Working lessons (abstract lessons)

Secondary education

Line Ukk B. A. Vorontsova-Veliamnova. Astronomy (10-11)

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The purpose of the lesson

Reveal the empirical and theoretical foundations of the laws of heavenly mechanics, their manifestations in astronomical phenomena and use in practice.

Tasks lesson

• Check the justice of the law of the World Committee on the basis of the analysis of the movement of the Moon around the Earth; Prove that from the laws of Kepler it follows that the Sun reports the planet acceleration, inversely proportional to the square of the distance from the Sun; explore the phenomenon of the indignant movement; Apply the law of world community to determine the masses of the celestial bodies; Explain the phenomenon of tides as a consequence of the manifestation of the world of global gravity in the interaction of the Moon and the Earth.

Activities

Build logical oral statements; hypothesize; Perform logical operations - analysis, synthesis, comparison, generalization; formulate research objectives; draw up a study plan; turn on the group's work; implement and adjust the study plan; submit the results of the Group's work; Reflection of cognitive activity.

Key concepts

The law of global gravity, the phenomenon of the perturbed movement, the phenomenon of tides, refined the third law of Kepler.

№	Stage name	Methodical comment
1	1. Motivation to activities	During the discussion of the issues, the mean elements of the laws of Kepler are emphasized.
2	2. Actualization of experience and preceding knowledge of students and fixation of difficulties	The teacher organizes a conversation about the contents and boundaries of the applicability of the laws of Kepler, the law of the World Committee. The discussion is based on the knowledge of students from the course of physics about the law of world community and its applications to the explanation of physical phenomena.
3	3. Statement of the educational task	Using the slideshow, the teacher organizes a conversation about the need for evidence of the justice of the law of world community, the study of the perturbed movement of the celestial bodies, finding a method for determining the masses of heavenly bodies and studies of the phenomenon of tides. The teacher accompanies the process of dividing students to problem groups that decisive one of the astronomical tasks, and initiates a discussion of the objectives of the Group.
4	4. Drawing up a plan to overcome difficulties	Students in groups based on the goal, formulate questions that they want to get answers, and make up a plan for achieving the goal. The teacher corrects together with the group each of the plans of activity.
5	5.1 Implementation of the selected activity plan and independent work	Portrait I. Newton is presented on the screen during the execution of independent group activities. Students implement a plan using the textbook content § 14.1 - 14.5. The teacher adjusts and sends work in groups, supporting the activities of each student.
6	5.2 Implementation of the selected activity plan and independent work	The teacher organizes the representation of the group 1 of the work results, based on the tasks presented on the screen. The remaining students outline the main ideas expressed by the group members. After submitting data, the teacher focuses on the correction of the plan, which participants carried out in the process of its implementation, asks to formulate the concepts with which students first met during the work.
7	5.3 Implementation of the selected activity plan and independent work	The teacher organizes the presentation of the group 2 of the results of the work. The remaining students outline the main ideas expressed by the group members. After submitting data, the teacher focuses on the correction of the plan, which participants carried out in the process of its implementation, asks to formulate the concepts with which students first met during the work.
8	5.4 Implementation of the selected activity plan and independent work	The teacher organizes the representation of a group of 3 results of work. The remaining students outline the main ideas expressed by the group members. After submitting data, the teacher focuses on the correction of the plan, which participants carried out in the process of its implementation, asks to formulate the concepts with which students first met during the work.
9	5.5 Implementation of the selected activity plan and independent work	The teacher organizes the representation of the group 4 of the results of work. The remaining students outline the main ideas expressed by the group members. After submitting data, the teacher focuses on the correction of the plan, which participants carried out in the process of its implementation, asks to formulate the concepts with which students first met during the work.
10	5.6 Implementation of the selected activity plan and self-work	The teacher, using the animation, discusses the dynamics of the occurrence 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. Reflexing of activity	During the discussion of the answers to reflective questions, it is necessary to focus on the methodology for performing tasks with groups, the correction of the activity plan in its implementation, the practical significance of the results obtained.
12	7. Homework

The significance of the world of global

The law of global gravity underlies the heavenly mechanics- sciences about the movement of planets.

With the help of this law, the provisions of heavenly bodies are determined with great accuracy on the heavenly arch for many dozens of years ahead and their trajectories are calculated.

The law of global gravity is also applied in the calculations of the movement of artificial satellites of the Earth and interplanetary automatic devices.

Perturbations in motion planets

Planets do not move strictly according to the laws of Kepler. The laws of Kepler would definitely comply with the movement of this planet only when one of the planet would appeal around the Sun. But there are many planets in the solar system, they are all attracted both the sun and each other. Therefore, there are perturbations of the motion of the planets. In the solar perturbation system is small, because the attraction of the planet Sun is much stronger than the attraction by other planets.

When calculating the visible position of the planets have to take into account the indignation. When launching artificial celestial bodies and, when calculating their trajectories, use the approximate theory of movement of the celestial bodies - perturbation theory.

Opening Neptune

One of the bright examples of the Triumph of the World Act is the discovery of the planet Neptune. In 1781, the English astronomer William Herschel opened Uranian Planet.

Its orbit was calculated and the table of the positions of this planet was drawn up for many years ahead. However, checking this table, conducted in 1840, showed that its data disagree with reality.

Scientists suggested that the deviation in the movement of uranium was caused by attraction of an unknown planet from the Sun even further than uranium. Knowing deviations from the calculated trajectory (perturbation of the movement of uranium), the Englishman Adams and the Frenchman Leerright, using the world of global gravity, calculated the position of this planet in the sky.

Adams used to finish the calculations, but the observers to whom he told his results did not hurry with the inspection. Meanwhile, Leverrier, having completed the calculation, pointed to German Astronoma Galle, where it is necessary to look for an unknown planet.

Both discoveries, as they say, were made "at the tip of the pen."

The correctness of the World Act of the World Act is confirmed by the fact that with the help of this law and the second law of Newton can withdraw the laws of Kepler. We will not give this conclusion.

With the help of the World Act, it is possible to calculate the mass of the planets and their satellites; Explain such phenomena as tides and flowing water in the oceans, and much more.

2.1 Opening Neptune

One of the bright examples of the Triumph of the World Act is the discovery of the planet Neptune. In 1781, the English astronomer William Herschel opened Uranian Planet. Its orbit was calculated and the table of the positions of this planet was drawn up for many years ahead. However, checking this table, conducted in 1840, showed that its data disagree with reality.

Scientists suggested that the deviation in the movement of uranium was caused by attraction of an unknown planet from the Sun even further than uranium. Knowing deviations from the calculated trajectory (perturbation of the movement of uranium), the Englishman Adam and the Frenchman Leerright, using the world of global, calculated the position of this planet in the sky. Adam used to finish the calculations, but the observers to whom he told his results did not hurry with the inspection. Meanwhile, Leverrier, having completed the calculation, pointed to German Astronoma Galle, where it is necessary to look for an unknown planet. On the first evening, September 28, 1846, Galle, sending a telescope to the specified place, discovered a new planet. She was called Neptune.

In the same way, on March 14, 1930, Planet Pluto was opened. The discovery of Neptune, made, in the expression of Engels, on the "tip of the pen", is a convincing proof of the justice of the law of Newton's World Act.

With the help of the World Act, it is possible to calculate the mass of the planets and their satellites; Explain such phenomena as tides and flowing water in the oceans, and much more.

World forces are the most universal of all the forces of nature. They act between any bodies with mass, and the mass has all the bodies. For the forces of grave there are no obstacles. They act through any bodies.

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Lesson 1(Record the topic and purpose of the lesson in notebooks)

The law of global gravity. Acceleration of free fall on earth and other planets

The purpose of the lesson:

Examine the law of global gravity, show its practical significance.

During the classes

I.. New material (make a summary in notebooks)

Danish astronomer quietly Braga, many years watching the movement of the planets, has accumulated numerous data, but failed to process them. This made his student Johann Kepler. Using the idea of \u200b\u200bCopernicus about the heliocentric system and the results of observations of Quiet Brage, Kepler installed the laws of motion of the planets around the Sun. But Kepler failed to explain the dynamics of movement. Why do the planets turn around the sun according to such laws? This question was able to answer Isaac Newton, using the laws of movement established by Kepler, and the general laws of speakers.

Newton suggested that a number of phenomena seemingly not having anything to do anything (the fall in the bodies on the ground, the appeal of the planets around the sun, the movement of the moon around the earth, tides and flow, etc.), caused by one reason. Having spent numerous calculations, Newton came to the conclusion that heavenly bodies are attracted to each other with force, directly proportional to the product of their masses and inversely proportional to the square of the distance between them. Let us show how Newton came to this conclusion.

From the second law, "the dynamics follows that the acceleration that receives the body under the action of force is inversely proportional to the mass of the body. But the acceleration of the free fall does not depend on body weight. This is possible only if the force with which the earth attracts the body, changes in proportion Mass body.

According to the third law of force with which the bodies interact are equal. If the force acting on one body is proportional to the mass of this body, then the force equal to it acting on the second body is obviously proportional to the mass of the second body. But the forces acting on both bodies are equal, therefore, they are proportional to the mass and the first and second body.

Newton calculated the ratio of the radius of the moon orbits to the radius of the Earth. The ratio was 60. And the ratio of the acceleration of the free fall on the ground to the centripetal acceleration, with which it turns around the Moon's Earth, was 3600. Consequently, the acceleration is inversely proportional to the square of the distance between the bodies.

But according to the second Newton law, the force and acceleration are associated with direct dependence, therefore, the force is inversely proportional to the square of the distance between the bodies.

Isaac Newton discovered this law at the age of 23, but 9 years did not publish, since incorrect data on the distance between the Earth and the Moon did not confirm his idea. And only when this distance was clarified, Newton in 1667 published the law of global gravity.

The strength of the gravitational interaction of two bodies (material points) with the masses t.1 I. t.2 equal:

where G. - gravitational constant, r. - Distance between bodies.

The gravitational constant is numerically equal to the module of the force acting on the body weighing 1 kg from the other body of the same mass at the distance between the bodies equal to 1 m.

For the first time, the gravitational constant was measured by the English physicist in the city of Cavendis in 1788 with the help of a device called twisted scales. G. Cavendish secured two small lead balls (with a diameter of 5 cm and weighing 775 g each) at the opposite ends of the two-meter rod. The rod was suspended on a thin wire. Two large lead balls (20 cm with a diameter and a mass of 45.5 kg) were close to small. The forces of attraction from large balls were forced to move small, while the wire was twisted. The degree of twisting was a measure of force acting between the balls. The experiment showed that the gravitational is in-sintic G \u003d 6.66 × 1011 Nm2 / kg2.

Limits of the applicability of the Law

The world's law is applicable only for material points, i.e. for bodies, the dimensions of which are significantly less than the distances between them; bodies having a shape of a ball; For a ball of a large radius that interacts with bodies, the dimensions of which are significantly less than the sizes of the ball.

But the law is not applicable, for example, to interact the infinite rod and ball. In this case, the strength of gravity is inversely proportional to only the distance, and not the square of the distance. And the force of attraction between the body and the infinite plane is generally independent of the distance.

Gravity

A special case of gravitational forces is the force of attraction to the Earth. This force is called the power of gravity. In this case, the law of world community has the form:

where t. - body weight [kg],

M. - Mass of the Earth [kg],

R. - the radius of the Earth [m],

h. - Height above the surface [m].

But the power of gravity F.T \u003d. mG.From here, and the acceleration of free fall.

On the surface of the earth ( h. = 0) .

Acceleration of free fall depends

♦ from height above the surface of the Earth;

♦ from the latitude of the terrain (land - non-inertial reference system);

♦ from the density of the rocks of the earth's crust;

♦ From the form of the Earth (the poles are closed).

In the above formula for G, the last three dependences are not taken into account. At the same time once again we emphasize that the acceleration of the free fall is not 1 depends on body weight.

Application of the law when opening new planets

When the Planet Uranus was opened, on the basis of the law of world community, it was calculated by its orbit. But the true orbit of the planet did not coincide with the calculated one. They suggested that the indignation of the orbit caused the presence of another planet behind the uranium, which his orbit changes its strength. To find a new planet, it was necessary to solve the system of 12 differential equations with 10 unknown. This task was performed by the Ang - Jai's student Adamc; He sent the decision to the British Academy of Sciences. But there they did not pay attention to his work. And the French mathematician Leverage, having decided the task, sent the result to Italian Astronoma Galle. And he, on the first evening, to bring his pipe at the specified point, discovered a new planet. She was given the name Neptune. Similarly, the 9th Planet of the Solar System - Pluto was also open in the zo-e years of the twenty-century.

On the question of what the nature of the forces of grave, Newton answered: "I do not know, but I do not want to fulfill hypotheses."

III. Exercises and questions for repetition (orally)

How is the law of global gravity formulating?

What species does the formula of the world of world gravity for material points?

What do they call the gravitational constant? What is her physical meaning? What is the value in si?

What is called a gravitational field?

Does the force depend on the properties of the environment in which the bodies are located?

Does the acceleration of the free fall of the body depend on its mass?

Is the power of gravity at different points of the globe?

Explain the effect of the rotation of the Earth around the axis to accelerate the free fall.

How is the acceleration of free fall when removing from the surface of the Earth?

Why doesn't the moon fall on Earth? ( The moon draws around the Earth, held by the power of attraction. The moon does not fall on the ground, because having the initial speed, moves by inertia. If the effect of the force of attraction of the moon to the ground ceases, the moon in a straight line will be twisted into the abyss of the outer space. Stop movement on inertia - and the moon would fall on the ground. The fall would continue four days nineteen hours fifty four minutes seven seconds. So Calcated Newton.)

IV.. Solving tasks (in writing in notebooks with registration !!!)

Task 1.

At what distance the force of attraction of two balls by the masses of 1 g is equal to 6.7 · 10-17 N?

Task 2.

Which height from the surface of the Earth, a spacecraft rose, if the instruments noted the decrease in the acceleration of the free fall to 4.9 m / s2?

Task 3.

The force of gravity between two balls 0.0001 N. What is the mass of one of the balls, if the distance between their centers is 1 m, and the mass of another ball 100 kg?

Homework

1. To learn §11;

2. Exercise 5.1-5.10 (orally), 5.11-5.5.20 (in writing in notebooks with registration);

3. Answer the question of Microtest:

Space rocket is removed from the ground. How will the force of grave acting on the part of the earth on the rocket, with an increase in the distance to the center of the Earth 3 times?

a) will increase 3 times; b) will decrease 3 times;

c) will decrease by 9 times; d) will not change.

Opening and application of the law of world gravity10-11 class
UMK B.A. Vorontsova-Vel'aminova
Razmov Viktor Nikolaevich,
Teacher MOU "Bobelovskaya School"
Lyambir Municipal District of the Republic of Mordovia

The Law of the World Health

The Law of the World Health
All bodies in the Universe are attracted to each other.
with strength, directly proportional to their
masses and back proportional square
Distances between them.
Isaac Newton (1643-1727)
where T1 and T2 - mass bodies;
R is the distance between the bodies;
G - gravitational constant
The discovery of the world of world agreed in many ways
The laws of motion of the planets formulated by Kepler,
and other achievements of Astronomy XVII century.

Distance to the Moon allowed Isaac Newton to prove
The identity of the force holding the moon when it moves around the Earth, and
Forces causing the fall to the ground.
Since the strength of gravity changes inversely proportional to the square of the distance,
as it follows from the law of the world, then the moon,
located from the earth at a distance of about 60 of its radii,
should experience acceleration 3600 times less
Than accelerating gravity on the surface of the earth, equal to 9.8 m / s.
Consequently, the acceleration of the moon should be 0.0027 m / s2.

At the same time, the moon, like any body, evenly
Moving around the circle, has acceleration
where ω is its angular velocity, R is the radius of its orbit.
Isaac Newton (1643-1727)
If we assume that the land radius is 6400 km,
then the radius of the lunar orbit will be
r \u003d 60 6 400 000 m \u003d 3.84 10 m.
Star period of circulation of the moon T \u003d 27.32 days,
In seconds is 2.36 10 s.
Then the acceleration of the orbital movement of the moon
The equality of these two values \u200b\u200bof acceleration proves that the force holding
The moon in orbit, there is the power of earth attraction, weakened 3600 times
compared with the acting on the surface of the Earth.

When moving planets, according to the third
The law of Kepler, their acceleration and acting on
they are the strength of the attraction of the sun back
proportional to the square of the distance like this
It follows from the law of world community.
Indeed, according to the third law of Kepler
The ratio of cubes of large semi-axes of orbits d and squares
Periods of circulation T there is a permanent value:
Isaac Newton (1643-1727)
The acceleration of the planet is equal to
From the third law of Kepler follows
Therefore, the acceleration of the planet is equal
So, the strength of the interaction of the planets and the Sun satisfies the law of world community.

Indignation in the movements of the bodies of the solar system

The movement of the planets of the solar system does not exactly obey the laws
Kepler because of their interaction not only with the Sun, but also among themselves.
Deviations of bodies from the movement by ellipses are indignant.
Indignation is small, since the mass of the sun is much more mass not only
A separate planet, but also all the planets in general.
The deviations of asteroids and comets are especially noticeable when they pass.
Near Jupiter, the mass of which is 300 times higher than the mass of the Earth.

In the XIX century The calculation of disturbances allowed to open the planet Neptune.
William Herschel
John Adams.
Urben Leverier
William Herschel in 1781 opened Uranian Planet.
Even when registering perturbations from all
famous planets observable movement
Uranus was not agreed with calculated.
Based on the assumption about the presence of yet
one "Zaurantova" Planet John Adams in
England and Urben Leverier in France
independently of each other made calculations
Its orbits and positions in the sky.
Based on the calculations of Leverier German
Astronomer Johann Galle September 23, 1846
discovered in the constellation Aquarius unknown
Previously, the planet is Neptune.
Uranium and Neptune was disturbed
predicted, and in 1930 and found
Dwarf Planet Pluto.
Neptune's discovery has become a triumph
heliocentric system
The most important confirmation of justice
The law of the world.
Uranus
Neptune
Pluto
Johann Galle