At what altitude does weightlessness begin? What is this - weightlessness? Conditions for the occurrence of weightlessness

According to the law of universal gravitation, all bodies are attracted to each other, and the force of attraction is directly proportional to the masses of the bodies and inversely proportional to the square of the distance between them. That is, the expression “absence of gravity” makes no sense at all. At an altitude of several hundred kilometers above the Earth's surface - where manned spacecraft and space stations fly - the Earth's gravitational force is very strong and practically no different from the gravitational force near the surface.

If it were technically possible to drop an object from a tower 300 kilometers high, it would begin to fall vertically and with the acceleration of free fall, just as it would fall from the height of a skyscraper or from the height of a person. Thus, during orbital flights, the force of gravity is not absent or weakened to a significant extent, but is compensated. In the same way as for watercraft and balloons, the force of gravity of the earth is compensated by the Archimedean force, and for winged aircraft - by the lifting force of the wing.

Yes, but the plane flies and does not fall, and the passenger inside the cabin does not fly like astronauts on the ISS. During a normal flight, the passenger feels his weight perfectly, and what keeps him from falling to the ground is not the direct lifting force, but the ground reaction force. Only during an emergency or artificially caused sharp decline does a person suddenly feel that he stops putting pressure on the support. Weightlessness arises. Why? But because if the loss of height occurs with an acceleration close to the acceleration of free fall, then the support no longer prevents the passenger from falling - she herself falls.

spaceref.com It is clear that when the plane stops sharply descending, or, unfortunately, falls to the ground, then it will become clear that gravity has not gone away. For in terrestrial and near-Earth conditions, the effect of weightlessness is possible only during a fall. Actually, a long fall is an orbital flight. A spacecraft moving in orbit at escape velocity is prevented from falling to Earth by the force of inertia. The interaction of gravity and inertia is called “centrifugal force,” although in reality such a force does not exist, it is in some way a fiction. The device tends to move in a straight line (tangentially to the near-Earth orbit), but the Earth's gravity constantly “spins” the trajectory of movement. Here, the equivalent of gravitational acceleration is the so-called centripetal acceleration, as a result of which it is not the value of the speed that changes, but its vector. And therefore the speed of the ship remains unchanged, but the direction of movement is constantly changing. Since both the spacecraft and the astronaut are moving at the same speed and with the same centripetal acceleration, the spacecraft cannot act as a support on which the weight of a person presses. Weight is the force of a body acting on a support that arises in the field of gravity and prevents it from falling. But a ship, like a sharply descending airplane, does not prevent it from falling.

That is why it is completely wrong to talk about the absence of Earth’s gravity or the presence of “microgravity” (as is customary in English-language sources) in orbit. On the contrary, the gravity of the earth is one of the main factors in the phenomenon of weightlessness that occurs on board.

We can talk about true microgravity only when applied to flights in interplanetary and interstellar space. Far from a large celestial body, the gravitational forces of distant stars and planets will be so weak that the effect of weightlessness will arise. We have read more than once in science fiction novels about how to deal with this. Space stations in the form of a torus (steering wheel) will spin around a central axis and create an imitation of gravity using centrifugal force. True, in order to create the equivalent of gravity, you will have to give the torus a diameter of more than 200 m. There are other problems associated with artificial gravity. So all this is a matter of the distant future.

), arising in connection with gravitational attraction or the action of other mass forces (in particular, the force of inertia that arises during the accelerated movement of a body).

Sometimes the term is used as a synonym for the name of this phenomenon microgravity, which is incorrect (it gives the impression that gravity is absent or negligibly small).

Causes

The state of weightlessness occurs when the external forces acting on the body are only mass (gravitational forces), or the field of these mass forces is locally homogeneous, that is, the field forces impart to all particles of the body in each position the same acceleration in magnitude and direction (which when moving in the Earth's gravitational field practically takes place if the dimensions of the body are small compared to the radius of the Earth), or the initial velocities of all particles of the body are the same in magnitude and direction (the body moves translationally).

For example, a spacecraft and all the bodies in it, having received the appropriate initial speed, move under the influence of gravitational forces along their orbits with almost the same accelerations as free ones; neither the bodies themselves nor their particles exert mutual pressure on each other, that is, they are in a state of weightlessness. At the same time, in relation to the cabin of the device, the body located in it can remain at rest in any place (freely “hang” in space). Although gravitational forces during weightlessness act on all particles of the body, there are no external surface forces that could cause mutual pressure of particles on each other.

Thus, any body whose dimensions are small compared to the Earth’s radius, performing free translational motion in the Earth’s gravitational field, will, in the absence of other external forces, be in a state of weightlessness. The result will be similar for the movement in the gravitational field of any other celestial bodies.

Story

The change in the weight of a ball when it falls freely in a liquid was noted by Leibniz. In 1892-1893 several experiments demonstrating the occurrence of weightlessness during free fall were carried out by Moscow State University professor N.A. Lyubimov, for example, a pendulum removed from its equilibrium position during free fall did not swing.

Features of human activity and technology

In conditions of weightlessness on board a spacecraft, many physical processes (convection, combustion, etc.) proceed differently than on Earth. The absence of gravity, in particular, requires special design of systems such as showers, toilets, food heating systems, ventilation, etc. To avoid the formation of stagnant zones where carbon dioxide can accumulate, and to ensure uniform mixing of warm and cold air, The ISS, for example, has a large number of fans installed. Eating and drinking, personal hygiene, working with equipment and, in general, ordinary everyday activities also have their own characteristics and require the astronaut to develop habits and the necessary skills.

The effects of weightlessness are inevitably taken into account in the design of a liquid-propellant rocket engine designed to launch in zero gravity. Liquid fuel components in tanks behave exactly the same as any liquid (forming liquid spheres). For this reason, the supply of liquid components from the tanks to the fuel lines may become impossible. To compensate for this effect, a special tank design is used (with gas and liquid media separators), as well as a fuel sedimentation procedure before starting the engine. This procedure consists of turning on the ship's auxiliary engines for acceleration; the slight acceleration they create deposits the liquid fuel at the bottom of the tank, from where the supply system directs the fuel into the lines.

Impact on the human body

When transitioning from conditions of body weight near the Earth's surface to conditions of weightlessness (primarily when a spacecraft enters orbit), most astronauts experience an organism reaction called space adaptation syndrome.

When a person stays in space for a long time (more than a week), the lack of body weight begins to cause certain harmful changes in the body.

The first and most obvious consequence of weightlessness is the rapid atrophy of muscles: the muscles are actually turned off from human activity, as a result, all the physical characteristics of the body decrease. In addition, the consequence of a sharp decrease in the activity of muscle tissue is a reduction in the body's oxygen consumption, and due to the resulting excess hemoglobin, the activity of the bone marrow that synthesizes it (hemoglobin) may decrease.

There is also reason to believe that limited mobility will disrupt phosphorus metabolism in the bones, which will lead to a decrease in their strength.

Weight and gravity

Quite often the disappearance of weight is confused with the disappearance of gravitational attraction, but this is not true at all. An example is the situation on the International Space Station (ISS). At an altitude of 350 kilometers (the altitude of the station), the acceleration due to gravity is 8.8/², which is only 10% less than on the surface of the Earth. The state of weightlessness on the ISS does not arise due to the “lack of gravity,” but due to movement in a circular orbit at the first escape velocity, that is, the cosmonauts seem to constantly “fall forward” at a speed of 7.9 km/s.

Weightlessness on Earth

On Earth, for experimental purposes, a short-term state of weightlessness (up to 40 s) is created when an aircraft flies along a ballistic trajectory, that is, the trajectory along which the aircraft would fly under the influence of the force of gravity alone. This trajectory at low speeds turns out to be a parabola, which is why it is sometimes mistakenly called “parabolic”. In general, the trajectory is an ellipse or hyperbola.

Such methods are used to train astronauts in Russia and the USA. In the cockpit, a ball is suspended on a string, which usually pulls the string down (if the plane is at rest or moving uniformly and in a straight line). The lack of tension in the thread on which the ball hangs indicates weightlessness. Thus, the pilot must control the plane so that the ball hangs in the air without tension on the string. To achieve this effect, the plane must have a constant acceleration equal to g and directed downward. In other words, pilots create zero g-force. Such an overload can be created for a long time (up to 40 seconds) by performing a special aerobatic maneuver called “failure in the air.” Pilots abruptly begin to climb, entering a “parabolic” trajectory, which ends with the same sharp drop in altitude. Inside the fuselage there is a chamber in which future cosmonauts train; it is a completely upholstered passenger cabin without seats to avoid injuries both in moments of weightlessness and in moments of overload.

A person experiences a similar feeling of (partial) weightlessness when flying on civil aviation flights during landing. However, for flight safety reasons and due to the heavy load on the aircraft structure, any scheduled aircraft drops altitude, making several long spiral turns (from a flight altitude of 11 km to an approach altitude of about 1-2 km). That is, the descent is carried out in several passes, during which the passenger feels for a few seconds that he is slightly lifted up from the seat. The same feeling is experienced by motorists who are familiar with routes passing along steep hills when the car begins to slide down from the top.

Claims that the aircraft performs aerobatic maneuvers such as the “Nesterov loop” to create short-term weightlessness are nothing more than a myth. Training is carried out in slightly modified production passenger or cargo aircraft, for which aerobatic maneuvers and similar flight modes are supercritical and can lead to destruction of the aircraft in the air or rapid fatigue wear of the supporting structures.

The state of weightlessness can be felt at the initial moment of free fall of a body in the atmosphere, when air resistance is still small.

There are several aircraft capable of flying in a state of weightlessness without going into space. The technology is used both for training by space agencies and for commercial flights by individuals. Similar flights are carried out by the American airline Zero Gravity, Roscosmos (on the Il-76 MDK since 1988, flights are also available to private individuals), NASA (on the Boeing KC-135), the European Space Agency (on the Airbus A-310) A typical flight lasts about one and a half hours. During the flight, 10-15 weightlessness sessions are carried out, to achieve which the plane makes a steep dive. The duration of each zero-gravity session is about 25 seconds. More than 15,000 people have flown as of November 2017. Many famous people have flown in zero gravity on board an aircraft, including: Buzz Aldrin, John Carmack, Tony Hawk, Richard Branson, Artemy Lebedev. Stephen Hawking also made a short flight on April 26, 2007.

Centrifuge at the Central Processing Plant (Star City)

Once upon a time, in one of the premises of the CPC, a special centrifuge weighing 300 tons and with a diameter of 18 m. It is used to simulate overloads in terrestrial conditions and, in particular, allows you to experience physiological weightlessness. Anyone who wants to try the power of a 300-ton centrifuge is dressed in a pressure suit, then seated in a special chair, to which numerous sensors are first connected. A fully equipped chair with a volunteer seated in it is brought to the centrifuge and, having rolled inside, the engine is turned on. Rotation in a centrifuge lasts three minutes; weightlessness in this case is achieved due to the redistribution of fluid in the body. Doctors and an instructor will monitor the sensor readings for all three minutes. But there is also an emergency way to warn about unbearable overloads: inside the centrifuge, a person must hold tightly to a special lever. If he is released, doctors and specialists will receive an emergency signal that the person has lost consciousness and will immediately turn off the centrifuge.

Service cost: 55,000 rubles per person

Tel.:

Hydrolab (Star City)

This year marks thirty years since they began training cosmonauts before flights in the Star City hydrolab. The laboratory is a huge pool 23 m long and 12 m deep, at the bottom of which there is a mock-up of the ISS. This is where astronauts train before going into outer space for the first time. As in other CTC attractions, everyone undergoes a mandatory medical examination, then listens to a theoretical lecture, and after that - and this takes at least half an hour - they put on a complex, heavy and extremely clumsy spacesuit, equipped with special lead weights (all together weighs about 200 kg) . And only then, with the help of a crane, the volunteers are carefully lowered to the bottom. The dive takes place with an instructor, who at the same time gives the task of moving some part of the model underwater from one place to another. It is at maximum depth that a feeling of weightlessness appears - akin to that experienced by an astronaut working in outer space. The entire process lasts four hours; a person spends two underwater. Please note: orders are not accepted until June.

Service cost: 182,000 rubles per person

Tel.: 526 38 42, 526 38 79, 526 78 55

Flight on the MiG-29

Another way to experience weightlessness is to take part in a flight on MiG-29. During aerobatic maneuvers, those in the cockpit experience weightlessness, albeit for just a few seconds. Similar flights for civilians are organized in Nizhny Novgorod. The event takes the whole day and begins early in the morning: it is recommended to arrive and check into the hotel the day before. In this case, an instructor will come to the hotel and tell you about the upcoming program. It is necessary to register a month and a half in advance so that the security service has time to check whether the newcomer is a spy. Anyone who has been recognized as an honest citizen is invited to choose one of three possible programs: a flight to the troposphere at an altitude of 12 km, at an altitude of 18 km and a flight to the stratosphere at an altitude of 21 km. In the latter case, from the porthole, the starry sky will be visible on one side, and the rounded contour of the Earth on the other side. Depending on the altitude, flights last from 25 to 50 minutes. Before the flight, everyone undergoes a cursory medical examination: doctors check blood pressure and pulse.

Service cost: flight at an altitude of 12 km - 380,000 rub./person; flight at an altitude of 18 km - 480,000 rub./person; flight at an altitude of 21 km - 595,000 rub./person.

Tel.: 645 07 02

Flights on Il-76

While it may seem that Star City has a monopoly on true space weightlessness, there is another way to experience the everyday life of astronauts - a flight on the Il-76, a Soviet military transport aircraft. All the rules of the Cosmonaut Training Center apply here: a thorough medical examination, and then pre-flight preparation. One flight lasts up to an hour and a half, and during this time, as the organizers say, “up to ten weightlessness modes are performed” for 25 seconds each. Weightlessness finds 15 daredevils on board during a flight along the so-called Kepler curve. According to the organizers, tourists can order video filming on board, but here you should be prepared for some incidents - many people feel nauseous out of habit. Attention: flights have been temporarily suspended, but they are promised to resume soon.

Service cost: 1,800,000 for a group of 15 people

Wind tunnel

A wind tunnel allows you to feel like an aeronaut: the air flow picks up a person and suspends you in the air, throwing you in different directions. These sensations, of course, are not weightlessness in the strict sense of the word, but a wind tunnel allows you to soar at a height of up to 10 m with a flow width of 4 m. The main advantage of a wind tunnel compared to all the above methods is its relative cheapness and the absence of medical examinations. Plus, it's completely safe. Many skydivers, for example, train in wind tunnels. In the flight area, all walls are softly upholstered, there are no hard objects, and a special protective mesh softens the fall after the engine is turned off. In addition, there is always an experienced instructor nearby who controls the flight every minute. The recommended flight duration for a girl is five minutes; for a man - up to ten. Even children (from 5 years old) can fly in a wind tunnel, because this does not require being an athlete with a low self-preservation threshold. According to the schedule, those interested are required to listen carefully to the instructor, who will tell in detail how to stay in the air flow. Next, you have to dress in a special overall, put on a helmet, then a little training and - take off! Attention: the wind speed in the wind tunnel reaches 200 km/h.

Service cost: 4 minutes - 3500 rubles per person; 10 minutes - 6500 rubles

Sensory deprivation chamber (floating)

Another opportunity to find yourself in conditional weightlessness is to lie for an hour or two in a sensory deprivation chamber (float chamber). Clients are promised that “the buoyancy that the body acquires thanks to the salt solution nullifies the effects of gravity, bringing a person close to the experience of complete weightlessness.” The float tank, which is about 30 cm deep, is slightly wider than a double bed; it contains an aqueous solution prepared from 400 kg of salt. A thermostat maintains a constant temperature of about 35 degrees Celsius. It is believed that this is the optimal temperature regime, at which most people do not feel heat or cold and quickly cease to feel the contact of water with the body. Inside the float chamber, a person finds himself isolated from external stimuli: no sounds, no light, no smells penetrate into it.

Service cost: 2000 rubles per procedure in 1 hour

Weightlessness

Astronauts aboard the International Space Station

Burning a candle on Earth (left) and in zero gravity (right)

Weightlessness- a state in which the force of interaction of a body with a support (body weight), arising in connection with gravitational attraction, the action of other mass forces, in particular the inertial force that arises during the accelerated movement of a body, is absent. Sometimes you can hear another name for this effect - microgravity. This name is incorrect for near-Earth flight. Gravity (force of attraction) remains the same. But when flying at large distances from celestial bodies, when their gravitational influence is negligible, microgravity actually arises.

To understand the essence of weightlessness, you can consider an airplane flying along a ballistic trajectory. Such methods are used to train astronauts in Russia and the USA. In the cockpit, a weight is suspended from a string, which usually pulls the string down (if the plane is at rest or moving uniformly and in a straight line). When the thread on which the ball hangs is not tensioned, a state of weightlessness occurs. Thus, the pilot must control the plane so that the ball hangs in the air and the string is not taut. To achieve this effect, the plane must have a constant downward acceleration g. In other words, pilots create zero g-force. Such an overload can be created for a long time (up to 40 seconds) by performing a special aerobatics maneuver (which has no name other than “failure in the air”). The pilots sharply lower the altitude; at a standard flight altitude of 11,000 meters, this gives the required 40 seconds of “weightlessness”; Inside the fuselage there is a chamber in which future cosmonauts train; it has a special soft coating on the walls to avoid injuries when climbing and dropping altitude. A person experiences a feeling similar to weightlessness when flying on civil aviation flights upon landing. However, for the sake of flight safety and the heavy load on the aircraft structure, civil aviation drops the altitude by making several long spiral turns (from a flight altitude of 11 km to an approach altitude of about 1-2 km). Those. The descent is carried out in several passes, during which the passenger feels for a few seconds that he is being lifted up from the chair. (The same feeling is familiar to motorists who are familiar with routes passing along steep hills, when the car begins to slide down from the top) The claims that the aircraft performs aerobatic maneuvers such as the “Nesterov loop” to create short-term weightlessness are nothing more than a myth. Training is carried out in slightly modified production passenger or cargo class vehicles, for which aerobatic maneuvers and similar flight modes are supercritical and can lead to destruction of the vehicle in the air or rapid fatigue failure of the supporting structures.

Peculiarities of human activity and the operation of equipment in conditions of weightlessness

In conditions of weightlessness on board a spacecraft, many physical processes (convection, combustion, etc.) proceed differently than on Earth. The absence of gravity, in particular, requires a special design of systems such as showers, toilets, food heating systems, ventilation, etc. To avoid the formation of stagnant zones where carbon dioxide can accumulate, and to ensure uniform mixing of warm and cold air, the ISS, for example, has a large number of fans installed. Eating and drinking, personal hygiene, working with equipment and, in general, ordinary everyday activities also have their own characteristics and require the astronaut to develop habits and the necessary skills.

The effects of weightlessness on the human body

When transitioning from the conditions of earth's gravity to conditions of weightlessness (primarily when a spacecraft enters orbit), most astronauts experience an organism reaction called space adaptation syndrome.

When a person stays in space for a long time (several weeks or more), the lack of gravity begins to cause certain changes in the body that are negative.

There is also reason to believe that limited mobility will disrupt phosphorus metabolism in the bones, which will lead to a decrease in their strength.

Weight and gravity

Quite often the disappearance of weight is confused with the disappearance of gravitational attraction. This is wrong. An example is the situation on the International Space Station (ISS). At an altitude of 350 kilometers (the altitude of the station), the acceleration due to gravity is 8.8/², which is only 10% less than on the surface of the Earth. The state of weightlessness on the ISS does not arise due to the “lack of gravity,” but due to movement in a circular orbit at the first escape velocity, that is, the cosmonauts seem to constantly “fall forward” at a speed of 7.9 km/s.

Weightlessness on Earth

On Earth, for experimental purposes, a short-term state of weightlessness (up to 40 s) is created when an aircraft flies along a parabolic plane (and in fact, ballistic, that is, the one along which the aircraft would fly under the influence of the force of gravity alone; this trajectory is a parabola only if at low speeds; for a satellite it is an ellipse, circle or hyperbola) trajectory. The state of weightlessness can be felt at the initial moment of free fall of a body in the atmosphere, when air resistance is still small.

Notes

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Synonyms

See what “Weightlessness” is in other dictionaries: Weightlessness...

Spelling dictionary-reference book Lightness, ethereality, weakness, hydro-weightlessness, insignificance, airiness Dictionary of Russian synonyms. weightlessness see lightness 1 Dictionary of synonyms of the Russian language. Practical guide. M.: Russian language. Z. E. Alexandrova ...

Synonym dictionary A condition in which external forces acting on a body do not cause mutual pressure of its particles on each other. In the Earth's gravitational field, the human body perceives such pressures as a feeling of weight. Weightlessness occurs when...

Big Encyclopedic Dictionary

Modern encyclopedia Weightlessness, a state experienced by an object in which the effect of weight does not manifest itself. Weightlessness can be experienced in space or during free fall, although the gravitational attraction of a “weighty” body is present. Astronauts... ...

Scientific and technical encyclopedic dictionary The state of a material body moving in a gravitational field, in which the forces of gravity acting on it or the movement it makes do not cause pressure on the bodies on each other. If a body is at rest in the Earth's gravitational field on a horizontal plane,... ...

Physical encyclopedia Weightlessness - WEIGHTLESSITY, a state in which external forces acting on a body do not cause mutual pressure of its particles on each other. Weightlessness occurs when a body moves freely in a gravitational field (for example, during a vertical fall, movement along... ...

Illustrated Encyclopedic Dictionary

Why are bodies weightless in the center of the Earth? First of all, let's try to understand the baron's idea: he claims that in the center of the Earth the inhabitant will be attracted in all directions the same , and therefore will be in a state of weightlessness. To make this idea more clear, consider the situation when the point mass located in the center of a ring consisting of a large number of point masses M(Fig. 6.1).

It is clear that every two oppositely lying masses M pull the resident in opposite directions with forces of equal magnitude. Therefore, the resultant of all forces applied to a point mass , and therefore will be in a state of weightlessness. To make this idea more clear, consider the situation when the point mass, is equal to zero.

In a similar situation there will be a tenant located in the center of the Earth.

Why is the Professor afraid that the weight of the resident in the center of the Earth will be infinitely large? He simply remembered the formula for the law of universal gravitation from a school textbook: where , and therefore will be in a state of weightlessness. To make this idea more clear, consider the situation when the point mass And M- masses of bodies, and R- the distance between them. He decided that since at the center of the Earth the distance between the inhabitant and the Earth is zero, it turns out that

The professor forgot that the law of universal gravitation is valid only for point masses, that is, bodies whose sizes in the conditions of this problem can be neglected in comparison with the distances between them. Such an approximation, for example, is quite acceptable when calculating the motion of planets around the Sun, but in the conditions of our task, it is, of course, impossible to consider the Earth a point mass!

How will the body's weight change as it approaches the center of the Earth?

The businessman claims that as we dive deeper into the Earth, our body weight will be increase, and the baron, on the contrary, judging by the drawing shown on the poster, believes that the deeper underground the tenant is, the less he weights. Which one is right? Both are right! Indeed, when diving to a depth of up to 2000 km, body weight increases, with further immersion - decreases, and at the center of the Earth becomes equal to zero!

Let's look at this issue in more detail.

What weight does the body inside the spherical shell have?

Let the point mass m be at the point O" inside a spherical shell with radius R(Fig. 6.2) and let the mass per unit surface area of the sphere be equal to ρ.

Let us prove that the resultant of all gravitational forces acting on a point mass , and therefore will be in a state of weightlessness. To make this idea more clear, consider the situation when the point mass from the side of the sphere, is equal to zero.

1. Construct two narrow conical surfaces with a small opening angle α and a common vertex at the point O", as shown in Fig. 6.3. These conical surfaces will “cut out” pieces of the surface on the sphere that can be approximately considered flat, which is quite acceptable if the angle α is very small.

2. Areas of “pieces” cut out on the sphere S 1 And S 2 are proportional to the squares of their “diameters” - segments AB And CD. Let AB = k·CD, Then S 1 = k 2 ·S 2, the same relationship applies for the masses of cut pieces: m 1 = k 2· m 2

3. Consider the angles ABC And ADC. They are equal, as if inscribed in a circle and supported by a common arc AC, so let’s denote them with one letter φ.

4. Two angles (α and φ) of a triangle O"AB equal to two angles of a triangle O"DC, therefore, these triangles are similar. From the similarity of triangles it follows that if R 1,R 2 are the distances from the body to the centers of mass of the corresponding pieces of the sphere, then R 1 = k· R 2.

5. Let us find the ratio of forces acting on a body of mass , and therefore will be in a state of weightlessness. To make this idea more clear, consider the situation when the point mass, located at the point O", from the side of bodies with masses m 1 And m 2, which can be considered pointlike (since their sizes are very small).

That is F 1=F 2, which means the resultant of these forces is zero.

6. But the entire surface of the sphere can be divided into such pairs of oppositely lying “pieces”, and each such pair will give a resultant equal to zero.

This means that the total force acting from the sphere on the point mass , and therefore will be in a state of weightlessness. To make this idea more clear, consider the situation when the point mass, is equal to zero. That is, the sphere doesn't work at all to a point mass located inside it, no matter where this point mass is located (it is not at all necessary that it be in the center of the sphere!).

What weight does the body inside the spherical layer have?

Now we move from a thin sphere to a spherical layer of finite thickness. Let the point mass , and therefore will be in a state of weightlessness. To make this idea more clear, consider the situation when the point mass is now inside the spherical layer (Figure 6.4).

It is clear that a spherical layer of finite thickness can be divided into many very thin concentric spherical layers of very small thickness - practically spheres. And each such sphere, as we just found out, does not affect the point mass located inside it. Consequently, the spherical layer won't work at all to a point mass located inside it.

Point mass inside a homogeneous sphere

Now let's move on to a more complicated case: let the point mass , and therefore will be in a state of weightlessness. To make this idea more clear, consider the situation when the point mass is located inside a uniform ball of radius R and density ρ at a distance r from the center of the ball (Fig. 6.5). The part of the ball external to the point mass is the outer spherical layer, which, as we have just proved, acts on the point mass will not, and the inner part of the large ball (small ball with radius r) will attract our point mass with a force where M= is the mass of the small ball. Substituting the value M into the formula for F, we get:

That is, the force of gravity is directly proportional to the distance to the center of the ball. It is clear that if r= 0, then F = 0.

So, if the Earth were homogeneous ball, then the weight of the body actually gradually decreased with depth, and Baron Munchausen would be absolutely right. But in reality the Earth is not a homogeneous ball: its density changes with depth - namely, it increases.

When diving into a mine, the magnitude of gravity is affected by two factors: on the one hand, the distance to the center of the Earth decreases, so the force of gravity increases:

and on the other hand, the mass of the “small” ball located under immersed body:

The question is which factor will have a greater influence on the magnitude of gravity. Let's look at two extreme cases.

1. Let the spherical layer above point mass , and therefore will be in a state of weightlessness. To make this idea more clear, consider the situation when the point mass(see Fig. 6.5) has a negligibly small density (ρ → 0), then the mass of a “small” ball with a radius r exactly the same as the mass of a “large” ball with a radius R. Then gravity at a distance r < R it will be clear from the center more gravity at a distance R from the center. That is, in this case, when diving into the mine, the force of gravity will increase.

2. Let a “small” ball have zero density (see Fig. 6.5), that is, all the mass is concentrated in the spherical layer above point mass , and therefore will be in a state of weightlessness. To make this idea more clear, consider the situation when the point mass. Then already at a distance r from the center the force of gravity will be zero:

As we have already said, the Earth is a heterogeneous ball, and the density of the upper layers is much less than the density of the inner layers. Therefore, when diving underground to a depth of approximately 2000 km, the first effect prevails - the force of gravity increases: and then the force of gravity begins to decrease - the effect of the decrease in the mass of the “small” ball prevails.

How long will it take to get to the bottom floor?

Now let's answer our Engineer, who is interested primarily in the practical feasibility of the project: how long will it take the tenant of an inverted skyscraper to get down to his apartment if he lives in the very center of the Earth?

Let's assume that the elevator will first accelerate to some very decent speed (say, 1 km/s), then it will move at this speed for some time, and at the end of the journey it will slow down. Then it will take time to descend to the center of the Earth

In conclusion, we note another difficulty in the practical implementation of the project: the house must be absolutely sealed, firstly, and Very durable, secondly, since the atmospheric pressure in the center of the Earth will be simply monstrous!

Let’s estimate what the air pressure will be in a mine “only” 100 km deep. (Note that the deepest modern wells do not yet exceed 12 km.) We will assume that on the Earth’s surface the atmospheric pressure is 100,000 Pa, and the air density is 1.29 kg/m3 and does not change with depth (in fact In fact, the density, of course, increases with depth, so our estimate will be underestimated).

Then the required pressure will be equal to:

p=p a+ ρ gh≈ 100000 Pa + 1.29 kg/m 3 9.8 m/s 2 100000 m =

1364200 Pa ≈ 13.6 atm.

The same pressure under water at a depth of 136 m! But for now we are only talking about a depth of 100 km, and the center of the Earth is at a depth of 6400 km!

We will not dwell on the difficulties associated with the fact that deep underground the Earth is, to put it mildly, a little hot. Perhaps someone will suggest a principle for cooling an inverted skyscraper?