James E. MILLER
The huge increase in the number of young energetic workers working in the scientific field is a happy consequence of the expansion scientific research in our country, encouraged and cherished by the Federal Government. Exhausted and twitchy scientific supervisors these neophytes are abandoned to their fate, and they are often left without a pilot to guide them through the pitfalls of government subsidies. Fortunately, they can be inspired by the story of Sir Isaac Newton, who discovered the law universal gravity. Here's how it happened.
In 1665, young Newton became professor of mathematics at Cambridge University- his alma mater. He was in love with his work, and his abilities as a teacher were beyond doubt. However, it should be noted that this was in no way a person not of this world or an impractical inhabitant of a tower from Ivory. His work in the college was not limited to the classroom: he was an active member of the Schedule Commission, sat on the management of the university branch of the Young Christian Association of Noble Birth, served on the Dean's Assistance Committee, on the Publications Commission and other and other commissions that were necessary for proper management of the college in the distant 17th century. Careful historical research shows that in just five years, Newton sat on 379 commissions that studied 7,924 problems of university life, of which 31 problems were solved.
Once (and this was in 1680), after a very busy day, a meeting of the commission, scheduled for eleven o’clock in the evening, was not ahead of time, did not gather the necessary quorum, because one of the oldest members of the commission suddenly died of nervous exhaustion. Every moment conscious life Newton had been carefully planned, and then it suddenly turned out that he had nothing to do that evening, since the start of the meeting of the next commission was scheduled only for midnight. So he decided to walk a little. This short walk changed world history.
It was autumn. In the gardens of many good citizens, who lived next door to Newton’s modest house, the trees were breaking under the weight of ripe apples. Everything was ready for harvest. Newton saw a very tasty apple fall to the ground. Newton's immediate reaction to this event—typical of the human side of a great genius—was to climb over the garden fence and put the apple in his pocket. Having moved a decent distance from the garden, he took a bite of the juicy fruit with pleasure.
That's when it dawned on him. While pondering, without preliminary logical reasoning, the thought flashed in his brain that the fall of an apple and the movement of planets in their orbits must obey the same universal law. Before he had time to finish the apple and throw away the core, the formulation of the hypothesis about the law of universal gravitation was already ready. There were three minutes left before midnight, and Newton hurried to a meeting of the Commission for the Suppression of Opium Smoking Among Students of Ignoble Origin.
In the following weeks, Newton's thoughts returned again and again to this hypothesis. He devoted the rare free minutes between two meetings to plans to check it. Several years passed, during which, as careful calculations show, he spent 63 minutes and 28 seconds thinking about these plans. Newton realized that testing his hypothesis required more free time than he could count on. After all, it was necessary to determine with great accuracy the length of one degree of latitude per earth's surface and invent differential calculus.
Having no experience in such matters, he chose a simple procedure and wrote short letter of 22 words to King Charles, in which he outlined his hypothesis and pointed out what great opportunities it promises if confirmed. Whether the king saw this letter is unknown, it is quite possible that he did not see it, since he was overloaded state problems and plans for future wars. However, there is no doubt that the letter, having passed through the appropriate channels, reached all the heads of departments, their deputies and their deputies who had full opportunity express your thoughts and recommendations.
Eventually Newton's letter, along with the voluminous file of comments it had acquired along the way, reached the office of the secretary of PCEBIR/KINI/PPABI (His Majesty's Planning Commission for Research and Development, Committee for the Study of New Ideas, Sub-Committee for the Suppression of Anti-British Ideas). The Secretary immediately recognized the importance of the matter and brought it before the Subcommittee, which voted to allow Newton to testify before the Committee. This decision was preceded by a brief discussion of Newton's ideas to see if there was anything anti-British in his intentions, but the record of this discussion, which filled several quarto volumes, clearly shows that no serious suspicion fell on him.
Newton's testimony before PCEVIR/KINI should be recommended reading for all young scientists who do not yet know how to behave when their time comes. The college showed delicacy by granting him a two-month leave without pay during the Committee meetings, and the deputy dean for research sent him off with a humorous parting wish not to return without a “fat” contract. The Committee meeting was held at open doors, and quite a lot of people crowded in, but later it turned out that most of those present had the wrong door, trying to get to the meeting of KEVORSPVO - His Majesty’s Commission for Exposing Depravity Among Representatives of High Society.
After Newton had been sworn in and solemnly declared that he was not a member of His Majesty's Loyal Opposition, had never written immoral books, had never traveled to Russia or seduced milkmaids, he was asked to briefly state the essence of the matter. In a brilliant, simple, crystal-clear ten-minute speech, delivered impromptu, Newton outlined Kepler's laws and his own hypothesis, born of the sight of a falling apple. At this moment one of the members of the Committee, an imposing and dynamic man, real man actions, wanted to know what means Newton could offer to improve the organization of apple growing in England. Newton began to explain that the apple was not an essential part of his hypothesis, but was interrupted by several members of the Committee, who unanimously expressed support for the project to improve English apples. The discussion continued for several weeks, during which Newton, with his characteristic calm and dignity, sat and waited for the Committee to wish to consult him. One day he was several minutes late for the start of a meeting and found the door locked. He knocked carefully, not wanting to disturb the Committee members' thoughts. The door opened slightly, and the gatekeeper, whispering that there was no room, sent him back. Newton, always distinguished by his logical thinking, came to the conclusion that the Committee no longer needed his advice, and therefore returned to his college, where he was expected to work on various commissions.
A few months later, Newton was surprised to receive a bulky package of PCEVIR/KINI. Opening it, he discovered that the contents consisted of numerous government forms, five copies each. Natural curiosity - main feature every true scientist - forced him to carefully study these questionnaires. Having spent on this study certain time, he realized that he was being invited to apply for a contract to conduct a scientific study to clarify the relationship between the way apples are grown, their quality and the speed at which they fall to the ground. The ultimate goal The project, he realized, was to develop a variety of apples that would not only taste good, but also fall to the ground softly without damaging the skin. This, of course, was not exactly what Newton had in mind when he wrote the letter to the king. But he was a practical man and realized that by working on the proposed problem, he could simultaneously test his hypothesis. So he will respect the interests of the king and do a little science - for the same money. Having made this decision, Newton began filling out the forms without further hesitation.
One day in 1865, Newton's precise daily routine was disrupted. On Thursday afternoon, he was preparing to receive a commission of vice-presidents of the companies that were part of the fruit syndicate, when the news that plunged Newton into horror and the whole of Britain into grief arrived that the entire composition of the commission had been killed during a terrible collision of stagecoaches. Newton, as had happened once before, had an unoccupied “window” and decided to take a walk. During this walk, the idea came to him (he doesn’t know how) about a new, completely revolutionary mathematical approach, with the help of which one can solve the problem of attraction near large sphere. Newton realized that solving this problem would allow him to test his hypothesis with the greatest accuracy, and immediately, without resorting to ink or paper, he proved in his mind that the hypothesis was confirmed. One can easily imagine how delighted he was with such a brilliant discovery.
This is how His Majesty's Government supported and encouraged Newton during these intense years of work on the theory. We will not dwell on Newton's attempts to publish his proof, Fr. misunderstandings with the editors of the Gardeners' Journal and how his article was rejected by the Amateur Astronomer and Physics for Housewives magazines. Suffice it to say that Newton founded his own journal in order to be able to print the message about his discovery without abbreviations or distortions.
Published in The American Scientist, 39, No. 1 (1951).
J.E. Miller is chairman of the Department of Meteorology and Oceanography at New York University.
/brief historical perspective/
The greatness of a true scientist is not in the titles and awards with which he is marked or awarded by the world community, and not even in the recognition of his services to Humanity, but in the discoveries and theories that he left to the World. Unique discoveries made during our bright life, famous scientist Isaac Newton is difficult to overestimate or underestimate.
Theories and discoveries
Isaac Newton formulated the basic laws classical mechanics , was opened law of universal gravitation, theory developed movements of celestial bodies, created fundamentals of celestial mechanics.
Isaac Newton(independently of Gottfried Leibniz) created theory of differential and integral calculus , opened light dispersion, chromatic aberration, studied interference and diffraction, developed corpuscular theory Sveta, gave a hypothesis that combined corpuscular And wave representations, built mirror telescope.
Space and time Newton considered absolute.
Historical formulations of Newton's laws of mechanics
Newton's first law
Every body continues to be maintained in a state of rest or uniform and rectilinear movement, until and as long as it is not forced by applied forces to change this state.
Newton's second law
IN inertial system reference acceleration, which receives material point, directly proportional to the resultant of all forces applied to it and inversely proportional to its mass.
The change in momentum is proportional to the applied driving force and occurs in the direction of the straight line along which this force acts.
Newton's third law
An action always has an equal and opposite reaction, otherwise the interactions of two bodies on each other are equal and directed in opposite directions.
Some of Newton's contemporaries considered him alchemist. He was the director Mint, established coinage in England, headed the society Prior-Zion, studied the chronology of ancient kingdoms. Several theological works ( for the most part unpublished) devoted to the interpretation of biblical prophecies.
Newton's works
– « New theory light and flowers", 1672 (message Royal Society)
– “Motion of bodies in orbit” (lat. De Motu Corporum in Gyrum), 1684
– “Mathematical principles of natural philosophy” (lat. Philosophiae Naturalis Principia Mathematica), 1687
- “Optics or a treatise on the reflections, refractions, bendings and colors of light” (eng. Opticks or a treatise of the reflections, refractions, inflections and colors of light), 1704
– “On the quadrature of curves” (lat. Tractatus de quadratura curvarum), supplement to "Optics"
– “Enumeration of lines of the third order” (lat. Enumeratio linearum tertii ordinis), supplement to "Optics"
– “Universal arithmetic” (lat. Arithmetica Universalis), 1707
– “Analysis using equations with infinite number members" (lat. De analysi per aequationes numero terminorum infinitas), 1711
– “Method of Differences”, 1711
According to scientists around the world, Newton's work was significantly ahead of the general scientific level of his time and were little understood by his contemporaries. However, Newton himself said about himself: “ I don’t know how the world perceives me, but to myself I seem to be only a boy playing seashore who amuses himself by occasionally finding a pebble more colorful than the others, or a beautiful shell, while the great ocean of truth lies unexplored before me. »
But according to the conviction of no less a great scientist, A. Einstein “ Newton was the first to try to formulate elementary laws, which determine the time course of a wide class of processes in nature with high degree completeness and accuracy" and “... with his works he showed deep and strong influence to the entire worldview as a whole. »
Newton's grave bears the following inscription:
“Here lies Sir Isaac Newton, the nobleman who, with an almost divine mind, was the first to prove with the torch of mathematics the motion of the planets, the paths of comets and the tides of the oceans. He investigated the differences in light rays and the various properties of colors that appeared thereby, which no one had previously suspected. A diligent, wise and faithful interpreter of nature, antiquity and Holy Scripture, he affirmed with his philosophy the greatness of Almighty God, and with his disposition he expressed evangelical simplicity. Let mortals rejoice that such an adornment of the human race existed. »
Prepared Lazarus Model.
I.Newton ()
A widely known story is that Newton's discovery of universal gravitation was prompted by the unexpected fall of an apple from a tree in Woolsthorpe. This story is apparently reliable and is not a legend. Stekeley conveys the following scene relating to Newton’s old age: “The afternoon (in London, at Newton’s) the weather was hot; we went into the garden and drank tea under the shade of several apple trees; it was just the two of us. By the way, Sir Isaac told me that he was in exactly the same situation when the idea of gravity first occurred to him. It was caused by an apple falling while he was sitting deep in thought. Why does the apple always fall vertically, he thought to himself, why not to the side, but always to the center of the Earth. There must be an attractive force in matter concentrated at the center of the Earth. If matter pulls other matter in this way, then there must be a proportionality 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.” For some reason, Stekelei's story remained little known, but a similar retelling of Voltaire from the words of Newton's niece spread throughout the world. I liked the story, they began to show the apple tree, which supposedly served as the reason for the emergence of “Principles,” poets and philosophers used the grateful metaphor, comparing Newton’s apple with the apple that killed Adam, or with the apple of Paris; people far from science liked it simple mechanics emergence of complex scientific idea. There are still quite a few people who know about Newton only what is connected with this story about the apple. There is no reason to doubt that Newton was working on gravity in 1666. This was just another task, and many people were interested in it at that time. In a letter to Halley in 1686, Newton writes quite affirmatively that already in 1665 or 1666 he deduced from Kepler’s laws that the force of gravity must decrease in inverse proportion to the square of the distance between attracting bodies. In another letter to Halley from the same year, Newton writes the following: “In papers written more than 15 years ago (I cannot give the exact date, but in any case it was before the beginning of my correspondence with Oldenburg), I expressed the inverse quadratic proportionality the gravitational pull of the planets towards the Sun depending on the distance and calculated right attitude the earth’s gravity and the conatus recedendi (striving) of the Moon towards the center of the Earth, although not entirely accurately.” In Newton's papers, in addition, there is the following more detailed entry: “In the same year (1666) I began to think about gravity extending to the orbit of the Moon, and found how to estimate the force with which a ball rotating inside a sphere presses on the surface this sphere. From Kepler's rule that the periods of planets are in one and a half proportions to the distance from the centers of their orbits, I deduced that the forces holding the planets in their orbits must be in inversely squares of their distances from the centers around which they rotate. From here I compared the force required to keep Lupa in its orbit with the force of gravity on the surface of the Earth and found that they were almost identical. All this happened in two plague years, 1665 and 1666, for at that time I was at the height of my inventive powers and thought about mathematics and philosophy more than ever since.” In any case, if in 1666 Newton could derive the law of gravitation from Kepler’s laws, then he should have known the expression of centrifugal force, and, so to speak, the “Principles” were already being drafted by Newton the student. As often happened with Newton, for no apparent reason, the question of gravitation and other mechanical problems were put aside for a long time, and he concentrated entirely on optical problems. Newton apparently returned to mechanics only around 1679, i.e. almost 15 years later. Despite the undoubted connection noted above between the optical and mechanical research of Newton and other physicists, his contemporaries, the transition for Newton was quite abrupt. It was not only about a change in the field of research, but also about a new method. From experience Newton moved to the field mathematical physics. In 1675, Collins wrote to Gregory that “mathematical speculation now seems to Barrow and Newton after all dry and sterile.” In the eighties, during the era of the publication of Principia, Newton, on the contrary, liked to call himself a mathematician and gave the title to the book itself - “Mathematical Principia of Natural Philosophy.” Newton combined the qualities of a brilliant experimenter, theoretician and mathematician, but in the eighties we have to note a clear change in his penchant for experimentation into a penchant for math problems. Newton continued chemical work, but to the exact physical experience in any case, he returned very rarely.
So, the movement of planets, for example the Moon around the Earth or the Earth around the Sun, is the same fall, but only a fall that lasts indefinitely (in any case, if we ignore the transition of energy into “non-mechanical” forms).
The conjecture about the unity of causes governing the movement of planets and the fall of earthly bodies was expressed by scientists long before Newton. Apparently, the first to clearly express this idea was the Greek philosopher Anaxagoras, a native of Asia Minor, who lived in Athens almost two thousand years ago. He said that the Moon, if it did not move, would fall to the Earth.
However, Anaxagoras’ brilliant guess, apparently, did not have any practical impact on the development of science. She was destined to be misunderstood by her contemporaries and forgotten by her descendants. Ancient and medieval thinkers, whose attention was attracted by the movement of the planets, were very far from the correct (and more often than not any) interpretation of the causes of this movement. After all, even great Kepler, who, at the cost of enormous labor, was able to formulate the exact mathematical laws of planetary motion, believed that the cause of this motion was the rotation of the Sun.
According to Kepler's ideas, the Sun, rotating, constantly pushes the planets into rotation. True, it remained unclear why the time of revolution of the planets around the Sun differs from the period of revolution of the Sun around own axis. Kepler wrote about this: “if the planets did not have natural resistance, then it would be impossible to give reasons why they should not follow exactly the rotation of the Sun. But although in reality all the planets move in the same direction in which the rotation of the Sun occurs, the speed of their movement is not the same. The fact is that they mix, in certain proportions, the inertia of their own mass with the speed of their movement.”
Kepler failed to understand that the coincidence of the directions of motion of the planets around the Sun with the direction of rotation of the Sun around its axis is not associated with the laws of planetary motion, but with the origin of our solar system. An artificial planet can be launched both in the direction of rotation of the Sun and against this rotation.
Robert Hooke came much closer than Kepler to the discovery of the law of attraction of bodies. Here are his actual words from a work entitled An Attempt to Study the Motion of the Earth, published in 1674: “I will develop a theory which is in every respect consistent with the generally accepted rules of mechanics. This theory is based on three assumptions: firstly, that all celestial bodies, without exception, have a gravity directed towards their center, due to which they attract not only their own parts, but also all celestial bodies within their sphere of action. According to the second assumption, all bodies moving in a rectilinear and uniform manner will move in a straight line until they are deflected by some force and begin to describe trajectories in a circle, an ellipse, or some other less simple curve. According to the third assumption, the forces of attraction act the more strongly, the closer to them the bodies on which they act are located. I have not yet been able to establish by experience what various degrees attraction. But if we develop this idea further, astronomers will be able to determine the law according to which all celestial bodies move.”
Truly, one can only be amazed that Hooke himself did not want to engage in the development of these ideas, citing being busy with other work. But a scientist appeared who made a breakthrough in this area
The history of Newton's discovery of the law of universal gravitation is quite well known. For the first time, the idea that the nature of the forces that make a stone fall and determine the movement of celestial bodies is one and the same arose with Newton the student, that the first calculations did not give the correct results, since the data available at that time on the distance from the Earth to the Moon were inaccurate, that 16 years later new, corrected information about this distance appeared. To explain the laws of planetary motion, Newton applied the laws of dynamics he created and the law of universal gravitation that he himself established.
He named the Galilean principle of inertia as the first law of dynamics, including it in the system of basic laws-postulates of his theory.
At the same time, Newton had to eliminate the error of Galileo, who believed that uniform motion in a circle - this is movement by inertia. Newton pointed out (and this is the second law of dynamics) that the only way To change the movement of a body - the value or direction of speed - is to act on it with some force. In this case, the acceleration with which a body moves under the influence of a force is inversely proportional to the mass of the body.
According to Newton's third law of dynamics, “to every action there is always an equal and opposite reaction.”
Consistently applying the principles - the laws of dynamics, he first calculated the centripetal acceleration of the Moon as it moves in orbit around the Earth, and then was able to show that the ratio of this acceleration to the acceleration free fall bodies near the Earth's surface is equal to the ratio of the squares of the Earth's radii and lunar orbit. From this Newton concluded that the nature of gravity and the force that holds the Moon in orbit are the same. In other words, according to his conclusions, the Earth and the Moon are attracted to each other with a force inversely proportional to the square of the distance between their centers Fg ≈ 1∕r2.
Newton was able to show that the only explanation The independence of the acceleration of free fall of bodies from their mass is the proportionality of the force of gravity to the mass.
Summarizing the findings, Newton wrote: “there can be no doubt that the nature of gravity on other planets is the same as on Earth. In fact, let us imagine that the earth's bodies are raised to the orbit of the Moon and sent together with the Moon, also devoid of any movement, to fall to the Earth. Based on what has already been proven (meaning the experiments of Galileo), there is no doubt that at the same times they will pass through the same spaces as the Moon, for their masses are related to the mass of the Moon in the same way as their weights are to its weight.” So Newton discovered and then formulated the law of universal gravitation, which is rightfully the property of science.
2. Properties of gravitational forces.
One of the most remarkable properties forces of universal gravitation, or, as they are often called, gravitational forces, are already reflected in the very name given by Newton: universal. These forces, so to speak, are “the most universal” among all the forces of nature. Everything that has mass - and mass is inherent in any form, any kind of matter - must experience gravitational influences. Even light is no exception. If you visualize gravitational forces with the help of threads that stretch from one body to another, then an innumerable number of such threads would have to permeate space anywhere. At the same time, it is worth noting that it is impossible to break such a thread and protect yourself from gravitational forces. There are no barriers to universal gravity; their radius of action is unlimited (r = ∞). Gravitational forces are long-range forces. This is " official name"of these forces in physics. Due to long-range action, gravity connects all bodies of the Universe.
The relative slowness of the decrease of forces with distance at each step is manifested in our earthly conditions: after all, all bodies do not change their weight when transferred from one height to another (or, to be more precise, they change, but extremely insignificantly), precisely because with a relatively small change in distance – in in this case from the center of the Earth - gravitational forces practically do not change.
By the way, it is for this reason that the law of measuring gravitational forces with distance was discovered “in the sky.” All the necessary data was drawn from astronomy. One should not, however, think that a decrease in gravity with height cannot be detected under terrestrial conditions. For example, pendulum clock with an oscillation period of one second, they will lag by almost three seconds per day if they are lifted from the basement to the top floor of Moscow University (200 meters) - and this is only due to a decrease in gravity.
Heights at which they move artificial satellites, are already comparable to the radius of the Earth, so to calculate their trajectory, taking into account the change in force gravity with distance is absolutely necessary.
Gravitational forces have another very interesting and unusual property, which will be discussed now.
For many centuries, medieval science accepted as an unshakable dogma Aristotle's statement that a body falls the faster the greater its weight. Even everyday experience confirms this: it is known that a piece of fluff falls slower than a stone. However, as Galileo was able to show for the first time, the whole point here is that air resistance, coming into play, radically distorts the picture that would be if only earthly gravity acted on all bodies. There is a remarkable experiment with the so-called Newton tube, which makes it possible to very easily evaluate the role of air resistance. Here short description this experience. Imagine an ordinary glass tube (so that you can see what is happening inside) in which various items: pellets, pieces of cork, feathers or fluffs, etc. If you turn the tube over so that all this can fall, then the pellet will flash quickly, followed by pieces of cork and, finally, the fluff will smoothly fall. But let’s try to monitor the fall of the same objects when the air is pumped out of the tube. The fluff, having lost its former slowness, rushes along, keeping pace with the pellet and the cork. This means that its movement was delayed by air resistance, which had a lesser effect on the movement of the plug and even less on the movement of the pellet. Consequently, if it were not for air resistance, if only the forces of universal gravity acted on bodies - in a particular case, gravity - then all bodies would fall exactly the same, accelerating at the same pace.
But “there is nothing new under the sun.” Two thousand years ago Lucretius Carus in his famous poem“On the Nature of Things” wrote:
everything that falls in rare air,
Should fall faster according to its own weight
Only because water or air is a subtle essence
I am not able to put obstacles in the way of things that are the same,
But it is more likely to yield to those with greater severity.
On the contrary, I am never capable of anything anywhere
The thing holds the emptiness and appears as some kind of support,
By nature, constantly giving in to everything.
Therefore, everything, rushing through the void without obstacles,
Have the same speed despite the difference in weight.
Of course, these wonderful words were a great guess. To turn this guess into a reliable established law, required many experiments, starting with famous experiments Galileo, who studied the fall of balls of the same size, but made of various materials(marble, wood, lead, etc.), and ending with the most complex modern measurements of the influence of gravity on light. And all this variety of experimental data persistently strengthens us in the belief that gravitational forces impart equal acceleration to all bodies; in particular, the acceleration of free fall caused by gravity is the same for all bodies and does not depend on the composition, structure, or mass of the bodies themselves.
This seemingly simple law expresses perhaps the most remarkable feature of gravitational forces. There are literally no other forces that accelerate all bodies equally, regardless of their mass.
So, this property of the forces of universal gravity can be compressed into one short statement: the gravitational force is proportional to the mass of bodies. Let us emphasize that here we're talking about about the very mass that acts as a measure of inertia in Newton’s laws. It is even called inert mass.
The four words “gravitational force is proportional to mass” contain a surprising deep meaning. Large and small bodies, hot and cold, of all kinds chemical composition, any structure - they all experience the same gravitational interaction if their masses are equal.
Or maybe this law is really simple? After all, Galileo, for example, considered it almost self-evident. Here is his reasoning. Let two bodies of different weights fall. According to Aristotle, a heavy body should fall faster even in vacuum. Now let's connect the bodies. Then, on the one hand, the bodies should fall faster, since the total weight has increased. But, on the other hand, adding a part to a heavy body that falls more slowly should slow down this body. There is a contradiction that can be eliminated only if we assume that all bodies under the influence of gravity alone fall with the same acceleration. It's like everything is consistent! However, let us think again about the above reasoning. It is based on the common method of proof “by contradiction”: by assuming that a heavier body falls faster than a lighter one, we have arrived at a contradiction. And from the very beginning there was an assumption that the acceleration of free fall is determined by weight and only weight. (Strictly speaking, not by weight, but by mass.)
But this is not at all obvious in advance (i.e., before the experiment). What if this acceleration was determined by the volume of the bodies? Or temperature? Let's imagine that there is a gravitational charge, similar to an electric charge and, like the latter, completely unrelated directly to mass. Comparison with electric charge very helpful. Here are two specks of dust between the charged plates of a capacitor. Let these specks of dust equal charges, and the masses are related as 1 to 2. Then the accelerations must differ by a factor of two: the forces determined by the charges are equal, and when equal forces body doubled greater mass accelerates at half the rate. If you connect dust particles, then, obviously, the acceleration will have a new, intermediate value. No speculative approach without experimental research electrical forces cannot provide anything here. The picture would be exactly the same if the gravitational charge were not associated with mass. But only experience can answer the question of whether such a connection exists. And we now understand that it was the experiments that proved the identical acceleration due to gravity for all bodies that essentially showed that the gravitational charge (gravitational or heavy mass) is equal to the inertial mass.
Experience and only experience can serve as a basis for physical laws, and the criterion of their fairness. Let us at least recall the record-breaking precision experiments conducted under the leadership of V.B. Braginsky at Moscow State University. These experiments, in which an accuracy of about 10-12 was obtained, once again confirmed the equality of heavy and inert mass.
It is on experience, on the wide testing of nature - from the modest scale of a small laboratory of a scientist to the grandiose cosmic scale - that the law of universal gravitation is based, which (to summarize everything said above) says:
The force of mutual attraction of any two bodies whose dimensions are much smaller than the distance between them is proportional to the product of the masses of these bodies and inversely proportional to the square of the distance between these bodies.
The proportionality coefficient is called the gravitational constant. If we measure length in meters, time in seconds, and mass in kilograms, the gravitational force will always be equal to 6.673*10-11, and its dimension will be m3/kg*s2 or N*m2/kg2, respectively.
G=6.673*10-11 N*m2/kg2
3. Gravitational waves.
In Newton's law of universal gravitation on the time of transmission gravitational interaction nothing is said. It is implicitly assumed that it occurs instantly, no matter how large the distances between the interacting bodies are. This view is generally typical of supporters of action at a distance. But from " special theory relativity” by Einstein, it follows that gravity is transmitted from one body to another at the same speed as the light signal. If some body moves from its place, then the curvature of space and time caused by it does not change instantly. This will first affect close proximity from the body, then the change will capture more and more distant areas, and finally, a new distribution of curvature will be established throughout space, corresponding to the changed position of the body.
And here we come to a problem that has caused and continues to cause greatest number disputes and disagreements - the problem of gravitational radiation.
Can gravity exist if there is no mass creating it? According to Newton's law– definitely not. It makes no sense to even raise such a question there. However, as soon as we agreed that gravitational signals are transmitted, although at a very high, but still not infinite speed, everything changes radically. Indeed, imagine that at first the mass causing gravity, for example a ball, was at rest. All bodies around the ball will be affected by ordinary Newtonian forces. Now let’s remove the ball from its original place with great speed. At first, the surrounding bodies will not feel this. After all, gravitational forces do not change instantly. It takes time for changes in the curvature of space to spread in all directions. This means that the surrounding bodies will experience the same influence of the ball for some time, when the ball itself is no longer there (at least, in the same place).
It turns out that the curvatures of space acquire a certain independence, that it is possible to tear a body out of the region of space where it caused the curvatures, and in such a way that these curvatures themselves, at least over large distances, will remain and develop in their own way internal laws. Here is gravity without gravitating mass! We can go further. If you make the ball oscillate, then, as it turns out from Einstein’s theory, on Newton's picture gravity, a kind of ripple is superimposed - waves of gravity. To better imagine these waves, you need to use a model - a rubber film. If you not only press your finger on this film, but at the same time make it oscillatory movements, then these vibrations will begin to be transmitted along the stretched film in all directions. This is an analogue of gravitational waves. The further away from the source, the weaker such waves are.
And now at some point we will stop putting pressure on the film. The waves won't go away. They will exist independently, scattering further and further across the film, causing geometry to bend along the way.
In exactly the same way, waves of space curvature - gravitational waves - can exist independently. Many researchers draw this conclusion from Einstein’s theory.
Of course, all these effects are very weak. For example, the energy released during the combustion of one match is many times greater than the energy of gravitational waves emitted by our entire planet. solar system for the same time. But what is important here is not the quantitative, but the principled side of the matter.
Proponents of gravitational waves - and they seem to be in the majority now - predict one more thing. amazing phenomenon; the transformation of gravity into particles such as electrons and positrons (they must be born in pairs), protons, antitrons, etc. (Ivanenko, Wheeler, etc.).
It should look something like this. A wave of gravity reached a certain area of space. At a certain moment, this gravity sharply, abruptly, decreases and at the same time, say, an electron-positron pair appears there. The same can be described as an abrupt decrease in the curvature of space with the simultaneous birth of a pair.
There are many attempts to translate this into quantum mechanical language. Particles are introduced into consideration - gravitons, which are compared to a non-quantum image gravitational wave. In the physical literature, the term “transmutation of gravitons into other particles” is in circulation, and these transmutations - mutual transformations - are possible between gravitons and, in principle, any other particles. After all, there are no particles that are insensitive to gravity.
Even if such transformations are unlikely, that is, they happen extremely rarely, cosmic scale they may turn out to be fundamental.
4. Curvature of space-time by gravity,
"Eddington's Parable"
Parable English physicist Eddington from the book “Space, Time and Gravity” (retelling):
“In an ocean that has only two dimensions, there once lived a breed of flat fish. It was observed that the fish generally swam in straight lines as long as they did not encounter obvious obstacles in their path. This behavior seemed quite natural. But there was a mysterious area in the ocean; when the fish fell into it, they seemed enchanted; some sailed through this area but changed the direction of their movement, others endlessly circled around this area. One fish (almost Descartes) proposed a theory of vortices; she said that in this area there are whirlpools that make everything that gets into them spin. Over time, a much more advanced theory was proposed (Newton's theory); they said that all fish are attracted to a very large fish - the sun fish, dormant in the middle of the region - and this explained the deviation of their paths. At first this theory seemed perhaps a little strange; but she's with amazing accuracy confirmed by a wide variety of observations. All fish have been found to have this attractive property, proportionate to their size; the law of attraction (analogous to the law of universal gravitation) was extremely simple, but despite this, it explained all movements with such precision that the accuracy of scientific research had never reached before. True, some fish, grumbling, declared that they did not understand how such an action at a distance was possible; but everyone agreed that this action was carried out by the ocean, and that it would be easier to understand when the nature of water was better studied. Therefore, almost every fish that wanted to explain gravity began by suggesting some mechanism by which it spread through water.
But there was a fish who looked at things differently. She noticed the fact that the big fish and the small ones always moved along the same paths, although it might seem that it would take a lot of force to deflect the big fish from its path. (The sunfish imparted equal accelerations to all bodies.) Therefore, instead of trying, she began to study in detail the paths of movement of fish and thus came to an astonishing solution to the problem. There was a high place in the world where the sunfish lay. The fish could not directly notice this because they were two-dimensional; but when the fish in its movement fell on the slope of this elevation, then although it tried to swim in a straight line, it involuntarily turned a little to the side. This was the secret of the mysterious attraction or curvature of paths that occurred in the mysterious area. »
This parable shows how the curvature of the world in which we live can give the illusion of gravity, and we see that an effect like gravity is the only way such curvature can manifest itself.
Briefly this can be formulated in the following way. Since gravity bends the paths of all bodies in the same way, we can think of gravity as the curvature of space-time.
5. Gravity on Earth.
If you think about the role that gravitational forces play in the life of our planet, entire oceans open up. And not only oceans of phenomena, but also oceans in the literal sense of the word. Oceans of water. air ocean. Without gravity they would not exist.
A wave in the sea, the movement of every drop of water in the rivers that feed this sea, all currents, all winds, clouds, the entire climate of the planet are determined by the play of two main factors: solar activity and gravity.
Gravity not only holds people, animals, water and air on Earth, but also compresses them. This compression at the Earth's surface is not so great, but its role is important.
The ship is sailing on the sea. What prevents him from drowning is known to everyone. This is the famous buoyant force of Archimedes. But it appears only because water is compressed by gravity with a force that increases with increasing depth. Inside spaceship in flight there is no buoyant force, just as there is no weight. The globe itself is compressed by gravitational forces to colossal pressures. At the center of the Earth, the pressure appears to exceed 3 million atmospheres.
Under the influence for a long time active forces pressure under these conditions, all substances that we are accustomed to consider solid behave like pitch or resin. Heavy materials sink to the bottom (if you can call the center of the Earth that way), and light materials float to the surface. This process has been going on for billions of years. It has not ended, as follows from Schmidt’s theory, even now. The concentration of heavy elements in the region of the Earth's center is slowly increasing.
Well, how does the attraction of the Sun and the closest to us manifest itself on Earth? celestial body Moon? Watch this attraction without special devices only residents of the ocean coasts can.
The sun acts in almost the same way on everything on and inside the Earth. The force with which the Sun attracts a person at noon, when he is closest to the Sun, is almost the same as the force acting on him at midnight. After all, the distance from the Earth to the Sun is ten thousand times greater than the Earth’s diameter, and an increase in the distance by one ten-thousandth when the Earth rotates half a turn around its axis practically does not change the force of gravity. Therefore, the Sun imparts almost identical accelerations to all parts globe and all bodies on its surface. Almost, but still not quite the same. Because of this difference, the ebb and flow of the ocean occurs.
On the part of the earth's surface facing the Sun, the force of gravity is slightly greater than that necessary for the movement of this part along an elliptical orbit, and on opposite side The land is somewhat smaller. As a result, according to Newton's laws of mechanics, the water in the ocean bulges slightly in the direction facing the Sun, and on the opposite side it recedes from the Earth's surface. Tidal forces, as they say, arise, stretching the globe and giving, roughly speaking, the surface of the oceans the shape of an ellipsoid.
The smaller the distances between interacting bodies, the greater the tidal forces. This is why the Moon has a greater influence on the shape of the world's oceans than the Sun. More precisely, tidal influence is determined by the ratio of the mass of a body to the cube of its distance from the Earth; this ratio for the Moon is approximately twice that for the Sun.
If there were no cohesion between the parts of the globe, then tidal forces would tear it apart.
Perhaps this happened to one of Saturn's satellites when it came close to this big planet. That fragmented ring that makes Saturn such a remarkable planet may be debris from the satellite.
So, the surface of the world's oceans is like an ellipsoid, the major axis of which faces the Moon. The earth rotates around its axis. Therefore, along the surface of the ocean towards the direction of rotation of the Earth, it moves tidal wave. When it approaches the shore, the tide begins. In some places the water level rises to 18 meters. Then the tidal wave goes away and the tide begins to ebb. The water level in the ocean fluctuates, on average, with a period of 12 hours. 25min. (half a lunar day).
This simple picture is greatly distorted by the simultaneous tidal action of the Sun, water friction, continental resistance, and the complexity of the configuration of the ocean shores and bottom in coastal areas and some other private effects.
It is important that the tidal wave slows down the Earth's rotation.
True, the effect is very small. Over 100 years, the day increases by a thousandth of a second. But, acting for billions of years, the braking forces will lead to the fact that the Earth will be turned to the Moon all the time with one side, and the Earth’s days will become equal lunar month. This has already happened to Luna. The Moon is slowed down so much that it always faces the Earth with one side. To "look" at reverse side Moon, we had to send a spaceship around it.
Newton's life and the history of his discoveries have become the subject of close attention of scientists and historians. However, there are many contradictions in Newton's biographies; This is probably due to the fact that Newton himself was very secretive person and even suspicious and not so frequent were the moments in his life when he slightly opened his true face, your way of thinking, your passions. Scientists are still trying to recreate his life and, most importantly, his work from surviving papers, letters, and memories, but, as one of the English researchers of Newton’s work noted, “this is largely the work of a detective.”Perhaps Newton's secrecy, his reluctance to let outsiders into his creative laboratory and gave impetus to the emergence of the legend of the falling apple. In any case, there are memoirs of Newton’s friend, Stukeley, where he, allegedly from the words of Newton himself, says that the scientist’s idea of the law of universal gravitation matured at the moment when he saw an apple fall from an apple tree to the ground. This legend is so firmly rooted in history that the tree in Newton's garden from which this famous apple fell was a museum exhibit for many years until a storm broke it, almost a century. Everyone who was lucky enough to visit the family estate of the Newton family in Woolsthorpe, near Cambridge, certainly wanted to look at it. At the same time, another friend of Newton, Pemberton, highly doubted the possibility of such an event. The famous Voltaire, who received information from Newton’s niece, had a similar opinion. A little later, Carl Gauss, the outstanding German mathematician and the astronomer wrote of the notorious apple: “I do not see how this incident could hasten or retard this discovery.” Gauss believed that Newton deliberately made up an anecdotal story in order to get rid of “the annoying, stupid and impudent interrogator.” It is not clear who he had in mind—was it Stukelei?
Probably, true story no one can restore the discoveries; one can only try to assess the reliability of certain facts and their interpretations.
What was certain? That after graduating from college and receiving his bachelor's degree, Newton left Cambridge in the fall of 1665 for his home in Woolsthorpe. Cause? The plague epidemic that swept through England - in the village there is still less chance of becoming infected. It is now difficult to judge how necessary this measure was medical point vision; in any case, she was not superfluous. Although Newton apparently had excellent health- in his old age he retained thick hair, did not wear glasses and lost only one tooth - but who knows how the history of physics would have turned out if Newton had remained in the city.
What else happened? There was undoubtedly also a garden at the house, and in the garden there was an apple tree, and it was autumn, and at this time of year, apples, as you know, often spontaneously fall to the ground. Newton also had a habit of walking in the garden and thinking about the problems that worried him at that moment; he himself did not hide this: “I constantly keep the subject of my research in my mind and patiently wait until the first glimpse gradually turns into a full and brilliant light.” . True, if we assume that it was at that time that the glimmer of a new law illuminated him (and we can now assume so: in 1965 Newton’s letters were published, in one of which he directly speaks about this), then the expectation of “full brilliant light” It took quite a long time - twenty years. Because the law of universal gravitation was published only in 1687. Moreover, it is interesting that this publication was not made on Newton’s initiative; he was literally forced to express his views by his colleague at the Royal Society, Edmund Halley, one of the youngest and most gifted “virtuosos” - that’s what people who were “sophisticated in the sciences” were called at that time. Under his pressure, Newton began to write his famous “Mathematical Principles of Natural Philosophy.” First, he sent Halley a relatively small treatise, “On Movement.”
Halley, instantly appreciating the full significance of Newton's ideas, went to him to convince him to present them in more detail. At the same time, he took upon himself all the financial costs and hassles of publishing. This time he did not have to persuade Newton much: perhaps that rare moment had come when the scientist felt the need to express his views publicly. And within a year and a half, he wrote all three books of his “Principles,” which were fully published in the summer of 1687. And then the whole world, and not just members of the Royal Society, could learn that two particles are attracted to each other with a force directly proportional to the product of their masses and inversely proportional to the square of the distance between them.
That's exactly what happened. In the entire chain of these events, as you can see, there is not much room left for chance, except perhaps a plague epidemic. If not for her, Newton would not have gone to Woolsthorpe, and who knows whether in Cambridge he would have had the opportunity to watch the fall of the apple, and at that moment when the scientist’s imagination is just waiting for a push to head along a completely new, unknown path. But if Newton himself had regarded the story of the apple as a happy accident that unexpectedly led him to outstanding discovery, if he had felt that way about it, would he have waited twenty years to tell the world about this discovery?
However, he was in no hurry to notify the world about accidental discovery. Only in 1673, eight years later, therefore, did he hint in a very vague form in one of his letters to the Dutch scientist Christiaan Huygens that he knew something that made it possible to calculate the magnitude of the mutual attraction of the Earth with the Moon and the Sun. But the hint was so mysterious that it remained ununderstood. Perhaps Newton really had the intention of saying more, but either because in the correspondence between “virtuosos” he was supposed to be mysterious, or simply suspicion or secrecy shackled his good intention, but it remained unfulfilled. Although many years later, Newton assured that his discovery could have long been guessed from a letter to Huygens.
On June 20, 1886, in a letter to Halley regarding the first book of the Principia, Newton hints - again a hint! - that only last year, that is, in 1865, he managed to obtain evidence that the law inverse squares valid not only in space, but also at the surface of the Earth. It took twenty years for the first thought about the identity of the force of attraction governing the movement of planets with the force of gravity on Earth to be embodied in quantity law. Apparently, Newton did not consider it convenient to publish a bare idea that was not supported by calculations, and at first the calculations did not work out. Another legend was even created along the way - that the calculations did not converge due to the fact that Newton used the wrong value of the Earth’s radius, and the correct value was obtained many years later, so he had to wait.
Generally speaking, if we look carefully at when the law of universal gravitation could have been discovered - in the very general view at least - it turns out that it could have been discovered at least as early as the 3rd century BC new era, when it was first suggested that the ebb and flow of tides on Earth are influenced by the Sun and Moon. And in any case, this law should have appeared - if only a falling apple was not enough - in 1596, when Johannes Kepler published the work “The Secret of the Universe”, where he boldly asserted that the Moon moves due to gravity.
But nevertheless the law in its strictest mathematical expression never appeared, although scientists at that time already had an idea of the inverse square law.
Robert Hooke also knew about it when in 1666 he reported to the Royal Society about experiments proving the dependence of body weight on height, and when in 1674 he published the study “On the Motion of the Earth,” where he directly says that “not only the Sun and the Moon influence on the shape and movement of the Earth, and it, in turn, influences their movement, but Mercury, Venus, Mars, Jupiter and Saturn also influence the movement of the Earth with their attraction...” However, at first, Hooke, like Newton, did not dare, or rather, did not guess to extend the action of the inverse square law to the models under consideration and believed that the force of action increases simply in inverse proportion to the distance; Only in 1680 did he decide to introduce the square of distance, which he reported in a letter to Newton, but it was too late: Newton himself had already done it.
In a word, the apple, even if it fell and even if it prompted Newton’s assumption, did not play such a role. big role in the birth of a new law, as the legend attributes to him: you must admit, in twenty years an idea could take shape in the mind of a scientist without his visual help.
But even if we assume that chance played famous role in the emergence of an idea, then the subsequent twenty years of waiting until it is embodied in a formula do not give reason to talk about the ease of such an accidental discovery.