflection angle was measured using a telescope.

Having attributed the twisting of the thread to the magnetic interaction of the iron rod and lead balls, Cavendish replaced it with copper, obtaining the same results.

You numerical value

IN Britannica it is stated that G. Cavendish obtained the value G = 6.754·10 -11 m?/(kg s?) . This is also stated by E. P. Cohen, K. Crowe and J. Dumond and A. Cook. .

L. Cooper in his two-volume physics textbook gives a different value: G=6.71·10 -11 m?/(kg s?) .

O. P. Spiridonov - third: G=(6.6 ± 0.04) 10 -11 m?/(kg s?) .

However, Cavendish's classic work did not give any value for G. He only calculated the mean density Earth: 5.48 densities water (modern meaning 5.52 g/cm?). Cavendish's conclusion that the average density of the planet is 5.48 g/cm? more than the surface ~2 g/cm?, confirmed that heavy substances are concentrated in the depths.

The gravitational constant was first introduced, apparently for the first time, only S.D. Poisson in "Treatise on Mechanics" (1811) . The value of G was later calculated by other scientists from data from the Cavendish experiment. Historians do not know who first calculated the numerical value of G.

Marenkov Alexey

History of experiments to determine the gravitational constant and calculate the mass of the planet.

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Presentation on physics on the topic: “Henry Cavendish’s experiment to determine the gravitational constant and measure the mass of the planet” 9th grade student of GBOU secondary school No. 1465 Alexey Marenkov Physics teacher: L.Yu. Kruglova Moscow, 2013

Plan 1. History 2. Installation for the experiment 3. Calculated value of the gravitational constant 4. Physical meaning of the gravitational constant. 5. Cavendish's experience revived the law of gravity. 6. The role of Henry Cavendish's experience 7. Determination of the mass of the Earth

History Newton's establishment of the law of universal gravitation was the most important event in the history of physics. Its significance is determined primarily by the universality of gravitational interaction. One of the central branches of astronomy - celestial mechanics - is based on the law of universal gravitation. We feel the force of gravity towards the Earth, but the attraction of small bodies to each other is imperceptible. It was necessary to experimentally prove the validity of the law of universal gravitation for ordinary bodies. This is exactly what Cavendish did, simultaneously determining the average density of the Earth. The experiment was originally proposed by John Michell. It was he who designed the main part in the experimental installation - the torsion balance, but died in 1793 without completing the experiment. After his death, the experimental setup passed to Henry Cavendish. Cavendish modified the setup, carried out experiments, and described them in the Philosophical Transactions in 1798.

Installation The installation was a wooden rocker about 1.8 m long with small lead balls with a diameter of 5 cm and a mass of 775 g attached to its ends, suspended on a thread of silver-plated copper 1 m long. To these balls, using a special rotary truss, the axis of rotation which coincides as accurately as possible with the axis of the thread, two larger lead balls were brought in - with a diameter of 20 cm and a mass of 49.5 kg, rigidly fixed to the truss. Due to the gravitational interaction of small balls with large ones, the rocker arm was deflected by a certain angle. Knowing the elastic properties of the thread, as well as the angle of rotation of the rocker, we can calculate the force of attraction of the small ball to the large one, and hence the gravitational constant. The torsional elasticity of the thread was determined based on the period free vibrations rocker, which was 15 minutes. Since the measured forces are negligibly small, a number of measures were taken to compensate for errors arising from the influence of physical conditions of the experiment that are not directly related to the measured ones. gravitational forces, but can have an impact on the result comparable to or even greater than the effect of these forces. Among these measures the following can be noted.

The experiment is carried out in two steps: first, large balls are brought to small ones using a rotating truss mechanism on one side (for example, counterclockwise, as shown in the figure), and then on the opposite side, and measured double angle twisting the thread - from deflecting the rocker in one direction to the opposite. This increases the directly measured value of the angle, and most importantly, it compensates for the influence of possible inclination or deformation of the installation and/or building when moving heavy balls during the experiment, as well as the impact on the result of all sorts of asymmetric factors: the technically inevitable asymmetry of the installation itself, gravitational influence massive objects located nearby (buildings, mountains, etc.), magnetic field The Earth, its rotation, the position of the Sun and Moon, etc. To prevent the influence of convection air flows in the room, the torsion balances were enclosed in a wooden casing. Assuming that thread twisting may be influenced magnetic interaction iron truss rods and lead balls, Cavendish replaced the rods with copper ones, obtaining the same results.

ABCDDCBAEFFEA is a fixed wooden casing within which a torsion balance is suspended. m - thin wooden rocker rod. g - a stretcher made of thin silver wire, imparting rigidity to the rocker arm. X - small balls suspended from a beam on a wire. K - handle for the initial installation of the rocker arm. RrPrR - rotating truss, with large balls attached to it MM - pulley for the turning mechanism of the truss. L - lighting devices T - telescopes for observing the deflection of the rocker arm through glazed holes in the end walls of the casing, opposite the ends of the rocker arm. At the lower edges of these holes with inside scales were installed on the casing ivory with graduations of 1/20 inch (about 1.2 mm). At the ends of the rocker arms were attached verniers made of the same material, with the same divisions, divided into 5 equal segments. The accuracy of measuring the deflection of the rocker arm end was therefore 1/100 of an inch. The presence of two telescopes made it possible to control the correctness of the experiment: if the readings of the telescopes were noticeably different, this would indicate the presence of some kind of defect in the design of the installation, or some unaccounted physical factor that significantly influenced the result. For its time, this installation was an unparalleled masterpiece of the art of physical experimentation.

Calculated value The Britannica states that G. Cavendish obtained the value G = 6.754·10 −11 m³/(kg s²). This is also stated by E. P. Cohen, K. Crowe, J. Dumond and A. Cook. L. Cooper in his two-volume physics textbook gives a different value: G = 6.71·10 −11 m³/(kg s²). O.P. Spiridonov - third: G = (6.6±0.04)·10 −11 m³/(kg s²). Cavendish himself in his experiment did not set the task of determining the gravitational constant, about which in his time a unified idea had not yet been developed in the scientific community. In his classic work, he calculated the average density of the Earth: 5.48 densities of water (the modern value of 5.52 g/cm³ differs only 0.7% from Cavendish's result). Average density The planet turned out to be significantly larger than the surface one (~2 g/cm³), from which it followed that heavy substances were concentrated in the depths of the Earth. The gravitational constant was apparently introduced for the first time only by S. D. Poisson in his Treatise on Mechanics (1811). The value of G was later calculated by other scientists from data from the Cavendish experiment. Historians do not know who first calculated the numerical value of G.

The role of the Cavendish experiment The law of universal gravitation received experimental proof The law of universal gravitation became applicable to quantitative calculations. Now it was possible to calculate the masses and densities of various celestial bodies, including the Earth, trajectories artificial satellites Earth. Determine the time and place of solar and lunar eclipses. Discover new planets and stars. Predict new physical patterns.

Determination of the mass of the Earth. Let us assume that a body of mass 1 kg located at its surface interacts with the Earth. Then the force of attraction of a body to the Earth can be found in two ways - using the formulas: Equating the right sides of these equalities, we obtain: It is known that g = 9.81 m/s 2, G = 6.67 ∙ 10 -11 N ∙ m 2 /kg 2, R =6370000 m, substituting their values, we obtain the mass of the Earth:

Feynman quote. ... Cavendish scales, two attracting balls, this is a small model solar system. If you increase it by 10 million times, and here you have galaxies that attract each other according to the same law, embroidering their own pattern. Nature uses only the longest threads and anyone, even the smallest example, can open our eyes to the structure of the whole.

Physical meaning of the gravitational constant. Let's find out physical meaning– G, for this we express it through quantities that are included in the law: If the masses of bodies are equal to 1 kg, the distance between the bodies is 1 m, then G = F, where the gravitational constant is numerically equal to the modulus of the force of attraction between two material points weighing 1 kg each, when the distance between them is 1m. Its name.

The need to calculate the gravitational constant. When analyzing the law of universal gravitation, attention is drawn to the fact that without knowledge of (G), it cannot be applicable for quantitative calculations. To measure (G), one must independently determine the values ​​of the other physical quantities included in the formula of the law. About the complexity of conducting similar experiments The fact that it was possible to “revive” the law of universal gravitation only more than a century after its discovery gives an idea.

Cavendish's experiment revived the law of gravity. This was done in 1798 by the English scientist Cavendish. The main purpose of Cavendish's experiment was to measure the force with which spherical bodies were attracted to each other. Cavendish took advantage torsion scales- a very sensitive device that was invented by his compatriot F. Mitchell. The Cavendish Experience Henry CAVENDISH (), English physicist and chemist. Determined the composition of air (1781) and chemical composition water (1784). With the help of the torsion balances he invented, he confirmed the law of universal gravitation. Determined the mass of the Earth (1798).

The role of the Cavendish experience 1. The law of universal gravitation received experimental proof 2. The law of universal gravitation became applicable for quantitative calculations. 3. Now it was possible to calculate the masses and densities of various celestial bodies, including the Earth, and the trajectories of artificial Earth satellites. 4. Determine the time and place of solar and lunar eclipses. 5.Discover new planets and stars. 6.Predict new physical patterns.

Determination of the mass of the Earth. Let us assume that a body of mass 1 kg located at its surface interacts with the Earth. Then the force of attraction of a body to the Earth can be found in two ways - using the formulas: Equating the right sides of these equalities, we obtain: It is known that g = 9.81 m/s 2, G = 6.67 * nm 2 / kg 2, R = m, Substituting their values, we get the mass of the Earth:

Feynman quote. ... Cavendish scales, two attracting balls, this is a small model of the solar system. If you increase it by 10 million times, and here you have galaxies that attract each other according to the same law. Embroidering your own pattern. Nature uses only the longest threads and anyone, even the smallest example, can open our eyes to the structure of the whole.

- celestial mechanics. We feel the force of gravity towards the Earth, but the attraction of small bodies to each other is imperceptible. It was necessary to experimentally prove the validity of the law of universal gravitation for ordinary bodies. This is exactly what Cavendish did, simultaneously determining the average density of the Earth.

Modern expression of the law of universal gravitation:

Where Unable to parse expression (Executable file texvc not found; See math/README for setup help.): G- gravitational constant, Unable to parse expression (Executable file texvc not found; See math/README - help with setup.): m_1 And Unable to parse expression (Executable file texvc not found; See math/README - help with setup.): m_2- masses of material points, Unable to parse expression (Executable file texvc not found; See math/README for setup help.): R- the distance between them, a Unable to parse expression (Executable file texvc not found; See math/README for setup help.): F- the strength of interaction between them.

Until the beginning of the 19th century, the constant G was not introduced into the law of universal gravitation, since for all calculations in celestial mechanics it is enough to use constants GM, having kinematic dimension. Constant G appeared for the first time, apparently, only after the unification of units and the transition to a single metric system of measures at the end of the 18th century. Numerical value G can be calculated through the average density of the Earth, which had to be determined experimentally. It is obvious that for known values ​​of density ρ and radius R Earth, as well as acceleration due to gravity g on its surface you can find G:

The experiment was originally proposed by John Michell. It was he who designed the main part in the experimental installation - the torsion balance, but died in , without having carried out the experiment. After his death, the experimental setup passed to Henry Cavendish. Cavendish modified the setup, conducted experiments and described them in Philosophical Transactions in 1798.

Installation

The installation was a wooden rocker about 1.8 m long with small lead balls with a diameter of 5 cm and a mass of 775 g attached to its ends, suspended on a thread of silver-plated copper 1 m long. To these balls using a special rotary truss, the axis of rotation of which coincides as accurately as possible with the axis of the thread, two larger lead balls were brought in - with a diameter of 20 cm and a mass of 49.5 kg, rigidly fixed to the truss. Due to the gravitational interaction of small balls with large ones, the rocker arm was deflected by a certain angle. Knowing the elastic properties of the thread, as well as the angle of rotation of the rocker, we can calculate the force of attraction of the small ball to the large one, and hence the gravitational constant.

The torsional elasticity of the thread was determined based on the period of free oscillation of the rocker arm, which was 15 minutes.

Since the measured forces are negligibly small, a number of measures were taken to compensate for errors arising from the influence of physical conditions of the experiment that are not directly related to the measured gravitational forces, but can have an influence on the result comparable to or even greater than the effect of these forces. Among these measures the following can be noted.

1. The experiment is carried out in two steps: first, large balls are brought to small ones using a rotating truss mechanism on one side (for example, counterclockwise, as shown in the figure), and then on the opposite side, and the double angle of twist of the thread is measured - from the deflection of the rocker in one direction to the opposite. This increases the directly measured value of the angle, and most importantly, it compensates for the influence of possible inclination or deformation of the installation and/or building when moving heavy balls during the experiment, as well as the impact on the result of various asymmetric factors: the technically inevitable asymmetry of the installation itself, the gravitational influence of massive objects located nearby (buildings, mountains, etc.), the Earth’s magnetic field, its rotation, the position of the Sun and Moon, etc.
2. To prevent the influence of convection air currents in the room, the torsion scales were enclosed in a wooden casing.
3. Assuming that the twisting of the thread could be influenced by the magnetic interaction of the iron rods of the truss and the lead balls, Cavendish replaced the rods with copper ones, obtaining the same results.

Cavendish himself in his experiment did not set the task of determining the gravitational constant, about which in his time a unified idea had not yet been developed in the scientific community. In his classic work, he calculated the average density of the Earth: 5.48 densities of water (the modern value of 5.52 g/cm³ differs only 0.7% from Cavendish's result). The average density of the planet turned out to be significantly higher than the surface density (~2 g/cm³), which meant that heavy substances were concentrated in the depths of the Earth.

The gravitational constant was apparently introduced for the first time only by S. D. Poisson in his Treatise on Mechanics (1811). The value of G was later calculated by other scientists from data from the Cavendish experiment. Historians do not know who first calculated the numerical value of G.

Further development of the experiment

See also

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Notes

Literature

• Cavendish G. Experiments to determine the density of the Earth // / Golin G. M. Filonovich S. R. - M., 1989. - P. 255-268.
• Filonovich S. R. Physical experiment and its perception // Studies in the history of physics and mechanics. M., 1988. P.5-36 (I); right there. 1989. pp.38-69 (II).
• Milyukov V.K., Sagitov M.U. Gravitational constant in astronomy // Knowledge. 1985. No. 9.
• Poynting J.H. The mean density of the Earth. L., 1894. 156 p.
• MacCormach R. John Michell and Henry Cavendish. Weighting the stars //Brit. J. Hist. Sci. 1968. Vol.4. No. 14. P.126-155.
• Poisson S.D. Traité de mecanique. Paris, 1811. T.1-2.

Excerpt describing the Cavendish Experiment

– Is this really the Grail, Sever? – I couldn’t resist, I asked.
- No, Isidora. The Grail was never what this amazing Smart Crystal is. People simply “attributed” what they wanted to Radomir... like everything else, “alien.” Radomir, all his adult life, was the Guardian of the Key of the Gods. But people, naturally, could not know this, and therefore did not calm down. First, they were looking for the Chalice that supposedly “belonged” to Radomir. And sometimes his children or Magdalene herself were called the Grail. And all this happened only because the “true believers” really wanted to have some kind of proof of the veracity of what they believe in... Something material, something “holy” that could be touched... (which, Unfortunately, this is happening even now, after many hundreds of years). So the “dark ones” came up with a beautiful story for them at that time in order to ignite sensitive “believing” hearts with it... Unfortunately, people always needed relics, Isidora, and if they didn’t exist, someone simply made them up. Radomir never had such a cup, because he did not have the “Last Supper” itself... at which he supposedly drank from it. The cup of the “Last Supper” was with the prophet Joshua, but not with Radomir.
And Joseph of Arimathea actually once collected a few drops of the prophet’s blood there. But this famous “Grail Cup” was really just a simple clay cup, which all Jews usually drank from at that time, and which was not so easy to find later. A golden or silver bowl, completely strewn with precious stones (as the priests like to portray it) never existed in reality, neither in the time of the Jewish prophet Joshua, nor even more so in the time of Radomir.
But this is another, albeit most interesting, story.

You don't have much time, Isidora. And I think you will want to know something completely different, what is close to your heart, and what, perhaps, will help you find in yourself more strength to survive. Well, in any case, this tangled tangle of two lives that are alien to each other (Radomir and Joshua), too closely tied by “dark” forces, cannot be unraveled so soon. Like I said, you simply don't have time for this, my friend. Forgive me...
I just nodded in response, trying not to show how much I was interested in all this real true story! And how I wanted to know, even if I was dying, all the incredible amount of lies brought down by the church on our gullible earthly heads... But I left it to the North to decide what exactly he wanted to tell me. It was his free will- to say or not to tell me this or that. I was already incredibly grateful to him for his precious time, and for his sincere desire to brighten up our sad remaining days.
We found ourselves again in the dark night garden, “listening” last hours Radomir and Magdalena...
– Where is this Great Temple, Radomir? – Magdalena asked in surprise.
- In a wonderful far away country... At the very “top” of the world... (meaning North Pole, former country Hyperborea - Daaria), Radomir whispered quietly, as if going into the infinitely distant past. “There stands a holy, man-made mountain, which neither nature, nor time, nor people can destroy. For this mountain is eternal... This is the Temple of Eternal Knowledge. Temple of our old Gods, Mary...
Once upon a time, a long time ago, their Key sparkled on the top of the holy mountain - this green crystal that gave the Earth protection, opened souls, and taught the worthy. Only now our Gods have left. And since then, the Earth has plunged into darkness, which man himself has not yet been able to destroy. There is still too much envy and anger in him. And laziness too...

– People need to see the light, Maria. – After a short silence, Radomir said. – And YOU are the one who will help them! – And as if not noticing her protesting gesture, he calmly continued. – YOU will teach them KNOWLEDGE and UNDERSTANDING. And give them real FAITH. You will become theirs Guiding Star no matter what happens to me. Promise me!.. I have no one else to trust with what I had to do myself. Promise me, my darling.
Radomir carefully took her face in his hands, carefully peering into the radiant Blue eyes and... unexpectedly smiled... How much endless love shone in those wondrous, familiar eyes!.. And how much deepest pain there was in them... He knew how scared and lonely she was. Knew how much she wanted to save him! And despite all this, Radomir could not help but smile - even in such a terrible time for her, Magdalena somehow remained as amazingly bright and even more beautiful!.. Like a clean spring with life-giving clear water...
Shaking himself, he continued as calmly as possible.
– Look, I’ll show you how this ancient Key opens...
An emerald flame blazed on Radomir’s open palm... Each smallest rune began to open up into a whole layer of unfamiliar spaces, expanding and opening into millions of images that smoothly flowed through each other. The marvelous transparent “structure” grew and spun, revealing more and more floors of Knowledge, never seen by today’s man. It was stunning and endless!.. And Magdalene, unable to take her eyes off all this magic, plunged headlong into the depths of the unknown, experiencing a burning, sizzling thirst with every fiber of her soul!.. She absorbed the wisdom of the centuries, feeling, like a powerful wave, filling every cell of it, unfamiliar Ancient Magic flows through it! The knowledge of the Ancestors flooded, it was truly immense - from the life of the slightest insect it was transferred to the life of the universes, flowed over millions of years into the lives of alien planets, and again, in a powerful avalanche, returned to Earth...
With her eyes wide open, Magdalene listened to the wondrous Knowledge Ancient world... Her light body, free from earthly “shackles,” bathed like a grain of sand in the ocean distant stars, enjoying the grandeur and silence of universal peace...
Suddenly, the fabulous Star Bridge unfolded right in front of her. Stretching out, it seemed, into infinity, it sparkled and sparkled with endless clusters of large and small stars, spreading out at her feet like a silver road. In the distance, in the very middle of the same road, all enveloped in a golden glow, a Man was waiting for Magdalene... He was very tall and looked very strong. Coming closer, Magdalena saw that not everything in this unprecedented creature was so “human”... What struck him most were his eyes - huge and sparkling, as if carved from gemstone, they sparkled with cold edges, like a real diamond. But just like a diamond, they were insensitive and aloof... The stranger’s courageous facial features were surprising with their sharpness and immobility, as if a statue stood in front of Magdalene... Very long, lush hair sparkled and shimmered with silver, as if someone had accidentally scattered stars on it ... The “man” was, indeed, very unusual... But even with all his “icy” coldness, Magdalena clearly felt a wonderful, soul-enveloping peace and warm, sincere kindness coming from the strange stranger. Only for some reason she knew for sure that this kindness was not always the same to everyone.
The “man” raised his palm facing her in greeting and said affectionately:
– Stop, Star... Your Path is not over yet. You can't go Home. Return to Midgard, Maria... And take care of the Key of the Gods. May Eternity protect you.
And then, the powerful figure of the stranger suddenly began to slowly oscillate, becoming completely transparent, as if about to disappear.
- Who are you?.. Please tell me who you are?! – Magdalena shouted pleadingly.
- Wanderer... You will meet me again. Goodbye, Star...
Suddenly the wondrous crystal slammed shut... The miracle ended as unexpectedly as it began. Everything around immediately became chilly and empty... As if it was winter outside.