VI district scientific conference of students named after Lobachevsky
abstract
On the topic: "Why does the moon not fall to the Earth?"
Done by: 9th grade student Isenbaev secondary school Nagimova Anastasia
Supervisor:
Ismagilova Farida Mansurovna
2008-2009 academic year
I. Introduction.
II. Why doesn't the moon fall to earth?
1. The law of universal gravitation
2. Can the force with which the Earth attracts the Moon be called the weight of the Moon?
3. Is there a centrifugal force in the Earth-Moon system, what does it act on?
4. Can the Earth and the Moon collide? Their orbits around the Sun intersect, and not even once
III. Conclusion
IV. Literature
Introduction
Why did I choose this topic? Why is she so interesting to me?
After all, the starry sky has always occupied the imagination of people. Why do stars light up? How many of them shine at night? Are they far from us? Does the stellar universe have boundaries? Since ancient times, man has thought about these and many other questions, sought to understand and comprehend the structure of the big world in which we live. This opened the widest area for the study of the Universe, where the forces of gravity play a decisive role.
Among all the forces that exist in nature, the force of gravity differs, first of all, in that it manifests itself everywhere. All bodies have mass, which is defined as the ratio of the force applied to the body to the acceleration that the body acquires under the action of this force. The force of attraction acting between any two bodies depends on the masses of both bodies; it is proportional to the product of the masses of the considered bodies. In addition, the force of gravity is characterized by the fact that it obeys the law inversely proportional to the square of the distance. Other forces may depend on distance quite differently; many such forces are known.
All weighty bodies mutually experience gravity, this force determines the movement of the planets around the sun and satellites around the planets. The theory of gravity - the theory created by Newton, stood at the cradle of modern science. Another theory of gravity developed by Einstein is the greatest achievement of theoretical physics of the 20th century. During the centuries of the development of mankind, people observed the phenomenon of mutual attraction of bodies and measured its magnitude; they tried to put this phenomenon at their service, to surpass its influence, and, finally, very recently, to calculate it with extreme accuracy during the first steps deep into the universe.
The story is widely known that the discovery of Newton's law of universal gravitation was caused by the fall of an apple from a tree. How reliable this story is, we do not know, but the fact remains that the question that we have gathered today to discuss: "Why does the moon not fall to the Earth?" interested Newton and led him to the discovery of the law of gravitation. Newton argued that between the Earth and all material bodies there is a gravitational force, which is inversely proportional to the square of the distance.
The forces of universal gravitation are otherwise called gravitational.
Law of gravity
Newton's merit lies not only in his brilliant conjecture about the mutual attraction of bodies, but also in the fact that he was able to find the law of their interaction, that is, a formula for calculating the gravitational force between two bodies.
The law of universal gravitation says: any two bodies are attracted to each other with a force directly proportional to the mass of each of them and inversely proportional to the square of the distance between them.
Newton calculated the acceleration imparted to the Moon by the Earth. The acceleration of freely falling bodies near the Earth's surface is equal to g=9.8 m/s 2 . The Moon is distant from the Earth at a distance equal to about 60 Earth radii. Therefore, Newton reasoned, the acceleration at this distance would be: 9.8 m/s 2:60 2 =0.0027 m/s 2. The moon, falling with such an acceleration, should approach the Earth in the first second by 0.0013 m. But the Moon, in addition, moves by inertia in the direction of the instantaneous velocity, i.e. along a straight line tangent at a given point to its orbit around the Earth.(rice. 25)
Moving by inertia, the Moon should move away from the Earth, as the calculation shows, in one second by 1.3 mm. Of course, such a motion, in which in the first second the Moon would move along the radius to the center of the Earth, and in the second second along the tangent, does not really exist. Both movements add up continuously. As a result, the Moon moves along a curved line close to a circle.
Consider an experiment that shows how the force of attraction acting on a body at right angles to the direction of its motion transforms a rectilinear motion into a curvilinear one. A ball, having rolled down from an inclined chute, by inertia continues to move in a straight line. If, however, a magnet is placed on the side, then under the influence of the force of attraction to the magnet, the trajectory of the ball is curved (Fig. 26)
The moon revolves around the earth, held by the force of gravity.
A steel rope that could keep the moon in orbit would have to have a diameter of about 600 km. But despite such a huge The force of gravity, the Moon does not fall to the Earth, because, having an initial speed, it moves by inertia.
Knowing the distance from the Earth to the Moon and the number of revolutions of the Moon around the Earth, Newton determined the centripetal acceleration of the Moon. We got the number already known to us: 0.0027 m / s 2.
Stop the force of attraction of the Moon to the Earth, and the Moon will rush in a straight line into the abyss of outer space. So in the device, shown in Figure 27, the ball will fly away tangentially if the thread holding the ball on the circle breaks. In the device you know on a centrifugal machine (Fig. 28), only the connection (thread) keeps the balls in a circular orbit.
When the thread breaks, the balls scatter along the tangents. It is difficult to catch their rectilinear movement with the eye when they are devoid of connection, but if we make a drawing (Fig. 29), it will be seen that the balls move in a rectilinear manner, tangentially to the circle.
Using the formula of the law of universal gravitation, you can determine with what force the Earth attracts the Moon , whereG- gravitational constant, M andm- the masses of the earth,r- the distance between them. The earth pulls on the moon with a force of about 2. 10 20 N.
The law of universal gravitation applies to all bodies, which means that the Sun also attracts the Moon. Let's count with what force?
The mass of the Sun is 300,000 times the mass of the Earth, but the distance between the Sun and the Moon is 400 times greater than the distance between the Earth and the Moon. Therefore, in the formulaF= G mm: r 2 the numerator is increased by 300,000 times, and the denominator by 400 2 , or 160,000 times. The gravitational force will be almost twice as large.
But why doesn't the moon fall on the sun?
The Moon falls on the Sun in the same way as on the Earth, i.e. only long enough to stay about the same distance as it orbits the Sun.
The following question arises: The moon does not fall to the Earth, because, having an initial speed, it moves by inertia. But according to Newton's third law, the forces with which two bodies act on each other are equal in absolute value and oppositely directed. Therefore, with what force the Earth attracts the Moon to itself, with the same force the Moon attracts the Earth. Why doesn't the Earth fall on the Moon? Or does it revolve around the moon?
The fact is that both the Moon and the Earth revolve around a common center of mass. Recall the experience with balls and a centrifugal machine. The mass of one of the balls is twice the mass of the other. In order for the balls connected by a thread during rotation to remain in equilibrium relative to the axis of rotation, their distances from the axis, or center of rotation, must be inversely proportional to the masses. The point around which these balls revolve is called the center of mass of the two balls.
Newton's third law is not violated in the experiment with balls: the forces with which the balls pull each other towards the common center of mass are equal. The common center of mass of the Earth and the Moon revolves around the Sun.
Can the force with which the Earth is pulled by the Moon be called the weight of the Moon?
No! We call the weight of the body the force caused by the attraction of the Earth, with which the body presses on some support, for example, a scale pan, or stretches the spring of a dynamometer. If you put a stand under the Moon (from the side facing the Earth), then the Moon will not put pressure on it. The moon would not stretch the spring of the dynamometer, if we could hang it. The entire action of the force of attraction of the Moon by the Earth is expressed only in keeping the Moon in orbit, in imparting centripetal acceleration to it. It can be said about the Moon that in relation to the Earth it is weightless in the same way as objects in a space ship-satellite are weightless when the engine stops working and only the force of attraction to the Earth acts on the ship, but this force cannot be called weight. All items released by the astronauts from their hands (pen, notepad) do not fall, but float freely inside the cabin. All bodies on the Moon, in relation to the Moon, of course, are weighty and will fall onto its surface if they are not held by something, but in relation to the Earth, these bodies will be weightless and cannot fall to the Earth.
Is there a centrifugal force in the Earth-Moon system, what does it act on?
In the Earth-Moon system, the forces of mutual attraction of the Earth and the Moon are equal and oppositely directed, namely to the center of mass. Both of these forces are centripetal. There is no centrifugal force here.
The distance from the Earth to the Moon is approximately 384,000 km. The ratio of the mass of the Moon to the mass of the Earth is 1/81. Therefore, the distances from the center of mass to the centers of the Moon and the Earth will be inversely proportional to these numbers. Dividing 384,000 km by 81, we get approximately 4,700 km. So the center of mass is at a distance of 4700 km from the center of the earth.
Look up, there's a ceiling or sky. Look down, there is floor or ground. We use the words "up" and "down" dozens of times a day without thinking about their meaning. We say: "What you throw up will surely fall down." The ball flies up to the sky and then falls down. But here we see a lot of stars in the sky. Why don't they fall down like a ball?
What is top and bottom
Wait a minute! Do the words "up" and "down" really mean what we ascribe to them? If we fly to the South Pole, to Antarctica, then we will by no means have to walk upside down there. Wherever we go on Earth, everywhere there will be sky above, and solid ground under our feet.
What we call "down" is most directly related to the force of gravity (gravity). Objects fall towards the ground - we call this "down" because they are attracted by the gravity under our feet. But if we move away from the Earth in a spaceship, then the concepts of "up" and "down" will lose their meaning. During space flight, there is only a huge empty space between planets and stars. Shooting or "flying" stars are actually meteorites, fragments of stone or ice, pulled from space to the Earth by its gravity.
Space, gravity, up and down
In space it is impossible to determine where is up and where is down.. Since there really is no gravity in space, the astronaut is not able to determine which is up and which is down. The astronaut can walk on the ceiling of the ship or on the floor. At the same time, he will not feel any difference: “up” and “down” appear when we are somehow oriented in the gravitational field, that is, in the gravitational field. As soon as gravity decreases or practically disappears, the concepts of "up" and "down" lose their meaning.
Everything, however, changes during the landing of the spacecraft. The force of gravity begins to show. When the ship approaches the Earth, the astronaut immediately remembers where is up and where is down. Every planet, like every star, has the power of attraction. Giant gravity is the force that keeps nine planets in our solar system, including the Earth, in orbit around the Sun.
So why don't the stars fall?
The stars of the night sky are cosmic bodies that are trillions and trillions of kilometers away from us. The attraction between them and the Earth is negligible. But if someday these stars approached the Earth, then it would fall on the stars, attracted by their gigantic attraction, and not vice versa. So, alas! Stars do not fall and will not fall to Earth. Only meteorites fall to Earth - these pieces of rocks or ice that people mistook for stars. Romantic but wrong.
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Warm sunlight, without which life on Earth would be impossible, is also a cunning way for the Sun to destroy us. With the help of light, the star causes us and our planet to slowly fall on itself, in order to eventually absorb it. This process is explained by the Poynting-Robertson effect and applies to all objects of the Solar System, especially small ones.
All objects belonging to our planetary system smoothly and slowly rotate in a spiral, with each turn becoming closer and closer to the Sun.
The Poynting-Robertson effect follows the same principle that is used in laboratories to heat tiny particles of matter with a laser - the particles radiate light energy in all directions, even if they received it from only one source. Bring a piece of iron to the fire: the side that faces the flame directly will be hotter, but nevertheless, if you touch the opposite side of the piece, you will feel that it is also warm. Although the degree to which an object radiates heat depends on the thermal conductivity of the substance, its dimensions, and the heat source, almost every object will radiate heat received from the source. Orbital particles receive energy from only one source - the Sun - and radiate it in all directions. Therefore, the radiated energy gently pushes them towards the Sun.
But why do particles fall on the Sun? After all, the impacts of solar photons, on the contrary, should repel them in the opposite direction. This would be the case if the particles were stationary, but they rotate. For example, imagine standing in vertical rain. As long as you're just standing there, the rain doesn't interfere with your movements. But as soon as you start moving, the rain seems to stop being vertical. It starts to look like it's pouring at a slight angle and hitting you in the face. With particles - the same case. As particles move around the sun, they come into conflict with solar energy. Instead of just moving in a neutral direction, the particles are attracted to the Sun like rain to your face. If particles could only radiate energy in one direction, they would simply pick up more and more speed, but since they radiate in all directions, they generally slow down. And when they slow down their orbit, they fall into the power of solar gravity.
This is such a cunning trap created by the Sun for you and me. Of course, its proximity gives us warmth and energy to sustain life, but the Earth will slow down sooner or later and eventually fall into its star. Of course, cosmic dust has a harder time in this regard than planets, but we are also spiraling towards the end.
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Why doesn't the Earth-Moon system fall into the Sun?
attraction by the sun systems Earth-Moon very large.
Why does this system not fall on the Sun?
After all, the mass of the Sun is 329,000 times greater than the total mass of the Earth and the Moon.
tides, caused by the mutual attraction of the Earth and the Moon, is stronger than the sun. The Sun also causes relatively weak tides in the Earth-Moon system, stretching the Moon's orbit around the Earth and compressing it from the sides.
Tidal actions from the Sun are weak, because they depend on the DIFFERENCE of forces acting on the near and far sides of attracting objects, and the sizes of these objects are small compared to the distance to the Sun.
At the same time, the attraction of the ENTIRE Earth-Moon SYSTEM by the Sun is very strong.
Why doesn't it fall on the sun? After all, the mass of the Sun is 329,000 times greater than the total mass of the Earth and the Moon. Of course, it would have fallen directly on the Sun if the Earth had stopped in orbit, and would not have moved, as it is now, around the Sun at a speed of 30 kilometers per second. (At this speed, you can drive to Samara in 7 seconds!). And if it were not for the attraction of the Sun, the Earth would fly away tangentially to its orbit. The sun prevents this and forces all the bodies of the solar system to revolve around it.
Why do the bodies of the solar system rotate in orbits at such high speeds?
Because the solar system was formed from a rapidly rotating cloud. The increase in its angular velocity was a consequence of the gravitational contraction of the cloud towards its center of mass, in which the Sun subsequently formed. Even before the compression, the cloud already had angular and translational velocities. Therefore, the solar system not only rotates, but also moves in the direction of the constellation Hercules at a speed of 20 kilometers per second. And the Earth and the Moon also participate in this movement.
What is the reason for the translational and rotational motions of the cloud prior to its gravitational contraction? "Our" cloud is a small part of one of the huge gas and dust complexes that fill our Galaxy. Of the numerous reasons that cause the complex movement of these complexes, we will name a few main ones.
Non-rigid rotation of the Galaxy. The galaxy is not a solid body. The speed of rotation of that part of the complex, which is closer to the center of the Galaxy, is greater than that which is farther away, a pair of forces appears, turning the gas-dust complex.
Magnetic fields of the Galaxy. The gas component contains ions, and the dust component contains iron and other metals. Interacting with complex galactic fields, the complexes move along magnetic field lines.
Supernova explosions. The supernova substance released during the explosion accelerates the surrounding dusty substance at a speed of thousands of kilometers per second. Less effective are the "new" and other stars that shed their atmospheres.
Stellar wind. Hot giant stars with their stellar wind disperse the gas and dust substance from which they were formed,
There are many reasons. In the Galaxy, all objects have their own rotational and translational speeds.
The problem, which is discussed in this note, refers to the tasks of cosmogony. Scientists have puzzled over it since the moment of a common understanding of the structure of our solar system. This problem is at least three hundred years old. Now, in general, the problem is qualitatively solved. Rakhil Menashevna's informative note was written about this.
However, many mysteries still remain, especially in the quantitative calculation of the parameters of the solar system. We have already written about some of these riddles. Some of them were described by Rakhil Menashevna. For example, why is there a lot of water on Earth, and how this water got to us.
I would very much like to understand how the formation of our Sun and the Solar System took place. But this problem may never be completely solved. The period of revolution of the Sun around the center of the Galaxy is approximately 250 million years. During the lifetime of the Sun, which is approximately 4.5 billion years, the Sun has made 16-17 revolutions. During this time, apparently, our Sun has diverged very far with its sisters, who were born with her. Therefore, in order to deal with the initial conditions, it would be necessary to establish which stars are sisters to our Sun. But, unfortunately, we cannot do this yet. And it would be great to say that that star was born from the same cloud as the Sun, but this one was next to it at the time of birth.
For example, within a radius of 15 light years from the Sun, there are two systems with a white dwarf. This is Sirius and Procyon. These systems are similar to each other. Were they born together with the Sun or not?
Your unexpected question also interested me. I think that the assumption about the formation of the Sun, Sirius and Procyon from one common cloud is true.
I also found in the reference book P.G. Kulikovsky that these stars have rather small relative radial velocities: they approach the Sun at velocities of 8 and 3 km/s, respectively, while most of the radial velocities of stars lie within 20–30 km/s. Perhaps these stars revolve together around the center of the Galaxy.
The purpose of my short articles is to explain the essence of the phenomena under consideration. I could add many details to them, but I try not to do this, even more details could be taken from the literature, and even more, as you rightly noted, are unknown to science.
Dear RMR_stra! Very interesting information! I have been spinning one idea for a long time!
Let's pretend that Sirius or Procyon were born with sun from the same cloud. We know the age of the Sun. This is about 4.5 billion years. This is about half the life of the Sun. White dwarfs cannot have a mass greater than twice the mass of the Sun. More likely somewhere 1.5 masses of the Sun. But stars with a mass two to one and a half times more than the sun and live the same number of times less than the Sun, approximately, of course. But this means that white dwarfs in the systems of Saturn and Procyon appeared quite recently. It is possible that our ancestors saw the shedding of the shells of these stars in the form of some grandiose celestial fireworks. There is a so-called disk Nebra. It is estimated to be about 5000 years old. It has some arcs in the starry sky. The discarded shell should have looked like such sparkling arcs in the Earth's sky. On the disk, the arcs are said to be adjacent to the seven stars of the Pleiades. And they are just located almost in the same sector of the sky as Sirius and Procyon.
Moreover, it can even be assumed that reaching the ejected shell of the Solar System several hundred years after the ejection could cause increased condensation of moisture in the Earth's atmosphere (due to an increase in the flux of charged particles), i.e. rain. Such rain could last all the time during which the central part of the shell passes the Earth. And this time should be calculated in several tens of days.