What is the form of the law of universal gravitation? Law of universal gravitation Newton's formula

Almost all the planets of the Solar System (except Pluto) move in orbits that are close to circular.

Kepler's second law (1609): “The radius vector of a planet describes equal areas in equal periods of time” (Fig. 2).

Figure 2 - Law of areas - Kepler's second law

Kepler's second law shows the equality of areas described by the radius vector of a celestial body over equal periods of time. In this case, the speed of the body changes depending on the distance to the Earth (this is especially noticeable if the body moves along a highly elongated elliptical orbit). The closer the body is to the planet, the greater the speed of the body.

Kepler's third law (1619): “The squares of the periods of revolution of the planets are related as the cubes of the semi-major axes of their orbits”:

Kepler's third law is true for all planets in the solar system with an accuracy of greater than 1%.

Figure 3 shows two orbits, one of which is circular with radius R, and the other is elliptical with semi-major axis a. The third law states that if R=a, then the periods of revolution of bodies in these orbits are the same.

Figure 3 - Circular and elliptical orbits

When R=a, the periods of revolution of bodies in these orbits are the same

Kepler's laws, which forever became the basis of theoretical astronomy, were explained in the mechanics of I. Newton, in particular in the law of universal gravitation.

Despite the fact that Kepler's laws were a major step in understanding the motion of the planets, they still remained only empirical rules derived from astronomical observations; Kepler was unable to find the reason that determines these patterns common to all planets. Kepler's laws needed theoretical justification.

And only Newton made a private but very important conclusion: there must be a connection between the centripetal acceleration of the Moon and the acceleration of gravity on Earth. This relationship had to be established numerically and verified.

It was precisely this that Newton's considerations differed from the guesses of other scientists. Before Newton, no one was able to clearly and mathematically prove the connection between the law of gravity (a force inversely proportional to the square of the distance) and the laws of planetary motion (Kepler's laws).

Two of the greatest scientists, far ahead of their time, created a science called celestial mechanics, discovered the laws of motion of celestial bodies under the influence of gravity, and even if their achievements were limited to this, they would still have entered the pantheon of the greats of this world.

It so happened that they did not intersect in time. Only thirteen years after Kepler's death Newton was born. Both of them were supporters of the heliocentric Copernican system.

After studying the motion of Mars for many years, Kepler experimentally discovered three laws of planetary motion, more than fifty years before Newton discovered the law of universal gravitation. Not yet understanding why the planets move the way they do. It was a brilliant foresight.

But Newton used Kepler’s laws to test his law of gravitation. All three of Kepler's laws are consequences of the law of gravity. And Newton discovered it. The results of Newton's calculations are now called Newton's law of universal gravitation, which we will look at in the next chapter.

2 Law of Gravity

2.1 Discovery of Isaac Newton

The law of universal gravitation was discovered by I. Newton in 1682. According to his hypothesis, attractive forces (gravitational forces) act between all bodies of the Universe, directed along the line connecting the centers of mass (Fig. 4). For a body in the form of a homogeneous ball, the center of mass coincides with the center of the ball.

Newton's law of gravity

the law of universal gravitation, one of the universal laws of nature; according to N. z. i.e. all material bodies attract each other, and the magnitude of the gravitational force does not depend on the physical and chemical properties of the bodies, on the state of their motion, on the properties of the environment where the bodies are located. On Earth, gravity manifests itself primarily in the existence of gravity, which is the result of the attraction of any material body by the Earth. Associated with this is the term “gravity” (from the Latin gravitas - heaviness), equivalent to the term “gravity”.

Gravitational interaction in accordance with the New Law. m plays a major role in the movement of stellar systems such as double and multiple stars, inside star clusters and galaxies. However, the gravitational fields inside star clusters and galaxies are of a very complex nature and have not yet been sufficiently studied, as a result of which the movements inside them are studied by methods different from the methods of celestial mechanics (see Stellar astronomy). Gravitational interaction also plays a significant role in all cosmic processes in which accumulations of large masses of matter participate. N. z. t. is the basis for studying the movement of artificial celestial bodies, in particular artificial satellites of the Earth and the Moon, and space probes. On N. z. t. relies on Gravimetry. The forces of attraction between ordinary macroscopic material bodies on Earth can be detected and measured, but do not play any noticeable practical role. In the microcosm, the forces of attraction are negligible compared to intramolecular and intranuclear forces.

Newton left open the question of the nature of gravity. The assumption about the instantaneous propagation of gravity in space (i.e., the assumption that with a change in the positions of bodies the gravitational force between them instantly changes), which is closely related to the nature of gravity, was also not explained. The difficulties associated with this were eliminated only in Einstein's theory of gravitation, which represented a new stage in the knowledge of the objective laws of nature.

Lit.: Isaac Newton. 1643-1727. Sat. Art. to the tercentenary of his birth, ed. acad. S. I. Vavilova, M. - L., 1943; Berry A., A Brief History of Astronomy, trans. from English, M. - L., 1946; Subbotin M.F., Introduction to theoretical astronomy, M., 1968.

Yu. A. Ryabov.

Great Soviet Encyclopedia. - M.: Soviet Encyclopedia. 1969-1978 .

See what "Newton's law of gravity" is in other dictionaries:

- (law of universal gravitation), see Art. (see GRAVITY). Physical encyclopedic dictionary. M.: Soviet Encyclopedia. Editor-in-chief A. M. Prokhorov. 1983 ... Physical encyclopedia

NEWTON'S LAW OF GRAVITY, the same as the law of universal gravitation... Modern encyclopedia

The same as the law of universal gravitation... Big Encyclopedic Dictionary

Newton's law of gravity- NEWTON'S LAW OF GRAVITY, the same as the law of universal gravitation. ... Illustrated Encyclopedic Dictionary

NEWTON'S LAW OF GRAVITY- the same as (see) ...

The same as the law of universal gravitation. * * * NEWTON'S LAW OF GRAVITY NEWTON'S LAW OF GRAVITY, the same as the law of universal gravitation (see UNIVERSAL GRAVITATION LAW) ... Encyclopedic Dictionary

Newton's law of gravity- Niutono gravitacijos dėsnis statusas T sritis fizika atitikmenys: engl. Newton's law of gravitation vok. Newtonsches Gravitationsgesetz, n; Newtonsches Massenanziehungsgesetz, n rus. Newton's law of gravity, m; Newton's law of gravity, m pranc.… … Fizikos terminų žodynas

Gravity (universal gravitation, gravitation) (from Latin gravitas “gravity”) is a long-range fundamental interaction in nature to which all material bodies are subject. According to modern data, it is a universal interaction in that... ... Wikipedia

LAW OF GRAVITY- (Newton’s law of gravity) all material bodies attract each other with forces directly proportional to their masses and inversely proportional to the square of the distance between them: where F is the modulus of the gravitational force, m1 and m2, the masses of interacting bodies, R... ... Big Polytechnic Encyclopedia

Law of Gravity- I. Newton’s law of gravitation (1643–1727) in classical mechanics, according to which the force of gravitational attraction of two bodies with masses m1 and m2 is inversely proportional to the square of the distance r between them; proportionality coefficient G gravitational... Concepts of modern natural science. Glossary of basic terms

… Let mortals rejoice that such an adornment of the human race lived among them.

(Inscription on Isaac Newton's grave)

Every schoolchild knows the beautiful legend about how Isaac Newton discovered the law of universal gravitation: an apple fell on the great scientist’s head, and instead of getting angry, Isaac wondered why this happened? Why does the Earth attract everything, but what is thrown always falls down?

But most likely it was a beautiful legend invented later. In reality, Newton had to do difficult and painstaking work to discover his law. We want to tell you about how the great scientist discovered his famous law.

The principles of the natural scientist

Isaac Newton lived at the turn of the 17th and 18th centuries (1642-1727). Life at this time was completely different. Europe was rocked by wars, and in 1666, England, where Newton lived, was struck by a terrible epidemic called the “Black Death.” This event would later be called the “Great Plague of London.” Many of the sciences were just emerging; there were few educated people, as well as what they knew.

For example, a modern weekly newspaper contains more information than the average person at that time would learn in his entire life!

Despite all these difficulties, there were people who strived for knowledge, made discoveries and moved progress forward. One of them was the great English scientist Isaac Newton.

The principles that he called “rules of philosophizing” helped the scientist make his main discoveries.

Rule 1.“No other causes should be accepted in nature other than those that are true and sufficient to explain phenomena... nature does nothing in vain, and it would be in vain for many to do what can be done by fewer. Nature is simple and does not luxury with superfluous causes of things...”

The essence of this rule is that if we can exhaustively explain a new phenomenon with existing laws, then we should not introduce new ones. This rule in general form is called Occam's razor.

Rule 2.“In experimental physics, propositions derived from occurring phenomena using induction (that is, the method of induction), despite the possibility of assumptions contrary to them, should be revered as true, either exactly or approximately, until such phenomena are discovered by which they are further clarified or will be subject to exclusion.” This means that all laws of physics must be proven or disproved experimentally.

In his principles of philosophizing, Newton formulated the principles scientific method. Modern physics successfully explores and applies phenomena whose nature has not yet been clarified (for example, elementary particles). Since Newton, natural science has developed in the firm belief that the world can be known and that Nature is organized according to simple mathematical principles. This confidence became the philosophical basis for the tremendous progress of science and technology in human history.

Shoulders of Giants

You probably haven't heard of the Danish alchemist Quiet Brahe. However, it was he who was Kepler's teacher and the first to compile an accurate table of planetary motions based on his observations. It should be noted that these tables merely represented the coordinates of the planets in the sky. Quietly bequeathed them Johannes Kepler, to his student, who, after carefully studying these tables, realized that the movement of the planets is subject to a certain pattern. Kepler formulated them as follows:

1. All planets move around in an ellipse, with the Sun at one of the focuses.
2. The radius drawn from the Sun to the planet “sweeps” equal areas in equal periods of time.
3. The squares of the periods of two planets (T 1 and T 2) are related as the cubes of the semi-major axes of their orbits (R 1 and R 2):

What immediately strikes the eye is that the Sun plays a special role in these laws. But Kepler could not explain this role, just as he could not explain the reason for the movement of planets around the Sun.

Isaac Newton will once say that if he saw further than others, it was only because he stood on the shoulders of giants. He undertook to find the root cause of Kepler's laws.

World Law

Newton realized that in order to change the speed of a body, it is necessary to apply a force to it. Today every schoolchild knows this statement as Newton's first law: the change in the speed of a body per unit time (in other words, acceleration a) is directly proportional to the force (F), and inversely proportional to the mass of the body (m). The greater the mass of the body, the more effort we must expend to change its speed. Please note that Newton uses only one characteristic of a body - its mass, without considering its shape, what it is made of, what color it is, etc. This is an example of the use of Occam's razor. Newton believed that body mass is a necessary and sufficient “factor” to describe the interaction of bodies:

Newton imagined the planets as large bodies that move in a circle (or nearly a circle). In everyday life, he often observed a similar movement: children played with a ball to which a thread was tied, they twirled it over their heads. In this case, Newton saw the ball (planet) and that it was moving in a circle, but did not see the thread. Drawing a similar analogy and using his rules of philosophizing, Newton realized that it was necessary to look for a certain force - a “thread” that connects the planets and the Sun. Further reasoning was simplified after Newton applied his own laws of dynamics.

Newton, using his first law and Kepler's third law, obtained:

Thus, Newton determined that the Sun acts on the planets with force:

He also realized that all planets revolve around the Sun, and considered it natural that the mass of the Sun should be taken into account in the constant:

It was in this form that the law of universal gravitation corresponded to Kepler's observations and his laws of planetary motion. The value G = 6.67 x 10 (-11) H (m/kg) 2 was derived from observations of the planets. Thanks to this law, the movements of celestial bodies were described, and, moreover, we were able to predict the existence of objects invisible to us. In 1846, scientists calculated the orbit of a previously unknown planet, which by its existence influenced the movement of other planets in the solar system. It was.

Newton believed that simple principles and “mechanisms of interaction” underlie the most complex things. That is why he was able to discern a pattern in the observations of his predecessors and formulate it into the Law of Universal Gravitation.

Law of Gravity

Gravity (universal gravitation, gravitation)(from Latin gravitas - “gravity”) - a long-range fundamental interaction in nature, to which all material bodies are subject. According to modern data, it is a universal interaction in the sense that, unlike any other forces, it imparts the same acceleration to all bodies without exception, regardless of their mass. Mainly gravity plays a decisive role on a cosmic scale. Term gravity also used as the name of the branch of physics that studies gravitational interaction. The most successful modern physical theory in classical physics that describes gravity is the general theory of relativity; the quantum theory of gravitational interaction has not yet been constructed.

Gravitational interaction

Gravitational interaction is one of the four fundamental interactions in our world. Within the framework of classical mechanics, gravitational interaction is described law of universal gravitation Newton, who states that the force of gravitational attraction between two material points of mass m 1 and m 2 separated by distance R, is proportional to both masses and inversely proportional to the square of the distance - that is

Here G- gravitational constant, equal to approximately m³/(kg s²). The minus sign means that the force acting on the body is always equal in direction to the radius vector directed to the body, that is, gravitational interaction always leads to the attraction of any bodies.

The law of universal gravitation is one of the applications of the inverse square law, which also occurs in the study of radiation (see, for example, Light Pressure), and is a direct consequence of the quadratic increase in the area of ​​the sphere with increasing radius, which leads to a quadratic decrease in the contribution of any unit area to area of ​​the entire sphere.

The simplest problem of celestial mechanics is the gravitational interaction of two bodies in empty space. This problem is solved analytically to the end; the result of its solution is often formulated in the form of Kepler's three laws.

As the number of interacting bodies increases, the task becomes dramatically more complicated. Thus, the already famous three-body problem (that is, the motion of three bodies with non-zero masses) cannot be solved analytically in a general form. With a numerical solution, instability of the solutions relative to the initial conditions occurs quite quickly. When applied to the Solar System, this instability makes it impossible to predict the motion of planets on scales larger than a hundred million years.

In some special cases, it is possible to find an approximate solution. The most important case is when the mass of one body is significantly greater than the mass of other bodies (examples: the solar system and the dynamics of the rings of Saturn). In this case, as a first approximation, we can assume that light bodies do not interact with each other and move along Keplerian trajectories around the massive body. The interactions between them can be taken into account within the framework of perturbation theory, and averaged over time. In this case, non-trivial phenomena may arise, such as resonances, attractors, chaos, etc. A clear example of such phenomena is the non-trivial structure of the rings of Saturn.

Despite attempts to describe the behavior of a system of a large number of attracting bodies of approximately the same mass, this cannot be done due to the phenomenon of dynamic chaos.

Strong gravitational fields

In strong gravitational fields, when moving at relativistic speeds, the effects of general relativity begin to appear:

• deviation of the law of gravity from Newton's;
• delay of potentials associated with the finite speed of propagation of gravitational disturbances; the appearance of gravitational waves;
• nonlinearity effects: gravitational waves tend to interact with each other, so the principle of wave superposition in strong fields no longer holds true;
• changing the geometry of space-time;
• the emergence of black holes;

Gravitational radiation

One of the important predictions of general relativity is gravitational radiation, the presence of which has not yet been confirmed by direct observations. However, there is indirect observational evidence in favor of its existence, namely: energy losses in the binary system with the pulsar PSR B1913+16 - the Hulse-Taylor pulsar - are in good agreement with a model in which this energy is carried away by gravitational radiation.

Gravitational radiation can only be generated by systems with variable quadrupole or higher multipole moments, this fact suggests that the gravitational radiation of most natural sources is directional, which significantly complicates its detection. Gravity power l-field source is proportional (v / c) 2l + 2 , if the multipole is of electric type, and (v / c) 2l + 4 - if the multipole is of magnetic type, where v is the characteristic speed of movement of sources in the radiating system, and c- speed of light. Thus, the dominant moment will be the quadrupole moment of the electric type, and the power of the corresponding radiation is equal to:

Where Q ij- quadrupole moment tensor of the mass distribution of the radiating system. Constant (1/W) allows us to estimate the order of magnitude of the radiation power.

From 1969 (Weber's experiments) to the present (February 2007), attempts have been made to directly detect gravitational radiation. In the USA, Europe and Japan, there are currently several operating ground-based detectors (GEO 600), as well as a project for a space gravitational detector of the Republic of Tatarstan.

Subtle effects of gravity

In addition to the classical effects of gravitational attraction and time dilation, the general theory of relativity predicts the existence of other manifestations of gravity, which under terrestrial conditions are very weak and their detection and experimental verification are therefore very difficult. Until recently, overcoming these difficulties seemed beyond the capabilities of experimenters.

Among them, in particular, we can name the entrainment of inertial frames of reference (or the Lense-Thirring effect) and the gravitomagnetic field. In 2005, NASA's robotic Gravity Probe B conducted an experiment measuring these effects near Earth, unprecedented in its accuracy, but its full results have not yet been published.

Quantum theory of gravity

Despite more than half a century of attempts, gravity is the only fundamental interaction for which a consistent renormalizable quantum theory has not yet been constructed. However, at low energies, in the spirit of quantum field theory, gravitational interaction can be represented as an exchange of gravitons - gauge bosons with spin 2.

Standard theories of gravity

Due to the fact that quantum effects of gravity are extremely small even under the most extreme experimental and observational conditions, there are still no reliable observations of them. Theoretical estimates show that in the overwhelming majority of cases one can limit oneself to the classical description of gravitational interaction.

There is a modern canonical classical theory of gravity - general theory of relativity, and many hypotheses and theories of varying degrees of development that clarify it, competing with each other (see the article Alternative theories of gravity). All of these theories make very similar predictions within the approximation in which experimental tests are currently carried out. The following are several basic, most well-developed or known theories of gravity.

• Gravity is not a geometric field, but a real physical force field described by a tensor.

• Gravitational phenomena should be considered within the framework of flat Minkowski space, in which the laws of conservation of energy-momentum and angular momentum are unambiguously satisfied. Then the motion of bodies in Minkowski space is equivalent to the motion of these bodies in effective Riemannian space.

• In tensor equations to determine the metric, the graviton mass should be taken into account, and gauge conditions associated with the Minkowski space metric should be used. This does not allow the gravitational field to be destroyed even locally by choosing some suitable reference frame.

As in general relativity, in RTG matter refers to all forms of matter (including the electromagnetic field), with the exception of the gravitational field itself. The consequences of the RTG theory are as follows: black holes as physical objects predicted in General Relativity do not exist; The universe is flat, homogeneous, isotropic, stationary and Euclidean.

On the other hand, there are no less convincing arguments by opponents of RTG, which boil down to the following points:

A similar thing occurs in RTG, where the second tensor equation is introduced to take into account the connection between non-Euclidean space and Minkowski space. Due to the presence of a dimensionless fitting parameter in the Jordan-Brans-Dicke theory, it becomes possible to choose it so that the results of the theory coincide with the results of gravitational experiments.

Sources and notes

Literature

• Vizgin V. P. Relativistic theory of gravity (origins and formation, 1900-1915). M.: Nauka, 1981. - 352c.
• Vizgin V. P. Unified theories in the 1st third of the twentieth century. M.: Nauka, 1985. - 304c.
• Ivanenko D. D., Sardanashvili G. A. Gravity, 3rd ed. M.: URSS, 2008. - 200 p.

See also

• Gravimeter

Links

• The law of universal gravitation or “Why doesn’t the Moon fall to Earth?” - Just about difficult things

James E. MILLER

The enormous increase in the number of young energetic workers working in the scientific field is a happy consequence of the expansion of scientific research in our country, encouraged and cherished by the Federal Government. Exhausted and nervous, scientific leaders abandon these neophytes to their fate, 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 of universal gravitation. Here's how it happened.

In 1665, young Newton became professor of mathematics at the University of Cambridge, 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 man of this world or an impractical inhabitant of an ivory tower. 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 of Newton’s conscious life was 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 in the neighborhood of 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 thinking, 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 on the earth’s surface and to invent differential calculus.

Having no experience in such matters, he chose a simple procedure and wrote a short letter of 22 words to King Charles, in which he outlined his hypothesis and pointed out the great possibilities it promised if confirmed. It is unknown whether the king saw this letter; it is quite possible that he did not, since he was overloaded with state problems and plans for future wars. However, there is no doubt that the letter, having passed through the appropriate channels, reached all heads of departments, their deputies and their deputies, who had every opportunity to express their 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 meeting of the Committee was held with open doors, and there was quite a lot of public, but it later turned out that most of those present had entered 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 not 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, a real man of action, wished to know what means Newton could suggest for improving the management 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 - the main trait of any true scientist - forced him to carefully study these questionnaires. After spending some time on this study, he realized that he was being invited to apply for a contract to conduct a scientific study to clarify the connection between the way apples are grown, their quality and the speed at which they fall to the ground. The ultimate goal of the project, he realized, was to develop a variety of apples that not only tasted good, but also fell 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 came, which plunged Newton into horror and the whole of Britain into grief, 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 himself does not know how) about a new, completely revolutionary mathematical approach, with the help of which one can solve the problem of attraction near a 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 mentally proved 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.