Keywords

annotation scientific article on Earth sciences and related ecological sciences, author of scientific work - Bondarenko Yury Sergeevich, Medvedev Yury Dmitrievich

A technique has been developed to determine trajectory celestial body in the Earth's atmosphere, parameters heliocentric orbit body before it enters the atmosphere, as well as assess the main factors of damage by a shock wave. The technique provides for the study of several scenarios for the development of events due to the passage of an object in the Earth's atmosphere. If the object passed through the atmosphere without colliding with the Earth, the moments of entry and exit of the body from the Earth's atmosphere are determined. An object can collide with the Earth without being destroyed. In this case, the differential equations are integrated until the celestial body reaches the Earth's surface. It was believed that an object burns up in the atmosphere if its radius becomes less than 1 cm. Separately, the case was considered when the object is destroyed during the movement, and only fragments reach the Earth's surface. The developed technique was implemented in a software-computer complex. One of the advantages of the complex is the ability to save calculation results in a .kml file, which allows displaying three-dimensional geospatial data in the Google Earth program, as well as on two-dimensional Google maps. In our case, this is the flight path and its projection on the Earth's surface, the places of destruction, explosion and fall of the meteorite, the area of ​​fragments falling and shock wave damage, as well as other useful information. The efficiency of the software and computing system was tested on the motion of the asteroid 2008 TC3 and the Chelyabinsk meteorite. It was shown that the orbits of the 2008 TC3 and Chelyabinsk meteorites before entering the atmosphere turned out to be close to the orbits obtained by other authors, and the parameters air bursts coincide with the original data within their accuracy. The resulting areas of fall of fragments of these meteorites are only a few kilometers from the discovered fragments. The zones of destruction as a result of the action of an air shock wave in the case of the Chelyabinsk meteorite coincide with real data.

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Determination of the trajectory of motion of celestial bodies in the Earth""s atmosphere

The authors have developed and realized the method, allowing to determine the trajectory of motion of celestial bodies in the Earth's atmosphere, to determine the parameters of heliocentric orbit of celestial bodies prior to its entry into the atmosphere, as well as to estimate major factors of damage due to the blast wave . The method researches several scenarios due to the passage of the object in the Earth's atmosphere. In case the object passed through the atmosphere, without colliding with the Earth, the moments of an entrance and exit of a body from the Earth’s atmosphere are determined. The object can collide with the Earth without breakup. In this case, the differential equations are integrated until the celestial body reaches the Earth's surface. It was assumed that the object burns in the atmosphere, if its radius becomes less than 1 cm. The case when object breaks up during the motion and only the fragments reach the Earth's surface was considered separately. The developed method has been implemented in the software package. One of the advantages of the package is the ability to save the results of calculations in the.kml format, allowing to display threedimensional geospatial data in the “Google Earth” as well as two-dimensional data in “Google” maps. In our case these data are the flight trajectory and its projection to the Earth’s surface, the places of meteorite break up and air burst, the impact areas of the fragments, the overpressure areas due the blast wave , as well as other useful information. Using this method the motion of Chelyabinsk and 2008 TC3 meteorites were simulated. It was shown that heliocentric orbital elements of the Chelyabinsk and 2008 TC3 meteorites before entering the Earth 's atmosphere calculated using the developed software are close to the parameters obtained by other authors, the trajectory parameters are in good agreement with the initial data within their accuracy . Estimated impact areas of meteorites fragments are only in a few kilometers from the recovered one. The overpressure areas due to the blast wave in case of “Chelyabinsk” meteorite coincide with the real data.

The text of the scientific work on the topic "Determination of the trajectory of the movement of celestial bodies in the Earth's atmosphere"

UDC 521.35; 523.628.4

Bulletin of SibGAU 2014. No. 4(56). pp. 16-24

DETERMINATION OF THE TRAJECTORY OF MOVEMENT OF CELESTIAL BODIES IN THE EARTH'S ATMOSPHERE

Yu. S. Bondarenko, Yu. D. Medvedev

Institute of Applied Astronomy of the Russian Academy of Sciences Russian Federation, 191187, St. Petersburg, nab. Kutuzova, 10 [email protected]

A technique has been developed that makes it possible to determine the trajectory of a celestial body in the Earth's atmosphere, the parameters of the body's heliocentric orbit prior to its entry into the atmosphere, and also to evaluate the main factors of damage by a shock wave. The technique provides for the study of several options for the development of events due to the passage of an object in the Earth's atmosphere. If the object passed through the atmosphere without colliding with the Earth, the moments of entry and exit of the body from the Earth's atmosphere are determined. An object can collide with the Earth without being destroyed. In this case, the differential equations are integrated until the celestial body reaches the Earth's surface. It was believed that an object burns up in the atmosphere if its radius becomes less than 1 cm. The case was considered separately when the object is destroyed during the movement, and only fragments reach the Earth's surface. The developed technique was implemented in a software-computer complex. One of the advantages of the complex is the ability to save calculation results in a .kml file, which allows displaying three-dimensional geospatial data in the Google Earth program, as well as on two-dimensional Google maps. In our case, this is the flight path and its projection on the Earth's surface, the places of destruction, explosion and fall of the meteorite, the area of ​​fragments falling and shock wave damage, as well as other useful information. The efficiency of the software and computing system was tested on the motion of the asteroid 2008 TC3 and the Chelyabinsk meteorite. It was shown that the orbits of the 2008 TC3 and Chelyabinsk meteorites before entering the atmosphere turned out to be close to the orbits obtained by other authors, and the parameters of air explosions coincide with the original data within their accuracy. The resulting areas of fall of fragments of these meteorites are only a few kilometers from the discovered fragments. The zones of destruction as a result of the action of an air shock wave in the case of the Chelyabinsk meteorite coincide with real data.

Key words: celestial body, asteroid, meteorite, heliocentric orbit, motion trajectory, Earth's atmosphere, air burst, shock wave, impact area.

Vestnik SibGAU 2014, no. 4(56), P. 16-24

DETERMINATION OF THE TRAJECTORY OF MOTION OF CELESTIAL BODIES

IN THE EARTH'S ATMOSPHERE

Yu. S. Bondarenko, Yu. D. Medvedev

Institute of Applied Astronomy of Russian Academy of Sciences 10, Kutuzova nab., St. Petersburg, 191187, Russian Federation [email protected]

The authors have developed and realized the method, allowing to determine the trajectory of motion of celestial bodies in the Earth's atmosphere, to determine the parameters of heliocentric orbit of celestial bodies prior to its entry into the atmosphere, as well as to estimate major factors of damage due to the blast wave. The method researches several scenarios due to the passage of the object in the Earth's atmosphere. In case the object passed through the atmosphere, without colliding with the Earth, the moments of an entrance and exit of a body from the Earth's atmosphere are determined. The object can collide with the Earth without breakup. In this case, the differential equations are integrated until the celestial body reaches the Earth's surface. It was assumed that the object burns in the atmosphere, if its radius becomes less than 1 cm. The case when object breaks up during the motion and only the fragments reach the Earth's surface was considered separately. The developed method has been implemented in the software package. One of the advantages of the package is the ability to save the results of calculations in the .kml format, allowing to display three-dimensional geospatial data in the "Google Earth" as well as two-dimensional data in "Google" maps. In our case these data are the flight trajectory and its projection to the Earth"s surface, the places of meteorite break up and air burst, the impact areas of the fragments, the overpressure areas due the blast wave, as well as other useful information.

Using this method the motion of Chelyabinsk and 2008 TC3 meteorites were simulated. It was shown that heliocentric orbital elements of the Chelyabinsk and 2008 TC3 meteorites before entering the Earth's atmosphere calculated using the developed software are close to the parameters obtained by other authors, the trajectory parameters are in good agreement with the initial data within their accuracy The overpressure areas due to the blast wave in case of "Chelyabinsk" meteorite coincide with the real data.

Keywords: celestial body, asteroid, meteorite, heliocentric orbit, trajectory of motion, Earth's atmosphere, air blast, blast wave, impact area.

Introduction. The main disturbing factors in the motion of small bodies in the solar system are the attraction of large planets, which in most cases are considered as material points. However, in the case of a close approach or collision of the object under study with the Earth, it is necessary to take into account such factors as the influence of non-sphericity, the perturbation exerted by the Earth's atmosphere, the mass, composition and shape of the body itself, which presents a certain difficulty for researchers. In this regard, there is a need to develop a technique that allows one to make a fairly accurate estimate of the trajectory of a body when it moves both near and in the Earth's atmosphere.

dynamic model. In the developed dynamic model, if the object under study moves outside the earth's atmosphere, the equations of motion are given in a rectangular heliocentric coordinate system and have the form

where " - gravitational acceleration from the Sun; W2" - perturbing accelerations determined by the attraction of the object under study by the planets; W," - relativistic corrections.

If the body entered the Earth's atmosphere, then there is a transition to the geocentric coordinate system, and the equations of motion change. They add terms that take into account the compression of the Earth and the resistance of the atmosphere. A differential equation is also added that describes the change in the size of an object due to its deceleration in the atmosphere:

7 = W + W2 + W3; I = VI

where W - gravitational acceleration from the Earth, taking into account compression; G2 - gravitational perturbations from the Sun and planets of the Solar system; W, - atmospheric resistance; V is the rate at which the object's size changes.

The perturbing acceleration W, which takes into account the resistance of the atmosphere, is given in the form

W = -1 Cd рУ (

speed; the ratio of the midsection to the mass of the object m characterizes the windage. For convenience, the letter P denotes the pressure exerted by air on the body, and the letter A denotes air resistance.

Assuming that part of the energy arising from atmospheric resistance goes to heating and evaporation of matter from the surface of the body, and the object itself has and retains a spherical shape as a result of evaporation, the rate of change in the body radius will be determined by the following expression:

where y is the amount of energy spent on the sublimation of matter; I is the radius of the object; K is the heat required to vaporize 1 kg of a substance.

Possible development of events. The technique provides for the study of several options for the development of events due to the passage of an object in the Earth's atmosphere. If the object passed through the atmosphere without colliding with the Earth, the moments of entry and exit of the body from the Earth's atmosphere are determined. An object can collide with the Earth without being destroyed. In this case, the differential equations are integrated until the celestial body reaches the Earth's surface. It was believed that an object burns up in the atmosphere if its radius R becomes less than 1 cm. The case was considered separately when the object is destroyed during its movement, and only fragments reach the Earth's surface.

The destruction of the body occurs when the air pressure on the body P reaches the critical value Рmax. The values ​​of critical pressure for various materials of the object under study are presented in Table. one . Depending on the given density, the critical pressure values ​​​​are determined from Table. 1 by interpolation.

Table 1

Critical pressure values ​​for various materials

Material Density, kg/m3 Pmax; Pa

Porous rock 1500 105

Hard Rock 3600 10"

Iron 8000 108

where Sp is the coefficient of air resistance; pa - air density; u is the object's velocity vector relative to the Earth's atmosphere; and - vector modulus

Having reached the critical pressure, the body is destroyed, however, for some time the fragments of the body move as a single whole, moving away from each other at a speed

bodies at the moment of destruction; p is the density of the body. After destruction, the rate of resizing

object V in the system is taken equal to V. Due to the difference in pressures on the front and rear surfaces, the fragmented body, as it were, expands perpendicular to the motion trajectory until the ratio of the current radius to the radius of the body at the moment of destruction R(t)/R reaches the specified limit. Estimates of this value by different authors vary from 2 to 10. In the developed dynamic model, it is considered that an air explosion occurs at the moment when the value of R(t) = 5R, provided that the body has not reached the Earth's surface by this moment. From this moment, it is considered that the fragments begin to move along independent trajectories, and the consequence of their rapid deceleration is a shock wave.

The parameter of the shock wave, which determines its effect on various objects, is the maximum overpressure at the front Apm. On the basis of experimental data for a spherical shock wave, an empirical dependence 1 2

Apm = 0.084 - + 0.27 U- + 0.7 E Fm l l2 l3

where E is the energy of the explosion, measured in kg of TNT equivalent; l - distance from the explosion center, m; excess pressure at the front of the shock wave Apm is measured in MPa. This formula is valid for high power explosions: E > 100 kg TNT in the range 0.01< Apm < 1 МПа.

The direct impact of excess pressure at the front of the shock wave leads to partial or complete destruction of buildings, structures and other objects. Depending on the magnitude of the excess pressure, various destruction zones are distinguished, the values ​​of which are presented in Table. 2. The lesion on flat terrain is conditionally limited to a radius with an overpressure of 10 kPa (0.1 kgf/cm).

The energy of an air explosion is determined by the amount of energy released during deceleration of a collapsing body, according to the formula

E = l-tiT, 2

where m is the mass of the body at the moment of destruction; n is the fraction of energy released almost instantaneously during deceleration of small fragments. Thus, knowing the energy and height of the explosion, the dimensions of the destruction zones are found.

table 2

Destruction under the influence of a shock wave

Destruction zones Apm, kPa

Glass strength threshold 1

10% glass broken 2

Minor damage to buildings 5

Partial destruction 10

Medium destruction 20

Strong Destruction 30

Complete destruction 50

destruction of the object into fragments. To estimate the area of ​​impact, the developed method integrates together the movement of 4 fragments, which fly apart in opposite directions in a plane perpendicular to the velocity vector of the body at the moment of destruction um with velocities V = -\[p~1rot. These

directions are shown in fig. 1. In this case, the velocity vectors of each of the four fragments u, uE, and are given by the formulas

Tl Yu - - Tl Yu X°T

uW = uT + V-; uN \u003d uT + V--g

Suppose that during the movement of the body in the Earth's atmosphere at some point in time T,

uE = uT - VuW ; uS = uT - VuN,

where rä = uT x ¥T ; ¥T - body position vector at the moment of destruction. The fragment radius is taken equal to Rf = RT/n , where n is the number of fragments; RT - radius

object at the time of destruction. The coordinates of the fall fragments indicated in fig. 1 points W, E, N and S are calculated taking into account the parameters of precession and nutation of the Earth's axis, and the area of ​​incidence is approximated by an ellipse passing through these points.

The developed technique was implemented in a software-computer complex. One of the advantages of the complex is the ability to save the calculation results in a .kml file, which allows you to display three-dimensional geospatial data in the Google Earth program

And also on two-dimensional Google maps. In our case, this is the flight path and its projection on the Earth's surface, the places of destruction, explosion and fall of the meteorite, the area of ​​fragments falling and shock wave damage, as well as other useful information. The efficiency of the software and computing complex was tested on the motion of the asteroid 2008 TC3 and the Chelyabinsk meteorite.

Asteroid 2008 TC3. Asteroid 2008 TC3 was discovered on the morning of October 6, 2008 at Mount Lemmon Observatory. Operational calculations of the preliminary orbit showed that this asteroid should collide with the Earth in the next 24 hours. It was the first celestial body discovered before entering the Earth's atmosphere. Its diameter was estimated in the range from 2 to 5 m. On October 7, the meteorite was destroyed when it fell in the atmosphere over the desert territory of Sudan at an altitude of 37 km with coordinates of 20.8 ° N. sh. and 32.2° E. d.

More than 600 asteroid fragments with a total mass of 10.7 kg were later found.

At the first stage, using the method of determining orbits based on the enumeration of orbital planes , the elements of the heliocentric orbit were obtained (Table 3), which represent 589 positional observations of the asteroid 2008 TC3 with a root-mean-square error c = 2.0"" for epoch 2454746.5 JD (7 October 2008). These elements define the so-called nominal orbit, i.e., satisfying the conditions of the least squares method. For comparison in table. Figure 3 also shows orbital elements obtained by the Jet Propulsion Laboratory (JPL).

Further, using the obtained elements of the orbit, the motion of the asteroid 2008 TC3 was simulated until the moment of its collision with the Earth. In the adopted model, the equations of motion take into account gravitational perturbations from all the major planets, the Moon and Pluto. The coordinates of the perturbing planets were calculated from the numerical ephemeris EPM. Numerical integration of the equations of motion was performed by the 4th order Runge-Kutta method with automatic step selection according to the velocity value. The air density was calculated from the US 1976 Standard Atmosphere Tables, in which the atmosphere is divided into seven consecutive layers with a linear dependence of temperature on height. The Earth's surface was approximated by an ellipsoid of revolution. Assuming that the object was spherical, the drag coefficient

air Cn was taken equal to 2 . The amount of energy spent on the sublimation of matter y was taken equal to 10-3 for the main body, and 10-2 for fragments. It was also believed that 600 cal/g is needed to evaporate 1 kg of the substance of the asteroid 2008 TC3.

The results of simulation of the motion of the asteroid 2008 TC3 in the Earth's atmosphere are shown in Figs. 2, which shows a satellite image of the area, on which the black line shows the trajectory of the meteorite, obtained from the elements of the nominal orbit, and the white line shows its projection onto the Earth's surface. The places of the beginning of the destruction and explosion of the meteorite are designated by the letters A and B, respectively, and their parameters in comparison with satellite data are given in Table. 4. The numbers mark the places of the discovered fragments of the meteorite, and their masses and coordinates are given in Table. 5.

Rice. 1. Determining the area of ​​falling fragments

IPA 330.7502 234.4474 194.1011 2.5416 0.311995 0.658783

CXR 330.7541 234.4490 194.1011 2.5422 0.312065 0.658707

Table 4

Parameters of the places where the destruction and explosion of the asteroid 2008 TSZ began

IPA parameter Satellite data (KABA/KHR, 2008)

Destruction Explosion

Altitude, km 36.9 35.2 37

Time, IT 02:45:51 02:45:51 02:45:45

Latitude, ° with. sh. 20.72 20.71 20.8

Longitude, ° in. 32.15 32.19 32.2

Table 5

Parameters of found fragments of asteroid 2008 TZ

Parameter 1 2 3 4 5 6 7

Weight, g 4.412 78.201 65.733 141.842 378.710 259.860 303.690

Latitude, ° with. sh. 20.77 20.74 20.74 20.70 20.68 20.70 20.70

Longitude, ° in. 32.29 32.33 32.36 32.49 32.50 32.50 32.52

Rice. 2. Simulation results of the motion of the 2008 TC3 meteorite in the Earth's atmosphere

From Table. Figure 5 shows that the masses of the detected fragments do not exceed a kilogram, therefore, after the explosion of the meteorite, the motion of fragments with masses in the range from 100 to 700 g was simulated. to files. The figure shows the probable regions of impact of fragments of various masses, obtained from the nominal orbit and its two variations. The letters A and B denote the regions where the fragments with the smallest and largest masses fell out, respectively. On fig. 2 shows a good agreement between the results of the assessment of the impact areas with the found fragments, and small deviations can be explained, for example, by the effect of wind. Table data. 4 also indicate a good agreement between the simulation results and satellite data.

Meteorite "Chelyabinsk". On the morning of February 15, 2013, a bright flash was observed in the sky over Chelyabinsk, which was caused by a relatively small asteroid approximately 17-20 m in diameter, which entered the Earth's atmosphere at high speed and at a small angle. At that moment, a huge amount of energy was released, and the body itself collapsed into many parts of different sizes, which fell to the ground. Since this event took place over a populous city, it differs from similar events in the number of eyewitness accounts. It was recorded by a large number of video recorders and video cameras. In addition, meteorological satellites

MyeoBa! 9 and MeleoBa1 10 were able to photograph the condensation trail from the passage of a meteorite in the Earth's atmosphere, and from the bottom of Lake Chebarkul a fragment of a meteorite about a meter in size and weighing approximately 600 kg was raised.

To model the movement of the meteorite, the most accurate data to date were used as the initial parameters, which were obtained by equipment installed on geostationary satellites operating in the interests of the US Department of Defense and the US Department of Energy. This equipment makes it possible to track nuclear air explosions, as well as to measure the luminosity curves of fireballs burning up in the atmosphere. According to these data, the moment of maximum brightness occurred on February 15, 2013 at 03:20:33 GMT at an altitude of 23.3 km with coordinates of 54.8° N. sh. and 61.1° E. e. The speed of the object at the moment of maximum brightness was 18.6 km / s, and the released energy was 440 Kg in TNT equivalent.

The trajectory azimuth and inclination, obtained by Colombian astronomers from numerous records from video recorders and surveillance cameras, were taken to be 285 ± 2° and 15.8 ± 0.3°, respectively. The found remains of a meteorite indicate that it was an ordinary chondrite with a density of approximately 3.6 g / cm3. The diameter of the object before entering the atmosphere was taken to be 18 m.

These parameters were used to calculate the elements of the object's heliocentric orbit prior to its entry into the atmosphere at epoch 2456336.5 AR (February 13, 2013). These elements, in comparison with the results of other authors, are presented in Table. 6 in the first line.

Table 6

Comparison of the parameters of the resulting heliocentric orbit

IPA 0.70 0.56 100.90 326.46 4.27 1.60

7u1^a 0.71 0.48 97.98 326.47 4.31 1.37

1Аu 3423 0.77 0.5 109.7 326.41 3.6 1.55

INASAN 0.74 0.58 108.3 326.44 4.93 1.76

KhNU 0.65 0.65 97.2 326.42 12.06 1.83

Rice. 3. Heliocentric orbit of the Chelyabinsk meteorite

Rice. 4. Simulation results of the motion of the Chelyabinsk meteorite in the Earth's atmosphere

Rice. 5. Areas of falling fragments of the meteorite "Chelyabinsk"

On fig. 3 shows the heliocentric orbit of the Chelyabinsk meteorite in the plane of the ecliptic according to the calculated elements, obtained using the NLBU software complex. As can be seen from fig. 3, the asteroid's orbit reaches the orbit of Venus at perihelion and the asteroid belt at aphelion. A numerical calculation of evolution shows that the asteroid could move along this orbit for thousands of years, repeatedly crossing the Earth's orbit. It is likely that this asteroid was formed as a result of collisional processes in the main belt. Being at the perihelion of its orbit approximately two and a half months before the collision, it approached the Earth from the side of the Sun, which prevented its early detection by observatories that constantly monitor the small bodies of the solar system.

Table 7

Parameters of the beginning of the destruction and explosion of the meteorite "Chelyabinsk"

Parameter Destruction Explosion

Height, km 27.7 24.5

Time, IT 03:20:32 03:20:33

Latitude, ° with. sh. 54.78 54.81

Longitude, ° in. d. 61.20 61.04

The black line in Fig. 4 shows the trajectory of the fall, white is the projection of the trajectory, the places of destruction

and explosion at points L and B, respectively, the area where the fragments fell, as well as the nearest settlements superimposed on a satellite image of the area.

According to calculations, 474 kt of TNT energy was released at the moment of the explosion. In this case, the radius of the destruction zone with an excess pressure at the front of a shock wave of 1 kPa turns out to be equal to 127 km and 51 km for 2 kPa. Such pressure values ​​correspond to the glass strength threshold (see Table 2). The destruction zones are shown in fig. 4 white circles.

After the explosion of the meteorite, the motion of 20 groups of fragments with sizes ranging from 1.8 to 0.4 m was simulated. 5 asterisk marks the place where the largest fragment of a meteorite fell, about a meter in size and weighing 654 kg, found in Lake Chebarkul. Numbers 1, 2, and 3 designate the obtained probable areas of fall of the fragments, located in the immediate vicinity of the found fragment, and their parameters are presented in Table. eight.

Table 8

Fragment Drop Area Parameters

Parameter 1 2 3

Fragment size, m 0.7 0.6 0.6

Fragment weight, kg 646 517 420

Latitude of the center of the region, ° N sh. 54.94 54.93 54.93

Longitude of the center of the region, ° E 60.31 60.33 60.35

Area size, m 1270x354 1216x346 1166x336

Conclusion. The results obtained in the work show that the developed method allows calculating the trajectory of a celestial body in the Earth's atmosphere, the parameters of the body's heliocentric orbit before it enters the atmosphere, to evaluate the region where fragments fall and the main factors of damage. It was shown that the orbits of the 2008 TC3 and Chelyabinsk meteorites before entering the atmosphere turned out to be close to the orbits obtained by other authors, and the parameters of air explosions coincide with the initial data within their accuracy. The resulting areas of fall of fragments of these meteorites are only a few kilometers from the discovered fragments. The zones of destruction as a result of the action of an air shock wave in the case of the Chelyabinsk meteorite coincide with real data, according to which about 7320 buildings were damaged. In some buildings, windows were broken, in others the frames were completely knocked out of the windows. In the Etkulsky district, which became the epicenter of the explosion, 865 windows in residential buildings and 1.1 thousand windows in other buildings were damaged.

1. E. P. Aksenov, Theory of Movement of Artificial Satellites of the Earth. M. : Nauka, 1977. 360 p.

2. Svetsov V. V., Nemtchinov I. V. Disintegration of Large Meteoroids in Earth's Atmosphere: Theoretical Models // Icarus. 1995. Vol. 116. P. 131-153.

3. Passey Q. R., Melosh H. J. Effects of atmospheric breakup on crater field formation // Icarus. 1989. 42. P. 211-233.

4. Ivanov B. A., Deniem D., Neukum G. Implementation of dynamic strength models into 2D hydrocodes: Applications for atmospheric breakup and impact cratering // International Journal of Impact Engineering. 1997. P. 411-430.

5. Chyba C. F., Thomas P. J., Zahnle K. J. The 1908 Tunguska explosion: Atmospheric disruption of a stony asteroid // Nature. 1993. P. 40-44.

6. Physics of explosion / S. G. Andreev [and others]; ed. L. P. Orlenko. In 2 vols. T. 1. 3rd ed., revised. M. : FIZMATLIT, 2002. 832 p.

7. Atamanyuk V. G., Shirshev L. G., Akimov N. I. Civil defense: a textbook for universities / ed. D. I. Mikhailika. M. : Vyssh. school, 1986. 207 p.

8. Google [Electronic resource]. URL: http://www. google.com/earth/ (date of access: 07/15/2014).

9. NASA/JPL [Electronic resource]. URL: http://neo. jpl.nasa.gov/news/2008tc3.html/ (Accessed 7/15/2014).

10. The recovery of asteroid 2008 TC3 / ​​M. H. Shaddad // Meteoritics & Planetary Science. 2010. P. 1-33.

11. Bondarenko Yu. S., Vavilov D. E., Medvedev Yu. D. Method for determining the orbits of small bodies of the solar system based on enumeration of orbital planes. 2014. V. 48, No. 3. S. 229-233.

12. JPL Solar System Dynamics, 2014, SPK-ID: 3430291 [Electronic resource]. URL: http://ssd.jpl.nasa.gov/ (date of access: 07/15/2014).

13. Pit'eva E. V. Fundamental national ephemerides of the planets and the Moon (EPM) of the Institute of Applied Astronomy RAS: dynamic model, parameters, accuracy // Proceedings of the IAA RAS. SPb. : Nauka, 2012. Issue. 23. S. 364-367.

14. U.S. Standard Atmosphere / U.S. Government Printing Office. Washington, D.C., 1976.

15. Groten E. Report of the IAG. Special Commission SC3, Fundamental Constants. XXII. 1999. IAG General Assembly.

16. NOAA [Electronic resource]. URL: http://www.nnvl. noaa. gov/MediaDetail2 .php?MediaID=1290&MediaTypeID=1/ (Accessed 07/15/2014).

17. NASA/JPL [Electronic resource]. URL: http://neo.jpl.nasa. gov/news/fireball_130301. html/ (date of access: 07/15/2014).

18. Zuluaga J. I., Ferrin I., Geens S. The orbit of the Chelyabinsk event impactor as reconstructed from amateur and public footage. 2013.arXiv:1303.1796.

19. Mineralogy, reflectance spectra, and physical properties of the Chelyabinsk LL5 chondrite - Insight into shock induced changes in asteroid regoliths / T. Kohout // Icarus. 2014. V. 228. P. 78-85.

20. Central Bureau for Astronomical Telegrams, IAU. Electronic Telegram No. 3423: Trajectory and Orbit of the Chelyabinsk Superbolide, 2013 [Electronic resource]. URL: http://www.icq.eps.harvard.edu/CBET3423.html/ (accessed 07/15/2014).

21. Astronomical and physical aspects of the Chelyabinsk event of February 15, 2013 / V. V. Emelyanenko [et al.] // Astr. Vestn., 2013. V. 47, No. 4. C. 262277.

22. A. V. Golubev, “Main characteristics of meteoroid motion during the Chelyabinsk meteor shower on February 15, 2013,” Asteroids and Comets. The Chelyabinsk event and the study of the fall of a meteorite into Lake Chebarkul: Proceedings of the Conf. 2013. C. 70.

23. Bondarenko Yu. S. Halley - electronic ephemeris // Proceedings of the Main Astronomical Observatory in Pulkovo. Pulkovo-2012: Tr. Vseros. astrometric conference. 2013. No. 220 S.169-172.

24. URA.RU, The Chelyabinsk meteorite was delivered to the local history museum [Electronic resource]. URL: http://ura.ru/content/chel/17-10-2013/news/1052167381.html (date of access: 07/15/2014).

25. Gazeta.Ru, Non-emergency meteorite [Electronic resource]. URL: http://www.gazeta.ru/social/2013/03/05/50003 89.shtml/ (date of access: 07/15/2014).

1. Aksenov E. P. Teorija dvizhenija iskusstvennykh sputnikov Zemli. . Moscow, Nauka Publ., 1977, 360 p.

2. Svetsov V. V., Nemtchinov I. V., Disintegration of Large Meteoroids in Earth's Atmosphere: Theoretical Models. Icarus, 1995, vol. 116, p. 131-153.

3. Passey Q. R., Melosh H. J. Effects of atmospheric breakup on crater field formation. Icarus 1989, vol. 42, p. 211-233.

BecmnuK Cu6FAy. 2014. No. 4(56)

4. Ivanov B. A., Deniem D., Neukum G. Implementation of dynamic strength models into 2D hydrocodes: Applications for atmospheric breakup and impact cratering. International Journal of Impact Engineering, 1997, p. 411-430.

5. Chyba C. F., Thomas P. J., Zahnle K. J. The 1908 Tunguska explosion: Atmospheric disruption of a stony asteroid. Nature, 1993, p. 40-44.

6. Andreev S.G., Babkin A.V. Fizika vzryva. . Vol. 1. Moscow, FIZMATLIT Publ., 2002, 832 p.

7. Atamanjuk V. G., Shirshev L. G., Akimov N. I. Grazhdanskaja oborona: Uchebnik dlja vuzov. . Moscow, Vysshaya shkola Publ., 1986, 207 p.

8. Google. Available at: http://www.google.com/earth/ (accessed: 07/15/2014).

9 NASA/JPL. Available at: http://neo.jpl.nasa.gov/news/2008tc3.html/ (accessed: 07/15/2014).

10. Muawia H. Shaddad, Peter Jenniskens et. al. The recovery of asteroid 2008 TC3. Meteoritics & Planetary Science, 2010, p. 1-33.

11. Bondarenko Yu. S., Vavilov D. E., Medvedev Yu. D. . Astronomicheskij Vestnik. 2014, vol. 48, no 3, p. 229-233. (In Russ.)

12. JPL Solar System Dynamics, 2014, SPK-ID: 3430291. Available at: http://ssd.jpl.nasa.gov/ (accessed: 07/15/2014).

13. Pit "eva EV Fundamental" nye natsional "nye jefemeridy planet i Luny (EPM) Instituta prikladnoj astronomii RAN: dinamicheskaja model", parametry, tochnost" St. Petersburg, Nauka Publ., Proc. of IAA RAS., 2012, vol 23, pp. 364-367 (In Russ.).

14. U.S. Standard Atmosphere, 1976, U.S. Government Printing Office, Washington, D.C., 1976.

15. Groten, E. Report of the IAG. Special Commission SC3, Fundamental Constants, XXII, 1999, IAG General Assembly.

16 NOAA. Available at: http://www.nnvl.noaa.gov/ MediaDetail2.php?MediaID=1290&MediaTypeID=1/ (accessed: 07/15/2014).

17 NASA/JPL. Available at: http://neo.jpl.nasa.gov/news/fireball_130301. html/ (accessed: 07/15/2014).

18. Zuluaga J. I., Ferrin I., Geens S., The orbit of the Chelyabinsk event impactor as reconstructed from amateur and public footage, 2013, arXiv:1303, 1796.

19. Kohout T. et al. Mineralogy, reflectance spectra, and physical properties of the Chelyabinsk LL5 chondrite -Insight into shock induced changes in asteroid regoliths. Icarus, 2014, vol. 228, p. 78-85.

20. Central Bureau for Astronomical Telegrams, IAU. Electronic Telegram No. 3423: Trajectory and Orbit of the Chelyabinsk Superbolide, 2013 Available at: http://www.icq.eps.harvard.edu/CBET3423.html/ (accessed: 07/15/2014).

21. Emel "janenko V. V., Popova O. P., Chugaj N. N. i dr. Astronomicheskij Vestnik. 2013, vol. 47, no 4, p. 262-277 (In Russ.).

22. Golubev A. V. Materialy konferentsii "Asteroidy i komety. Cheljabinskoe sobytie i izuchenie padenija meteorita v ozero Chebarkul" 2013, p. 70 (In Russ.).

23. Bondarenko J. S. Izvestija Glavnoj astronomicheskoj observatorii v Pulkove. Trudy vserossijskoj astrometricheskoj konferencii "Pulkovo-2012". . St. Petersburg, 2013, vol. 220, p. 169-172 (In Russ.).

On February 15, 2013, the inhabitants of the Southern Urals witnessed a small asteroid collide with the Earth. In the sky over Chelyabinsk, a celestial body collapsed with an explosion that knocked out windows and damaged several buildings in the city, led to numerous injuries to people from glass fragments ... Numerous surveillance cameras and car DVRs recorded the flight of the car and the consequences of the shock wave - perhaps this is the first in history a case when so many people and so many video cameras watched the fall of a meteorite. Thanks to the results of these video recordings, it is possible to very accurately restore the trajectory of its flight, determine the area where fragments fell, and evaluate the characteristics of the meteorite. Let's try and conduct such a study.

Video recordings from car recorders are probably the most impressive, but it is difficult to use them for our purposes, since the wide-angle lenses of the recorders greatly distort the image and, without knowing the parameters of a particular device, one can hardly count on any results. In addition, on many records it is difficult to identify the location of the shooting. So I chose for analysis two recordings of stationary surveillance cameras installed on the streets of Chelyabinsk - on Revolution Square and near the railway station on Razin Street.

True, the meteorite itself is not visible on these records, but the shadow cast by buildings and pillars is perfectly visible.

Below are satellite images from the Google Earth program, we will use this program for measurements.

Chelyabinsk. Razin street

Let's try to determine where the meteorite explosion occurred. Since the trajectory of its flight passed almost horizontally, in the first approximation it can be considered that its section closest to the observer is located at the maximum height. Therefore, consider the frame with the shortest shadows.

Having restored the position of the column shadow on the satellite image, it is possible to measure its length, the height of the column can be approximately determined from the photographs of the area relative to the height of the cars - it is 12 meters. Now you can determine the maximum height of the meteorite trajectory:

φ=arctan(h/L shadow)=arctan(12/16)=37°, where

h - column height;

Shadow L - the length of the column shadow.

Similar calculations can be repeated for the second video, the building in the lower left corner of the frame is the Ostrov shopping center, its height is about 15 meters.

The distance to the nearest point of the trajectory can be estimated from the shock wave delay time. It was to the nearest point, since the meteorite was moving at a speed much higher than the speed of sound. The above videos were recorded without sound, but the moment of arrival of the shock wave can be literally seen by the alarms of parked cars. On the video from Razin Street, we will determine the moment of the shortest shadow from the shopping center and the moment the car alarms are triggered:

T 1 =0 min 48 s;

T 2 =3 min 11 s;

ΔT=T 2 -T 1 =143 s;

d=ΔT*v sound =143*331=47.3 km, where

v sound - speed of sound in air = 331 m/s;

d is the slant range to the trajectory.

Knowing the maximum angular height of the trajectory and the slant range, we can determine the distance to the nearest point over which the trajectory passed and its height above the ground:

D=d*cos(φ)=37.8 km;

H=d*sin(φ)=28.5 km.

Here it is necessary to make several remarks. This calculation is correct assuming the meteorite's trajectory was horizontal, but it is not. Unfortunately, it is impossible to determine the complete spatial position of the flight path from observation from one point, but we can at least estimate it qualitatively. Since the meteorite was descending and approaching the city (this can be seen from the greater speed of the shadows at the end of the flight), the nearest point of the trajectory must necessarily lie further in the direction of flight than the highest point, that is, to the west, which means that the meteorite did not move exactly from east to west, and from southeast to northwest. Consequently, the height of this point may be somewhat lower than we have determined, and the distance to the projection of the trajectory on the earth's surface is greater.

Let's build a circle on the map with a radius D=38.8 km (yellow arrow) - the trajectory should be tangent to it (More precisely, as mentioned above, the radius of the circle should be slightly larger, but not exceed the slant range d=47 km). In addition, we note approximately the directions to the meteorite at the moments of the beginning and end of the flare (at least 45 ° in each direction from the direction to the south) - this angle not only determines the length of the flare segment, but also sets the limiting directions of the trajectory, which must necessarily cross the sides of this angle. Therefore, the direction of flight lies in the sector from 270° to 315° (counting clockwise from the north direction). Below on the map the real path of the meteorite flight is also marked (red arrow) - as we see, it practically coincides with our estimates, taking into account corrections for a decrease in the flight trajectory.

It remains to estimate the speed of the meteorite. To improve accuracy, this should be done for the closest part of the trajectory, and therefore, in the sector of the fastest shadow movement in the video. Looking again at the video from the Revolution Square, we see that the entire flash lasted about 5.5-6s, and the time of flight of the meteorite for the second half of the trajectory - from the south until the end of the flash is no more than one and a half seconds. During this time, the meteorite flew at least 20 kilometers, that is, its speed in the final section of the outbreak was at least 12-13 km / s, and it entered the atmosphere at an even higher speed.

On the map - the approximate trajectory of the fall of the meteorite

Chelyabinsk meteorite- a stone meteoroid that fell on February 15, 2013 near Lake Chebarkul in the Chelyabinsk region. The meteorite fell at 9:20 local time 80 km west of Chelyabinsk. As a result of the fall of the meteorite, 1491 people were injured.

According to experts, the mass of the meteorite was up to 10,000 tons, and the diameter was about 15-17 m. The flight of the meteorite body from the moment it entered the atmosphere lasted 32.5 seconds. During the flight in the atmosphere, the meteorite collapsed into many pieces, and therefore fell to the ground in the form of a meteor shower. At a height of 15-25 meters, the meteorite broke up into several parts as a result of a series of explosions. The fall speed of the car was from 20 to 70 km/s. During the fall, the space object left a bright trace, which was visible even in Kazakhstan and the Samara region.

When the meteorite was destroyed into several parts, shock waves were formed. According to experts, the total amount of energy released during the destruction of the cosmic body amounted to 500 kilotons in TNT equivalent.

Chronicle of the fall of the Chelyabinsk meteorite

At 9:15 local time, the movement of the cosmic body was seen by residents of the Kostanay and Aktobe regions of Kazakhstan. At 9:21 am, a meteor trail was seen in the Orenburg region. The witnesses of the fall of the meteorite were residents of the Sverdlovsk, Tyumen, Kurgan, Samara and Chelyabinsk regions, as well as the Republic of Bashkortostan.

At 9:20 local time, the meteorite fell into Chebarkul Lake, located 1 km from the city of Chebarkul. The fall of parts of the meteorite was observed by fishermen who were fishing near the lake. According to eyewitnesses, about 7 fragments of a cosmic body flew over the lake, one of which fell into the lake, raising a column of water 3-4 meters high. On the satellite map you can see Chebarkul Lake, where the meteorite fell.

As a result of the fall of the meteorite, a blast wave was formed, which, in terms of released energy, exceeded the energy of the atomic bombs dropped on Hiroshima and Nagasaki. Due to the gentle trajectory of the entry of the body into the atmosphere, only part of the released energy reached the settlements.

The consequences of the fall of the Chelyabinsk meteorite

As most of the energy dissipated, the blast mostly shattered windows in buildings in nearby communities. A total of 1,491 people were injured in the meteorite impact, but most of the injuries were cuts and bruises from broken windows. Nevertheless, the number of victims of the Chelyabinsk meteorite has no equal in the world.

The greatest damage from the disaster was suffered by 6 settlements of the Chelyabinsk region: the cities of Yemanzhelinsk, Chelyabinsk, Korkino, Kopeysk, Yuzhnouralsk and the village of Etkul. The shock wave damaged many buildings: the damage from it was estimated from 400 million to 1 billion rubles.

Chelyabinsk zinc plant, the roof of which collapsed from the blast wave of a meteorite

Research and study of the Chelyabinsk meteorite

On February 15, 2013, it was found that fragments of a meteorite fell in the Chebarkul and Zlatoust districts of the Chelyabinsk region. Scientists from URFU have collected meteorite fragments for further study.

Later, the researchers told the press that the meteorite was an ordinary chondrite, which is composed of sulfites, iron, olivine and melting crust.

Early February morning in 2013 unexpectedly became tragic for 1613 residents of Chelyabinsk and its environs. There has never been such a large number of people affected by a fallen meteorite in the history of the Earth's population. During the impact, windows were broken in many buildings, trees were broken and people were injured to varying degrees of severity, as a result of which about 1,613 people were recognized as victims, of which, according to various sources, from 50 to 100 people ended up in hospitals. People who watched the fall of the meteorite that morning were simply shocked by the events taking place. The first versions of what was happening sounded like: a plane crash, a rocket crash and even an alien attack ...

At the moment, the picture of the events of that tragic morning has been fully restored and it is reliably known when and where the meteorite fell in Chelyabinsk.

How it was

At about 9 am on February 15, this “unexpected guest” appeared high in the sky over Chelyabinsk, as a result of which a state of emergency was declared in Chelyabinsk and its surroundings. Previously, the same meteorite was observed by residents of other regions of the Russian Federation, but they were much more fortunate than the residents of Chelyabinsk, because it simply flew past them without causing absolutely no harm. For example, at 7.15 Moscow time or at 9.15 local time, residents of the Aktobe and Kostanay regions of Kazakhstan saw it, and residents of Orenburg observed this amazing phenomenon at 7.21 Moscow time. This meteorite was also clearly visible in Sverdlovsk, Kurgan, Tyumen and their environs, and even 750 km from the place of impact in the village of Prosvet, Volzhsky district, Samara region.

Bright flash

According to the US National Aeronautics and Space Administration (NASA), a meteorite weighing about 10 tons and a diameter of about 17 meters, with a speed of 17 km / s, entered the Earth's atmosphere and after 32 seconds split into many pieces. The destruction of the meteorite was accompanied by a series of explosions, the first of three explosions was the strongest and caused the destruction. It was a bright flash, it lasted about five seconds, and a minute later it came to Earth in the form of a destructive wave. According to scientists, the destruction of the meteorite led to the release of energy, which was approximately equal to 100 to 500 kilotons of TNT. The center of the explosion was not the city of Chelyabinsk itself, but its area, which is located a little to the south and is called Yemanzhelinsk - Yuzhnouralsk.

Locations of the fall of fragments

As a result of research conducted by a specially created group, four places were discovered where fragments of the meteorite are supposed to be located. The first two places are in the Chebarkulsky district of the Chelyabinsk region, the third in the Zlatoustovsky district, and the fourth in the Chebarkul lake area. The information that the meteorite is located in the lake was confirmed by the fishermen who were at the crash site. From their stories, members of the search group learned that at the moment the meteorite fell into the lake, a column of water and ice about 3-4 meters high rose from it.

Second largest after Tunguska

As a result of the work carried out in the area of ​​​​Emanzhelinsk and the village of Travniki, about a hundred fragments were found, and about 3 kg of fragments were collected in the lake area. All of them are currently being studied by scientists, according to whom, the meteorite that fell in Chelyabinsk is the second largest after the Tunguska meteorite that fell on the territory of Russia on June 30, 1908.

Full cut video from the event

Based on the foregoing, desperate The May Day boys were in the distance 340×(25+8)= 11220 meters= 11.22 km (340 is the speed of sound in air) from the epicenter of the explosion. The plume break was at an angle of 45-60° from the observer with respect to the horizon (see photo above). Sin50° = 0.766, hence the height at which the explosion occurred, equals 11.22 × 0.766 = 8.58 km, and not 20-30, and even more so not 50 km, as it was stated in the media. This is also evidenced by the shape of the cloud formed by the plume, it is rather cumulus than cirrus. The distance from the observer to a point on the earth's surface under the epicenter will be 11.22 × Cos50° = 11.22 × 0.64 = 7.1 km. We mark this point on the Google Earth map, 7 km from the village of Pervomaisky in the direction opposite to the village of Chebarkul, it will be useful for us to plot the flight path of the “celestial body”.
And here is video footage from Kopeysk, located 30 kilometers from the epicenter, the camera is turned on immediately after the flash, and people behind the scenes are discussing why there was a light, but there was no explosion. The shock wave came to Kopeysk much later, which once again confirms the epicenter we have identified. The shock wave came in 1 minute 13 seconds from the start of the shooting.



Pictures from Kopeysk.
Now let's define the trajectory of the flight of a celestial body.

“According to the chairman of the regional branch of the Russian Geographical Society, candidate of geographical sciences Sergey Zakharov, the body flew from the southeast to the northwest, the flight path was in azimuth about 290 degrees along the Yemanzhelinsk-Miass line.
The reconstruction of the meteoroid trajectory is based on the study of the records of two surveillance cameras, one of which is located on the Revolution Square in the center of Chelyabinsk, and the other in Korkino, as well as the assumption of the impact site in Chebarkul Lake. http://en.wikipedia.org/ ←
Well, the "scientists" were wrong again! In fact, the map shows the flight path of the largest fragment of a celestial body from the explosion site to the impact site. Using two cameras, they determined the place of the explosion and drew a line from it to an ice hole in Lake Chebarkul, where, presumably, something had fallen. But this is not true, since the explosion could change the trajectory of the fall of debris, scattering them over a large area and the real trajectory of the flight of the fireball must be sought differently (author's note).
Only great scientists can accurately calculate the trajectory from two surveillance cameras that are close to each other. We, based on our school knowledge in mathematics and physics, will use three points. We have already found one of them, located near the village of Pervomaisky (see above).
In order to most accurately determine the flight path of the fireball, it was necessary to find two more cameras located at a great distance from the explosion site. We were lucky, and we found videos made in Kustanai (Kazakhstan) 240 km and Kurgan 270 km from the explosion site.

In the picture from Kustanai, the car flies from right to left. And in the picture from Kurgan from left to right. Therefore, the flight path passed between these cities.
The closer the observer is to the inclined line, the greater the angle of its inclination to the horizon seems to be. Being directly under the inclined line, it will appear vertical to him.
Using the Google Earth program, we drew the exact flight path of the meteorite. You can check yourself.
We determine the angles of inclination of the plume to the horizon line, given that in Kurgan the surveillance camera is tilted, so we draw the horizon line along the roof ridge. And in Kustanai we will take into account the slope of the video recorder, drawing a vertical axis parallel to the poles. It turned out in Kurgan 38.3 °, and in Kustanai 31.6 °. Consequently, the trajectory passed closer to Kurgan. Let's move on to construction. From the point marked by us, near the village of Pervomaisky, we draw two lines, one to Kurgan (blue), the other to Kustanai (green) and measure the distances. Then, on the line Kurgan - Pervomaisky, we set aside a distance equal to the distance from Pervomaisky to Kustanai. From this point we will draw an auxiliary line to Kustanay and measure it. Next, we divide this line in the proportion of 38.3° / 31.6° = 1.21 and put the resulting segments (green and orange) on this line in order to determine the point over which the bolide's flight path passed between Kustanai and Kurgan. Now we draw a straight line through the village of Pervomaisky and the point we found, this is the real flight path of the celestial body, in the picture it is yellow. We hope you get the same picture:


Let's take a closer look at the place of the explosion and the fall of the fireball.


The flight path of the fireball over the villages of Pervomaisky and Timiryazevsky.


Place of fall, Timiryazevsky, Chebarkul and Miass ..
We found another video taken by the DVR of a car moving perpendicular to the trajectory of the car (see freeze-frames below). According to it, we determined the angle at which the celestial body fell to the earth. Let us remind once again that the true angle of inclination of the plume to the horizon will be the minimum observable, located perpendicular to the trajectory, in all other angles the angle will be greater than the true one. It is 13.3° (see image below). Sin 13.3° = 0.23. From here the path that the body must fly after the explosion, is equal to 8.58: 0.23 = 37,3 km. The distance from the place of impact to the epicenter of the explosion will be 8.58: Tg 13.3° = 8.58: 0.236 = 36.4 km. The calculated drop point is located between the village of Timiryazevsky and Chebarkul, along the trajectory. Without a doubt, fragments of the body scattered by the explosion over a large area.


The same camera shows the moment when the glow of the fireball starts (24 seconds of recording), and the time of the climax of the explosion (30 seconds of recording).

23 seconds, clear skies.


24 seconds, a luminous dot appeared.


30 seconds, the beginning of the explosion.


34 seconds, climax.


35 seconds, the end of the explosion.


38 seconds, everything burned down.
Based on this video recording, we calculate the height at which the glow began (24 seconds) and the average speed of the body in the period from the beginning of the glow to the culmination of the explosion (34 seconds). 10 seconds have passed. We already know the height of the explosion. Having made the necessary constructions, based on the similarity of the obtained right-angled triangles, we find: glow start height H=19.5 km,path, traversed from the beginning of the glow to the climax S= 47.5 km, time t=10 sec, respectively average body flight speed, υ=4.75 km/s = 4750 m/s. As you can see, this speed is less than the first cosmic speed (7900 m/s) required to put the body into the earth's orbit. This is another fact against the meteorite version.
And according to the following video recording (see below), you can determine the start time, the end of the glow of the body and the moment of the explosion with an accuracy of hundredths of a second. The camera of this video recorder is located almost opposite the previous one, to the left of the flight path of the fireball. Total glow time 15 seconds, time from the beginning of the glow to the explosion 10 seconds the values ​​are exactly the same as those of the previous DVR. As you can see, the flight speed can be calculated with great accuracy.

Of course, we doubted the declared power of the explosion, as well as the likelihood of a meteorite explosion in general. Can a stone meteorite explode, forming such a bright and powerful flash, and burn out, disappearing without a trace? Let's try to answer this question. Moreover, it is quite simple, you still remember the school physics course. Who does not remember, can look into the reference book from which we extracted the following formula:
F = c A ρ/2 υ²
Where F- aerodynamic drag force, it will impede the movement of the body, and put pressure on its surface, warming it up.
For simplicity, we will make the calculation with certain assumptions that do not significantly affect the result, experts will forgive us.
Let's take the diameter of a stone meteorite equal to D = 3 meters, you will understand later why.
A- body cross-sectional area, A=π D²/4= 7 m²; c is a coefficient depending on the shape of the body, for simplicity we will consider it spherical, the value from the table, c = 0.1; ρ - air density, at a height of 11 km it is four times less, and at a height of 20 km it is 14 times less than normal, for calculations we will reduce it by 7 times, ρ = 1.29/7 = 0.18; and υ is the speed of the body, υ=4750 m/sec.
F = 0.1 7 0.18: 2 4750² = 1421438 N
When entering the dense layers of the atmosphere, the surface of the body will be pressure air is less than:
R= F/A = 1421438: 7 = 203063 N/m = 0.203 MPa, (since the cross-sectional area, 7 m², is significantly less than the area of ​​half the surface of the ball, 14.1 m²). Any builder will tell you that even the worst brick or concrete block will not collapse from such pressure, you can see for yourself by looking at the building guide, the compressive strength of clay bricks is 3-30 MPa, depending on the quality. When a brick falls from space, only its surface will be destroyed, heated by the resisting air and cooled by it. The heating energy can approximately be calculated by the formula: W = F · S, where S is the distance traveled. And the heat that flies away with the air flowing onto the brick is calculated by the formula: Q=α · A · t · ∆T; where α=5.6+4υ; А= 14.1 m² - surface area, in our case, half of the ball surface, t=10sec - flight time, ∆T=2000° - temperature difference between the body surface and the incoming air. We suggest you do these calculations yourself, and we will calculate power required to move in the stream according to the formula:
P\u003d c A ρ / 2 υ³ \u003d 0.1 7 0.18: 2 4750³ \u003d 6.75 10 9 W
Energy is released in ten seconds of flight equal to:
W\u003d P t \u003d 6.75 10 9 10 \u003d 67.5 10 9 J
And dissipate in space in the form of heat :
Q=α A t ∆T = (5.6 +4 4750) 14.1 10 2000 = 5.36 10 9 J
Remaining energy: 67.5 10 9 - 3.5 10 9 = 62.14 10 9 J, will go to heat the car.
She might be enough to blow him up, but completely not enough, for this stone to burn, evaporating in the air. In TNT equivalent, this energy is equal to 14.85 tons of TNT. 1 ton of TNT \u003d 4.184 10 9 J. The energy of the explosion of the nuclear bomb "Kid" over Hiroshima on August 6, 1945, according to various estimates, is from 13 to 18 kilotons of TNT, that is, a thousand times more.
"We literally just finished the study, we confirm that the particles of matter found by our expedition (Ural Federal University) in the area of ​​Lake Chebarkul really have a meteorite nature. This meteorite belongs to the class of ordinary chondrites, it is a stone meteorite with an iron content of about 10% Most likely, it will be given the name "Chebarkul meteorite," Viktor Grokhovsky, a member of the RAS Committee on Meteorites, quotes RIA Novosti.
Calculate the energy released if chondrite with a diameter of 3 meters hit about the earth.
W\u003d m υ² / 2 \u003d 31.6 10³ 4750²: 2 \u003d 356.5 10 9 J, this is equivalent to 85.2 tons of TNT.
m \u003d V ρ \u003d 14.14 2.2 \u003d 31.6 tons, the mass of the ball. ρ=2.2 tons/m³ - chondrite density.
V \u003d 4 π r³ / 3 \u003d 4 3.14 1.5³: 3 \u003d 14.13 m³, the volume of the ball.
As you can see, this power clearly does not reach the kilotons announced in the media.
"The total amount of released energy according to NASA amounted to about 500 kilotons in TNT equivalent, according to RAS estimates - 100-200 kilotons».
http://ru.wikipedia.org/ ← "They went completely crazy, 15 kilotons exploded over Hiroshima, and there was no wet place left from it, and what would happen to Chelyabinsk with such an explosion power" (author's note).
We decided to calculate the explosion power of 30 tons of high-energy hydrocarbon fuel, for example, gasoline, although, of course, gasoline is not carried in rockets.
An explosion of 30 tons of gasoline will release energy equal to:
Q\u003d m H \u003d 30 10³ 42 10 6 \u003d 1.26 10 12 J, which is equivalent to 300 tons of TNT, and this is more like the power of the explosion in Chelyabinsk.
Why did we think about the rocket? Yes, because everything that was reported in the media and what we actually saw on the screens did not coincide at all. The plume was similar in color and shape to a jet engine contrail rather than a meteor trail. The inclination of the trajectory was not as advertised, 20°, but actually 13°, and is more suitable for a body falling from near-Earth orbit, rather than bursting from the depths of space. Explosion height, judging by the shape of the loop, clearly did not correspond to the declared one. And in fact, as the calculations showed, it turned out to be equal to 8.58 km and not 30-50 km. In addition, the flight path of the “meteorite” was somehow vaguely spoken about, it flew in Tyumen and Kazakhstan and Bashkiria, in short circled half the country, and fell in Chelyabinsk. And most importantly, having not yet found the fragments of the "celestial body", they declared it a meteorite, and it was absolute stupidity - they called it a symbol of the Krasnoyarsk forum. A good symbol, the millionth city and the surrounding villages ended up with broken windows in the cold, thousands of people suffered.
That is why we undertook an independent investigation of the incident. Of course, our calculations are very approximate, and the arguments we give may seem dubious and controversial to you, it’s difficult for us to resist the informational pressure of the media ourselves, but we did not find mathematics and physics exact sciences and errors in our calculations. And to convince you of the plausibility, we present our assumptions and calculations Ultima ratio(the last argument), which shocked us too. After we discovered IT, we have no doubt that "Chelyabinsk Meteorite" was sent towards Russia by someone's evil will.

After plotting the flight path of the fireball (yellow line), we, out of curiosity, extended it beyond the place where the body fell ( Red line). We were amazed, she walked right through Moscow, having enlarged the image, we were even more amazed, the red line rested directly on Kremlin center, and it's already can't be a coincidence. You can see for yourself.


The Chelyabinsk meteorite flew there.


And here o should have fallen.
You may have an objection: the round hole found on Lake Chebarkul (the place where a large fragment fell) does not coincide with the trajectory laid by us. The answer is simple.


The only whole fragment of an exploded and burned-out rocket could only be a fairing - the most durable and heat-resistant part of the rocket. http://russianquartz.com/ « The fairings are so strong that they can only be cut with diamond blades. The head part heats up to 2200 degrees.
After the explosion, he somersaulted in the air, forming a loop on the plume (there was another small flash in this place), and flew on. Due to its aerodynamic shape (hemisphere), having lost speed, it glided vertically onto the lake, as children's flying saucers do, and, having melted the ice, went under water, crumbling into small pieces from impact and a large temperature difference.
“On the one hand, ceramics are fragile. If you hit it with a hammer, it will shatter. On the other hand, it can be affected simultaneously when heated to one and a half thousand degrees,” said Vladimir Vikulin, director general of NPP Tekhnologiya. http://russianquartz.com/ Therefore, a round hole was left in the ice. A stone flying at an angle of 13° would form an oval hole in the ice, elongated along the trajectory.


The video, filmed from the roof of one of the houses from Chelyabinsk, clearly shows that there was more than one explosion. You can also see fragments of the fireball flying out during the explosions.


It may seem to someone that they flew forward and upward, but this is not so. Imagine: the observer looks from below, and the car flies on an inclined path, moving away from the observer. This is easy to understand by taking two pencils in your hand, perpendicular to each other, looking at them slightly from below. All fragments flew to the right of the fireball's trajectory, therefore, the remaining part received an impulse to the left. Therefore, the rest of the rocket (fairing), deviating to the left of the original trajectory, fell directly into the lake.
Another argument confirming our version of the stones in the rocket is the fact that the stones that the searchers find lie in the snow, almost on the surface, which indicates that they had a low temperature when they fell. That is, they were not heated by friction against the air and the explosion, as would happen with a real meteorite, but were slightly heated at the time of the explosion, since the container with the stones was in the bow, which was the least exposed to the thermal effects of the explosion. The pictures clearly show how the fireball was torn apart by the blast wave into two parts and the front one, by inertia, flew forward and went out faster than the fuel that burned out and was thrown off by the blast wave. That is why a gap 3-5 kilometers long appeared on the plume.
And look again at the train.


It is clearly seen that a volumetric body was flying, carrying with it the remnants of burning fuel and combustion products.


And in this place the fuel burned out, and the luminous hot body (rocket fairing) continued to fly, this is clearly seen in the video:


You can find many more details confirming our version, but it is already clear that the official statements about the meteorite do not hold water.
This case is not similar to the invasion of an extraterrestrial civilization, their shot would definitely hit the target, besides, the Kremlin was not seen in connection with aliens. But the Americans are hiding something about little green men.
We have many versions explaining this fact, for example: Islamic terrorists loaded a rocket with stones and sent it to Moscow to simulate a meteorite falling on the Kremlin, as a symbol of heavenly punishment (it is difficult to find terrorists). Option number two: high-ranking Russian officials and oligarchs are taking revenge for being deprived of the opportunity to have real estate and bank accounts abroad (those who were not in Moscow that day are under suspicion). The third option: international currency speculators and financiers decided to make money again, big, once again, bringing down the market, destabilizing the situation in the world (they can be calculated if you find the place where the rocket was fired from). US business activity indices are at the maximum of the third wave, which will overwhelm and turn the entire world economy. So friends, merge shares and go to cash and do not forget to thank us for the information, put some money in the wallet, how much is not a pity. And subscribe to our magazine, as we have not told you the main thing yet.
We can only guess who threw a stone at Russia, we have no means to find out, the maps show that the trace of the trajectory leads to the Pacific Ocean.
All our assumptions seem fantastic and we are ready to sell them as an idea for a script for another cool action movie.
By the way, the version of the rocket with stones is very plausible. The error in pitch (height) was due to the fact that during the transition to horizontal flight, the stones, which were not covered tightly, poured into the container in bulk, and, having shifted the center of gravity, changed the rocket's flight path. And this was not taken into account by ballistics. We noticed the deviation late, turned on the main engines (the luminous dot on the video appeared suddenly), when the rocket had already begun to descend.
Other scenarios for the development of events in the Chelyabinsk region are also possible, and it was not in vain that we mentioned lasers at the beginning of the article. We invite you to imagine the further course of our thoughts.

P.S.
Frankly, we were hesitant to post this information online, it seems unbelievably cruel. But there is a lot of evil in the world, and the governments of most countries are not able to cope with it, but rather contribute to its multiplication. Therefore, we decided that everyone should take care of their own safety and well-being.
Don't take our word for it, do your own research, maybe we were wrong after all.
If the end of the world did not happen and the Chelyabinsk meteorite did not hit you, this does not mean at all that all the dangers are behind. They are all ahead. And soon you will know about them. Happiness and prosperity to you.
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