Current progress in the understanding of the physics ...

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Proceedings of the IMC, Egmond, 2016

Current progress in the understanding of the physics of large bodies recorded by photographic and digital fireball networks Manuel Moreno-Ibáñez1,2, Maria Gritsevich2,3,4, Josep Ma. Trigo-Rodríguez1 and Esko Lyytinen4 1

Institute of Space Sciences (IEEC-CSIC), Meteorites, Minor Bodies and Planetary Science Group, Campus UAB, Carrer de Can Magrans, s/n E-08193 Cerdanyola del Vallés, Barcelona, Spain [email protected], [email protected] 2 3

Finnish Geospatial Research Institute, Geodeetinrinne 2, FI-02431 Masala, Finland

Institute of Physics and Technology, Ural Federal University, 620002 Ekaterinburg, Russia [email protected] 4

Finnish Fireball Network, Helsinki, Finland [email protected]

The basic equations of motion of a meteor in the atmosphere require a concise knowledge about the body physical properties, such as the bulk density, shape, mass, etc. These properties do change during the flight and they also depend on the observations¶ reliability and camera resolution. The usual way of tackling this problem relies on using average values which are retrieved either from previous experience or from the observations available from the astrometric reduction of each specific event. Alternatively, a different approach is suggested. Instead of using the average values as input data, all unknowns can be gathered into dimensionless parameters, retrievable from the observations with the help of inverse techniques. This methodology has already been implemented in several scientific studies. In order to demonstrate the applicability of the model, we have already used archived data from the Meteorite Observation and Recovery Project (MORP) operated in Canada between 1970 and 1985 as well as selected recent fireball records from the Spanish Fireball and Meteorite Recovery (SPMN) Network. Recently, a correction which accounts for real atmosphere conditions has also been successfully included in the model. Our next steps foresee fireball data processing obtained by the Finnish Fireball Network (FFN) and the SPMN.

1 Introduction 7KH VWXG\ RI PHWHRURLGV LQWHUDFWLQJ ZLWK WKH (DUWK¶V atmosphere relies on both, the observations and the mathematical modelling. Current ground based observations consists of a distribution of photographic and video cameras managed by local entities or national institutions. Observations usually provide meteor atmospheric trajectory data, height and velocity (h, v); in some cases, for equipped instrumentation, spectroscopy data is released as well. Due to weather conditions and/or individual camera resolution, the observation accuracy is affected and data pre-analysis treatment is normally required. Meteor physical properties and flight dynamic behavior can be derived from well adjusted (h,v) data (see Ceplecha et al., 1998 for a detailed review) Initial meteor mass, terminal height, ablation, etc., are essential properties for further meteor science. Since Hoppe (1937) elaborated a strong mathematical formulation for these phenomena (known as Single body theory or classical theory), it has been extensively used in common meteor studies. This formulation relies on considering as constant a series of flight variables which cannot be known beforehand and cannot be obtained directly through observations. In addition, other input flight parameters required in the formulation are assumed to be the median values of previous studies, for instance the bulk meteor density is usually introduced in the equations of motion as a fixed value which depends on the assumed

meteor classification. Other relevant assumption is the atmospheric model required to solve the equations. An exponential atmospheric model behavior does work fairly well and leads to good results. However, the atmosphere conditions vary with time, location and height; thus, in some events this should be taken into account. Due to the large number of unknowns required by the classical theory, the resolution of the equations and the results shall be treated with care and extreme attention. Slight modifications in any parameter may lead to different results. Alternatively, the introduction of scale laws and dimensional study in the mathematical formulation can overcome these problems. Based on this, lead Stulov et al. (1995), Stulov (1997) and Gritsevich (2007) suggested a new way of resolving the equations of motion. As we will see later on this paper, their methodology reduces the number of unknowns down to two, which still show physical meaning. These two new parameters . DQG are easily retrievable from (h,v) data in most of the cases. On top of that, recent studies have succeeded in introducing alternative atmospheric models in this new mathematical formulation. In this paper we will take an overlook to this recent methodology and its applicability. The mathematical


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formulation will be described in Section 2. We will show the state-of-the-arts on this methodology in Section 3. In Section 4 we will discuss its capabilities and show further utilities. Finally, we will go through the main conclusions in Section 5.

retrieved from the observations (see Gritsevich, 2007, for further details). In principle, at least three (h,v) points, LQFOXGLQJWKHHQWU\YHORFLW\DUHUHTXLUHGWRGHULYH.DQG

3 State-of-the-art 2 Mathematical formulae The equations of the meteor atmospheric motion are well known and are usually projected to the tangent and normal of the trajectory (Gritsevich, 2007): / ×Û ×ç

×Ï ×ç

5

L F ?× éÔ 8 6 5 6

L F8 I Û

×Æ *Û ×ç

5

L F ?Û éÔ 8 7 5 6

(1) (2) (3)

In order to solve the system (1-3) extra equations are required. On the one hand the relationship between the instant meteor mass and dragging surface is considered: S/Se = (M/Me)µ , where µ expresses the rotation of the meteor during the flight. On the other hand, as stated previously, the atmosphere is usually considered as isothermal: !!0 = exp(-h/h0), where !0 is the atmospheric density at sea level and h0 =7.16 x 103 m is the scale height. Introducing dimensionless variables (M = Mem, V = Vev, h = h0y, S = Ses and !a !0!) and solving the resulting equations with the conditions \ and v = 1 (for details see Gritsevich (2007) : I L >F:s F R 6 ;Ú :s F ä;?

(4)

U L HJtÙ E Ú F HJ¿á % :Ú; F ' % :ÚR 6 ; ¿L ' ß

Where

% :T; L ìë Ø ' ?¶ ç

The resolution of these equations depends on two new variables. The parameter . is related to the drag intensity suffered by the meteor during its flight. It is called the ballistic coefficient and can be expressed as: 5

Ù L ?× 6

, Û, ÌÐ ÆÐ æÜá

(6)

The mass loss parameter characterizes the ablation of the meteor. It can be expressed as the fraction of the kinetic energy of the unit mass of the body that is transferred to the body in the form of heat divided by the effective destruction enthalpy:

Ú L :s F ä;

ÖÓ ÏÐ. 6ÖÏ Á Û

(7)

The derivation of parameters .DQG LVGRQH YLD a least squared method which adjusts (5) with the (h,v) data

This methodology was first implemented by Gritsevich (2008). She used the (h,v) data for four well known meteorite recoveries in order to discuss the accuracy of the methodology. This first study did also remark that, similarly to the classical theory, this recent methodology finds difficulties when meteor fragmentation is significantly present in the atmospheric flight. Gritsevich (2009) deULYHG . DQG SDUDPHWHUV IRU objects from the Meteor Observation and Recovery Project (MORP, Canada) and 121 objects from the Prairie Network (PN) database. This allowed the first large classification of fireballs and meteorites using accurate parameters. As can be seen in Figure1, meteorites (Innisfree, Lost City, Annama and Neuschwanstein) fall in a defined distant region of the diagram compared to the rest of fireballs. The location of the few Taurids registered in the PN database is also plotted. These carbonaceous chondrites mostly fall in another delimited area of the diagram. Thus, it seems that this methodology probes to be useful to set up a new classification based on this new accurate parameters. Gritsevich and Koschny (2011) included this dimensionless methodology when they tried to constrain the percentage of meteor kinetic energy emitted as light. This allowed them to include the meteor mass and velocity variations avoiding further assumptions on meteor bulk density, shape and initial mass. Later on, Moreno-Ibáñez et al. (2015) studied the efficiency of simplifications of the equations (4, 5) to describe accurately the terminal height of fireballs and meteorites. A global standard deviation of 0.75 km between observed and derived terminal heights was achieved when approximated functions were introduced in the simplified solutions. Finally, Lyytinen and Gritsevich (2016) suggested the way to successfully incorporate different atmospheric models in the dimensionless equation of motion. Using detailed height and atmospheric pressure probes to increase accuracy. If possible, local weather station information should be used. However, for most of meteor observations these data are not available. Detailed models such as the International Standard Atmosphere (ISA) model or MSIS-E-90 could also provide good results. A revised mathematical formulation should be done when real atmospheric conditions are to be considered (see Lyytinen and Gritsevich, 2016). Otherwise, for detailed atmospheric models, the exponential atmospheric model is still valid as along as individual heights are corrected for appropriate pressure values.

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Figure 1 ± 'LDJUDPVKRZLQJWKHFRPELQDWLRQRI/RJ.DQG/RJIRU0253DQG31GDWDEDVHHYHQWV based on Gritsevich et al. (2012), where the few Taurids registered by the PN are marked separately. We have also printed those values for Annama, Innisfree, Neuschwanstein and Lost City meteorites. Circles mark clearly different regions on the diagram for meteorites and the Taurids shower.

4 Discussion and further utilities The use of scaling laws and dimensionless variables in the meteor equations of motion lead Stulov et al. (1995), Stulov (1997) and Gritsevich (2007) to reduce the QXPEHURIXQNQRZQYDULDEOHVGRZQWRWZRSDUDPHWHUV. DQG7KHVHSDUDPHWHUVFDQEHH[SODLQHGSK\VLFDOO\DQG given that they are directly obtained by a least squared adjustment of the observational data, their accuracy mainly depends on that of the observations (thought the number of h,v points recorded and the part of the trajectory they represent is also relevant). This is also very convenient to set up new reliable classifications. We have printed in Figure 1 the few Taurids present within the Prairie Network data. The graphic expands results previously shown in (Gritsevich et al., 2012). In SDUWLFXODULWDOVRGHPRQVWUDWHVKRZWKHFRPELQDWLRQRI. DQGSDUDPHWHUVIRUWKH7DXULGVUHPDUNDEO\GLIIHUVIURP those of recovered meteorites. The inclusion of different atmosphere models is quite straightforward in this methodology compared to the single body theory, and provides more accurate results. This is quite helpful when dealing with extensive databases or particularly difficult events where atmospheric conditions could be crucial to determine further flight parameters. Furthermore, the dimensionless methodology has proved to adequately describe individual flight parameters. The terminal height is considered a key parameter that helps understanding the deceleration suffered by the meteor. An accurate derivation of its value from the mathematical formulae not only increases chances of any suitable meteorite recovery, but it also gives the opportunity of solving the inverse problem: obtaining the . DQG

parameters from complicated observations where maybe the last part of the fireball trajectory was recorded. Besides, other relevant parameters such as the ending mass or the ablation coefficient, are easily derived frRP. DQG The utilities of this new approach are various and most of them are still to be studied. For example, the time dependency of some final parameters (such as terminal height) could be used in the inverse problem to estimate the time length of the meteor flight. Systematic studies are also very convenient for these methodology, which will ultimately increase statistics and, hence, scientific knowledge. For instance, we foresee the derivation of . DQG YDOXHV IRU WKH 6SDQLVK 0HWHRU 1HWZRUN 6301 and the Finnish Fireball Network (FFN) databases. The SPMN scans the sky of the Iberian Peninsula either at day or night. Since its official kick off in 1997 (see Trigo et al., 2004; Madiedo and Trigo-Rodríguez, 2008), the cooperation between scientists and amateurs, along with fully equipped instrumentation (CCD all sky cameras, video cameras, photographic cameras, and spectrographs) and self-developed software have led to the registration of numerous fireballs and two meteorites: Villalbeto de la Peña ordinary chondrite and Puerto Lápice eucrite (e.g. Trigo-Rodríguez et al., 2006). Similarly, FFN spreads over Finland and neighboring countries in about 400000 km2 and does also rely on the co-work of amateur astronomers and scientists (Gritsevich et al., 2014). The initial operational start was in 2002 and it counts on the already mentioned instrumentation and their own software too (e.g. Lyytinen and Gritsevich, 2013). One of the latest cooperation between both networks led to the recovery, orbit

Proceedings of the IMC, Egmond, 2016 determination and parental relationship of the Annama H5 chondrite (Trigo-Rodríguez et al., 2015).

5 Conclusions The methodology reviewed in this paper has proved to work efficiently and accurately. Parameters .DQGVKRZ physical meaning and are potentially the basis of a new fireball and meteorite classification. The mathematical formulation is flexible enough so as to include different atmospheric models or real data provided by local weather stations. Besides, relevant meteor atmospheric flight parameters are easily derived from the main equations. Simplifications of the equations are also possible, and the accuracy of their results have already been checked. Future applications and improvements of this methodology are being studied. Problems such as fragmentation will require more study to be overcome. Finally, far from being opposite, the combination of both methodologies, classical and dimensionless, would be quite helpful in some cumbersome cases.

Acknowledgments This study was supported, by the Spanish grant AYA 2015-67175-P, by the Academy of Finland project No 260027, by the Magnus Ehrnrooth Foundation, and by the Act 211 of the Government of the Russian Federation (agreement No 02.A03.21.0006). This study was done in the frame of a PhD. on Physics at the Autonomous University of Barcelona (UAB).

195 ERGLHV ZLWK WKH (DUWK DWPRVSKHUH DQG VXUIDFH´ Cosmic Research, 50, 56±64. Gritsevich M., Lyytinen E., Moilanen J., Kohout T., Dmitriev V., Lupovka V., Midtskogen V., Kruglikov N., Ischenko A., Yakovlev G., Grokhovsky V., Haloda J., Halodova P., Peltoniemi J., Aikkila A., Taavitsainen A., Lauanne J., Pekkola M., Kokko P., Lahtinen P. and Larionov M. (2014). ³)LUVWPHWHRULWHUHFRYHU\ based on the observations by the Finnish Fireball 1HWZRUN´ In Rault J.±L. and Roggemans P., editors, Proceedings of the International Meteor Conference, Giron, France 18-21 September 2014. IMO, pages 162±169. Hoppe J. (1937). ³Die physikalischen Vorgänge beim Eindringen meteoritischer Körpe in die Erdatmosphäre´. Astronomsche Nachrichten, 262, 169±198. Lyytinen E. and Gritsevich 0 ³$IOH[LEOHILUHEDOO entry track calculaWLRQ SURJUDP´ ,Q *\VVHQV M. and Roggemans P., editors, Proceedings of the International Meteor Conference, La Palma, Canary Islands, Spain, 20±23 September 2012. IMO, pages 155±167 Lyytinen E. and Gritsevich M. (2016). ³Implications of the atmospheric density profile in the processing of fireball observations´ Planetary and Space Science, 120, 35±42.

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