Physical properties of meteoroids based on observations Maria Gritsevich 1,, Johan Kero 3, Jenni Virtanen 1, Csilla Szasz 3, Takuji Nakamura 4, Jouni Peltoniemi 1, and Detlef Koschny 5 (1) Finnish Geodetic Institute, Geodeetinrinne, P.O. Box 15, FI-0431 Masala, Finland; () Institute of Mechanics, Lomonosov Moscow State University, Russia; (3) Swedish Institute of Space Physics (IRF), Box 81, 9818 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 99, 00 AG Noordwijk, The Netherlands maria.gritsevich@fgi.fi, kero@irf.se
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 013)
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, km Different types of impact events, examples: formation of a massive single crater (Vredefort, Barringer)
Past terrestrial impacts ~300 km ~1, km ~1,8 km Different types of impact events, examples: formation of a massive single crater (Vredefort, Barringer, Lonar Lake)
Past terrestrial impacts ~1, km Dispersion of craters and meteorites over a large area (Sikhote-Alin)
Past terrestrial impacts ~1, km Tunguska ~1,8 km
Area over 000 km Tunguska after 100 years
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 Impacts as a hazard
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 010-08-13 at 1:56:11 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 1 M c V S dt d a, dh dt V sin, dm 1 3 H* c VS dt h a
Introducing dimensionless parameters m dv dy 1 0hS 0 evs cd ; M sin e dm dy 1 c h h V v H * sin 0 0 e e s M e S m = M/M e ; M e pre-atmospheric mass v = V/V e ; V e velocity at the entry into the atmosphere y = h/h 0 ; h 0 height of homogeneous atmosphere s = S/S e ; S e 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 S ( M e M e ) assumption of the isothermal atmosphere =exp(-y)
Analytical solutions of dynamical eqs. Initial conditions y =, v = 1, m = 1 m( v) 1 v exp 1 y( v) ln ln( Ei( ) Ei( v )) where by definition: Ei(x) x e dz z z
The key dimensionless parameters used 1 c d M 0 e h0 Se, sin c h e 1, log s c d V H m 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 and On the right: Data of observations of Innisfree fireball (Halliday et al., 1981) y(v) ln ln( Ei( ) Ei( v x Ei( x) )) z e dz z The problem is solved by the least squares method t, sec h, km V, km/sec 0,0 58,8 14,54 0, 56,1 14,49 0,4 53,5 14,47 0,6 50,8 14,44 0,8 48, 14,40 1,0 45,5 14,34 1, 4,8 14,3 1,4 40, 14,05 1,6 37,5 13,79 1,8 35,0 13,4,0 3,5 1,96, 30, 1,35,4 7,9 11,54,6 5,9 10,43,8 4, 8,89 3,0,6 7,4 3, 1,5 5,54 3,3 1,0 4,70
The desired parameters are determined by the following formulas: the necessary condition for extremum: n n yi yi e i e ; i1 i1 n n n exp( y) exp( y) exp( y) ( ( ) ) 0 i i i i i i i i1 i1 i1 n n i i i i yi i i i i1 i1 n ((( ) ) ( exp( ) (( ) ( ) ) i1 the sufficient condition: exp( yi)( i ( i) ) 1
Result of calculations for well registered meteorite falls fireball Ve, km/s sin 10, s /km íbram 0,887 0,68 8,34 13,64 6,5 Lost City 14,1485 0,61 11,11 1,16 1,16 Innisfree 14,54 0,93 8,5 1,70 1,61 Neuschwanstein 0,95 0,76 3,9,57 1,17
Graphical comparison íbram h Lost City 60 40 Innisfree 0 5 10 15 0 V Analytical solution with parameters found by the method (solid lines) is compared to observation results (dots)
Neuschwanstein 1 Spurny et al. ReVelle et al., 004 Initial mass, kg 50-670 * 300 600 1 400 530 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 and for MORP fireballs ln 3 1 0-1 0 1 3 4 5 6 7 ln -1 - -3 Innisfree
Looking for Meteorite region ln M t M min, v t 1 3 1 0-1 0 1 3 4 5 6 7 ln -1 3ln ln m min - -3 sin = 0.7 and 1; M min = 8 kg Innisfree
Meteorite falls prediction (down to 50 g) ln Halliday et al., 1996 3 1 0-1 0 1 3 4 5 6 7 ln -1 - -3 sin = 0.7 and 1; M min = 8 kg and 0.05 kg Innisfree
Some historical events Event Original mass, t Collected meteorites, kg 1 Canyon Diablo meteorite (Barringer Crater) > 10 6 > 3010 3 0.1 0.1 Tunguska 0.10 6-0.3 30 3 Sikhote Alin 00 > 810 3 1. 0.15 4 Neuschwanstein 0.5 6. 3.9.5 5 Benešov 0. - 7.3 1.8 6 Innisfree 0.18 4.58 8.3 1.7 7 Lost City 0.17 17. 11.1 1.
Same events on the plane (ln, ln) (1) Crater Barringer ( ) ln () Tunguska 3 (3) Sikhote Alin (4) Neuschwanstein (5) Benešov (6) Innisfree 1 ( 4) (5 ) (7) Lost City (6) 0-3 - -1 0 1-1 (7) ln (1) - ( 3 ) -3 ~1, km
Same events on the plane (ln, ln) (1) Crater Barringer () Tunguska ( ) 3 ln (3) Sikhote Alin (4) Neuschwanstein 0 < < 1, > 1 >1, > 1 (5) Benešov 1 ( 4) (5 ) (6) Innisfree (6) (7) Lost City 0-3 - -1 0 1 (7) ln (1) 0 < < 1, 0 < < 1-1 - ( 3 ) > 1, 0 < < 1-3 ~1, km
Meteorites /craters prediction (1) Crater Barringer () Tunguska ( ) 3 ln (3) Sikhote Alin (4) Neuschwanstein (5) Benešov (6) Innisfree 1 ( 4) (5 ) (6) (7) Lost City 0-3 - -1 0 1-1 (7) ln (1) - ( 3 ) -3 ~1, km
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 near- Earth space and can be used to predict and quantify fallen meteorites, and thus to speed up recovery of their fragments.
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A dynamical methods: special case M c V S dt d a A dv S M 1 /3 b /3 Halliday et al. Wetherill, ReVelle, d ( c ) d b 0,306 V V 3 a av V 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 d 0,101 av d V 3 3 3
Why do we pass from y to exp(-y)? y 8 e y 0.04 6 0.03 0.0 4 0.01 0 0. 0.4 0.6 0.8 1 v 0 0. 0.4 0.6 0.8 1 v e, Ei - Ei(v ), Ei( x) x e dz z z
Newton's Second Law of Motion dv 1 dv 1 sin M c V S dt d a M c V S Mg dt d a dmv dt lim t o MV t MV ( M M )( V V ) M ( V U ) MV dmv MV M V MU dv lim lim M dt t o t t o t dt
Mass computation M e 1 c d h 0 0 sin A e / 3 m 3 Initial Mass depends on ballistic coefficient 1 0h0 A e M( v) cd exp (1 v ) /3 sin m 1 3