Physical properties of meteoroids
based on observations
Maria Gritsevich 1, 2, Johan Kero 3, Jenni Virtanen 1, Csilla Szasz 3,
Takuji Nakamura 4, Jouni Peltoniemi 1, and Detlef Koschny 5
(1) Finnish Geodetic Institute, Geodeetinrinne 2, P.O. Box 15, FI-02431 Masala, Finland;
(2) Institute of Mechanics, Lomonosov Moscow State University, Russia;
(3) Swedish Institute of Space Physics (IRF), Box 812, 98128 Kiruna, Sweden;
(4) National Institute of Polar Research (NIPR), 10-3 Midoricho, Tachikawa, 190-8518 Tokyo, Japan;
(5) European Space Agency, ESTEC, Keplerlaan 1, Postbus 299, 2200 AG Noordwijk, The Netherlands
[email protected], [email protected]
“A space rock a few metres across exploded in
Earth’s atmosphere above the city of Chelyabinsk,
Russia today at about 03:15 GMT. The numerous
injuries and significant damage remind us that what
happens in space can affect us all…”
Sourse: www.esa.int (News, 15 February 2013)
Outline
Introduction
Physical model
Result testing
General statistics and consequences
Basic definitions
A meteoroid is a solid object moving in interplanetary space, of a
size considerably smaller than an asteroid and larger than an atom
A meteor is event produced by a meteoroid entering atmosphere.
On Earth most meteors are visible in altitude range 70 to 100 km
A fireball (or bolide) is essentially bright meteor with larger
intensity
A meteorite is a part of a meteoroid or asteroid that survives its
passage through the atmosphere and impact the ground
Past terrestrial impacts
~300 km
The largest verified impact crater on Earth (Vredefort)
Past terrestrial impacts
~300 km
~1,2 km
Different types of impact events, examples: formation of a massive single crater
(Vredefort, Barringer)
Past terrestrial impacts
~300 km
~1,2 km
~1,8 km
Different types of impact events, examples: formation of a massive single crater
(Vredefort, Barringer, Lonar Lake)
Past terrestrial impacts
~1,2 km
Dispersion of craters and meteorites over a large area (Sikhote-Alin)
Past terrestrial impacts
~1,2 km
~1,8 km
Tunguska
Tunguska after 100 years…
Area over 2000 km2
Impacts as a hazard
Impacts as a hazard
The population of
very small
meteoroids,
only possible to
study with radar ,
are a hazard to
satellites and
manned space
flight
Another reason why we are interested
…or:
The three forms of extraterrestrial bodies. Meteorites (right) are remnants of the
extraterrestrial bodies (asteroids, comets, and their dusty trails, left) entering Earth’s
atmosphere and forming an event called a meteor or fireball (middle). The dark
fusion crust on the meteorite is a result of ablation during atmospheric entry.
Radar measurements
allow us to calculate time profiles of:
meteor height
meteor velocity
meteor radar cross section
(ionization)
which gives us:
meteoroid atmospheric trajectory
meteoroid solar system orbit
possibility to model dynamics
Immediate objectives
understanding of meteorite origins, physical properties and
chemical composition
meteor orbital characteristics and their association with parent
objects
possible identification of when and where a meteor can enter
the Earth’s atmosphere and potentially become a meteorite
understanding of how to predict the consequences based on
event observational data
Radar measurements
An example of a Shigaraki MU radar meteor detected 2010-08-13 at 12:56:11 JST.
The entry into the atmosphere contains detailed dynamic observational data.
Important model input parameters are: height h (t) and velocity V (t).
Data interpretation
dV
M
dt
dh
dt
dM
H*
dt
1
cd
2
2
V
S,
a
V sin ,
1
ch aV 3 S
2
Introducing dimensionless parameters
dv
m
dy
vs
1
0 h0 Se
cd
;
Me sin
2
dm
dy
1
ch
2
2
2
h
S
V
v
s
0 0 e
e
M e H * sin
m = M/Me; Me – pre-atmospheric mass
v = V/Ve; Ve – velocity at the entry into the atmosphere
y = h/h0; h0 – height of homogeneous atmosphere
s = S/Se; Se – middle section area at the entry into the atmosphere
0;
0
– gas density at sea level
Two additional equations
variations in the meteoroid shape can be
described as (Levin, 1956)
S
Se
M
(
)
Me
assumption of the isothermal atmosphere
=exp(-y)
Analytical solutions of dynamical eqs.
Initial conditions
y = , v = 1, m = 1
m(v) exp
1 v2
1
y (v) ln 2
2
ln( E i ( ) E i ( v ))
x
where by definition:
Ei( x)
e z dz
z
The key dimensionless parameters used
1
0 h0 S e
,
cd
2 M e sin
1
2
e
ch V
,
2c d H
log m s
characterizes the aerobraking efficiency, since it is proportional
to the ratio of the mass of the atmospheric column along the
trajectory, which has the cross section S , to the body’s mass
is proportional to the ratio of the fraction of the kinetic energy of
the unit body’s mass to the effective destruction enthalpy
characterizes the possible role of the meteoroid rotation in the
course of the flight
Next step: determination of
On the right:
Data of observations of Innisfree
fireball (Halliday et al., 1981)
y (v) ln 2
2
ln(Ei( ) Ei( v ))
x
Ei( x )
e z dz
z
The problem is solved by the least
squares method
t, sec
0,0
0,2
0,4
0,6
0,8
1,0
1,2
1,4
1,6
1,8
2,0
2,2
2,4
2,6
2,8
3,0
3,2
3,3
h, km
58,8
56,1
53,5
50,8
48,2
45,5
42,8
40,2
37,5
35,0
32,5
30,2
27,9
25,9
24,2
22,6
21,5
21,0
and
V, km/sec
14,54
14,49
14,47
14,44
14,40
14,34
14,23
14,05
13,79
13,42
12,96
12,35
11,54
10,43
8,89
7,24
5,54
4,70
The desired parameters are determined by the following
formulas:
the necessary condition for extremum:
n
n
yi
e
i
i 1
n
n
i 1
;
i 1
n
exp( 2yi )
i
e
2
2 yi
i
i 1
exp( yi ) exp( yi )
(
i
( i) )
0
i 1
the sufficient condition:
n
n
2
i 1
((( i )
i
2
)
(
i
i
2 exp(
yi ) (( i )
i 1
2
n
exp( yi )(
i 1
i
( i) )
2( i )
i
)
1
Result of calculations for well
registered meteorite falls
fireball
102 , s2/km2
Ve, km/s
sin
20,887
0,68
8,34
13,64
6,25
Lost City
14,1485
0,61
11,11
1,16
1,16
Innisfree
14,54
0,93
8,25
1,70
1,61
Neuschwanstein
20,95
0,76
3,92
2,57
1,17
íbram
Graphical comparison
íbram
h
60
Lost City
40
Innisfree
20
5
10
15
20
V
Analytical solution with parameters found by the method (solid lines) is
compared to observation results (dots)
Neuschwanstein
1Spurny
et al.
2ReVelle
et al., 2004
Initial mass, kg
520 - 670 *
300 – 600 1
400 – 530 2
Our result corresponds to the estimates done based on the analysis of recorded
acoustic, infrasound and seismic waves caused by the meteorite fall
Distribution of parameters
MORP fireballs
and for
ln
3
2
1
0
-1
0
1
2
3
4
5
6
7
ln
-1
-2
-3
Innisfree
Looking for Meteorite ‘region’
Mt
M min , vt
1
ln
3
2
1
0
-1
0
1
2
3
4
5
6
7
ln
-1
3ln
ln mmin
-2
-3
sin = 0.7 and 1; Mmin = 8 kg
Innisfree
Meteorite falls prediction (down to 50 g)
Halliday et al., 1996
ln
3
2
1
0
-1
0
1
2
3
4
5
6
7
ln
-1
-2
-3
sin = 0.7 and 1; Mmin = 8 kg and 0.05 kg
Innisfree
Some historical events
Event
Original mass,
t
Collected meteorites,
kg
1
Canyon Diablo meteorite
(Barringer Crater)
> 106
> 30 103
0.1
0.1
2
Tunguska
0.2 106
-
0.3
30
3
Sikhote Alin
200
> 28 103
1.2
0.15
4
Neuschwanstein
0.5
6.2
3.9
2.5
5
Benešov
0.2
-
7.3
1.8
6
Innisfree
0.18
4.58
8.3
1.7
7
Lost City
0.17
17.2
11.1
1.2
Same events on the plane (ln , ln )
ln
( 2)
(1)
Crater Barringer
(2)
Tunguska
(3)
Sikhote Alin
(4)
Neuschwanstein
(5)
Benešov
(6)
Innisfree
(7)
Lost City
3
2
( 4)
1
(5 )
(6)
(7)
0
-3
-2
-1
0
1
-1
(1)
-2
-3
~1,2 km
(3 )
2
ln
Same events on the plane (ln , ln )
ln
( 2)
(1)
Crater Barringer
(2)
Tunguska
(3)
Sikhote Alin
(4)
Neuschwanstein
(5)
Benešov
(6)
Innisfree
(7)
Lost City
3
0<
< 1,
>1
2
>1, > 1
( 4)
1
(5 )
(6)
(7)
0
-3
-2
-1
0
1
2
-1
0<
(1)
< 1, 0 < < 1
> 1, 0 < < 1
-2
-3
~1,2 km
(3 )
ln
Meteorites /craters prediction
ln
(1)
Crater Barringer
(2)
Tunguska
(3)
Sikhote Alin
(4)
Neuschwanstein
(5)
Benešov
(6)
Innisfree
(7)
Lost City
( 2)
3
2
( 4)
1
(5 )
(6)
(7)
0
-3
-2
-1
0
1
-1
(1)
-2
-3
~1,2 km
(3 )
2
ln
Radar meteors
Conclusions
Consideration of non-dimensional parameters
and
allow us to predict consequences of the meteor impact.
These parameters effectively characterize the ability of
entering body to survive an atmospheric entry and reach
the ground. The set of these parameters can be also used to
solve inverse problems, e.g. evaluating properties of the
entering bodies when applied to high resolution radar
meteor observations (like MU and EISCAT).
The results are applicable to study the properties of nearEarth space and can be used to predict and quantify fallen
meteorites, and thus to speed up recovery of their
fragments.
Tack så mycket!
Kiitos kaikille!
Thank you very much!
A dynamical methods: special case
dV
M
dt
S
A
M
1
cd
2
2
V S,
(
a
2/3
b
2/3
Halliday et al.
Wetherill, ReVelle
d
3
V
2V
2
V
2V
2
3
V
2V
2
3
cd )
a
2
b
d
d
0,306
0 ,101
3
a
a
The main drawback is approximation of constant meteoroid shape, which
adopted in the majority of publications in Meteor Physics
The values of deceleration are obtained with the numerical differentiation
Why do we pass from y to exp(-y) ?
y
e
y
8
0.04
0.03
6
0.02
0.01
4
0
0.2
0.4
0.6
0.8
v
1
0
0.2
0.4
0.6
0.8
x
e
2
,
Ei
- Ei( v 2 ) ,
Ei( x )
e z dz
z
v
1
Newton's Second Law of Motion
dV
M
dt
1
cd aV 2 S Mg sin
2
dMV
dt
lim
MV
(M
dMV
dt
t
o
lim
t
o
dV
M
dt
1
2
cd aV S
2
MV
t
M )(V
MV
t
V)
lim
t
o
M (V U )
M V
MU
t
MV
dV
M
dt
Mass computation
3
Me
h
sin
1
cd
2
0 0
Ae
2/3
m
Initial Mass depends on ballistic coefficient
M (v)
1
cd
2
h
sin
0 0
Ae
2/3
m
3
exp
2
1
(1 v )