The history of the discovery of the law of universal gravitation. Practical use of the law of gravity Significance of the discovery of the law of universal gravitation
Lesson development (lesson notes)
The average general education
B.A. Vorontsov-Velyaminov's UMK line. Astronomy (10-11)
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The purpose of the lesson
Expand empirical and theoretical basis laws celestial mechanics, their manifestations in astronomical phenomena and their application in practice.
Lesson Objectives
- Check the fairness of the law universal gravitation based on the analysis of the motion of the Moon around the Earth; prove that it follows from Kepler's laws that the Sun imparts acceleration to the planet, which is inversely proportional to the square of the distance from the Sun; investigate the phenomenon of indignant movement; apply the law of universal gravitation to determine the masses celestial bodies; explain the phenomenon of tides as a consequence of the manifestation of the law of universal gravitation during the interaction of the Moon and the Earth.
Activities
- Build logical oral statements; put forward hypotheses; perform logical operations - analysis, synthesis, comparison, generalization; formulate research objectives; draw up a research plan; get involved in the work of the group; implement and adjust the research plan; present the results of the group's work; to carry out reflection of cognitive activity.
Key concepts
- The law of universal gravitation, the phenomenon of disturbed motion, the phenomenon of tides, Kepler's refined third law.
| № | Stage name | Methodical comment |
|---|---|---|
| 1 | 1. Motivation for activity | During the discussion of issues, the substantive elements of Kepler's laws are emphasized. |
| 2 | 2. Updating the experience and previous knowledge of students and fixing difficulties | The teacher organizes a conversation about the content and limits of applicability of Kepler's laws, the law of universal gravitation. The discussion is based on the knowledge of students from the physics course about the law of universal gravitation and its applications to the explanation of physical phenomena. |
| 3 | 3. Staging learning task | Using a slide show, the teacher organizes a conversation about the need to prove the validity of the law of universal gravitation, study the disturbed motion of celestial bodies, find a way to determine the masses of celestial bodies and study the phenomenon of tides. The teacher accompanies the process of dividing students into problem groups that solve one of the astronomical problems, and initiates a discussion of the goals of the groups. |
| 4 | 4. Making a plan to overcome difficulties | Students in groups, based on the set goal, formulate the questions to which they want to get answers, and draw up a plan to achieve the set goal. The teacher corrects, together with the group, each of the action plans. |
| 5 | 5.1 Implementation of the selected activity plan and implementation of independent work | The portrait of I. Newton is presented on the screen in the course of students' independent group activity. Students implement the plan using the content of the textbook § 14.1 - 14.5. The teacher corrects and guides the work in groups, supporting the activities of each student. |
| 6 | 5.2 Implementation of the selected activity plan and implementation of independent work | The teacher organizes the presentation of the results of the work by the students in Group 1, based on the tasks presented on the screen. The rest of the students take notes of the main ideas expressed by the group members. After presenting the data, the teacher focuses on the correction of the plan, which the participants carried out in the process of its implementation, asks to formulate the concepts with which the students first met in the process of work. |
| 7 | 5.3 Implementation of the selected activity plan and implementation of independent work | The teacher organizes the presentation of the results of the work by the students of Group 2. The rest of the students take notes of the main ideas expressed by the group members. After presenting the data, the teacher focuses on the correction of the plan, which the participants carried out in the process of its implementation, asks to formulate the concepts with which the students first met in the process of work. |
| 8 | 5.4 Implementation of the selected activity plan and implementation of independent work | The teacher organizes the presentation of the results of the work by the students of Group 3. The rest of the students take notes of the main ideas expressed by the group members. After presenting the data, the teacher focuses on the correction of the plan, which the participants carried out in the process of its implementation, asks to formulate the concepts with which the students first met in the process of work. |
| 9 | 5.5 Implementation of the selected activity plan and implementation of independent work | The teacher organizes the presentation of the results of the work by the students of Group 4. The rest of the students take notes of the main ideas expressed by the group members. After presenting the data, the teacher focuses on the correction of the plan, which the participants carried out in the process of its implementation, asks to formulate the concepts that the students first met in the process of work. |
| 10 | 5.6 Implementation of the selected activity plan and implementation of independent work | The teacher, using animation, discusses the dynamics of the appearance of the tide on a certain part of the Earth's surface, emphasizes the influence of not only the Moon, but also the Sun. |
| 11 | 6. Reflection of activity | During the discussion of answers to reflexive questions, it is necessary to focus on the methodology for performing tasks by groups, correcting the plan of activities in the course of its implementation, and the practical significance of the results obtained. |
| 12 | 7. Homework |
DISCOVERY AND APPLICATION OF THE LAW OF WORLD GRAVITY 10-11 grade
UMK B.A. Vorontsov-Velyaminov
Razumov Victor Nikolaevich,
teacher of the Municipal Educational Institution "Bolsheelkhovskaya Secondary School"
Lyambirsky municipal district of the Republic of Mordovia
The law of universal gravitation
The law of universal gravitationAll bodies in the universe are attracted to each other
with a force directly proportional to the product of their
masses and inversely proportional to the square
the distance between them.
Isaac Newton (1643-1727)
where m1 and m2 are the masses of the bodies;
r is the distance between bodies;
G - gravitational constant
The discovery of the law of universal gravitation was largely facilitated by
the laws of planetary motion, formulated by Kepler,
and other achievements of astronomy in the 17th century. Knowing the distance to the moon allowed Isaac Newton to prove
the identity of the force that holds the moon as it moves around the earth, and
force causing bodies to fall to the Earth.
Since gravity varies inversely with the square of the distance,
as follows from the law of universal gravitation, the Moon,
located from the Earth at a distance of about 60 of its radii,
should experience acceleration 3600 times less,
than the acceleration of gravity on the surface of the Earth, equal to 9.8 m / s.
Therefore, the acceleration of the moon should be 0.0027 m / s2. At the same time, the moon, like any body, uniformly
moving in a circle, has an acceleration
where ω is its angular velocity, r is the radius of its orbit.
Isaac Newton (1643-1727)
If we assume that the radius of the Earth is 6400 km,
then the radius of the lunar orbit will be
r = 60 6 400 000 m = 3.84 10 m.
The sidereal period of the Moon's revolution is T = 27.32 days,
in seconds is 2.36 10 s.
Then the acceleration of the orbital motion of the Moon
The equality of these two values of acceleration proves that the force holding
The Moon in orbit, there is gravity, weakened by a factor of 3600
compared with that acting on the surface of the Earth. When the planets move, in accordance with the third
Kepler's law, their acceleration and acting on
them the pulling force of the sun back
proportional to the square of the distance, like this
follows from the law of universal gravitation.
Indeed, according to Kepler's third law
the ratio of cubes of semi-major axes d and squares
periods of circulation T is a constant value:
Isaac Newton (1643-1727)
The acceleration of the planet is
Kepler's third law implies
therefore the acceleration of the planet is
So, the force of interaction between the planets and the Sun satisfies the law of universal gravitation.
Disturbances in the movements of bodies in the solar system
The movement of the planets of the solar system does not exactly obey the lawsKepler because of their interaction not only with the Sun, but also with each other.
Deviations of bodies from motion along ellipses are called perturbations.
The perturbations are small, since the mass of the Sun is much greater than the mass, not only
an individual planet, but all planets as a whole.
The deviations of asteroids and comets during their passage are especially noticeable.
near Jupiter, whose mass is 300 times the mass of the Earth. In the XIX century. the calculation of perturbations made it possible to discover the planet Neptune.
William Herschel
John Adams
Urbain Le Verrier
William Herschel discovered the planet Uranus in 1781.
Even taking into account the indignation from all
known planets observed motion
Uranus did not agree with the calculated one.
Based on the assumption that there is still
one "zauranic" planet John Adams in
England and Urbain Le Verrier in France
independently made calculations
its orbit and position in the sky.
Based on calculations Le Verrier German
astronomer Johann Halle September 23, 1846
discovered an unknown in the constellation Aquarius
formerly the planet - Neptune.
Due to the indignation of Uranus and Neptune, there was
predicted, and discovered in 1930
dwarf planet Pluto.
The discovery of Neptune was a triumph
heliocentric system,
essential confirmation of justice
the law of universal gravitation.
Uranus
Neptune
Pluto
Johann Halle
This article will focus on the history of the discovery of the law of universal gravitation. Here we will get acquainted with the biographical information from the life of the scientist who discovered this physical dogma, consider its main provisions, the relationship with quantum gravity, the course of development and much more.
Genius
Sir Isaac Newton is a scientist from England. At one time he devoted a lot of attention and energy to such sciences as physics and mathematics, and also brought a lot of new things to mechanics and astronomy. He is rightfully considered one of the first founders of physics in its classical model. He is the author of the fundamental work "Mathematical Principles of Natural Philosophy", where he presented information about the three laws of mechanics and the law of universal gravitation. Isaac Newton laid the foundations of classical mechanics with these works. He also developed an integral type, a light theory. He also made major contributions to physical optics and developed many other theories in physics and mathematics.
Law
The law of universal gravitation and the history of its discovery go back to a distant beginning. Its classical form is the law, with the help of which the interaction of the gravitational type is described, which does not go beyond the framework of mechanics.
Its essence was that the indicator of the force F of the gravitational thrust arising between 2 bodies or points of matter m1 and m2, separated from each other by a certain distance r, observes proportionality in relation to both indicators of mass and is inversely proportional to the square of the distance between the bodies:
F = G, where by G we denote the constant of gravity equal to 6.67408 (31) .10 -11 m 3 / kgf 2.
Newton's gravity
Before considering the history of the discovery of the law of universal gravitation, let's get acquainted in more detail with its general characteristics.
In the theory created by Newton, all bodies with a large mass should generate a special field around them, which attracts other objects to itself. It is called the gravitational field, and it has potential.
A body with spherical symmetry forms a field outside of itself, similar to that created by a material point of the same mass located in the center of the body.
The direction of the trajectory of such a point in the gravitational field, created by a body with a much larger mass, obeys the Objects of the universe, such as, for example, a planet or a comet, also obeys it, moving along an ellipse or hyperbole. Allowance for the distortion created by other massive bodies is taken into account using the provisions of the perturbation theory.
Analyzing accuracy
After Newton discovered the law of universal gravitation, it had to be tested and proven many times. For this, a series of calculations and observations were made. Having come to agreement with its provisions and proceeding from the accuracy of its indicator, the experimental form of estimation serves as a clear confirmation of general relativity. Measurement of the quadrupole interactions of a body that rotates, but its antennas remain stationary, show us that the process of building up δ depends on the potential r - (1 + δ), at a distance of several meters and is in the limit (2.1 ± 6.2) .10 -3. A number of other practical confirmations allowed this law to be established and take a single form, without any modifications. In 2007, this dogma was rechecked at a distance less than a centimeter (55 μm-9.59 mm). Taking into account the experimental errors, the scientists investigated the range of the distance and found no obvious deviations in this law.
Observation of the Moon's orbit in relation to the Earth also confirmed its validity.
Euclidean space
Newton's classical theory of gravitation is associated with Euclidean space. The actual equality with a sufficiently high accuracy (10 -9) of the exponents of the measure of distance in the denominator of the equality considered above shows us the Euclidean basis of the space of Newtonian mechanics, with a three-dimensional physical form. At such a point of matter, the area of a spherical surface has exact proportionality with respect to the magnitude of the square of its radius.
Historical data
Consider summary history of the discovery of the law of universal gravitation.
Ideas were also put forward by other scientists who lived before Newton. Reflections about it were visited by Epicurus, Kepler, Descartes, Roberval, Gassendi, Huygens and others. Kepler put forward the assumption that the force of gravity has an inverse proportion to the distance from the star of the Sun and has propagation only in the ecliptic planes; according to Descartes, it was a consequence of the activity of vortices in the thickness of the ether. There were a number of guesses that reflected the correct guesses about distance dependence.
A letter from Newton to Halley contained information that the predecessors of Sir Isaac himself were Hooke, Ren and Buyo Ismael. However, before him, no one succeeded clearly, with the help of mathematical methods, to connect the law of gravitation and planetary motion.
The history of the discovery of the law of universal gravitation is closely connected with the work "Mathematical Principles of Natural Philosophy" (1687). In this work, Newton was able to derive the law under consideration thanks to Kepler's empirical law, which was already known by that time. He shows us that:
- the form of movement of any visible planet indicates the presence of a central force;
- the gravitational force of the central type forms elliptical or hyperbolic orbits.
About Newton's theory
Inspection brief history the discovery of the law of universal gravitation can also point us to a number of differences that set it apart from previous hypotheses. Newton was engaged not only in the publication of the proposed formula for the phenomenon under consideration, but also proposed a model of a mathematical type in an integral form:
- provision on the law of gravitation;
- regulation on the law of traffic;
- systematics of methods of mathematical research.
This triad could accurately investigate even the most complex movements of celestial objects, thus creating the basis for celestial mechanics. Until the beginning of Einstein's activity, this model did not require a fundamental set of corrections. Only the mathematical apparatus had to be significantly improved.
Object for discussion
Discovered and proven law throughout the eighteenth century became a well-known subject of active controversy and scrupulous checks. However, the century ended with a general agreement with his postulates and statements. Using the calculations of the law, it was possible to accurately determine the paths of motion of bodies in heaven. A direct check was made in 1798. He did this using a torsion balance with great sensitivity. In the history of the discovery of the universal law of gravitation, it is necessary to highlight a special place for the interpretations introduced by Poisson. He developed the concept of the potential of gravity and the Poisson equation, with which it was possible to calculate this potential. This type of model made it possible to study the gravitational field in the presence of an arbitrary distribution of matter.
There were many difficulties in Newton's theory. The main one could be considered the inexplicability of long-range action. It was impossible to accurately answer the question of how the forces of attraction are sent through vacuum space at infinite speed.
"Evolution" of the law
Over the next two hundred years, and even more, many physicists have attempted to suggest various ways to improve Newton's theory. These efforts ended in a triumph in 1915, namely the creation of the General Theory of Relativity, which was created by Einstein. He was able to overcome the whole set of difficulties. In accordance with the correspondence principle, Newton's theory turned out to be an approximation to the beginning of work on the theory in more general view that can be applied under certain conditions:
- The potential of a gravitational nature cannot be too large in the systems under study. The solar system is an example of compliance with all the rules for the movement of the celestial type of bodies. The relativistic phenomenon finds itself in a noticeable manifestation of the displacement of the perihelion.
- The indicator of the speed of movement in this group of systems is insignificant in comparison with the light speed.
The proof that in a weak stationary gravitational field the calculations of general relativity take the form of Newtonian ones is the presence of a scalar potential of gravity in a stationary field with weakly expressed characteristics of forces, which is able to satisfy the conditions of the Poisson equation.
Quantum scale
However, in history neither scientific discovery the law of universal gravitation, nor the general theory of relativity could not serve as the final gravitational theory, since both insufficiently satisfactorily describe the processes of the gravitational type on the scale of quanta. An attempt to create a quantum-gravitational theory is one of the most important tasks of modern physics.
From the point of view of quantum gravity, the interaction between objects is created through the interchange of virtual gravitons. In accordance with the uncertainty principle, the energy potential of virtual gravitons is inversely proportional to the time interval in which it existed, from the point of radiation by one object to the moment in which it was absorbed by another point.
In view of this, it turns out that on a small scale of distances, the interaction of bodies entails an exchange of virtual gravitons. Thanks to these considerations, it is possible to conclude a statement about Newton's law of potential and its dependence in accordance with the inverse exponent of proportionality with respect to distance. The existence of an analogy between the laws of Coulomb and Newton is explained by the fact that the weight of gravitons is equal to zero. The weight of the photons is of the same importance.
Delusion
V school curriculum the answer to the question from history, how Newton discovered the law of universal gravitation, is the story of a falling apple. According to this legend, it fell on the scientist's head. However, this is a widespread misconception, and in reality everything could do without such a case of possible head injury. Newton himself sometimes confirmed this myth, but in reality the law was not a spontaneous discovery and did not come in a burst of momentary insight. As it was written above, it was developed for a long time and was presented for the first time in the works on the "Mathematical Principles", which were released to the public in 1687.
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 an infinitely long (at least, if we ignore the transition of energy into "non-mechanical" forms).
The conjecture about the unity of the reasons governing the motion of the 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, had no practical influence 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 from any whatsoever) interpretation of the reasons for this movement. After all, even the great Kepler, who, at the cost of gigantic labor, was able to formulate the exact mathematical laws of planetary motion, believed that the reason for this motion was the rotation of the Sun.
According to Kepler's ideas, the Sun, rotating, with constant jerks, draws 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 its own axis. Kepler wrote about this: “If the planets did not possess natural resistance, then it would be impossible to indicate the reasons why they should not follow exactly the rotation of the Sun. But although in reality all the planets move in the same direction as the rotation of the Sun, their speed of 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 could not 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 connected not with the laws of motion of the planets, but with the origin of our solar system. An artificial planet can be launched both in the direction of the Sun's rotation and against this rotation.
Robert Hooke came much closer than Kepler to the discovery of the law of attraction of bodies. Here are his original words from a work entitled "An Attempt to Study the Motion of the Earth", published in 1674: "I will develop a theory that is consistent in all respects with the generally accepted rules of mechanics. This theory is based on three assumptions: first, that all celestial bodies, without exception, have a directed towards their center or gravity, due to which they attract not only their own parts, but also all celestial bodies in 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, ellipse, or some other less simple curve. According to the third assumption, the forces of attraction act the more, the closer to them are the bodies on which they act. I have not yet been able to establish by experience what the various degrees of attraction are. But if you develop this idea further, astronomers will be able to determine the law according to which all celestial bodies move. "
Truly, one can only amaze that Hooke himself did not want to take up the development of these ideas, referring to being busy with other work. But a scientist appeared who made a breakthrough in this field.
The history of Newton's discovery of the law of universal gravitation is 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 the same, arose even in Newton the student, that the first calculations did not give 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 motion of the planets, Newton applied the laws of the dynamics he created and the law of universal gravitation established by him.
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 mistake of Galileo, who believed that uniform motion along a circle is motion by inertia. Newton pointed out (and this is the second law of dynamics) that the only way to change the motion of a body - the value or direction of speed - is to act on it with some force. In this case, the acceleration with which the body moves under the action of the force is inversely proportional to the body's mass.
According to Newton's third law of dynamics, "action 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 its orbit around the Earth, and then was able to show that the ratio of this acceleration to the acceleration free fall bodies at the surface of the Earth is equal to the ratio of the squares of the radii of the Earth and the lunar orbit. From this, Newton concluded that the nature of the force of gravity and the force that holds the moon in orbit is 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 for the independence of the acceleration of gravity 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. Indeed, let us imagine that terrestrial bodies are lifted to the orbit of the Moon and launched together with the Moon, also devoid of any motion, to fall to the Earth. On the basis of what has already been proved (meaning Galileo's experiments), there is no doubt that at the same times they will pass the same space as the Moon, because their masses relate to the mass of the Moon in the same way as their weight 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 of the forces of universal gravitation, or, as they are often called, gravitational forces, is reflected already in the very name given by Newton: universal. These forces, so to speak, are "the most universal" among all the forces of nature. Anything that has mass - and mass is inherent in any form, any kind of matter - must experience gravitational influences. Even light is not an exception. If we visualize gravitational forces with the help of threads that stretch from one body to another, then the countless 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, to block oneself from gravitational forces. There are no barriers for universal gravitation, the range of their action is not limited (r = ∞). Gravitational forces are long-range forces. This is the "official name" of these forces in physics. Due to long-range action, gravity binds all the bodies of the Universe.
The relative slowness of the decrease in forces with distance at each step is manifested in our earthly conditions: after all, all bodies do not change their weight, being transferred, from one height to another (or, to be more precise, change, but extremely insignificantly), precisely because with a relatively small change in distance - in this case from the center of the Earth - the 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. However, one should not think that the decrease in the force of gravity with height cannot be detected in terrestrial conditions. For example, a pendulum clock with an oscillation period of one second will lag behind almost three seconds per day if it is lifted from the basement to the upper floor of Moscow University (200 meters) - and this is only due to a decrease in gravity.
The heights at which artificial satellites move are already comparable to the radius of the Earth, so that to calculate their trajectory, taking into account the change in the force of gravity with distance is absolutely necessary.
Gravitational forces have another very interesting and extraordinary property, which will be discussed now.
For many centuries, medieval science accepted as an unshakable dogma the assertion of Aristotle that the body falls the faster, the greater its weight. Even everyday experience confirms this: after all, it is known that a feather falls more slowly than a stone. However, as Galileo was able to show for the first time, the whole point here is that air resistance, when it comes into play, radically distorts the picture that would be if only earth's gravity acted on all bodies. There is an experiment, remarkable in its clarity, with the so-called Newton tube, which makes it very easy to assess the role of air resistance. Here short description this experience. Imagine an ordinary glass tube (so that you can see what is going on inside), into which various objects are placed: pellets, pieces of cork, feathers or fluffs, etc. , behind it are pieces of cork and, finally, the fluff will smoothly go down. But let's try to follow the fall of the same objects when air is pumped out of the tube. The fluff, having lost its former sluggishness, rushes, keeping up with the pellet and the cork. This means that its movement was delayed by air resistance, which affected the movement of the plug to a lesser extent and even less on the movement of the pellet. Consequently, if it were not for the air resistance, if only the forces of universal gravity acted on the bodies - in a particular case, the earth's gravity - then all the bodies would fall exactly the same, accelerating at the same rate.
But "nothing new under the moon." Two thousand years ago, Lucretius Carus, in his famous poem On the Nature of Things, wrote:
all that falls in the rare air,
Should fall faster in accordance with its own weight
Just because water or air is a subtle essence
Not in the state of things to put the same obstacles,
But it is inferior to those who have greater weight.
On the contrary, it is never capable of anything anywhere.
The thing is to hold back emptiness and appear as some kind of support,
By virtue of his nature, he is constantly yielding to everything.
Therefore, everything, sweeping through the void without obstacles, must
Have the same speed, despite the difference in weight.
Of course, these wonderful words were a wonderful guess. It took a lot of experiments to turn this guess into a reliably established law, from the famous experiments of Galileo, who studied the fall from the famous inclined Leaning Tower of Pisa balls of the same size, but made of different materials (marble, wood, lead, etc.), and ending the most complex modern measurements of the effect of gravity on light. And all this variety of experimental data persistently strengthens us in the belief that gravitational forces impart the same acceleration to all bodies; in particular, the acceleration of gravity 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 gravitation can be compressed into one short statement: the gravitational force is proportional to the mass of bodies. We emphasize that here we are talking about the very mass, which in Newton's laws acts as a measure of inertia. It is even called an inert mass.
The four words "gravitational force is proportional to mass" has a surprisingly deep meaning. Bodies large and small, hot and cold, of the most varied chemical composition, of 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 emptiness. Now let's connect the bodies. Then, on the one hand, the bodies should fall faster as the total weight has increased. But, on the other hand, adding a part falling more slowly to a heavy body should slow down this body. There is a contradiction that can be eliminated only if we assume that all bodies under the action of only one gravity fall with the same acceleration. As if everything is consistent! However, let us ponder once again the above reasoning. It is based on a common method of proof "by contradiction": assuming that a heavier body falls faster than a light one, we have arrived at a contradiction. And from the very beginning, it was assumed that the acceleration of gravity is determined by weight and only by weight. (Strictly speaking, not weight, but 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 us imagine that there is a gravitational charge, analogous to the electric one and, like this last, is completely unrelated to the mass directly. Comparison with electrical charge is very helpful. Here are two specks of dust between the charged capacitor plates. Let these dust grains have equal charges, and the masses relate as 1 to 2. Then the accelerations should differ by a factor of two: the forces determined by the charges are equal, and with equal forces, a body with twice its mass is accelerated by half. If we combine the dust particles, then, obviously, the acceleration will have a new, intermediate value. No speculative approach without experimental research electrical forces can give nothing here. The picture would be exactly the same if the gravitational charge was not associated with mass. And only experience can answer the question of whether there is such a connection. And now it is clear to us that it was the experiments that proved the same acceleration due to gravity for all bodies that showed, in essence, that the gravitational charge (gravitational or heavy mass) is equal to the inert mass.
Experience and only experience can serve both as a basis for physical laws and as a criterion for their validity. Let us recall at least the record-breaking in accuracy experiments conducted under the direction of VB Braginsky at Moscow State University. These experiments, in which an accuracy of the order of 10-12 was obtained, once again confirmed the equality of the heavy and inert mass.
It is on experience, on a wide test 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 (if you summarize all of the above) reads:
The force of mutual attraction of any two bodies, the dimensions of which are much smaller than the distance between them, is proportional to the product of the masses of these bodies and is inversely proportional to the square of the distance between these bodies.
The proportionality coefficient is called the gravitational constant. If you measure the length in meters, time in seconds, and mass in kilograms, the gravitational constant will be equal to 6.673 * 10-11, and its dimension will be respectively m3 / kg * s2 or N * m2 / kg2.
G = 6.673 * 10-11 N * m2 / kg2
3. Gravitational waves.
In Newton's law of universal gravitation, nothing is said about the time of transmission of the gravitational interaction. It is implicitly assumed that it is carried out instantly, no matter how large the distances between the interacting bodies. This view is generally typical of advocates of action at a distance. But it follows from Einstein's "special theory of relativity" that gravity is transmitted from one body to another at the same speed as the light signal. If a body moves from its place, then the curvature of space and time caused by it does not change instantly. First, this will affect in the immediate vicinity of the body, then the change will capture more and more distant regions, and, finally, a new distribution of curvature will be established throughout the space, corresponding to the changed position of the body.
And here we come to the problem that has caused and continues to cause the greatest number of disputes and disagreements - the problem of gravitational radiation.
Can gravity exist if there is no mass that creates it? According to Newtonian law, definitely not. It makes no sense to even raise such a question there. However, once 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 gravitational mass, for example a ball, was at rest. All bodies around the ball will be affected by the usual Newtonian forces. And now, with great speed, we will remove the ball from its original place. At the first moment, the surrounding bodies will not feel it. 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 for some time the surrounding bodies will experience the same effect of the ball, 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 pull the body out of the area of space where it caused curvatures, and so that these curvatures themselves, at least at large distances, remain and will develop according to their internal laws. Here is gravity without gravitating mass! You can go further. If you make the ball vibrate, then, as it turns out from Einstein's theory, a kind of ripple is superimposed on the Newtonian picture of gravitation - gravitational waves. To better imagine these waves, you need to use a model - rubber film. If you not only press your finger on this film, but at the same time make vibrational movements with it, then these vibrations will begin to be transmitted along the stretched film in all directions. This is the analogue of gravitational waves. The farther from the source, the weaker such waves are.
Now, at some point, we will stop pressing on the film. The waves won't go away. They will also exist independently, scattering further and further along the film, causing the curvature of geometry on their way.
In exactly the same way, waves of curvature of space - gravitational waves - can exist independently. Many researchers draw this conclusion from Einstein's theory.
Of course, all of these effects are very weak. So, 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 solar system during the same time. But here it is not the quantitative, but the principled side of the matter that is important.
Proponents of gravitational waves — and they seem to be in the majority now — predict another surprising phenomenon; the transformation of gravity into particles such as electrons and positrons (they must be produced in pairs), protons, antitrons, etc. (Ivanenko, Wheeler, etc.).
It should look something like this. A gravitational wave has reached a certain area of space. At a certain moment, this gravitation abruptly, abruptly, decreases and at the same time there appears, say, an electron-positron pair. The same can be described as an abrupt decrease in the curvature of space with the simultaneous creation of a pair.
There are many attempts to translate this into quantum mechanical language. Particles - gravitons are introduced into consideration, which are compared to the non-quantum image of the 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.
Let such transformations be unlikely, that is, they occur extremely rarely, - in cosmic scales they may turn out to be principled.
4. Curvature of space-time by gravity,
"Eddington's parable".
The parable of the English physicist Eddington from the book "Space, Time and Gravity" (retelling):
“In the ocean, which has only two dimensions, there once lived a breed of flat fish. It was observed that the fish generally swam in straight lines until they encountered obvious obstacles in their path. This behavior seemed quite natural. But there was a mysterious area in the ocean; when fish fell into it, they seemed enchanted; some swam through this area, but changed their direction of movement, others circled endlessly in this area. One fish (almost Descartes) proposed the theory of vortices; she said that in this area there are whirlpools that make everything that falls into them swirl. Over time, a much more perfect theory was proposed (Newton's theory); it was said that all fish are attracted to a very large fish - the sunfish, dormant in the middle of the region - and this explained the deviation of their paths. At first this theory seemed a little strange, perhaps; but it was confirmed with surprising accuracy in the most varied observations. All fish have been found to have this attractive property, proportional to their size; the law of attraction (an analogue of the law of universal gravitation) was extremely simple, but despite this, he explained all the movements with such accuracy, to which accuracy had never reached before scientific research... True, some fish, grumbling, declared that they did not understand how such an action was possible at a distance; but everyone agreed that this action was spread by the ocean, and that it would be easier to understand when the nature of water was better understood. Therefore, almost every fish that wanted to explain attraction started by assuming some mechanism by which it spreads through the water.
But there was a fish that looked at things differently. She drew attention to the fact that large fish and small ones always moved along the same path, although it might seem that it would take a lot of force to divert a large fish out of its path. (The sun fish imparted the same accelerations to all bodies.) Therefore, instead of forces, she began to study in detail the paths of movement of the fish and thus came to an amazing solution to the problem. There was an elevated place in the world where the sun fish lay. Pisces 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 took place in the mysterious area. "
This parable shows how the curvature of the world in which we live can give the illusion of the force of attraction, and we see that an effect similar to attraction is the only thing in which such curvature can manifest itself.
Briefly, this can be formulated as follows. Since gravity bends the paths of all bodies in the same way, we can think of gravity as a curvature of space-time.
5. Gravity on Earth.
If you think about what role the forces of gravity play in the life of our planet, then whole 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 feeding 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. Everyone knows what prevents him from drowning. This is the famous buoyancy force of Archimedes. But it appears only because water is compressed by gravity with a force that increases with 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 be in excess of 3 million atmospheres.
Under the influence of long-term pressure forces under these conditions, all substances that we are accustomed to consider as solid behave like var or resin. Heavy materials sink to the bottom (if you can call the center of the Earth that way), and the lungs float up. This process has been milking for billions of years. It has not ended, as follows from Schmidt's theory, and now. The concentration of heavy elements in the area of the center of the Earth is slowly increasing.
Well, how is the attraction of the Sun and the nearest celestial body of the Moon manifested on Earth? Only residents of the ocean coasts can observe this attraction without special devices.
The sun acts in almost the same way on everything on and within 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 around its axis by half a turn practically does not change the force of gravity. Therefore, the Sun imparts almost the same acceleration to all parts the globe and all bodies on its surface. Almost, but still not quite the same. This difference causes the ebb and flow of the ocean.
In the area facing the sun the earth's surface the force of attraction is somewhat greater than is necessary for the movement of this section along an elliptical orbit, and on the opposite side of the Earth it is somewhat less. As a result, according to the laws of Newtonian mechanics, the water in the ocean bulges slightly in the direction facing the Sun, and on the opposite side recedes from the Earth's surface. There are, as they say, tidal forces that stretch the globe and give, roughly speaking, the surface of the oceans the shape of an ellipsoid.
The smaller the distance between the interacting bodies, the greater the tidal forces. That is why the Moon has a greater influence on the shape of the world's oceans than the Sun. More precisely, tidal action is determined by the ratio of body mass to the cube of its distance from the Earth; this ratio for the Moon is about twice that for the Sun.
If there was no cohesion between parts of the globe, the tidal forces would tear it apart.
Perhaps this happened with one of the moons of Saturn, when he came close to this large planet. That ring of debris that makes Saturn such a remarkable planet may be the debris of the moon.
So, the surface of the world's oceans is like an ellipsoid, the major axis of which is directed towards the Moon. The earth rotates on its axis. Therefore, a tidal wave moves across the ocean surface towards the direction of the Earth's rotation. When it approaches the shore, the tide begins. In some places, the water level rises to 18 meters. Then the tidal wave leaves and the ebb tide begins. 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, friction of water, resistance of continents, the complexity of the configuration of oceanic shores and the bottom in coastal zones and some other particular effects.
It is important that the tidal wave slows down the Earth's rotation.
True, the effect is very small. For 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 by one side, and the Earth's day will become equal to the lunar month. This has already happened to the Moon. The moon is inhibited so much that it is turned to the Earth all the time with one side. To "look" at the far side of the moon, a spaceship had to be sent around it.
The presented materials can be used when conducting a lesson, conference or workshop on solving problems on the topic "The law of universal gravitation".
PURPOSE OF THE LESSON: to show the universal nature of the law of universal gravitation.
LESSON OBJECTIVES:
- study the law of universal gravitation and the limits of its application;
- consider the history of the discovery of the law;
- show the cause-and-effect relationships of Kepler's laws and the law of universal gravitation;
- show practical significance law;
- to consolidate the studied topic while solving qualitative and computational problems.
EQUIPMENT: projection equipment, TV set, VCR, video films “About the universal gravitation”, “About the power that rules the worlds”.
Let's start the lesson by reviewing the basic concepts of the mechanics course.
What branch of physics is called mechanics?
What do we call kinematics? (A section of mechanics that describes the geometric properties of motion without taking into account the masses of bodies and acting forces.) What types of motion do you know?
What question does the dynamics solve? Why, for what reason, in one way or another, the bodies are moving? Why does acceleration occur?
List the basic physical quantities of kinematics? (Moving, speed, acceleration.)
List the main physical quantities of the dynamics? (Mass, strength.)
What is body mass? (A physical quantity that quantitatively characterizes the properties of bodies, acquire different speeds during interaction, that is, characterizes the inert properties of a body.)
What physical quantity is called force? (Force - physical quantity, which quantitatively characterizes the external effect on the body, as a result of which it acquires acceleration.)
When does the body move evenly and in a straight line?
In what case does the body move with acceleration?
Formulate Newton's III law - the law of interaction. (Bodies act on each other with forces equal in magnitude and opposite in direction.)
We reviewed the basic concepts and basic laws of mechanics, which will help us explore the topic of the lesson.
(Questions and a drawing are on the board or screen.)
Today we must answer the questions:
- Why is the fall of bodies on Earth observed?
- why do planets move around the sun?
- why does the moon move around the earth?
- how to explain the existence on Earth of the ebb and flow of seas and oceans?
According to Newton's II law, a body moves with acceleration only under the action of a force. Force and acceleration are directed in the same direction.
AN EXPERIENCE... Raise the ball to a height and release it. The body falls down. We know that it is attracted by the Earth, that is, the ball is affected by gravity.
Is it only the Earth that has the ability to act on all bodies with a force called gravity?
Isaac Newton
In 1667, the English physicist Isaac Newton suggested that, in general, forces of mutual attraction act between all bodies.
They are now called the forces of gravity or gravitational forces.
So: between the body and the Earth, between the planets and the Sun, between the Moon and the Earth act gravitational forces summarized in the law.
THEME. THE LAW OF WORLD GRAVITY.
During the lesson, we will use knowledge of the history of physics, astronomy, mathematics, the laws of philosophy and information from popular science literature.
Let's get acquainted with the history of the discovery of the law of universal gravitation. Several students will give short presentations.
Message 1. If you believe the legend, then in the discovery of the law of universal gravitation the apple, whose fall from the tree was observed by Newton, is “to blame”. There is evidence from a contemporary of Newton, his biographer, on this score:
“After lunch… we went into the garden and drank tea under the shade of several apple trees. Sir Isaac told me that this was exactly the environment he was in when the thought of gravitation first occurred to him. It was caused by an apple falling. Why does an apple always fall vertically, he wondered to himself. There must be an attractive force of matter, concentrated in the center of the Earth, proportional to its quantity. Therefore, the apple attracts the Earth in the same way as the Earth attracts an apple. There must, therefore, be a force similar to what we call gravity, extending throughout the universe. "
These thoughts occupied Newton already in 1665-1666, when he, an aspiring scientist, was in his country house, where he left Cambridge in connection with the plague epidemic that swept the large cities of England.
This great discovery was published 20 years later (1687). Not everything was in agreement with Newton with his guesses and calculations, and being a man of the highest exactingness towards himself, he could not publish results that were not completed. (Biography of I. Newton.) (Appendix No. 1.)
Thank you for message. We cannot trace in detail the train of Newton's thoughts, but still we will try to reproduce them in general terms.
TEXT ON BOARD OR SCREEN. Newton used the scientific method in his work:
- from practice data,
- by processing them mathematically,
- to the general law, and from it
- to the consequences, which are verified again in practice.
What kind of practice data were known to Isaac Newton, which was discovered in science by 1667?
Message 2. Thousands of years ago it was noticed that by the location of heavenly bodies one can predict river floods, and hence harvests, make calendars. By the stars - find the right path for sea ships. People have learned to calculate the timing of eclipses of the Sun and Moon.
Thus the science of astronomy was born. Its name comes from two Greek words: "astronomer", which means a star, and "nomos", which means law in Russian. That is, the science of stellar laws.
Various assumptions have been made to explain the motion of the planets. The famous Greek astronomer Ptolemy in the II century BC believed that the center of the Universe is the Earth, around which the Moon, Mercury, Venus, the Sun, Mars, Jupiter, Saturn revolve.
The development of trade between the West and the East in the 15th century placed increased demands on navigation, gave impetus to the further study of the movement of celestial bodies, astronomy.
In 1515, the great Polish scientist Nicolaus Copernicus (1473-1543), a very brave man, refuted the doctrine of the immobility of the Earth. According to the teachings of Copernicus, the Sun is in the center of the world. Five planets known by that time and the Earth, which is also a planet, and is no different from other planets, revolve around the Sun. Copernicus argued that the rotation of the Earth around the Sun occurs in a year, and the rotation of the Earth around its axis occurs in a day.
The ideas of Nicolaus Copernicus were continued to develop by the Italian thinker Giordano Bruno, the great scientist Galileo Galilei, the Danish astronomer Tycho Brahe, the German astronomer Johannes Kepler. The first guesses were expressed that not only the Earth attracts bodies to itself, but the Sun also attracts planets to itself.
The first quantitative laws that opened the way to the idea of universal gravitation were the laws of Johannes Kepler. What do Kepler's conclusions say?
Communication 3. Johannes Kepler, an outstanding German scientist, one of the creators of celestial mechanics, for 25 years, under the conditions of the most severe need and adversity, generalized the data of astronomical observations of the motion of the planets. He received three laws about how the planets move.
According to Kepler's first law, planets move along closed curves called ellipses, in one of the focuses of which is the Sun. (A sample of the material design for projection on the screen is presented in the appendix.) (Appendix No. 2.)
The planets are moving at a changing speed.
The squares of the periods of revolution of the planets around the Sun are referred to as cubes of their semi-major axes.
These laws are the result of a mathematical generalization of astronomical observations. But it was completely incomprehensible why the planets were moving so “smartly”. Kepler's laws had to be explained, that is, deduced from some other, more general law.
Newton solved this difficult problem. He proved that if the planets move around the Sun in accordance with Kepler's laws, then the gravitational force must act on them from the direction of the Sun.
The force of gravity is inversely proportional to the square of the distance between the planet and the Sun.
Thanks for speaking. Newton proved that there is an attraction between the planets and the Sun. The force of gravity is inversely proportional to the square of the distance between the bodies.
But the question immediately arises: is this law valid only for the gravitation of the planets and the Sun, or does the attraction of bodies to the Earth obey it?
Message 4. The moon moves around the Earth approximately circular orbit... This means that a force acts on the Moon from the side of the Earth, imparting centripetal acceleration to the Moon.
The centripetal acceleration of the Moon as it moves around the Earth can be calculated by the formula:, where v is the speed of the Moon as it moves along its orbit, R is the radius of the orbit. The calculation gives a= 0.0027 m / s 2.
This acceleration is caused by the force of interaction between the Earth and the Moon. What is this power? Newton concluded that this force obeys the same law as the attraction of planets to the Sun.
The acceleration of falling bodies on the Earth g = 9.81 m / s 2. Acceleration when the Moon moves around the Earth a= 0.0027 m / s 2.
Newton knew that the distance from the center of the Earth to the orbit of the Moon is about 60 times the radius of the Earth. Based on this, Newton decided that the ratio of accelerations, and hence the corresponding forces, is equal to:, where r is the radius of the Earth.
From this it follows that the force that acts on the moon is the same one that we call the force of gravity.
This force decreases in inverse proportion to the square of the distance from the center of the Earth, that is, where r is the distance from the center of the Earth.
Thank you for message. Newton's next step is even more grandiose. Newton concludes that not only bodies gravitate to the Earth, planets to the Sun, but all bodies in nature are attracted to each other with forces obeying the inverse square law, that is, gravity, gravity is a universal, universal phenomenon.
Gravitational forces are fundamental forces.
Just think: universal gravitation. Worldwide!
What a magnificent word! All, all bodies in the Universe are connected by some kind of threads. Where is this all-pervading, not knowledgeable of boundaries the action of bodies on each other? How do bodies feel each other at gigantic distances through emptiness?
Does the force of universal gravitation depend only on the distance between bodies?
The force of gravity, like any force, obeys Newton's II law. F = ma.
Galileo found that the force of gravity F heavy = mg... The force of gravity is proportional to the mass of the body on which it acts.
But gravity is a special case of gravity. Therefore, we can assume that the force of gravity is proportional to the mass of the body on which it acts.
Let there are two attracting balls of masses m 1 and m 2. On the first from the side of the second, the force of gravity acts. But also on the second from the side of the first.
According to Newton's III law
If the mass of the first body is increased, then the force acting on it will also increase.
So. The force of gravity is proportional to the masses of the interacting bodies.
In its final form, the law of universal gravitation was formulated by Newton in 1687 in his work “Mathematical Principles of Natural Philosophy”: “ All bodies are attracted to each other with a force directly proportional to the products of masses and inversely proportional to the square of the distance between them. " The force is directed along the straight line connecting material points.
G - constant of universal gravitation, gravitational constant.
Why does the ball fall on the table (the ball interacts with the Earth), and the two balls lying on the table are not attracted to each other in any noticeable way?
Let's find out the meaning and units of measurement of the gravitational constant.
The gravitational constant is numerically equal to the force with which two bodies with a mass of 1 kg each, located at a distance of 1 m from each other, are attracted. The magnitude of this force is 6.67 · 10 –11 N.
; ; 
In 1798, the numerical value of the gravitational constant was first determined by the English scientist Henry Cavendish using a torsion balance.
G is very small, so two bodies on Earth are attracted to each other with very little force. She is imperceptible to the visible eye.
Fragment of the film "About universal gravitation". (About the Cavendish experience.)
The scope of the law:
- for material points (bodies, the dimensions of which can be neglected in comparison with the distance at which the bodies interact);
- for spherical bodies.
If the bodies are not material points, then the laws are fulfilled, but the calculations become more complicated.
It follows from the law of universal gravitation that all bodies have the property of being attracted to each other - the property of gravity (gravity).
From Newton's II law, we know that mass is a measure of the inertia of bodies. Now we can say that mass is a measure of two universal properties of bodies - inertia and gravity (gravity).
Let's get back to the concept scientific method: Newton generalized the data of practice by means of mathematical processing (which was known before him in science), derived the law of universal gravitation, and from it he received consequences.
Gravity is universal:
- On the basis of Newton's theory of gravitation, it was possible to describe the motion of natural and artificial bodies in the solar system, to calculate the orbits of planets and comets.
- Based on this theory, the existence of the planets was predicted: Uranus, Neptune, Pluto and the satellite of Sirius. (Appendix No. 3.)
- In astronomy, the law of universal gravitation is fundamental, on the basis of which the parameters of motion of space objects are calculated, their masses are determined.
- The onset of the ebb and flow of the seas and oceans is predicted.
- The flight paths of shells and missiles are being determined, and heavy ore deposits are being explored.
Newton's discovery of the law of universal gravitation is an example of solving the main problem of mechanics (to determine the position of a body at any time).
Fragment of the video "On the power that rules the worlds."
You will see how the law of universal gravitation is used in practice to explain the phenomena of nature.
THE LAW OF WORLD GRAVITY
1. Four balls have the same masses, but different sizes. Which pair of balls will attract more force?
2. What attracts to itself with greater force: the Earth - the Moon or the Moon - the Earth?
3. How will the force of interaction between bodies change with increasing distance between them?
4. Where will the body be attracted to the Earth with greater force: on its surface or at the bottom of the well?
5. How will the force of interaction of two bodies of masses m and m change if the mass of one of them is increased by 2 times, and the mass of the other is reduced by 2 times, without changing the distance between them?
6. What happens to the force of gravitational interaction of two bodies if the distance between them is increased by 3 times?
7. What will happen to the force of interaction of two bodies if the mass of one of them and the distance between them are doubled?
8. Why do we not notice the attraction of the surrounding bodies to each other, although the attraction of these bodies to the Earth is easy to observe?
9. Why does a button, tearing itself off from a coat, fall to the ground, because it is much closer to a person and is attracted to him?
10. The planets move in their orbits around the Sun. Where is the gravitational force acting on the planets from the sun? Where is the acceleration of the planet directed at any point in orbit? How is speed directed?
11. What explains the presence and frequency of sea tides on Earth?
PRACTICE ON SOLVING PROBLEMS
- Calculate the force of attraction of the moon to the earth. The mass of the Moon is approximately equal to 7 · 10 22 kg, the mass of the Earth is 6 · 10 24 kg. The distance between the Moon and the Earth is considered equal to 384,000 km.
- The Earth moves around the Sun in an orbit that can be considered circular, with a radius of 150 million km. Find the speed of the Earth in its orbit if the mass of the Sun is 2 · 10 30 kg.
- Two ships weighing 50,000 tons each are in the roadstead at a distance of 1 km from each other. What is the force of attraction between them?
SOLVE YOURSELF
- What is the force with which two bodies weighing 20 tons are attracted to each other, if the distance between their centers of mass is 10 m?
- With what force is attracted by the Moon a weight weighing 1 kg, located on the surface of the Moon. The Moon's mass is 7.3 10 22 kg, and its radius is 1.7 10 8 cm?
- At what distance the force of attraction between two bodies with a mass of 1 ton each will be equal to 6.67 · 10 -9 N.
- Two identical balls are at a distance of 0.1 m from each other and are attracted with a force of 6.67 · 10 -15 N. What is the mass of each ball?
- The masses of the Earth and the planet Pluto are almost the same, and their distances to the Sun are approximately 1: 40. Find the ratio of their gravitational forces to the Sun.
LIST OF LITERATURE:
- Vorontsov-Velyaminov B.A. Astronomy. - M .: Education, 1994.
- T.I. Gontaruk I get to know the world. Space. - M .: AST, 1995.
- Gromov S.V. Physics - 9.M .: Education, 2002.
- Gromov S.V. Physics - 9. Mechanics. M .: Education, 1997.
- Kirin L.A., Dick Yu.I. Physics - 10.collection of tasks and independent work... M .: ILEKSA, 2005.
- Klimishin I.A. Elementary Astronomy. - M .: Nauka, 1991.
- Kochnev S.A. 300 questions and answers about the Earth and the Universe. - Yaroslavl: "Development Academy", 1997.
- E.P. Levitan Astronomy. - M .: Education, 1999.
- Myakishev G.Ya., Bukhovtsev B.B., Sotskiy N.N. Physics - 10.M .: Education, 2003.
- G.P. Subbotin Collection of problems in astronomy. - M .: "Aquarium", 1997.
- Encyclopedia for children. Volume 8. Astronomy. - M .: "Avanta +", 1997.
- Encyclopedia for children. Supplementary volume. Cosmonautics. - M .: "Avanta +", 2004.
- Yurkina G.A. (compiler). From school to the universe. M .: "Young Guard", 1976.
