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Comments to Italian article on Tunguska  Andrei Ol'khovatov
 Jan 03, 2002 04:27 PST 
Dear All,

As I planned earlier, I post here my comments on the Italian announcement,
spread through BBC (below I comment the BBC story too):
I am emailing to some of the Italian researchers (to G. Longo, and L.
urging them to take part in the discussion of their article.
The BBC story refered to their article:
P. Farinella, L. Foschini, Ch. Froeschle, R. Gonczi, T.J. Jopek, G. Longo,
P. Michel: Probable asteroidal origin of the Tunguska Cosmic Body. Astronomy
and Astrophysics 377 (2001) 1081-1097 ( you could download the article from
here: http://www-th.bo.infn.it/tunguska/tu99public.htm ). If you don't have
Adobe Acrobat Reader, or it takes too long to download, you can use
to read text version of the article (with some minor distortions -
especially the converter likes to omit "f" and "fi"):
Below I place parts of the article's text gotten via the converter with my
comments (some of the minor converter distortions were not corrected and
formulas, tables and pictures are absent).
Each of my comments begins with ----BBBBBBBBBBBBB----- line and ends
with --------EEEEEEEE------- line.


Probable asteroidal origin of the Tunguska Cosmic Body
P. Farinella 1;? , L.Foschini 2 , Ch. Froeschle 3 , R. Gonczi 3 ,T. J.
Jopek 4 , G. Longo 5;6 , andP.Michel 3
1 Dipartimento di Astronomia, Universit a di Trieste, Via Tiepolo 11, 34131
Trieste, Italy
2 Istituto TeSRE { CNR, Via Gobetti 101, 40129 Bologna, Italy
3 Observatoire de la C^ote d'Azur, Departement Cassini, URA CNRS 1362, BP
229, 06304 Nice, France
4 Obserwatorium Astronomiczne Universytetu A. Mickiewicza, Sloneczna 36,
60286 Pozna n, Poland
5 Dipartimento di Fisica, Universita di Bologna, Via Irnerio 46, 40126
Bologna, Italy
6 INFN, Sezione di Bologna, Via Irnerio 46, 40126 Bologna, Italy

Received 18 May 2001 / Accepted 17 July 2001
Abstract. The complete characterisation of the Tunguska event of 30th June
1908 is still a challenge for astro-
physicists. We studied the huge amount of scientic literature to select
data directly available from measurements
and we introduced parameters calculated by the application of models, and
evaluated other possibilities. We then
selected a range of meaningful atmospheric trajectories, from which we
extracted a set of possible orbits. We
obtained 886 orbits, which were used to estimate the probabilities of the
possible origin of the Tunguska Cosmic
Body (TCB). We found that the probability that the TCB moved on an
asteroidal path is higher than it moved
on a cometary one, 83% to 17%, respectively.
1. Introduction
In the early morning of 30th June 1908, a powerful ex-plosion (10
15 Mton of energy) over the basin of the Podkamennaya Tunguska river attened
2150  50 km 2 of Siberian taig a. For more than ninety years, Tunguska
and still is a conundrum, although many scientists around the world have
written essays on the subject and proposed
their solutions. Shapley (1930) was the first to suggest that the Tunguska
event was caused by the impact of a comet.
Kulik (1939, 1940) subsequently proposed the first aster-oidal hypothesis
(iron body), followed shortly afterwards
by Fesenkov (1949), who hypothesised a stony meteorite of at least some
millions tons. Fesenkov (1961) later worked
out a definite model of an impact between a comet and the Earth's
From that time, the majority of
Russian scientists followed the cometary hypothesis, while many western
scientists preferred an asteroidal model (see,
e.g., Sekanina 1983; Chyba et al. 1993). For many reasons, these two
\schools" practically ignored each other until
the international workshop Tunguska96, held in Bologna (Italy) from
15th{17th July 1996 (see the special issue of
Planetary and Space Science, vol. 46, n. 2/3, 1996, ed. M. Di Martino, P.
Farinella, & G. Longo). There is no
reason to review here what is known about the Tunguska event and is reviewed
in Krinov (1966), Trayner (1997),
Vasilyev (1998), Bronshten (2000c).
Despite great e orts, the main question, i.e. the na-ture of the Tunguska
Cosmic Body (TCB), which caused
the explosion, is still open.

Please, pay attention that while the authors have recognized that the
event is still a conundrum, later they talk just about "Tunguska Cosmic Body
(TCB), which caused the explosion"! In other words, the field of
investigation was silently narrowed without any explanations.

Although almost every year there is an
expedition to Tunguska, so far no typical ma-
terial has permitted a certain discrimination to be made between an
asteroidal or cometary nature of the TCB.
Neither the chemical and isotopic analyses of peat (see, e.g., Kolesnikov et
al. 1998), nor studies on iridium in the
impact site (e.g. Rasmussen et al. 1999), nor the search of TCB
microremnants in tree resin (Longo et al. 1994) were
sucient to prove de nitely the nature of the TCB.
In July 1999, an Italian Scienti c Expedition, orga-nized by the University
of Bologna with the collaboration
of researchers from the Turin Astronomical Observatory and the CNR Institute
of Marine Geology, went to
Siberia in order to collect more data and samples (Longo et al. 1999;
Amaroli et al. 2000) 1 . The many samples col-
lected during the expedition are still under examination. This field
should be strengthened by theoretical
studies and modelling and the present paper is a step in that direction. In
this paper, we rst construct a sample
of possible TCB orbits, then we use a dynamic model to compute the most
probable source of the TCB if placed
on each of these orbits, thus obtaining the corresponding probabilities for
an asteroidal or a cometary origin.
Our paper is divided as follows: in Sect. 2, we dis-cuss the choice of the
di erent TCB parameters, which
are used to compute the possible orbits. This data includes the physical
parameters of the explosion, the speed values,
and the radiant coordinates. In Sect. 3, using the chosen set of parameters
we rst compute the lower and upper
boundaries of the dynamic elements of the heliocentric orbits, then we
deduce the dynamic geocentric parame-
ters (Sect. 4). We can thus build up a sample of possible TCB orbits and
calculate their respective initial osculat-
ing elements (Sect. 5). In Sect. 6, rst of all, we brie y recall the dynamic
method, which allows us to identify
the principal sources of small bodies, then we estimate for a ctitious TCB
on each orbit with orbital elements
(a, e, i) the probabilities of its coming from the di erent sources, and
discuss the results. In Sect. 7, we present a
sample of numerical integrations over a long timespan of the orbital
evolution of ctitious TCB coming from each
source according to our probability computations. Such numerical
integrations allow us to identify the various dy-
namic mechanisms at work and to compare their orbital behaviour. The
conclusions are presented in Sect. 8.

2. Choice of parameters
We assume that the Tunguska explosion was caused by a single solid body,
which collided with the Earth, and that
this body moved around the Sun on a closed orbit.

Here the authors were to recognize that they narrow their search field even
more strongly! And again without any arguments...

We can therefore describe
its cosmic trajectory as in the case of
meteoroids, namely, by means of the moment of time, the geocentric speed and
the radiant geocentric coordinates.
The values of these parameters should correspond to the point at which the
TCB entered the Earth's atmosphere.
Therefore within a short interval of time the TCB trajec-tory can be
modelled by a straight{line section whose ori-
entation relative to the local horizontal reference frame is given by the
azimuth and the height of its radiant point 2 .
We started (Sect. 2.1) with an extremely detailed anal-ysis of the
literature available on the Tunguska event, from
which we obtained the data summarized in Table 1. With the help of
theoretical models we then reduced the param-
eter ranges (Sects. 2.2 and 2.3) to those listed in Table 4. This choice of
parameters made it possible to make most
limited calculations whilst preserving the more plausible solutions.
2.1. Final trajectory data
In order to obtain the parameters necessary for the calcu-lations recorded
in this paper, we consider objective data
and testimonies of the Tunguska event. Two kinds of ob-jective data on the
Tunguska explosion are available: seis-
mic and barometric registrations, recorded immediately
2 The azimuth is calculated from North to East starting from
the meridian.
Tabl e 1. Selected parameters of the Tunguska explosion. In
the last column we state the sources used to nd the given
values: SM { seismic measurements, BM { barographic mea-
surements, FT { fallen tree direction, FD { forest devastation
data, EW { eyewitnesses.
Time of the explosion UT Remarks
Ben{Menahem (1975) 0 h 14 m 28 s SM
Pasechnik (1976) 0 h 14 m 30 s BM
Pasechnik (1986) 0 h 13 m 35 s SM
Geographic coordinates of the epicentre (; )
Fast (1967) (60530 0900 N;
101530 4000 E) FT
Zolotov (1969) (60530 1100 N
101550 1100 E) FT
Height of the explosion H [km]
Fast (1963) 10:5 FD
Ben{Menahem (1975) 8:5 SM
Bronshten & Boyarkina (1971) 7:5 FD
Korotkov & Kozin (2000) 6 10 FD
Trajectory azimuth a
Fast (1967) 115 FT
Zolotov (1969) 114 FT
Fast (1971), Fast et al. (1976) 99 FT
Andreev (1990) 123 EW
Zotkin & Chigorin (1991) 126 EW
Koval' (2000) 127 FT{FD
Bronshten (2000c) 122 EW
Bronshten (2000c) 103 FT{FD
Trajectory inclination h
Sekanina (1983) <5 EW
Zigel' (1983) 5 14 EW
Andreev (1990) 17 EW
Zotkin & Chigorin (1991) 20 EW
Koval' (2000) 15 FT{FD
Bronshten (2000c) 15 EW{FT
after the event, and data on forest devastation, systemat-ically collected
50{70 years later.
Seismic records from Irkutsk, Tashkent, and Ti is were published together,
two years after the event (Levitskij
1910); those from Jena { three years later (Catalogue 1913). However, it was
only in 1925, that the origin
of these seismic waves was connected to the Tunguska event and a rst
determination of the explosion time as
0 h 17 m 12 s UT was obtained (Voznesenskij 1925).
Barograms were recorded in a great number of ob-servatories throughout the
world. From the barograms of
13 Siberian stations, the explosion time was found equal to 0 h 16 m 36 s UT
(Astapovich 1933).
These two kinds of data were subsequently analysed more precisely taking
into account the exact distances
and the properties of seismic and atmospheric waves. A rst result (0 h 14 m
23 s UT), based on the seismic data of
Jena and Irkutsk only, was obtained by Pasechnik (1971).
Two more complete analyses, using the whole set of seis-mic and barographic
data, were independently performed
by Ben{Menahem (1975) and Pasechnik (1976). They found practically the same
value for the time the seismic
waves started (see Table 1). Pasechnik (1976) calculated that the time of
the explosion in the atmosphere was
30 s earlier depending on the height and energy of the explosion. This
interval was subsequently reduced to
20 s (Pasechnik 1986), which was much lower than the experimental
uncertainty quoted in 1976 (0:8 m ). In the
1986 paper, however, Pasechnik revised his previous re-sults obtaining a
value equal to 0 h 13 m 35 s
 5 s UT.

Please, pay attention that Pasechnik stated that the height of the explosion
can not be determined from poor-quality seismograms, and moreover, it even
can not be
determined whether there was a single explosion of several more or less
closely-spaced ones in place and time.

Taking into account the values given in Table 1 and the
uncertainties here discussed, in our calculations (Table 4)
we use the time given by Ben{Menahem with an uncer-tainty prudently
estimated equal to
 1 min.We consider this value as the instant at which the bolide entered
the Earth's atmosphere. That instant precedes both the time
of the atmospheric explosion and the time the seismic waves started.
However, the di erences are negligible when
compared with uncertainties a ecting other data.
The data on forest devastation is a second kind of ob-jective data on the
event. This data includes the directions
of attened trees, which can help us to obtain information on the coordinates
of the wave propagation centres and on
the final trajectory of the TCB. Although the radial ori-entation of the
fallen trees was discovered by Kulik since
1927 (see Fig. 1), systematic measurements of the azimuth of fallen trees
were begun during the two great post{war
expeditions organised by the Academy of Sciences in 1958 and 1961
(Florenskij 1960, 1963) and during the Tomsk
1960 expedition. Under the direction of Fast, with the help of Boyarkina,
this work was continued for two decades dur-
ing ten different expeditions from 1961 up to 1979. A total of 122 people,
mainly from Tomsk University, participated
in these measurements. The data collected is published in a catalogue in two
parts: the rst one (Fast et al. 1967)
contains the data obtained by six expeditions (1958{1965), which include the
measurement of the direction of more
than 60 thousands fallen trees on 859 trial areas equal to 2500 or 5000 m 2
and chosen throughout the whole dev-
astated forest. In the second part (Fast et al. 1983) the
data of the areas N 860{1475, collected by the six subse-quent expeditions
(1968{1976) were given.
From the data collected during the first three expe-ditions, Fast (1963)
obtained the epicentre coordinates
605304200 N and 1015303000 E. These values are very close to the nal ones
 0600 N, 1015304000  1300 E, calculated by Fast (1967) analysing the
whole set of data from the rst part of the catalogue (Fast et al. 1967).
Zolotov (1969) contemporarily performed an independent mathematical analysis
of the same data and obtained the
second values quoted in Table 1. The coordinates of Fast's epicentre 3 with
the uncertainties quoted, corresponding to
about 200 m on the ground, were subsequently con rmed in all Fast's papers
and are here used in our calculations
(Table 4).
Many witnesses have heard a single explosion. Some of them have heard
multiple explosions, that can be echoes.

Majority of witnesses heard several explosions. In many places the thunders
continued for a long time. For example, in the town of Kirensk the
explosions were heard for 45 minutes! Very special "echoes"...

Examining the directions of fallen trees seen on the aero{ photographic
survey performed in 1938, Kulik suggested
(1939, 1940) the presence of 2{4 secondary centres of wave propagation. This
hypothesis was not con rmed, though
not de nitely ruled out, by Fast's analyses and by seis-mic data
investigation (Pasechnik 1971, 1976, 1986). Some
hints on its likelihood were given e.g. by Serra et al. (1994) and Goldine
(1998). However, in absence of a sure conclu-
sion on the matter, in this paper we prefer to assume, as one usually does,
that a single explosion caused the
Tunguska event. If there were many bodies, like in the case of the
Shoemaker{Levy 9 comet, all orbits would be
very similar and the differences between the individual or-bits would be
smaller than the di erences due to the
uncertainties in the parameters chosen.

Of course this is plausible just in the case of the hypothesis that Tunguska
was a
space impact.

Data on forest devastation include, not only fallen tree directions, but
also the distances that di erent kind of
trees were thrown, the pressure necessary to do this, infor-mation on forest
res and charred trees, data on traumas
observed in the wood of surviving trees, and so on (see, e.g., Florenskij
1963; Vorobjev et al. 1967; Longo & Serra
1995; Longo 1996). From this data, other parameters of the trajectory can be
obtained. First of all, the height of
the explosion and the trajectory azimuth.
The height of the explosion is closely related to the value of the energy
emitted, usually estimated equal to
about 10{15 Mton (Hunt 1960; Ben{Menahem 1975), al-though some authors
considered the energy value to be
higher, up to 30{50 Mton (Pasechnik 1971, 1976, 1986). In correspondence
with the rst energy range, which seems
to have better grounds, the height of the explosion was found equal to 6{14
km. A height of 10:5
 3:5 km was obtained by Fast (1963) from data on forest devasta-tion. Using
more complete data on forest devastation,
Bronshten & Boyarkina (1971) subsequently obtained a
3 Even though the term \epicentre" is not proper, we will use
it because it is now common in this type of studies. However,
it is worth noting that by epicentre we understand the rst
contact point between the Earth surface and the shock wave
from the airburst. 3
3 Page 4 5
1084 P. Farinella et al.: Probable asteroidal origin of the Tunguska Cosmic
height equal to 7:5  2:5 km. From seismic data, Ben{ Menahem deduced an
explosion height of 8.5 km. Data on
the forest devastation examined, taking into account the wind velocity
gradient during the TCB's ight (Korotkov
& Kozin 2000), gave an explosion height in the range 6{ 10 km.

Please, pay attention that majority of the height estimations were done by
comparing with results on nuclear explosions. Of course, the comparasion is
rather arbitrary - that's why the estimates varies from a few Mt, to 150 Mt!
Probably the most well-grounded result in the frame of hypothesis of a
explosion was by group lead by V.Korobeinikov (~17Mt in total, Hmax=6.5 km).
Again, it means just the general shape of the forest-fall could be produced
by a specially shaped explosive charge. But: 1) there are some problems
trying to calculate how a meteoroid disintegration could be equal to such
charge explosion. 2) Some details of the forest-fall cannot be produced even
by this
charge explosion anyway!
Remarkably, that practically nobody took into account peculiarities of taiga
vegetation in the region, which probably could alter the data.

To calculate the TCB's geocentric speed we used a
height equal to 8:5 km (see Sect. 2.2), which agrees, tak-ing into account
the uncertainties quoted, with the data
summarized herein and listed in Table 1. Two other parameters are needed to
compute the pos-
sible TCB orbits: the nal trajectory azimuth (a) and its inclination (h)
the horizon.
A close inspection of seismograms of Irkutsk station, made by Ben{Menahem
(1975), showed that the ratio be-
tween East{West and North{South components is about 8:1, even though the
response of the two seismometers is
the same. Since the Irkutsk station is South of epicen-tre, Ben{Menahem
(1975) inferred that this was due to
the ballistic wave and therefore the azimuth should be be-tween 90 and
180, mostly eastward. However, it is not
possible to obtain more stringent constraints on the az-imuth from seismic
Analysing the data on attened tree directions from the rst part of his
catalogue, Fast found a trajectory
azimuth a = 115  2 as the symmetry axis of the \but-ter y" shaped region
(Fast 1967). An independent math-
ematical analysis of the same data gave a = 114  1 (Zolotov 1969). Having
made another set of measure-
ments, Fast subsequently suggested a value of a = 99 (Fast et al. 1976). In
this second work, the di erences be-
tween the mean measured azimuths of fallen trees and a strictly radial
orientation were taken into account. No
error was given for this new value, but a close examina-tion of Fast's
writings suggests that an uncertainty of 2
was considered. The Koval's group subsequently collected complementary data
on forest devastation and critically
re{examined Fast's work. They obtained a trajectory az-imuth a = 127
 3 and an inclination angle h = 15  3 (Koval' 2000). The witness
accounts can be analysed to obtain in-
formation on the trajectory azimuth. A great part of the testimonies were
collected more than 50 years after the
event. They are often contradictory or unreliable.

It is important to know that the first "most reliable" accounts collected
right after the event pointed to trajectory from SSW to NNE (so that was
trajectory of "Tunguska meteorite" till 1950s)! And most of
"unreliable" accounts collected 50-60 years later pointed to from SE to NW
or even practically from E to W...
In other words the trajectory of the hypothetical Tunguska Space body was
rotated by meteorite-fall advocates for 90 degrees! It demonstrates the
of the meteorite-fall interpretation.... Moreover, some accounts were even
not placed into catalog of witnesses because they gave even more
different trajectories, as there were many luminous bodies in the region, as
in the case of a single Tunguska Space Body flight many of the eyewitnesses
could not see it at all!

However a thorough
examination of this material can give reason-
able results. We here report some important results of such analyses (see
Fig. 2, re{elaborated from Bronshten 2000c).
From a critical analysis of all the eyewitness testi-monies collected in the
catalogue of Vasilyev et al. (1981),
Andreev (1990) deduced a = 123  4 and an inclination angle h = 17
 4. Zotkin & Chigorin (1991) using the data in the same catalogue
obtained: a = 126  12 and h = 20
 12, while, from partial data, Zigel' (1983) de-duced h = 5 14. A di
erent analysis of the eyewitness data (Bronshten 2000c), gave a = 122
 3 and h = 15. Inthe samebook ameanvaluea = 103  4, obtained from
forest devastation data, is given.
Sekanina (1983, 1998) studied the Tunguska event on the basis of superbolide
theories and analysed the data
available and eyewitness testimonies. He suggested a geo-centric speed of 14
kms 1 (see the discussion in Sect. 2.2),
an inclination over the horizon h <5, and an azimuth a = 110.
All these values for a and h are listed in Table 1 and were used to choose
the starting parameters of our calcu-
lations listed in Table 4. When the experimental error is not explicitly
given, we used 1.

Those who read articles on determination of Tunguska body trajectory are
aware how the trajectory is used to be obtained. From several hundred
witness's accounts 99% are claimed as "unreliable" ones, and just a few ones
which are in agreement with the trajectory (which is favourable by an
author) are claimed to be
reliable and pointing to the trajectory. So it is not surprising that the
number of
trajectories is about the same as the number of the authors...

2.2. Calculation of the geocentric speed
One of the most important parameters that can be in-ferred from atmospheric
studies is the geocentric speed.
Even though the fragmentation of a small asteroid or comet depends on
several parameters, the speed appears
to be the key in the understanding of the impact physics. Once the speed is
known, it allows us to calculate the
mass (from the energy released in the explosion), and to have a rst, but not
conclusive idea about the na-
ture of the TCB. Indeed, dynamic studies of minor bod-ies in the Solar
System have long suggested that it is
very unlikely to nd an asteroid with a geocentric speed higher than about 30
32 kms 1 . Generally speaking, it is common among researchers on impact
physics, to con-sider indicative values of speed associated to speci c bod-
ies. For example, Chyba et al. (1993) used 15 kms 1 for
iron/stone/carbonaceous bodies (asteroids), 25 kms 1
for short period comets, and 50 kms 1 for long period comets. Hills & Goda
(1993) considered a set of values in-
ferior to 30 kms 1 for asteroids, and up to 70 kms 1 for comets. So, a TCB
speed of, for example, 50 kms 1 would
strengthen the hypothesis of cometary nature of the TCB.
Speed is strictly related to the break{up height of the cosmic body. In the
TCB's case, the height is known from
studies on the devastated area and seismic records (see Table 1). It is
therefore possible to calculate the speed, but
we need a model for fragmentation. Present models con-sider that
fragmentation begins when the following condi-
tion is ful lled:
2 = S (1)
where fr is the density of the atmosphere at the frag-mentation height, V
is the speed of the body, S is the
material mechanical strength, and is the drag coe-cient, commonly set equal
to 1 (sphere). The term frV 2
refers to the dynamic pressure on the front of the cosmic body. Adopting
these criteria, Sekanina (1983) suggested
a geocentric speed of 14 kms 1 .
However, observations of very bright bolides prove that large meteoroids or
small asteroids disintegrate at dy-
namic pressures lower than their mechanical strength (e.g. Ceplecha 1996;
see also Foschini 2001 for a recent review).
Therefore, Foschini (1999, 2001) developed a new model studying the
hypersonic ow around a small asteroid en-
tering the Earth's atmosphere. This model is compatible with fragmentation
data from superbolides. According to
Foschini's model, the condition for fragmentation depends on two regimes:
steady state, when the Mach number does
not change, and unsteady state, when the Mach number has strong changes. In
the latter case, the distortion of
shock waves interacts with turbulence, producing a local ampli cation of
dynamic pressure (Foschini 2001). In the
rst case, when the Mach number is constant, the com-pression due to shock
waves tends to suppress the turbu-
lence and therefore the viscous heat transfer is negligible and we can
consider the ux as adiabatic (Foschini 1999).
The Tunguska Cosmic Body was under these condi-tions in the last part of its
trajectory in the atmosphere,
therefore it is possible to calculate the maximum possible speed at the
point of fragmentation (Foschini 1999):

I am unaware about this new principal contribution in rather
well-established physics of atmospheric entry, moreover with the words
which sound surprising to me. So I prefer not to comment this part of
the article, untill I will read details, or the contribution will be
by experts in hypersonic aerodynamics).

where is the speci c heat ratio, is the coecient of ionisation. Foschini
(1999), using h = 8:5 km, = 1(full
ionisation), and = 1:7, found that the only reasonable solution is with S =
50 MPa (typical of a stony asteroid),
which leads to a speed of 16 kms 1 and an inclination of 3.
However, Bronshten (2000a) raised a doubt about the validity of the value of
the speci c heat ratio , which,
according to him, should be equal to 1.15, calculated from using the
Tabl e 2. Evaluation of maximum speed of the TCB for four
di erent compositions of the TCB and four di erent states of
the shocked air: (A) = 3, = 1, plasma; (B) = 1:7, = 1,
fully ionised gas; (C) = 1:15, = 0:5, partially dissociated
and ionised air at high temperature; (D) = 1:15, = 1,
dissociated and ionised air at high temperature. The values of
speed are expressed in [kms 1 ].
Type S [MPa] A B C D
Cometary 1 2.7 3.5 7.1 6.2
Carbonaceous Ch. 10 8.7 11.0 22.6 19.6
Stony 50 19.4 24.6 50.5 43.8
Iron 200 38.7 49.3 101.0 87.5
where K is the density ratio across the shock, which in turn is given by the
equation (see Zel'dovich & Raizer
K = 4+ 3Q trans  (4)
In the Eq. (4), the sum of Q and trans gives the internal energy of the
gas, i.e. the sum of translational energy trans
and Q, the potential energy and the energy of the internal degree of freedom
of the particles (vibrational and rota-
tional, for molecules). According to Eqs. (3) and (4), for air molecules
under shock compression reaches the value
of 1.15 (Bronshten 2000a). Foschini (1999) used a value of = 1:7, according
the experimental investigation of hypervelocity impact by Kadono & Fujiwara
(1996). Their original experimental
results gave a value of = 2:6, that the authors considered too high. They
modi ed the calculations considering that
the expansion velocity of the leading edge of the plasma was about twice
that of the isothermal sound speed, ob-
taining a more reasonable = 1:7.
However, none of the above mentioned authors con-sidered that the gas
envelope around any cosmic body
entering the Earth's atmosphere is in the state of plasma, in which there
are electric and magnetic elds (see e.g.,
Beech & Foschini 1999) limiting the degree of freedom of particles.
According to the law of equipartition of energy,
the speci c heat ratio can be written (Landau & Lifshitz 1980):
where l is the degree of freedom of particles. For example, l = 3 for a
monatomic gas or metal vapours, because the
atom has three degrees of freedom (translation of atoms along x, y, z
directions) and = 5=3. For plasma, the
presence of electric elds forces the ions or even ionised molecules, if
present, to move along the eld lines, and
therefore l =1.This implies that = 3, close to Kadono & Fujiwara's original
experimental value of 2:6 (Kadono
& Fujiwara 1996).
Tabl e 3. Evaluation of the mechanical strength of the TCB for
two di erent velocities and four di erent states of the shocked
air: (A) = 3, = 1, plasma; (B) = 1:7, = 1, fully ionised
gas; (C) = 1:15, = 0:5, partially dissociated and ionised
air at high temperature; (D) = 1:15, = 1, dissociated and
ionised air at high temperature. The values of strength are
expressed in [MPa].
V [kms 1 ] ABCD
14 26 16 4 5
16 34 20 5 7
We calculated a set of possible speeds, depending on the mechanical
strength, for di erent values of speci c
heat ratio and ionisation coecient (Table 2). Concerning the air density at
the fragmentation height, we have to
consider that the height of the airburst is not the point of rst
fragmentation. Generally, studies on superbolides
show that the break{up begins about one scale height be-fore the airburst.
So, we consider that the TCB began to
break up at about 15 km, to which corresponds a value of fr
 0:2 kg/m 3 (Allen 1976). As already noted by Ceplecha (1999, personal com-
munication; cf. Foschini 2000), the key point in fragmen-tation is how the
ablation changes the hypersonic ow.
If the ablation does not appreciably modify the shocked air around the TCB,
the carbonaceous body hypothesis
could be plausible. However, if the shocked air is mixed with ionised atoms
from the TCB so that the gas around
the body is fully ionised or even plasma, the only possible solution appears
to be an asteroidal body (stony or even
iron). The values obtained in Table 2 show that, in any case, it is very
unlikely that a cometary body could reach
such a low height, because it would have an unphysical low value of speed.
It should be noted that these results are only indica-tive: for S we have
considered the commonly used val-
ues of 1, 10, 50, and 200 MPa. On the other hand, if we start to search for
the mechanical strength from the speed
value, we obtain comparable results, with some interest-ing aspects. We know
that Sekanina (1983) suggested
V = 14kms 1 and Foschini (1999) found V = 16 kms 1 .
With the new fragmentation theory, we can calculate the mechanical strength
that the TCB would have to
up at the given height. Table 3 shows some results ob-tained in the same conditions for air ow as in Table 2. It
appears clear that the asteroidal nature of the TCB is still the most probable, even though cases (C) and (D) { the
Bronshten's values { have the strength of a carbonaceous body. The cometary strength is very close and, given the
large uncertainties, it is not possible to exclude it at all.

This part o
f the article clea
rly demonstrates that estimations are very arbitrary.
Being unable to get reliable theoretical estimations, it is reasonable
to look at real data with large meteoroid entries. The data clearly shows
even a several-tonn-mass stony meteoroid disintegrates well above ~6.5 km
height assigned to the hypothetical Tunguska Cosmic Body. And there is a
law that with increasing mass/dimentions of a body, its averaged strength
decreases. So the giant hypothetical Tunguska stony meteorite was to
disintegrate much more higher!
Due to the above-mentioned, all following calculations in the article based
on the trajectory data are of little practical value. So the remaining part
of the
article is omitted.
And finally I would like to make a couple of comments on the BBC story:

By BBC News Online science editor Dr David Whitehouse
Astronomers may have solved the
puzzle of what it was that brought so much
devastation to a remote region of Siberia almost a ce
ntury ago.
In the early morning of 30 June, 1908, witnesses told of a gigantic
explosion and blinding flash. Thousands of square kilometres of trees were
burned and flattened.
Scientists have always suspected that an incoming comet or asteroid lay
behind the event - but no impact crater was ever discovered and no
expedition to the area has ever found any large fragments of an
extraterrestrial object.
Now, a team of Italian researchers believe they may have the definitive
answer. After combining never-before translated eyewitness accounts with
seismic data and a new survey of the impact zone, the scientists say the
evidence points strongly to the object being a low-density asteroid.
They even think they know from where in the sky the object came.
Completely disintegrated

The "never-before translated eyewitness accounts" are well-known to Russian
Tunguska researchers. To tell the truth, I don't understand from the
what was this "combining" with seismic data? And what is new in the "new
of the impact zone"? The value of the evidence is well seen from above....

"We now have a good picture of what happened," Dr Luigi Foschini, one of the
expedition's leaders, told BBC News Online.
The direction of the flattened trees is a vital clue
The explosion, equivalent to 10-15 million tonnes of TNT, occurred over the
Siberian forest, near a place known as Tunguska.
Only a few hunters and trappers lived in the sparsely populated region, so
it is likely that nobody was killed. Had the impact occurred over a European
capital, hundreds of thousands would have perished.
A flash fire burned thousands of trees near the impact site. An atmospheric
shock wave circled the Earth twice. And, for two days afterwards, there was
so much fine dust in the atmosphere that newspapers could be read at night
by scattered light in the streets of London, 10,000 km (6,213 miles) away.

In reality, well-known British astronomer W. Denning wrote in "Nature" right
after the event that the bright nights commenced on June 29. Russian
scientists in 1908 came to similar conclusion....

But nobody was dispatched to see what had happened as the Czars had little
interest in what befell the backward Tungus people in remote central
Soil samples
The first expedition to reach the site arrived in 1930, led by Soviet
geologist L A Kulik, who was amazed at the scale of the devastation and the
absence of any impact crater.

The first Kulik's expedition arrived in 1927.

Whatever the object was that came from space,
it had blown up in the atmosphere and completely disintegrated.

Again without any proofs it is stated that it was a cosmic impact....

Nearly a century later, scientists are still debating what happened at that
remote spot. Was it a comet or an asteroid? Some have even speculated that
it was a mini-black hole, though there is no evidence of it emerging from
the other side of the Earth, as it would have done.
What is more, none of the samples of soil, wood or water recovered from the
impact zone have been able to cast any light on what the Tunguska object
actually was.
Researchers from several Italian universities have visited Tunguska many
times in the past few years.

I advise to look at the www-page: http://www-th.bo.infn.it/tunguska/
to read about these "many" visits.

Now, in a pulling together of their data and
information from several hitherto unused sources, the scientists offer an
explanation about what happened in 1908.
Possible orbits
They analysed seismic records from several Siberian monitoring stations,
which combined with data on the directions of flattened trees gives
information about the objects trajectory. So far, over 60,000 fallen trees
have been surveyed to determine the site of the blast wave.
Over 60,000 fallen trees have been surveyed to determine the site of the
blast wave
"We performed a detailed analysis of all the available scientific
literature, including unpublished eye-witness accounts that have never been
translated from the Russian," said Dr Foschini. "This allowed us to
calculate the orbit of the cosmic body that crashed."
The object appears to have approached Tunguska from the southeast at about
11 km per second (7 miles a second).

If the words about "detailed analysis of all the available scientific
literature, including unpublished eye-witness accounts...." don't need any
comments due to their arbitrary nature, this 11 km per second speed
is already very remarkable. It is the lowest possible speed for a space
object, which is non-orbiting our planet. In other words, trying to
explain the
very low altitude of the hypothetical Tunguska Space Body explosion they
had to accept the lowest possible value!

Using this data, the researchers were
able to plot a series of possible orbits for the object.
Of the 886 valid orbits that they calculated, over 80% of them were asteroid
orbits with only a minority being orbits that are associated with comets.
But if it was an asteroid why did it break up completely?
"Possibly because the object was like asteroid Mathilde, which was
photographed by the passing Near-Shoemaker spaceprobe in 1997. Mathilde is a
rubble pile with a density very close to that of water. This would mean it
could explode and fragment in the atmosphere with only the shock wave
reaching the ground."

Here it is a one more stumbling stone for "Tunguska Space Impact"!
If the hypothetical Tunguska Space Body was a "rubble pile", it was to
disintegrate very high in the atmosphere, and could not produce main energy
deposition at 6-7 km altitude. If it was some unusually strong Space Body
penetrating to the low height, it must leave a lot of remnants....
TO SUMM UP: The article demonstrates once again that attempts to explain
Tunguska by space impact continue to fail!
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