MASTER THESIS

Impact hazard assessment from the automatic detection of meteoric and reentry fireballs recorded by the SPMN network

Eloy Peña Asensio

SUPERVISED BY Josep Maria Trigo Rodríguez

TUTOR Miquel Sureda Anfres

Universitat Politècnica de Catalunya Master in Aerospace Science & Technology February 2020

Title of the master thesis

BY

Eloy Peña Asensio

DIPLOMA THESIS FOR DEGREE

Master in Aerospace Science and Technology

AT

Universitat Politècnica de Catalunya

SUPERVISED BY:

Josep Maria Trigo Rodríguez Institut de Ciències de l'Espai (IEEC-CSIC)

TUTOR: Miquel Sureda Anfres Departamento de Física - ESEIAAT

ABSTRACT

The disruption of asteroids and comets can produce meteoroids that end up impacting the Earth’s atmo- sphere, creating shock waves or even excavating craters so they generate hazardous scenarios. In this thesis different software tools have been developed with the aim of automating the detection and analysis of fire- balls from multiple station video recordings.

Given the automatic video processing, it opens the possibility of providing early warnings associated with shock waves and massive meteorite arrival to the ground.

As an example of reduction procedure two meteoric events have been analyzed, obtaining their real atmo- spheric trajectories, characterizing their flight and computing their respective heliocentric orbits. A method to estimate meteorite-dropping likelihood has also been implemented. In one of the study cases, NASA satel- lite data has been used to reconstruct the fireball trajectory and compute its mass and luminosity.

Finally, the implications for impact hazard assessment associated to meter-sized meteoroids are dis- cussed and assess in view of recent evidence.

Barcelona, February 2020

i

CONTENTS

List of Figures v List of Tables vii 1 Introduction 1 1.1 Meteoric Phenomena...... 1 1.2 Impact Hazard...... 3 1.3 SPMN Network...... 4 1.4 Thesis Goals...... 5 2 Methodology and Frameworks7 2.1 Software...... 7 2.2 Databases and Libraries...... 7 2.2.1 SAO...... 8 2.2.2 Astropy and PyEphem...... 8 2.2.3 Orbit Calculator Software...... 8 3 Automatic Detection and Analysis of Meteors9 3.1 Computer Vision Techniques...... 9 3.1.1 Moving Object Tracking...... 10 3.1.2 False Positive Avoidance...... 13 3.1.3 Star Identification...... 14 3.2 Photometry: Magnitude Estimation...... 17 3.2.1 Extinction Correction...... 17 3.2.2 Atmospheric Refraction Correction...... 17 3.2.3 Aberration of Light Correction...... 18 3.2.4 Aperture Photometry...... 19 3.2.5 Photometric Mass...... 20 3.3 Reconstruction of the Atmospheric Trajectory...... 21 3.3.1 Standard and Equatorial Coordinates...... 21 3.3.2 Extended Method...... 23 3.3.3 Extension for Fish-eye and Wide-Field Lens...... 24 3.3.4 Simplex Method...... 26 3.3.5 Stereoscopic Intersection...... 28 3.3.6 Measured Points Projection on the Averaged Trajectory...... 29 3.3.7 Characterization of the Atmospheric Flight...... 31 3.3.8 Radiant Computation: Zenith Attraction and Diurnal Aberration...... 35 3.4 Calculation of Errors in Radiant Determination...... 36 4 Study Cases 39 4.1 Taurid Fireball: SPMN251019B...... 39 4.2 Sporadic Superbolide: SPMN160819...... 45 5 Discussion: Implication for Impact Hazard 53 6 Conclusions and Future work 57 Bibliography 59

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LISTOF FIGURES

1.1 Illustration of meteoroids, meteors, fireballs, superbolides, meteorites and micrometeorites. Adapted from [Rendtel, 1993]...... 2 1.2 Schematic figure shows the intersection of images taken from two stations resulting in the me- teor’s trajectory. Adapted from [Roggemans, 1987]...... 5

3.1 Image processing block diagram of each frame of the recorded video...... 10 3.2 Frames from a real video of SPMN300319B fireball, an intermediate step in the processing and the final result. Depicted temporarily from left to right, and from top to bottom in processing. It is shown a first frame without a meteor, a detection of the meteor, a false positives due to glare, a rejected frame when explosion, a detection of the meteor being larger and the detection of the meteor trail...... 12 3.3 Basic scheme of operation of a Kalman filter...... 13 3.4 Simple example of classification using DBSCAN clustering algorithm. Red dots are classified as core, since yellow dots are attainable only by A they are core too and blue N point is considered noise...... 14 3.5 Clustering algorithm and statistical calculations for discard false positives and automatically select the points corresponding to the trajectory in a real case (SPMN300319B fireball 2.1). From left to right: All detected points, clusters found and noise, and selected cluster...... 14 3.6 Block diagram of the star plate coordinates finder algorithm...... 15 3.7 Sequence of the process of obtaining the coordinates of the stars in the photo. Depicted tem- porarily from left to right. Sequence of the process of obtaining the coordinates of the stars in the photo. It shows the first frame of the video, the overlapping of all valid frames without detec- tion, the application of the ORB algorithm after a logarithmic correction, the classification with the clustering algorithm and the final result. The second application of the cluster algorithm to merge the points very close to the stars has been omitted in this figure...... 16 3.8 Illustration of the refraction produced by the atmosphere on an observed star. Adapted from [Tatum, 2019]...... 18 3.9 Schematic drawing on the aberration of the light produced by the speed of Earth’s translation with respect to that of the light. The apex A, the north polar P and a random star X are shown.. 19 3.10 Conceptual scheme showing misalignment between the standard axes (ξ, η) and the plate axes (x, y). Adapted from [Roggemans, 1987]...... 22 3.11 Illustration of stereographic projections. On the left, a star Q and its projection Q0 are repre- sented. Q0 is on the tangent plane to the sphere at the optical center point C, which is the standard coordinate system. On the right, the North Celestial Pole P, its projection P 0 and the spherical triangle that define CPQ are also represented. Adapted from [Tatum, 2019]...... 22 3.12 The basis of the extended method is to consider the equations of the movements between the coordinate axes in the plane. Adapted from [Tatum, 2019]...... 24 3.13 Conceptual correction of barrel distortion produced by a wide-field lens...... 25 3.14 Application example of the Simplex method. The initial triangle is represented in blue, with P the largest error and M the smallest one. R is the substitution point for reflection, E for expan- sion and C for contraction. The calculated plate centre is depicted in purple...... 27 3.15 Block diagram of the Simplex method. Adapted from [Steyaert, 1990] and [Trigo-Rodriguez et al., 2005]...... 27 3.16 Graphical representation of the real meteor trajectory calculation by intersecting the planes and obtaining the radiant by projecting backwards until the collision with the celestial sphere. It is shown the vertical projection as well...... 28 3.17 Schematic diagram for radiant error computation. On the left, the two largest possible devia- tions for each apparent trajectory are shown, which delimits the margin of error of the calcu- lated radiant. On the right, the four possibilities of deviation assuming the worst case...... 37

v vi LISTOF FIGURES

4.1 SPMN251019B apparent trajectory recorded and reduced from Eivissa (a), Folgueroles (b) and Montseny (c). Reference stars and constellation are pointed out...... 41 4.2 SPMN251019B apparent radiant based on the records from Eivissa (orange), Folgueroles (red) and Montseny (green) plotted into the celestial sphere with propagation errors. Ecliptic, equa- torial plane and the nearby constellations of the Northern hemisphere are show...... 42 4.3 SPMN251019B atmospheric trajectory based on the records from Eivissa (orange), Folgueroles (red) and Montseny (green). Vertical projection (white) and observation range are shown..... 43 4.4 Plot of observational data with velocity normalized to entry velocity and height normalized to the atmospheric scale height for the SPMN251019B event...... 44 4.5 The bounding line for a 50 g meteorite is shown in black for the case where there is no spin (µ 0) and in gray where spin allows uniform ablation over the entire surface (µ 2/3)...... 45 = = 4.6 SPMN160819 apparent trajectory recorded and reduced from Eivissa (a), Sardinia (b) and Costa Brava (c). Reference stars and constellation are pointed out...... 48 4.7 SPMN160819 apparent radiant based on the records from Eivissa (orange), Sardinia (green) and Costa Brava (purple) plotted into the celestial sphere with propagation errors. Ecliptic, equato- rial plane and the nearby constellations of the Northern hemisphere are shown...... 49 4.8 SPMN160819 atmospheric trajectory based on the records from (orange), Sardinia (green) and Costa Brava (purple). Vertical projection (white) and observation range are shown...... 50 4.9 Plot of observational data with velocity normalized to entry velocity and height normalized to the atmospheric scale height for the SPMN160819 event...... 51 4.10 SPMN160819 flight parametrization. The bounding line for a 50 g meteorite is shown in black for the case where there is no spin (µ 0) and in gray where spin allows uniform ablation over = the entire surface (µ 2/3)...... 51 = 5.1 Typical CREAs for chondritic meteorites. Adapted from [Eugster et al., 2006]...... 55 5.2 Comparison of bolides with the same initial conditions but different ablation coefficients.... 55 5.3 The radar appearance of recently discovered extinct comet 2015 TB145 (NAIC-Arecibo/NSF)... 56 LISTOF TABLES

1.1 Impact frequencies and estimated victims depending on the object size. [NASA, 2007]...... 4

2.1 Table with the different events recorded by the SPMN network. Only the SPMN300318 event is from a only station since it has been used to illustrate the operation of the code. Thanks to the previously studied event SPMN220514 it has been verified that the results of the software are correct.∗The observation point does not belong to the SPMN network...... 8

4.1 SPMN251019B data reduction for the station Eivissa, Folgueroles and Montseny. SAO number, plate coordinates in pixels (x, y), standard coordinates (ξ, η), right ascension and declination and their respective errors are shown...... 40 4.2 SPMN251019B observed, geocentric and heliocentric computed radiant and the velocity, with their corresponding errors...... 40 4.3 SPMN251019B computed orbital parameters and their errors...... 44 4.4 SPMN251019B computed trajectory, velocity and mass data obtained from the observations.. 45 4.5 SPMN160819 data reduction for the station Eivissa. SAO number, plate coordinates in pixels (x, y), standard coordinates (ξ, η), right ascension and declination and their respective errors are shown...... 46 4.6 SPMN160819 observed, geocentric and heliocentric computed radiant and the velocity, with their corresponding errors...... 47 4.7 SPMN160819 computed orbital parameters...... 47 4.8 SPMN160819 computed trajectory, velocity and mass data obtained from the observations.... 52

5.1 Orbital definitions of the Near Earth Object groups and their respective acronyms (Adapted from NEO JPL)...... 54

vii

1 INTRODUCTION

1.1. METEORIC PHENOMENA Meteoric phenomena are in between the most wonderful events of the astronomy at naked eye. The meteor phenomenon fascinates the humanity since time immemorial. It has been interpreted as manifestations of gods, mystical omens or atmospheric events. It was not until recently, in the 20th century, when it began to be understood in detail.

Commonly these flashes of light that appear at night in the sky are called "shooting stars" or meteors. This phenomenon happens when rocks arrived from asteroids, comets or even planets, following heliocen- tric orbits through the Solar System cross Earth’s path. Interplanetary particles, called meteoroids, penetrate the Earth’s atmosphere at hypervelocity producing ionized columns of gas during the ablation of the particles [Opik, 1959]. This luminous phase is the meteor itself.

Due to the high speeds at which the meteoroids penetrate in the atmosphere (from 11km/s up to 73km/s), they experience strong aerodynamic deceleration and high temperatures. As it enters the atmosphere, the outer layers of the body melt and vaporize as the number of surrounding air particles increases. This en- tails an ionization of the air and an ablation of the body that produces emissions of light, observable from hundreds of kilometers on the Earth’s surface and from space [Ceplecha et al., 1998]. This luminous column begins to form when meteoroid materials collides with the components of the Earth’s atmosphere become frequent enough to generate a dense and luminous plasma curtain behind the meteoroid [Opik, 1959].

Although the meteoric phenomenon is unpredictable, there are certain permanent streams that are re- peated cyclically. More than a dozen major showers have been reported. The continuous erosion of asteroids and comets by solar irradiation and collisional gardening is the cause for the formation of meteoroid streams that fallow, at least initially, orbits similar to their parent bodies [Mott et al., 1953]. The encounter of the Earth with these stream produces the so-called meteor showers,in which the meteors come from the same radiant1. They are usually faint meteors with similar speeds that have recently come off their parent body, keeping their relative orbital affinity [Jenniskens, 2006].

It is called a bolide or fireball every meteor with a brightness greater than Venus (apparent magnitude2 of -4). Those bolides with apparent magnitude lower than the full moon (-14) are called superbolides [Trigo- Rodriguez et al., 2009]. The flight dynamics of the meteor is extremely complex due to the nature of the high speed atmospheric entry and rapidly changing parameters in short periods of time, for instance: de- celeration, ballistic coefficient, mass lost ratio, heat transfer coefficient, or rarified wake [Bronshten, 1983]. Depending on several factors fragments could partially survive the atmospheric entry and reach the ground. These rocks are called meteorites. Only bolides that penetrate very deep into the atmosphere can produce meteorites. Once the luminous trajectory ends, a point known as terminal height, a dark-flight begins un- til impact on the ground [Ceplecha et al., 1998]. New models are still being improved to calculate terminal

1The radiant of a meteor is the celestial point in the sky from which its path seems to be originated. 2Apparent magnitude (m) is a measure of the relative brightness of an astronomical objects as seen by an observer from the Earth.

1 2 1.I NTRODUCTION height and dark-flight [Moreno-Ibañez, 2018] and terminal mass [Gritsevich, 2008].

Our planet acquires interplanetary matter daily. On average, it has been measured that after one year the Earth accretes approximately 40000 tons of material from space [Peucker-Ehrenbrink and Schmitz, 2001]. It is estimated that the meteorites that reach the ground on average represent only 3% of the entire incoming pre-atmospheric mass [Ceplecha et al., 1998].

The origin of these objects mainly comes from comets or asteroids but from planetary bodies like Mars or Moon as well produced by impacts or outgassing events [Jenniskens, 1998]. In any case, large meteoroids are dominated by rocks coming from asteroids and evolved comets. According to the International Astronomical Union (IAU) these bodies are defined as:

• Asteroids, or minor planets, are rocky/metal bodies from one meter to 1000 km in diameter. Often they are remnants of larger bodies that suffered collisional disruption, so the are irregularly shaped celestial bodies. The known majority of them orbit the Sun in the called Main Asteroid Belt, between the orbits of the planets Mars and Jupiter.

• A comet is a weakly-bounded agglomerate of rock and ice, typically a few kilometres in diameter, which orbits the Sun. Comets may pass by the Sun only once or go through the Solar System periodically. A comet’s tail is formed when the Sun’s heat warms it, which releases gas and dust into space.

• A meteoroid is a solid natural object moving in interplanetary space of a size between 30 micrometers and 1 meter. They could come from asteroids, comets or even planets.

In the Figure 1.1 is depicted conceptually meteors, fireballs, superbolides and meteorites.

Figure 1.1: Illustration of meteoroids, meteors, fireballs, superbolides, meteorites and micrometeorites. Adapted from [Rendtel, 1993]. 1.2.I MPACT HAZARD 3

The interest of the study of meteors lies in the estimation of the meteoroid’s orbit through the study of its luminous path and, from this, determine its heliocentric orbit and origin in the solar system. In addition, studying the different spectra of the meteors it is possible to deduce some physical properties of the atmo- spheric entry process. Both studies allow to relate the meteoroids with the other Solar System objects even when there is no meteorite surviving the ablation.

Furthermore, the study of the meteor leads to the calculation of its atmospheric trajectory and radiant, which is critical to estimate the possible area of meteorite fall, as well as the risk of impact. The collection of meteorites and their subsequent laboratory study gives fundamental keys to better understand the composi- tion and the physical processes at work in planetary bodies. They are also a source of extraterrestrial minerals never before seen on Earth [Rubin, 1997] by studying the strange composition of the meteorites the scientists are able to read the stories of other worlds [Trigo-Rodriguez, 2012].

Some of these minerals are formed in the ablation process, which is usually a differential ablation at var- ious heights due to different vaporization temperatures [Gómez Martín et al., 2017]. It is here where spec- troscopy techniques play a key role, they can provide information about the processes in ablation as well as the identification of emission lines from rock-forming elements. Some examples of meteor spectroscopy applications are the study of delivery processes of exogenous materials to Earth or the understanding of cometary meteoroids components, which do not survive the atmospheric entry [Trigo-Rodriguez, 2019].

The meteoroid composition is as diverse as the population they come from. In the bolide population it can be found carbonaceous chondrites, ordinary chondritic, soft and regular cometary materials and nickel- iron alloys [Trigo-Rodriguez and Blum, 2009]. Meteorites are classified into four main groups: iron meteorite, stony-iron meteorite, primitive meteorite or chondrite and achondrite. A chondrite is an agglomeration of protoplanetary disk materials coming from undifferentiated bodies while an achondrite is the product of partial melting and crystallization on their parent bodies (larger asteroids or planets) [McSween et al., 1999]. Chondrite falls represent 82% of total meteorite dropping events [Grady et al., 2000]. By analyzing their iso- topic signatures it can be estimated the meteorite’s age and their parent bodies.

The recording of the luminous trajectories of fireballs allows to retain valuable information about the pre- atmospheric orbits of meteoroids, so they add rewarding dynamic knowledge about the origin of these rocks and about the physical processes that deliver them to Earth.

1.2. IMPACT HAZARD Probably the most famous extinction occurred 65 million years ago, at the same time as the impact of a large asteroid (a diameter of 10 km or more) on the Yucatán Peninsula [Hildebrand et al., 1991]. The agreement between environmental conditions of this era (deductibles of fossils and the composition of geological lay- ers) and the long-term conditions foreseen by theoretical models as a result of an impact of this magnitude (in particular, the darkness due to dust in suspension in stratosphere, changes in the chemical composition of the atmosphere and the corresponding decrease in temperature) do not leave much doubt about the fact that this impact has been the cause (or one of the main causes) of that mass extinction [Grieve, 1990].

Luckily, catastrophic events of these magnitudes have an estimated frequency of around 100 million years. However, the frequency of impacts increases as the size of the object decreases, reaching that a meteoroid of only 50 meters in diameter could produce 5000 victims, being its typical range of impacts of less than 300 years, see Table 1.1. Obviously the number of victims depends on the luck of being in the impact location,

Depending on its size and composition, an asteroid could cause extensive damage even without directly impacting the ground. Two emblematic events of this type are known in detail:

• The aerial explosion (airbust) of asteroid or cometary body origin with a diameter between 50 and 100 meters [Sekanina, 1998] at a height between 5 and 10 km above Tunguska in 1908, which released an energy of 10-15 Megatons of TNT and destroyed about 2.150 km2 of Siberian taiga. It is important to note that this event could have been produced by a fragment of comet 2P/Encke [Kresak, 1978]. 4 1.I NTRODUCTION

Type of Event Diameter Victims Frequency

High altitude break-up <50 m 0 annual Tunguska-like event >50 m 5,000 250-500 y Regional event >140 m 50,000 5,000 y Large sub-global event >300 m 500,000 25,000 y Low global effect >600 m 5 M 70,000 y Nominal global effect >1 km 1000 M 1 My High global effect >5 km 2000 M 6 My Extinction-class Event >10 km 6000 M 100 My

Table 1.1: Impact frequencies and estimated victims depending on the object size. [NASA, 2007].

The Taurid meteor stream is associated with the fragments of this comet and currently has particular relevance in impact hazard [Trigo-Rodriguez and Blanch, 2017].

• The aerial explosion occurred over Chelyabinsk (Russian) on February 2013. It was produced by a 18 meter in diameter asteroid disrupting in the atmosphere with an energy equivalent to 500 Kilotons at a height of 6 km. Its shock wave destroyed windows of the urban area causing a high number of injured [Brown et al., 2013]. In addition, current evidence supports that evolved comets can produce meter- sized meteoroids that are potential meteorite droppers with significant danger by shock waves, as it happened in Chelyabinsk event [Trigo-Rodriguez and Williams, 2017].

These events demonstrate that in the forecasting and prevention of risk by comets and asteroids, it is not necessary to take into account only the effective impact by bodies larger than hundreds of meters or kilo- meters in diameter, but also bodies of much smaller size that can constitute an effective risk of human and material damage due to the effects induced by the shock wave [Tapia and Trigo-Rodriguez, 2016]. The Tun- guska air explosion did not cause fatalities solely because of the fact that the area was practically uninhabited, but taking into account that the central part (about 200 km2) of the affected area was exposed to tempera- tures of up to 1.500 degrees, it can be concluded that such an explosion over a metropolis such as Barcelona would result in a very high number of victims.

In fact, m-sized rocks are the cause of meteorite falls in which, despite the fact that most of the mass is pulverized, it gives rise to generally cm-sized fragments that do not pose a great danger when reaching the ground as it has been seen, for example, in the fall of the Villalbeto de la Peña meteorite [Llorca et al., 2005]. In order to quantify the possible consequences for planetary defense of small asteroids, the atmospheric flight analyses of centimeter-size meteoroids impacting the atmosphere is fundamental. These small fragments usually come from the comets or parent asteroids that suffer a disruption, being a source of dangerous aster- oids [Trigo-Rodriguez et al., 2007].

The scientific-technological knowledge can allow to take measures aimed at mitigating risk in the case that a potential impact hazard becomes a real and current forecast of it, by estimating the mechanical prop- erties of the chondritic meteorites that are representative of the potential projectile [Moyano-Cambero et al., 2016]. For all the reasons above mentioned, there is a need to develop a detecting system with the appropriate instruments and data processing in order to obtain the most information about these unexpected phenom- ena and their implications for impact hazard.

1.3. SPMNNETWORK The meteor observation task differs from most other types of astronomical observations since these events cannot be predicted either in time or direction. Analysis during hours of visual observation suggests that the frequency in which a fireball occurs brighter than -3 is approximately every 300 hours [Rendtel and Knoefel, 1989]. For this reason it is necessary to have a monitoring system that can detect meteors continuously in real time. That is the goal of current fireball networks 1.4.T HESIS GOALS 5

There are currently different detection technologies such optical, radio, radars or infrasounds [Pichon et al., 2019]. This work focuses on optical observation of meteors using digital sensors.

From a single observation point it is only possible to record the apparent trajectory of a meteor projected on the background stars. Having several cameras in different locations allows to calculate the parallactic dis- placement and obtain the atmospheric trajectory, the height, the radiant, the distance to the stations and the speed of the meteor. It is illustrated in the Figure 1.2 how two station record a meteor.

Figure 1.2: Schematic figure shows the intersection of images taken from two stations resulting in the meteor’s trajectory. Adapted from [Roggemans, 1987].

As the higher is the number of observation points, more accurate are the results. Consequently, detection networks have been built in many parts of the world. For example: the Harvard Meteor Project [Jacchia and Whipple, 1956], the European Fireball Network [Ceplecha, 1957], the continental scale Desert Fireball Net- work (DFN) [Bland, 2004], the SPanish Meteor Network (SPMN) [Trigo-Rodriguez et al., 2005], the Finnish Fireball Network (FFN) [Gritsevich et al., 2014] or the French Fireball Recovery and InterPlanetary Observa- tion Network (FRIPON) [Colas et al., 2014].

All the data used in this work have been obtained by the Spanish Fireball and Meteorite Network (SPMN) that is coordinated from the Institute of Space Sciences in Barcelona. The network is made up of 30 stations 3 and consists of two systems: 1) An all-sky CCD camera (180◦) with fish-eye lens and detectors of 4096x4096 pixels [Trigo-Rodriguez et al., 2005], and 2) a wide-field video system (90◦ to 120◦) working at 25 frames per second up to 50 frames per second by deinterlacing4 [Madiedo and Trigo-Rodríguez, 2007]. For the first sys- tem, the entire sky can be recorded with 100% time coverage and reaching stellar magnitude between 8 and 10. In the case of the second instrumentation, the typical configuration is using 3 cameras per station cover- ing 120x90◦ up to limiting magnitude 4. + The camera with the CCD sensor records both the stars of the sky and the apparent trajectory of the meteor in a discrete way, which is known as stereographic projection. This registered pixel position will be converted to a real position in the sky.

1.4. THESIS GOALS The aim of this work is to develop a software that automatically detects meteors from digital systems, com- pletes the astrometric measurements and computes their real trajectory, velocity and radiant. It will charac- terize the atmospheric flight, such as velocity, height, length and magnitude. In order to improve the accuracy,

3Charge-coupled device (CCD) is a technology for the movement of electrical charge used in digital image sensor. 4The ratio frames per second can be doubled by using even-odd sub-frames. 6 1.I NTRODUCTION in this process will be applied correction such light aberration, refraction, zenith attraction, diurnal aberra- tion and atmospheric extinction. The possibility of an event producing meteorites will also be estimated.

In addition to this, a graphic interface with a 3D model will be programmed, which allows to easily check the results and illustrate the calculation process. It will also facilitate star identification tasks and trajectory reconstruction.

The developed code is tested using two real cases detected by the SPMN network, one not producing meteorite and other from a clear meteorite-dropping bolide that was also recorded by NASA satellites, and reported in the online fireball list of the Center for Near Earth Object Studies (JPL/NASA).

To reduce elusive superbolides sometimes requires using different source of data. This is also exemplified as one of the events studied requires the interpretation of satellite data to reconstruct the fireball trajectory. From the trajectory data and the radiant computed, the heliocentric orbits of both events are estimated in order to understand their origin. It is particularly important to deduce if they are sporadic events or instead belong to a known meteor shower, because the later could reproduce the hazard in the future.

Finally, the main implications of these studies for impact hazard are discussed. 2 METHODOLOGYAND FRAMEWORKS

For the choice of development tools it has been decidedly to bet on open-source. Much of this work would not have been possible without the support and contribution of the entire community1 that openly shares its knowledge and progress.

The development of a graphical interface based on a three-dimensional model has a double function in this work. On the one hand it fulfils one objective of facilitating the tasks of identifying stars and disseminat- ing scientific content by making this tool more accessible to different users. On the other hand, throughout the development of the software, the graphic representation has been used to verify errors and confirm that the calculations were correct. This has been possible thanks to the geometric nature of the operations pre- formed.

2.1. SOFTWARE Given its growing expansion and settlement as a standard programming language in many fields, it has been chosen to program in Pyhton 3.7. Currently it is, without any doubt, the established language in computer vision and is increasingly used in the astrophysical community, having a multitude of tools already made and shared. In addition, thanks to developers, it has excellent libraries for data analysis and representation.

The development environment used has been JetBrains’s PyCharm, which provides an integrated and connected framework.

To facilitate mathematical operations, the well-known scientific computing libraries Scipy and Numpy have been used. It has been taken advantage of their vector calculation tools, system equations solver, matrix treatment, etc. For the computer vision part, the OpenCV library has been used, which provides multiple tools of image processing for real-time application. It is optimized to use GPU so it considerably reduces the calculation time. Given the large number of elements used on the graphic representations of the created ste- larium (more than 4000 stars), it has been necessary to use a rendering engine. The scientific data visualizer Mayavi has been chosen. This tool has allowed to make a representation of 3D objects with smoothed rota- tion and zoom capability.

2.2. DATABASES AND LIBRARIES For the realization of this work, three different events recorded by the SPMN network have been studied, which are shown in the Table 2.1. In addition to the data collected by the SPMN network itself, it has been necessary for the calculations to have access to different stellar datasets used to complete the astrometric measurements.

1Special emphasis on the platform https://stackoverflow.com/.

7 8 2.M ETHODOLOGYAND FRAMEWORKS

Name Stations Longitude Latitude Altitude Date Time (UTC)

SPMN300319B Santiago 08◦3301900W 42◦5203300N 236 m 2019/03/30 19h48m45s

Eivissa 01◦250450E 38◦5402100N 45 m SPMN251019B Folgueroles 02◦1903300E 41◦5603100N 580 m 2019/10/25 04h36m46s Montseny 02◦320010E 41◦4304700N 194 m

Eivissa 01◦250450E 38◦5402100N 45 m SPMN160819 Costa Brava∗ 03◦0401000E 41◦4900300N 2 m 2019/08/16 20h36m00s Sardinia∗ 08◦310430E 39◦5403700N 30 m

Table 2.1: Table with the different events recorded by the SPMN network. Only the SPMN300318 event is from a only station since it has been used to illustrate the operation of the code. Thanks to the previously studied event SPMN220514 it has been verified that the results of the software are correct.∗The observation point does not belong to the SPMN network.

2.2.1. SAO Files of the entire SAO2 catalog contain more than 250,000 stars, including positions, proper motions, magni- tudes and so on. It has been the most appropriate stellar catalog since it offers visual spectrum measurements similar to the range in which the detection cameras work, greatly facilitating the process. This has allowed the most visible stars to be easily identified and filtered.

To obtain the classified data, the VizieR3 tool has been used, which offers filtered search services for as- tronomical catalogs. Data referenced to J20004 have been used, which means that refers to the instant of 12 noon (midday) on January 1, year 2000. This correspond to the so-called 2000.00 equinox.

2.2.2. ASTROPYAND PYEPHEM Since in the photographs and videos taken, planets of the Solar System can also appear, which can be the brightest bodies at night, it has been necessary to introduce their location in the celestial sphere at the time of the observation, using ephemeris.

The complete calculation of the orbits of the planets has been avoided for a matter of time and limitation of computing power. This has been done using PyEphem5, a library that implements astronomical algo- rithms. Thanks to the software packages Astropy6, witch has an updated database, it is possible to access it with an internet connection. Entering the date and the planet of interest, returns its exact position.

These data packages has also been used for the identification of stars, being able to manually write the name of the star and automatically get the position. In addition, it facilitates various temporary calculations as well as unit handling. Finally, Astropy has assisted as well in the manually introduction of the constella- tions represented in the 3D model.

2.2.3. ORBIT CALCULATOR SOFTWARE Once the astrometry of the videos is done and the atmospheric trajectory has been reconstructed, it will be vital for the impact hazard study to be able to associate a given event with some meteor stream. For this purpose, it is necessary to obtain the origin orbit and apply some similarity method, for instance, criterion D, proposed by [Drummond, 1980], which analyses the angle between the Laplace vectors of the two orbits. In this regard, [Langbroek, 2004] did a spreadsheet to calculate the orbit of the meteor from radiant and velocity data. It will be used to compute the orbital parameters and their associated errors

2The Smithsonian Astrophysical Observatory (SAO) Star Catalog is an astrometric star catalogue published by the Smithsonian Astro- physical Observatory. 3http://vizier.u-strasbg.fr. 4A Julian year is an interval with the length of a mean year in the Julian calendar. 5https://rhodesmill.org/pyephem/. 6https://www.astropy.org/. 3 AUTOMATIC DETECTIONAND ANALYSIS OF METEORS

One of the main tasks of this thesis has been the development of a software package written in Python with multiple functionalities and as automated as possible, with the aim that in the future both the detection, as the characterization of atmospheric flight and the determination of the heliocentric orbit may be calculated immediately after the event. The software developed has been called SPMN 3D Fireball Trajectory and Orbital Calculator (3D-FireTOC), which produces realistic 3D representations. It will be used to analyze the cases of study and their implications for impact risk assessment.

In order to obtain the real trajectory of the meteor in the atmosphere, it is necessary to have recorded, at least from two far enough stations, a sequence of frames of its flight. It was previously tested that the minimum distance to get enough parallax to measure distance and proper radiant determination is about 20 km [Trigo-Rodriguez, 2002]. The obtained video data will have to be processed in parallel before it can be combined. It has been necessary to apply computer vision and astrometric data reduction techniques to be able to approximate the real meteor positions. For this purpose, computer vision techniques, coordinate system operations, optical distortion correction and parallax computation have been used. The main steps of the process are set out below:

• Meteor trace detection by using moving object tracking methods.

• Star identification.

• Equatorial coordinate transformation with optical distortion correction.

• Real atmospheric trajectory reconstruction by computing parallax.

3.1. COMPUTER VISION TECHNIQUES Computer vision is a engineering field focused in creating systems capable to understand digital videos or images [Ballard and Brown, 1982]. Roughly, it is an attempt to simulate and automate the human vi- sion.Acquiring, processing and analyzing digital data are the main tasks that computer vision has to accom- plish. Methods that, taking high-dimensional data from real world, generate numerical information.

This digital data, in this work, is a combination of video frames from multiple cameras located in record- ing stations separated by tens to hundreds of kilometers. These computer vision techniques have been used to detect the movement of the meteor in the monitored field and to identify the stars that appear in the im- ages.

9 10 3.A UTOMATIC DETECTIONAND ANALYSIS OF METEORS

3.1.1. MOVING OBJECT TRACKING To detect a movement in the image it is necessary to compare each frame with a reference frame in which it is known that there is no moving object.

The meteor path should be first obtained, together with each pixel for every frame that represents the evolution of the meteor. In practice this requires some treatment because the low resolution and the contrast found.

The first thing to be done is the image conversion into gray scale, in this way it can easily work with the image as an array, where each element represents the intensity of a pixel between black (0) and white (255).

Since often appears a flare along the meteor column as a consequence of a sudden release of micron- sized dust that is quickly ablated increasing the luminosity [Trigo-Rodríguez et al., 2006], it makes a correct position measurement impossible. Before continuing with the image processing, the average intensity of the pixels is calculated. If this mean is above a tolerance compared to the average reference frame, the frame is rejected. After that, it is applied a Gaussian function, called Gaussian blur. This operation smooths the image causing it to lose some detail but removing noise.

The next operation calculates the per-element absolute difference between two arrays. It is applied to each frame with the reference frame without movement, resulting in the change value of the pixels. Since due to the sensitivity of the optical system and the light conditions, as well as the stars present flashes, almost all the pixels of the image will show some variation, even if it is small. For this reason it is necessary to discrimi- nate changes that are not sufficiently relevant. This is achieved with a threshold.

In order to make the detection easier, morphological transformations have been applied. Specifically, the dilation transformation has been used. This operation consists of convoluting the image with a kernel. It cal- culates the highest value pixel within the kernel and replace the kernel center point with that maximal value.

Then, a finding contour algorithm is used [Suzuki and Abe, 1985]. This algorithm is based on topological structure analyzes and uses Green’s theorem and image moment 1. Basically this method detects the closed edges, being an edge a sharp change in an area of pixels. Having the contours, the area of each of them has been calculated to discriminate by size. Excessively small and large ones are eliminated. This prevents possible false positives such as flashes, improvised obstacles or incorrect trajectory points when the meteor explodes.

Finally, the centroids of the remaining contours are calculated, which represent the meteor path. This process is outlined conceptually in the block diagram of Figure 3.1.

Figure 3.1: Image processing block diagram of each frame of the recorded video.

1An image moment is a weighing of the image pixels’ intensities 3.1.C OMPUTER VISION TECHNIQUES 11

Sometimes because of the optical system or format conversion, some frames are corrupt. The code has become robust being able to deal with corrupt frames without stopping and warning what they are.

A very light image process is obtained, capable of being executed in real time thanks to the libraries used that are optimized for GPU 2.

The Figure 3.2 shows a selection of frames from a real event (SPMN300319B Table 2.1), an intermediate step in the process sing and the final result. They are depicted temporarily from left to right, and from top to bottom in processing. It is shown a first frame without a meteor, a fireball’s detection, a false positive due to glare, a rejected frame when explosion, a detection of the meteor and the detection of the meteor trail.

2A graphics processing unit (GPU) is a co-processor dedicated to graphics processing by fast altering memory. 12 3.A UTOMATIC DETECTIONAND ANALYSIS OF METEORS Figure 3.2: Frames from a realshown video a of first SPMN300319B frame fireball, without an a intermediate meteor, a step detection in of the the processing meteor, and a the false final positives result. due to Depicted glare, temporarily a from rejected left frame to when right, explosion, and a from detection top of to the bottom meteor in being processing. larger and It the is detection of the meteor trail. 3.1.C OMPUTER VISION TECHNIQUES 13

3.1.2. FALSE POSITIVE AVOIDANCE Due to the changing nature of fireball recordings, it is not possible to guarantee that false positives are com- pletely avoided with filters applied to frame processing. For this reason, two different methods are proposed to deal with this problem: a Kalman filter and a clustering algorithm.

A Kalman filter is an iterative mathematical process to quickly estimate values, that is, an optimal estima- tion algorithm to predict a future state of the system. The Figure 3.3 shows a scheme of the filter operations. Basically after collecting a series of input data, this is the first points detected, the filter adjusts itself to be able to make a prediction of the next point.

Figure 3.3: Basic scheme of operation of a Kalman filter.

The operation of the Kalman filter as a method to avoid false positives is simple: using the previous points, it generates a prediction of the next one. Focusing on this estimated point, it defines an area of validity, so any point outside this area will not be considered. This method gives good results as long as the first points detected are correct. As this is not always the case, since depending on the observation point the bolide can begin at its highest luminous peak phase, this method is only applicable to recordings where clearly the be- ginning of the light trace is smooth and constant. As an alternative to the Kalman filter, a method has been developed to avoid false positives based on a clustering algorithm that can work for all types of cases.

However, Kalmnan filter cannot always be applied successfully. The alternative is to apply criteria to rule false positives out after detection process. Unlike the Kalman filter method that works at the time of detec- tion, it will be apply clustering algorithms in a post-processing phase to remove incorrect detection. The designed discard method consists in applying a clustering algorithm and statistical calculations. The algo- rithm used is the density-based spatial clustering of applications with noise (DBSCAN) [Ester et al., 1996]. It finds a number of groups or clusters starting with an estimate of the density distribution of the corresponding nodes. It is a non-parametric algorithm.

In Figure 3.4 it can be seen that red dots are classified as core, since they are within a certain area and having at least a number of previously set elements. They form a single cluster since each of the red dots can reach any of the others. The same does not happen with the yellow dots but being attainable only by A already count as in the same cluster. The blue N point is considered noise.

To demonstrate the effectiveness of the algorithm, the brightness tolerance and the minimum size of de- tectable contours have been reduced, so that false positives increase and it can bee seen its behavior in the worst case.

As seen in Figure 3.5, the algorithm finds many different clusters, among them it can be observed the ap- parent trajectory of the meteor.

To automate the selection of the appropriate cluster, that is, the one corresponding to the trace, knowing 14 3.A UTOMATIC DETECTIONAND ANALYSIS OF METEORS

Figure 3.4: Simple example of classification using DBSCAN clustering algorithm. Red dots are classified as core, since yellow dots are attainable only by A they are core too and blue N point is considered noise. that the trajectory will be practically a straight line and that the false positives due to the flashes follow a random distribution, the linear regression of each cluster is computed and the one with the best coefficient of determination3 is chosen.

Figure 3.5: Clustering algorithm and statistical calculations for discard false positives and automatically select the points corresponding to the trajectory in a real case (SPMN300319B fireball 2.1). From left to right: All detected points, clusters found and noise, and selected cluster.

Apparent trajectory points are achieved in a fairly precise manner, the gaps observed in the middle of the trace correspond to the explosions, while some frames are discarded for exceeding the average brightness tol- erance. Just in case the automatic selection fails, a manually cluster selection option has been programmed.

The two proposed methods can be executed in parallel and perform a cross-matching to determine the reliability of the detected points and improve the final result.

3.1.3. STAR IDENTIFICATION In order to create an automated process that works for all cases, it has been excluded the classic star iden- tification image processing. This would have been to make a threshold at a certain value to only obtain the bright points, which would correspond to the stars and would be found by a finding contour algorithm. The limitation of this method is the changing nature of the images captured. They present too many light changes that make it impossible to find a threshold value that always works well. Nor can this value be estimated for each frame since there may be light pollution, clouds or obstacles.

For these reasons an alternative method is proposed. Figure 3.6 shows a conceptual scheme of the most important code steps to automatically find the coordinates of the stars in the frame.

Taking advantage of the motion detection process, each frame has been written in a folder and the associ- ated information has been saved. Thus, frames associated with an error, an excess of brightness or detection are known. This data will be used to overlap all frames that have not any of those characteristics. In essence,

3It is an estimate of how well the variance of the dependent variable can be predicted from the independent one. Typically written as R2. 3.1.C OMPUTER VISION TECHNIQUES 15

Figure 3.6: Block diagram of the star plate coordinates finder algorithm. an overlapping of the valid frames without detection is performed in order to soften the image to be identi- fied. This will highlight the stars and reduce noise or spontaneous flashes. As the last image processing, a logarithmic correction4 is applied to improve the result.

Since a star over the black sky is similar to a corner, it has been used Oriented FAST and Rotated BRIEF (ORB) descriptor [Rublee et al., 2011]. It is a method used to extract corners and infer features of an image. ORB uses the Features from Accelerated Segment Test (FAST) keypoint detector [Rosten and Drummond, 2006] and the Binary Robust Independent Elementary Features (BRIEF) descriptor [Calonder et al., 2010]. It is a quick process and the results are acceptable for images with very different conditions. The presence of clouds, artificial illumination sources or obstacles generates incorrect points, which will be subsequently eliminated. On the other hand the CCD chip contain failures or hot pixels5 that might produce wrong detec- tion and should be removed as well.

For the elimination of these wrong points, the same DBSCAN clustering algorithm is used as in the sub- section 3.1.2. For the motion detection was required to find the cluster that corresponds to the trajectory. However now, since stars appear in the sky far from each other in an apparently random distribution, the data labelled as noise by the cluster algorithm will be that is of interest.

Finally, due to the sparkles of the stars, ORB finds different corners in the surroundings near each star. The clustering algorithm is again used this time adjusted for these few nearby points, replacing all the points of each small cluster with their midpoint.

If the method fails, options have also been programmed to manually remove incorrect points and to add stars with the mouse over a zoomed area. Once the desired coordinates in the image are obtained, the code will loop over the stars allowing the user to manually enter their names, getting their right ascension and dec- lination thanks to Astropy.

Figure 3.7 shows some of the most relevant steps of this process applied to a real fireball case (SPMN300319B 2.1) filmed from the Montseny SPMN station (see Table 2.1 for more details).

4After scaling each pixel to the range 0 to 1, this function transforms the image according to the equation O g ain log(1 I). = ∗ + 5Pixels that appear when camera sensor gets hot during long exposures. 16 3.A UTOMATIC DETECTIONAND ANALYSIS OF METEORS Figure 3.7: Sequence of thephoto. process It of shows obtaining the the first coordinatesalgorithm frame of and of the the the final stars result. video, in The the the second overlapping photo. application of of Depicted all the temporarily valid cluster from frames algorithm left to without merge to detection, the right. the points application very Sequence of close of to the the the ORB process stars algorithm has of after been obtaining a omitted the in logarithmic coordinates this correction, of figure. the the classification stars with in the the clustering 3.2.P HOTOMETRY:MAGNITUDE ESTIMATION 17

3.2. PHOTOMETRY:MAGNITUDE ESTIMATION In order to properly estimate the bolide’s magnitude it is necessary to apply different corrections to the refer- ence stars that will be used as a comparison. The magnitudes associated with each star found in the catalog are not the magnitudes observed from Earth. This is due to different physical phenomena produced by the atmosphere and the Earth motion, which must be correct in order to obtain proper results.

3.2.1. EXTINCTION CORRECTION The extinction is the absorption and scattering of electromagnetic radiation by particles between an astro- nomical object and the observation point. The atmosphere of our planet absorbs by these physical processes the stellar light that is consequently attenuated. This fact is very significant when celestial objects are a few degrees above the horizon, the phenomenon is known as atmospheric absorption. The method proposed by International Comet Quarterly (ICQ) will be applied. This method will be applied for zenith distances greater than 70◦.

Atmospheric extinction is due to the fact that the light rays must travel more distance the further they are from the zenith. The correction used is based on tables that will modify the magnitude of the refer- ence stars. These tables were calculated based on theoretical values for different atmospheric conditions by [Green, 1992].

Using the tables, the variation of the magnitude ∆m corresponding to the observation height is obtained. Subtracting this difference from the reference magnitude mre f , the apparent magnitude mapp is obtained:

m m ∆m (3.1) app = re f − The intermediate values will be obtained by linear interpolation.

3.2.2. ATMOSPHERIC REFRACTION CORRECTION Applying Snell’s law, a relationship is reached between true zenith distance z and the apparent zenith distance ζ: sinζcos² cosζsin² n sinζ (3.2) + = being ² z ζ. Assuming ² is very small and dividing by : = − z ζ (n 1)tanζ (3.3) − = − Although the refractive index at sea level may change with pressure and temperature, it has been esti- mated that on average n-1 = 58"2 (in arcseconds).

It is necessary to calculate the local sidereal time (LST) of the station at the time of the event, which together with the right ascension allow calculate the hour angle of the star H. First it has to be computed the Julian date of the event:

7 (Y ear (Month 9)/12) 275 Month Hour Minute JD 367 Y ear · + + · Day 1721013.5 + (3.4) = · + 4 + 9 + + + 24

then, the Greenwich Mean Sidereal Time (GMST) can be calculated:

GMST 18.697374558 24.06570982441908 (JD 2451545) (3.5) = + · − being LST : Longi tude LST GMST (3.6) = + 15 and H: H LST α (3.7) = − 18 3.A UTOMATIC DETECTIONAND ANALYSIS OF METEORS

By applying spherical astronomy methods it can be obtained the true zenith distance z and azimuth A:

z arccos¡sinφsinδ cosδcosδcos H¢ (3.8) = + and µ sin H ¶ A arctan (3.9) = cosφtanδ sinφcos H − where φ is the latitude of the station. Applying spherical trigonometry and operating it can be computed the apparent declination δ0, apparent hour angle H 0: ¡ ¢ δ0 arcsin sinφcosζ cosφsinζcos A (3.10) = + and µ sin A tanζ ¶ H 0 arctan (3.11) = cosφ sinφcos A tanζ − And then, the apparent right ascension α0:

α0 LST H 0 (3.12) = − Just for example, when a bolide appears on the horizon, this correction could be up to a couple of degrees.

Figure 3.8: Illustration of the refraction produced by the atmosphere on an observed star. Adapted from [Tatum, 2019].

3.2.3. ABERRATION OF LIGHT CORRECTION The aberration of light is a phenomenon that occurs due to the vector difference between the Earth’s velocity and the light’s velocity. The effect of this aberration is to displace the star towards the direction of movement of the Earth, which is known as apex6. Because the speed of the earth is on average 29.8km/s, the error intro- duced by the aberration will not be too large, of the order of a few tenths of a degree. Even so, it is a factor to take into account to perform high accuracy astrometry.

By using Lorentz transformations the velocity components can be expressed as:

v cosχ c cosχ0 + = 1 ¡ v ¢cosχ + c (3.13) sinχ sinχ0 = γ¡1 ¡ v ¢cosχ¢ + c

p 2 7 where γ is the Lorentz factor 1/ 1 (v/c) and χ the true apical distance , being therefore χ0 the apparent − apical distance.

6The apex is where the ecliptic intersects the observer’s meridian at 6 hours local apparent solar time. 7The angle between the approach direction and with the direction to the apex. 3.2.P HOTOMETRY:MAGNITUDE ESTIMATION 19

From 3.13 and assuming v/c 1 << v sinχ δχ χ0 χ (3.14) = − ≈ − c p where γ is the Lorentz factor 1/ 1 (v/c)2. − Taking Figure 3.9 as a reference, it is calculated by spherical trigonometric ω and ψ. And applying cotan- gent formula and operating: sinωsinθδθ sinψcscχ2δχ (3.15) =

Figure 3.9: Schematic drawing on the aberration of the light produced by the speed of Earth’s translation with respect to that of the light. The apex A, the north polar P and a random star X are shown.

This enable to compute the apparent right ascension of the star:

¡ v ¢ c sinψcscχ α0 − α (3.16) = sinχsinω +

And, by using cosine formula, the apparent declination can be calculated:

δχ ¡ ¢ δ0 cosψsinχ sinψcosωcosχ δ (3.17) = cosδ − + +

3.2.4. APERTURE PHOTOMETRY To estimate the apparent magnitude of the bolide, a method knows as aperture photometry will be applied. This technique consists in selecting the minimum radius that encloses the stars, paying attention that this does not exceed the frame’s edges. It is necessary to choose a frame that does not appear the meteor in order to not alter the luminosity. A mask will be applied on each star leaving only the circle that contains it. Then, it will be add up the counts, that is, to count the each pixel value between 0 and 255 (gray scale), where 0 is black and 255 white.

The counts of each star in the image are associated with its magnitude in the S AO catalog, this apparent magnitude corresponds to optical V band between 500 and 600 nm. It is important to remark that digital CCD sensors usually have sensitivity in between 300 and 1000 nm, but meteor light is not a continuous, but produced by the emission in specific wavelengths [Trigo-Rodriguez et al., 2003].

Since the reference stars are light points that move slowly through the camera’s visual field, they will re- main a considerable time in the same position, activating the same group of pixels. This can cause these pixels to become saturated or because of the exposure time they could represent a higher brightness level 20 3.A UTOMATIC DETECTIONAND ANALYSIS OF METEORS than they would have with an instant exposure. Since what is observed from the meteor is its trail, which is an exposure of fleeting light, the brightness of the stars must have to be corrected depending on their an- gular velocity in the frame. This relative speed is related to declination. Consequently, it has to be reduced the star magnitudes to a reference declination. Using the method proposed by [Rendtel, 1993] the apparent magnitude of the stars can be corrected as follows:

1 m(δs ) m(δ0◦ ) 2.5p log (3.18) = − cosδs where p is the Schwarzschild exponent8, typically between 0.7 and 0.8.

Once the magnitudes are corrected, a linear regression of all the reference stars and their counts is made. In this way it is correlated from the meteor counts its apparent magnitude. The apparent magnitude is a value that includes the actual meteor-observer distance ratio. To obtain an useful value of the observation, the absolute magnitude of a meteor has been set by definition as: the magnitude observed at a distance of 100 km. This serves to standardize the information extracted from the fireball luminosity. The first step for this is to obtain the magnitude if the meteor would have been observed at the zenith, this is called zero-magnitude star. Then, the magnitude is corrected using its altitude recorded from the station:

m(δ ) m(δ ) 5logsin Al t (3.19) zeni th = m − m Once the magnitude is obtained from a reference point, taking into account the height of bolide, the magnitude at 100 km of distance is estimated as:

hm m m(δ0 ) 5log (3.20) abs = ◦ − 100 The magnitude is not only one of the main parameter for the identification of meteors, but it is also key to obtaining the photometric mass.

3.2.5. PHOTOMETRIC MASS The brightness emitted during the atmospheric flight of a bolide varies during its penetration. A proportional relationship between the emitted light and the ablation rate can be set assuming that the deceleration is not relevant from a frame to the following one. Thanks to the photometric techniques discussed above it can be obtained the measured luminosity flux Ip at zero-magnitude star units by:

2 m I 10 −5 abs (3.21) p = As suggested by [Ceplecha, 1988], the initial photometric mass mp can be computed thanks to the classi- cal mass-luminosity equation by integrating the meteor light curve:

t Z b Ip mp 2 2 dt (3.22) = te τv

where the integration limits tb and te correspond to the beginning and the end of the meteor, v the ve- locity and τ the luminous efficiency. The luminous efficiency is a critical parameter when estimating the meteoroid mass, which is poorly constrained by observational data. Different observational and experimen- tal techniques have been proposed to determine the mass from the light emitted by the fireball, however these methods give very different results reaching differences of up to several orders of magnitude. Due to the poor ability to characterize in detail the ablation process and the precision of the instruments used in the observations, this parameter is not too reliable. However, the method proposed by [Verniani, 1967] has been implemented as a first approximation in order to compare results with other methods not based on brightness and to draw conclusions about the limitations of photometric mass techniques. In this way, by integrating the luminosity equation and adding the drag equation results:

2 µ ¶3 2ρmE a τ 2 2 (3.23) = v¯ γAρa v

8It is a parameter that relate exposure time and speed. 3.3.R ECONSTRUCTIONOFTHE ATMOSPHERIC TRAJECTORY 21

being E: Z tb E 2 Ip dt (3.24) = te

where a is the deceleration, ρm the meteor density, γ the drag coefficient, A the shape factor, ρ0 the at- mospheric density, v¯ the velocity in some instant.

In addition the luminous efficiency errors are not well determined since several assumptions need to be made. This together with the fact that the error in the estimation of the magnitude is high, make the photometric mass an unreliable estimation.

3.3. RECONSTRUCTIONOFTHE ATMOSPHERIC TRAJECTORY Since meteors are a luminous phenomena that occur in our atmosphere, the perspective is completely lost and it is impossible to reconstruct their real trajectory by seeing them from a single place on the earth’s sur- face. For this reason the paths in the sky are known as apparent trajectories.

Therefore, in order to know the atmospheric trajectory followed by a meteoroid at its atmospheric entry, it is necessary to record it from at least two stations. From each station the meteor will appear projected on a different stellar background. With those images it can be reconstructed the geometry of the meteor’s appear- ance with respect to the recording stations and finally its real trajectory in the atmosphere can be computed by applying astrometric techniques.

The relevance of obtaining the atmospheric trajectory lies in the determination of the apparent radiant from which the meteor seems to originate in the celestial sphere. This will be described later on. Once a meteor has been registered from several stations there will be several of recordings in which the meteor is projected on the celestial background. Each station obtains an image in which the meteor, due to have been seen from a different place, will change its apparent trajectory among the stars. Knowing the start and end time of the pictures and the time of the meteor’s appearance, the meteoric path is first identified in the images depending on the location of the stations.

In each image a part of the sky is projected on a CCD chip device. The photographic objective provides a distorted image of the celestial sphere,as it is the result of the projection on the focal plane of a sphere. This is called stereographic projection.

3.3.1. STANDARD AND EQUATORIAL COORDINATES In order to determine the real trajectory of a meteor in the atmosphere, it is necessary to measure the ap- parent trajectory of the meteor with respect to the stars recorded in the video recording. Since the meteor appears projected on the sky, to obtain in detail the start and end positions of the meteor it is used equatorial coordinates9. This means that it has to be found a way to transform the position of a pixel into equatorial coordinates.

However, this transformation needs intermediate steps. Stereographic projection and camera sensor are not necessarily aligned: camera axis may not be perpendicular, so appear some unknown optical axis center or rotation and translation distortions. Figure 3.10 shows some possible misalignments. Thus, it is necessary to perform a transformation of the coordinates for each pixel in the image (plate coordinates) to stereographic projected coordinates, also known as standard coordinates. In Figure 3.11 it is assumed that the optical axis of the camera is pointing to the point C on the celes- tial sphere, with a right ascension and declination (A,D) and a focal length F . Also, the plane tangent to the sphere in point C is represented. This point marks the origin of the orthogonal axes (ξ, η), which is the bi-dimensional system of standard coordinates. It is depicted a star Q with coordinates (α, δ) on equatorial coordinates and its projection Q0 on the tangent plane. To help the interpretation of the image, the North Celestial Pole P and its projection P’ have also been drawn, defining a spherical triangle.

9It is a coordinate system with origin at the centre of Earth, a primary direction towards the vernal equinox and a right-handed conven- tion. 22 3.A UTOMATIC DETECTIONAND ANALYSIS OF METEORS

Figure 3.10: Conceptual scheme showing misalignment between the standard axes (ξ, η) and the plate axes (x, y). Adapted from [Rogge- mans, 1987].

Figure 3.11: Illustration of stereographic projections. On the left, a star Q and its projection Q0 are represented. Q0 is on the tangent plane to the sphere at the optical center point C, which is the standard coordinate system. On the right, the North Celestial Pole P, its projection P0 and the spherical triangle that define CPQ are also represented. Adapted from [Tatum, 2019]. 3.3.R ECONSTRUCTIONOFTHE ATMOSPHERIC TRAJECTORY 23

It can be obtained from the spherical system (α, δ) the position of the projected point P 0 or Q0 in a rect- angular coordinate system (xr , yr ,zr ) as:

x r cos(α A) cosδ r = · − · y r sin(α A) cosδ (3.25) r = · − · z r sinδ r = · where r is a parameter that represents the radius of the sphere.

From this expression it can be obtained the equations deduced by [Steyaert, 1990] that relate the equato- rial coordinates to standard coordinates:

cosδ sin(α A) ξ − · − = cosD cos(α A) cosδ sinD sinδ · − · + · (3.26) sinD cos(α A) cosδ cosD sinδ η − · − · + · = cosD cos(α A) cosδ sinD sinδ · − · + · Similarly, it is deduced the transformation of standard coordinates into equatorial coordinates:

µ ξ ¶ α A arctan = + η sinD cosD Ã · − ! (3.27) η cosD sinD δ arctan p · + = ξ2 (η sinD cosD)2 + · −

3.3.2. EXTENDED METHOD As a first approximation, the relation between standard and plate coordinates can be expressed linearly as:

ξ x ax by c − = + + (3.28) η y dx ey f − = + + Where a,b,c,d,e and f are parameters that must be adjusted and are called plate constants. The system will have to be resolved to obtain the relation between coordinates. This is known as the Schlesinger method.

But based on axis’s misalignment previously commented, it is necessary to introduce factors that model the possible variation in rotation, translation or scaling. Geometric elements appear that establish depen- dencies between the plate coordinates (x, y) and the standard coordinates (ξ, η).

Defining K as the scale ratio, (xo, yo) as the translation vector and β the rotation angle, from Figure 3.12 it fallows then the relation between the coordinates measured on the plate and the standards is:

µξ¶ µ cosβ sinβ¶ µx x ¶ K − o (3.29) η = sinβ cosβ · y y − − o Defining the following variables:

cosβ xo cosβ yo sinβ v1 v3 + = K = − K (3.30) sinβ xo sinβ yo cosβ v2 v4 − = K = − K

and being i 1,2,...,k, where k is the total number of reference star, the equation 3.29 can be expressed = as: 24 3.A UTOMATIC DETECTIONAND ANALYSIS OF METEORS

Figure 3.12: The basis of the extended method is to consider the equations of the movements between the coordinate axes in the plane. Adapted from [Tatum, 2019].

ξi xi v1 yi v2 v3 = + − (3.31) η y v x v v i = i 1 − i 2 + 4 Operating the previous expressions applying trigonometric formulas [Steyaert, 1990] obtains:

1 K q = v2 v2 1 + 2 µ ¶ v2 β arctan = v1 (3.32) v3v1 v4v2 xo − + = v2 v2 1 + 2 v3v2 v4v1 yo − − = v2 v2 1 + 2 It can be written, for a general system of n reference stars, the matrix equation as:

    ξ1 x1 y1 1 0 η  y x 0 1  1   1 − 1  ξ  x y 1 0v   2   1 2  1     η2  y2 x2 0 1v2    −   (3.33)   =  v3  ·   ····     v4  ·   ···· ξn  xn yn 1 0 η y x 0 1 n n − n

3.3.3. EXTENSIONFOR FISH-EYEAND WIDE-FIELD LENS As previously said, the SPMN network operates two systems: all-sky CCD [Trigo-Rodriguez et al., 2005] cam- eras and wide-field video cameras [Madiedo et al., 2009]. Both systems use wide-field lenses that produce barrel distortion, therefore, the correction method used is the same for both of them and from now on, only fish-eye lens will be named. This type of distortion causes the image to be much more deformed near the edges. A correction is necessary because, otherwise, the measured positions would have very large errors. Figure 3.13 shows a non-rigorous example of correction just to clarify what is being explained.

To model the distortion caused by the fish-eye lens, the measured radial distance from the center of the plate r is replaced by a function f (r ). It is used the proposed f (r ) by [Steyaert, 1990]. 3.3.R ECONSTRUCTIONOFTHE ATMOSPHERIC TRAJECTORY 25

Figure 3.13: Conceptual correction of barrel distortion produced by a wide-field lens.

f (r ) r a r 2 = + · q (3.34) r ξ2 η2 = +

Now it is necessary to modify the method to include a as an additional plate constant more. The system proposed above 3.33 is then replaced by:

  q 2 2 x1 y1 1 0 ξ1 ξ1 η1    − q +  ξ1  2 2  y1 x1 0 1 η1 ξ1 η1  η1   − − q +     2 2 v1 ξ  x1 y2 1 0 ξ2 ξ η   2   − 2 + 2  v    q  2 η2  y x 0 1 η ξ2 η2      2 − 2 − 2 2 + 2 v3 (3.35)   =     ·   v4    ·····   ·    a ξn   ·····q   2 2  η xn yn 1 0 ξn ξn ηn  n  − q +  y x 0 1 η ξ2 η2 n − n − n n + n

The parameter a can always be added, even when the camera has no fish-eye lens since its value would simply be close to zero.

This model has been tested for fish-eye correction in different cases and it has been found that it some- times creates a false impression that the method is converging but does not. Since it does not exhibit reliable behavior, the use of a new model is proposed.

Equivalent to the extended method 3.30, a quadratic relationship between the coordinates of the plate and the real ones is proposed by [Hawkes, 1993]:

ξ x ax2 2hx y by2 2g x 2f y c − = + + + + + (3.36) 2 2 η y a0x 2h0x y b0 y 2g 0x 2f 0 y c0 − = + + + + +

There are 12 plate constants so at least 6 reference stars will be necessary to solve the problem. The system of equations 3.36 for n reference stars is computed as follows: 26 3.A UTOMATIC DETECTIONAND ANALYSIS OF METEORS

 ξ x  x2 2x y y2 2x 2y 1 0 0 0 0 0 0 a  1 − 1 1 1 1 1 1 1 η y   0 0 0 0 0 0 x2 2x y y2 2x 2y 1 h   1 − 1   1 1 1 1 1 1    x  x2 2x y y2 2x 2y 1 0 0 0 0 0 0 b   ξ2 2   2 2 2 2 2 2    −   2 2   η2 y2   0 0 0 0 0 0 x2 2x2 y2 y2 2x2 2y2 1 g   −         f   ·   ············      c   ·   ············  (3.37)   =  a0  ·   ············     h      0  ·   ············     b0  ·   ············     g 0  ·   ············2 2   ξn xn   0 0 0 0 0 0 xn 2xn yn yn 2xn 2yn 1f 0 − 2 2 η y x 2x y y 2x 2y 1 0 0 0 0 0 0 c0 n − n n n n n n n

to simplify 3.37 can be expressed as X Mv. =

3.3.4. SIMPLEX METHOD The only thing missing to perform the coordinate transformation is to calculate the position of the optical axis (A,D). There is no analytical method to directly find the position, so iterative procedures that approxi- mate the solution are used, minimizing the error. This is done by applying the simplex algorithm [Motzkin, 1951].

A simplex is a polygon that has a vertex more than the dimension of the space where it is defined. Conse- quently a simplex in the plane is a triangle. The simplex method is a recursive algorithm applied to approx- imate the best value of the center of the plate based on the reference stars introduced, which minimizes the 10 2 T 1 T mean squared error J (Mv X ) , where v (M M)− M X . This method consists of previously assigning = − = an approximate value of the center (Ao,Do), which is linearly estimate, and computing an initial measure of the quadratic error J.

From that point (A ,D ) it is constructed a simplex with the vertices of the triangle: P(A ,D ), M(A o o o o o + ²,D ) and N(A ,D ²), where ² symbolizes a small angular increase. o o o +

The quadratic error is calculated for each vertex and it is discarded the largest one. As depicted in Figure 3.14, being JP the worst quadratic error vertex and JM the best one, P is replaced by another point generated according to any of the following mechanisms:

• Reflection: Being RO OP with O midpoint of MN, the new vertex R replaces P if JM JR JP. = < <

• Expansion: If R is that JR JM JP, then new vertex E is calculated with EO 2OP. If E is that < < = JE JR, E substitutes P. If not, R will be the new vertex. <

• Contraction: If R is that JZ JP JR, then new vertex C is calculated with CO OP/2. If C is that < < = JC JP, then C substitutes P. <

• Shrinkage: Finally if JP JC, a compression is made towards M with PS PM/2 and NS NM/2. < 1 = 1 =

One of the advantages of this method is that it always converges. As the block diagram of Figure 3.15 shows, the recursive process will end when a termination criterion is met, set in the number of iterations.

After applying the simplex method, the position of the optical axis (A,D) and the camera constants are obtained. The system of equations 3.36 to convert the plate coordinates (x, y) into standard coordinates (ξ,η). Finally it will be enough to apply 3.27 to obtain the equatorial coordinates of the apparent trajectory.

10It measures the average squared difference between the estimated values and the actual value. 3.3.R ECONSTRUCTIONOFTHE ATMOSPHERIC TRAJECTORY 27

Figure 3.14: Application example of the Simplex method. The initial triangle is represented in blue, with P the largest error and M the smallest one. R is the substitution point for reflection, E for expansion and C for contraction. The calculated plate centre is depicted in purple.

Figure 3.15: Block diagram of the Simplex method. Adapted from [Steyaert, 1990] and [Trigo-Rodriguez et al., 2005]. 28 3.A UTOMATIC DETECTIONAND ANALYSIS OF METEORS

3.3.5. STEREOSCOPIC INTERSECTION Once the equatorial coordinates of the apparent trajectory from each of the stations have been obtained, the stereoscopic intersection is calculated. The trace of the meteors in the sky defines a great circle11 in the celes- tial sphere. It is calculated the plane containing the apparent trajectory and the geographic coordinate from each observation point respectively. This results in two planes that intersect creating a line. This line con- tains the real trajectory of the meteor in the atmosphere. Figure 3.16 shows a representative illustration of the calculation of the real trajectory by intersecting the planes and obtaining the radiant by projecting backwards until the collision with the celestial sphere

Figure 3.16: Graphical representation of the real meteor trajectory calculation by intersecting the planes and obtaining the radiant by projecting backwards until the collision with the celestial sphere. It is shown the vertical projection as well.

The method was developed by [Ceplecha, 1987] performing all calculations in geocentric coordinates. For this purpose it is necessary to convert geographical latitude ϕ into geocentric latitude ϕ’:

ϕ0 ϕ 0.1924240867◦ sin2ϕ 0.000323122◦ sin4ϕ 0.0000007235◦ sin6ϕ (3.38) = − · + · − · It is also necessary to obtain the value of the geocentric vector radius at the zero height level R expressed in km:

s 1 0.0133439554 sin2 ϕ R 40680669.86 − · (3.39) = · 1 0.006694385096 sin2 ϕ − · Being h the height and θ the local sidereal time at the station, the geocentric rectangular coordinate sys- tem, with which the real point of each station is calculated, is defined as:

X (R h) cosϕ0 cosθ = + · · Y (R h) cosϕ0 sinθ (3.40) = + · · Z (R h) sinϕ0 = + · 11A great circle is a section of a sphere that contains a diameter of the sphere. 3.3.R ECONSTRUCTIONOFTHE ATMOSPHERIC TRAJECTORY 29

Similarly, any vector that defines an apparent trajectory point can be written in the rectangular system of the celestial sphere with:

ξ r cosδ cosα = sk y · · η r cosδ sinα (3.41) = sk y · · ζ r sinδ = sk y ·

where rsk y is a parameter that represents the radius of the celestial sphere, α the right ascension and δ the declination.

Since the recorded trajectory points do not represent an ideal case, some will be displaced so they will not all be contained in a great circle. This means that a plane containing the average trajectory has to be calculated minimizing the variations of the points. If (a,b,c) is a unit vector perpendicular to the average plane that contains the average meteor trajectory then it can be written:

aξ bη cζ ∆ (3.42) i + i + i = i where ∆ 0 represents the ideal case where all the measured points are exactly on the same great circle. i = From the condition:

k X 2 ∆i minimum (3.43) i 1 = = The solution of the unknown vector (a, b, c) is derived from 3.43 by the following relations:

k k k k X X X 2 X a0 ξi ηi ηi ζi ηi ξi ζi = i 1 · i 1 − i 1 · i 1 = = = = k k k k X X X 2 X b0 ξi ηi ξi ζi ξi ηi ζi = i 1 · i 1 − i 1 · i 1 = = = = k k à k !2 X 2 X 2 X c0 ξi ηi ξi ηi (3.44) = i 1 · i 1 − i 1 = = = p 2 2 2 d 0 a b c = 0 + 0 + 0 a a0/d 0 = b b0/d 0 = c c0/d 0 = By substituting this vector (a,b,c) obtained in the rectangular coordinate system (X ,Y , Z ) 3.40, written for station A for example, the geocentric position of the plane containing the apparent trajectory and the distance d from this plane to the station A is calculated:

aAξ bAη cAζ dA 0 + + + = (3.45) d a X b Y c Z A = A A + A A + A A This will allow a first approximation of the real trajectory, but it will have to be corrected later since it is unlikely that the computed trajectory is contained in a great circle, as it should be the meteor trajectory.

3.3.6. MEASURED POINTS PROJECTIONONTHE AVERAGED TRAJECTORY Given the inaccuracies in the measurements, not even the points that define the apparent trajectory of the meteor are contained exactly in the plane defined by the station and the calculated average trajectory. To overcome this problem by introducing the least possible inaccuracy, the perpendicular projection of such points measured from each station will be calculated, on the averaged trajectory defined by the vector (ξR ,ηR ,ζR ). 30 3.A UTOMATIC DETECTIONAND ANALYSIS OF METEORS

Considering any measured point (xn, yn), with the method explained above, it is possible to calculate its co- ordinates (ξn,ηn,ζn) determined from the astrometry of the plate.

It is defined the perpendicular plane to the meteor trajectory from the station A containing the straight line defined by the points (X A,YA, ZA) and (ξR ,ηR ,ζR ). The intersection of that plane with the trajectory of the bolide is the desired point, the closest one to the measured point which lies on the average trajectory of the meteor defined from two stations. This perpendicular plane can be written from station A as:

a ξ b η c ζ d 0 (3.46) n + n + n + n = Then the vector (an,bn,cn) can be calculated as:

a η c ζ b n = n A − n A b ζ a ξ c (3.47) n = n A − n A c ξ b η a n = n A − n A

Thus the corrected vector (ξn0 ,η0n,ζn0 ) is given as the intersection of the two planes (aA,bA,cA) and (an,bn,cn):

ξ b c c b An = n A − n A η c a a c An = n A − n A ζAn anbA bn aA = − (3.48) ξ0 ξ /L n = An An η0 η /L n = An An ζ0 ζ /L n = An An

where L An is the length of the cross product to keep vectors as unitary, that is: q L ξ2 η2 ξ2 (3.49) An = An + An + An

The sign of the vector (ξn0 ,η0n,ζn0 ) is defined by the condition that the calculated αn0 from 3.41 differs only by a small value from α. If this difference is close to 180◦, then it would only has to be changed the sign of the resulting vector (ξn0 ,η0n,ζn0 ).

Now the corrected points of the apparent trajectory are obtained and they are all contained in a great cir- cle. Therefore, by choosing two arbitrary points among them and the position of the station A in Cartesian coordinates (three plane’s points P1,P2,P3), the corrected plane containing the apparent trajectory and the station can be computed.

Having the three points of the plane:

P (ξ0 ,η0 ,ζ0 ) 1 = 1 1 1 P (ξ0 ,η0 ,ζ0 ) (3.50) 2 = 2 2 2 P (X ,Y , Z ) 3 = A A A the normal vector is computed as:       a0 ξ0 X ξ0 X A 1 − A 2 − A n~A b0  η0 YA  η0 YA  (3.51) = A = 1 − × 2 − c0 ζ0 Z ζ0 Z A 1 − A 2 − A

and the distance to the axe’s origin by using any of the points, for instance P3:

d 0 P n~ (3.52) A = − 3 · A It only remains to calculate the intersection of the averaged planes of each of the stations. This is a key step for define and compute the real trajectory of the meteor in the Earth’s atmosphere. Equivalent to 3.50, 3.51, 3.52, the corrected plane for B is obtained and the intersection of the two planes is calculated as follows: 3.3.R ECONSTRUCTIONOFTHE ATMOSPHERIC TRAJECTORY 31

ξ (b0 c0 b0 c0 )/d R = A B − B A η (a0 c0 a0 c0 )/d (3.53) R = B A − A B ζ (a0 b0 a0 b0 )/d R = A B − B A where d is: q d (b c b c )2 (a c a c )2 (a b a b )2 (3.54) = 0A B0 − B0 0A + B0 0A − 0A B0 + 0A B0 − B0 0A

being (ξR ,ηR ,ζR ) the direction vector that defines the line of the real trajectory.

By choosing a random component and making it zero, for instance ζ 0, it can be calculated a point P = l (being (Pl1,Pl2,0) in this example) contained in the line:

µa b ¶µξ¶ µ d ¶ A A − A (3.55) a b η = d B B − B Then the line containing the trajectory can be expressed in its general parametric form as:

x P λξ p = l1 + R y P λη (3.56) p = l2 + R z P λζ p = l3 + R where the parameter λ is a real value that determines each coordinate.

Being n each of the apparent trajectory points, the real point of the trajectory are computed by the inter- sections (Xn,Yn, Zn), which will be given by the three planes that contain the point:

a0 ξ b0 η c0 ζ d 0 0 A + A + A + A = a0 ξ b0 η c0 ζ d 0 0 (3.57) B + B + B + B = a ξ b η c ζ d 0 n + n + n + n = To compute these intersections the parametric equation of the line 3.56 and the collision with the plane anξ bnη cnζ dn 0 is calculated, which has a normal vector n~n(an,bn,cn) and contains a random point ¡ + d+n ¢ + = P 0,0, − : n cn   Xn (Pn Pl ) n~n Yn  Pl ¡ − ¢· (3.58) = + ξR ,ηR ,ζR n~n Zn ·

And the distance from this point seen from station A will be: q r (X X )2 (Y Y )2 (Z Z )2 (3.59) n = n − A + n − A + n − A

3.3.7. CHARACTERIZATION OF THE ATMOSPHERIC FLIGHT One of the critical parts of meteor detection is to express the flight performed by the bolide in terms of a mathematical model from which physical interpretations can be extracted. That is to say, to adjust the not necessarily precise observed data in a coherent way with the previous meteor knowledge. For example, the curves describing the velocity and height evolution during atmospheric entry are known, but if the raw data are used some errors are introduced as consequence of the inaccuracies. This is crucial both for the estima- tion of the initial velocity, which will be key in future work for the computation of the orbit of origin, and for the terminal mass calculations, which will define the possibilities of meteorite deposition.

The first step will be to compute the height corresponding to each detected point of the path. This can be used if wind profiles are used or to estimate ablation taking into account the variation in atmospheric density. 32 3.A UTOMATIC DETECTIONAND ANALYSIS OF METEORS

In order to calculate the vertical projection (not in the direction of the radius vector) on the Earth’s surface of the real point (Xn,Yn, Zn), it is necessary first to compute its geocentric latitude ϕ0, geographical longitude θ and height h: µ ¶ Yn θ arctan = Xn µ ¶ Zn ϕ0 arctan cosθ (3.60) = Xn · Zn h R = sinϕ0 −

where R is obtained by solving the Equation 3.39. The beginning and terminal height, hi and h f respec- tively, can be computed.

The geocentric latitude ϕnc will be obtained from 3.38. To obtain the vertical projection, since the inter- vals of sidereal time are equal to the longitude intervals, it only has to be corrected the ϕnc to obtain ϕn0 to the zero level height: hn (ϕn0 ϕnc ) ϕn ϕnc · − (3.61) = + R h + n which allows to obtain the rectangular coordinates of the vertical projection (Xv ,Yv , Zv ) using 3.40 with h 0. = A determining parameter in the characterization of the flight is the angle between the fireball trajectory and the local horizon, usually expressed as γ and named trajectory slope. From this value the depth of the atmospheric flight will depend considerably as well as the possibilities of producing a meteorite.

arcsin( ξR Xv ηR Yv ζR Zv ) γ | + + | (3.62) = q q X 2 Y 2 Z 2 ξ2 η2 ζ2 v + v + v R + R + R

The distances ln along the bolide’s trajectory can be determined from the first time mark (X1,Y1, Z1) by the formula: q l (X X )2 (Y Y )2 (Z Z )2 (3.63) n = n − 1 + n − 1 + n − 1 Now having the apparent covered distances from the recordings, data must be pre-processed before they can be used to compute velocities and deceleration, as suggested by [Whipple and Jacchia, 1957]. This is because during the meteor detection process, when fragmentation or fulgurations occur, the detected point could be not necessarily the meteoroid, but a part of the brightest shoch front of the wake. This data process- ing also assists in the subsequent characterisation of the bolide flight. By using this observed length, it can be obtained the pre-atmospheric velocity V with the first detected points by doing a regression and extrap- ∞ olating with a back-propagation. It is important for this estimation that the size of the chosen section is not too large, since the strong deceleration would produce an overestimation, nor too short, since the errors of a small sample are not reliable. Therefore, an initial sample is chosen away from the greatest fragmentation process but having a negative slope of the regression, which makes sense since the bolide only slows down.

Due to the gravitational attraction of the Earth, the meteoroid describes a hyperbolic orbit with a geo- centric velocity Vg . The apparent velocity of the meteor with respect to the Earth and the geocentric velocity match when the meteor is outside the terrestrial influence. When the meteoroid enters the atmosphere, the geocentric velocity con be approximated as:

q 2 2 Vg V VE km/s (3.64) = ∞ − where the terrestrial escape velocity is V 11.2km/s. E = In order to compute the velocity curve of the atmospheric flight, it is needed first to adjust the measure- ments associated with the computed length of the segments made in each video frame. Experience says that an optimal way to approximate these velocities is to adjust the distances with a least-squares to the following equation: 3.3.R ECONSTRUCTIONOFTHE ATMOSPHERIC TRAJECTORY 33

D a bt cekt (3.65) = + + where D is the path length, t time and a, b , c and k variables to be determined in the curve fitting. This adjustment has been made in segments: one first for most of the flight, and another for the final part that presents abrupt changes. It has been imposed as a condition in the adjustment continuity in both lengths and velocities, and in accordance with the maximum and minimum limits imposed by the observa- tion.

Once the adjustment is made, the speeds are obtained in a trivial way as follows:

V b kcekt (3.66) = + and re-deriving, the deceleration curve is obtained:

V˙ k2cekt (3.67) = Once the velocity and deceleration curve have been obtained, atmospheric flight can be characterized. Typically, the physical problem of meteor deceleration has been treated as a third-order dynamic system [Bronshten, 1983]. The classical dynamic third-order system is expressed by time dependent motion equation as: dV M D P sinγ dt = − + dγ MV 2 MV P cosγ cosγ L (3.68) dt = − R − dh V P sinγ dt = − +

being M(t) the mass, h(t) the height, V (t) the velocity, D 1 c ρ V 2S the drag force, L 1 c ρ V 2S the = 2 d a = 2 L a lift force, P Mg the body weight, ρ the atmospheric density, g the gravity and c , c the lift and drag coef- = a L d ficient, respectively.

By using the body’s variable mass equation can be written:

dM 1 3 H ∗ c ρaV S (3.69) dt = −2 h

where the heat exchange coefficient is ch and the sublimation heat is H ∗.

Based on these expressions and assuming that the body does not suffer any kind of fragmentation and that the cd and ch coefficients are constant, [Hoppe, 1937] developed the well-known Single Body Theory. However, the flight parameters change with time and are different depending on the event, to properly characterize the atmospheric flight, it is better to set up free these variables and to add more observed data. In order to solve 3.68 and 3.69 it is needed to introduced a shape factor A S/V olume2/3, which for a per- = fect sphere will be A 1.21. Also it is added a relation between the meteor mass and its cross-sectional area = as S/S (M/M )µ, where the subscript "e" indicates the moment when meteor starts and the parameter µ E = e characterizes the rotation of the body. If µ 0 there is no rotation, and for µ 2/3 the body ablation due the = = rotation is uniform, being constant the shape factor.

It can be passed to convenient dimensionless quantities by introducing a new variable h. Being h o = 7.16km the atmospheric scale height, it cab be expressed m M/M , v V /V , y h/h , ρ ρ /ρ and = e = e = 0 = a 0 s S/S . Taking into account the above mentioned considerations, the trajectory equations acquire the form: = e

dv 1 ρ0h0Se ρvs m cd d y = 2 Me sinγ 2 2 (3.70) dm 1 ρ0h0Se Ve ρv s ch d y = 2 Me H ∗ sinγ 34 3.A UTOMATIC DETECTIONAND ANALYSIS OF METEORS

In order to find an analytical solution, it is assumed the isothermal atmosphere model ρ exp y and = − according to [Levin, 1956] the body mass and its middle section is connected as s mµ being µ constant. = The following solution for 3.70 was proposed by [Stulov, 1995] with the initial conditions m 1, v 1, = = y : = ∞ µ β ¶ m exp (1 v2) = − 1 µ − − (3.71) ∆ y lnα β ln = + − 2

where:

∆ Ei(β) Ei(βv2) = − Z x et dt (3.72) Ei(x) dx = t −∞ showing that the trajectory depends on two dimensionless parameters, α the ballistic coefficient and β the mass loss parameter, defined as:

1 ρ0h0Se α cd = 2 Me sinγ 2 (3.73) chV β (1 µ) e = − 2cd H ∗

The derivation of these parameter can be done by least squared method for a particular event. The pa- rameter α characterizes how the meteoroid breaks apart, since it is proportional to the mass of a trajectory- aligned atmospheric column of cross section divided by the body mass. The parameter β is proportional to the fraction of the kinetic energy supplied to a unit mass of the body as heat divided by the effective vaporiza- tion enthalpy. β also avoids the computation of the luminous efficiency and the problems this entails, which was commented in 3.2.5.

These parameters bring great simplicity to the characterization of the atmospheric flight and can also be used to estimate how likely a fireball produces meteorites. In this regard, [Sansom et al., 2019] proposes a method for determining fireball fates using α β criterion. This method is enough of a graphical representa- − tion where y-axis is logβ and x-axis is log(αsinγ) and, following a series of assumptions, some curves delimit the area of meteorite-dropping candidate. The boundary curve are based on the definition of a macroscopic meteorite-dropping event if the final mass is greater than 50g [Campbell-Brown and Hildebrand, 2005] and the two extremes of the shape change coefficient µ: the body does not rotate µ 0 and the body shape doesn’t = change because the rotation allows homogeneous ablation around the entire surface µ 2/3. This method = provides an elegant way to classify fireballs.

Unlike the photometric mass discussed in the Section 3.2.5, thanks to the characterization of atmospheric flight, the so-called dynamic mass can be obtained. Continuing with the mathematical development, it can be computed the extra-atmospheric mass Me by doing some algebra on 3.73, leading to the expression:

à !3 1 ρ0h0 Ae Me cd (3.74) = 2 αsinγ 2/3 ρb To obtain the final mass of a bolide, it has to be apply the condition that the velocity becomes insignificant in relation to the pre-atmospheric velocity:

1 µ β ¶ M f Me exp (3.75) = α3 sinγ3 − 1 µ − 3 3 5 To calculate these masses, usually these values are used: ρ 1.29x10− g/cm (dry air), h 7,16x10 cm 0 = 0 = (scale factor), c 1.3 and A 1.21 (spherical body) or A 1.3. d = e = e = 3.3.R ECONSTRUCTIONOFTHE ATMOSPHERIC TRAJECTORY 35

3.3.8. RADIANT COMPUTATION:ZENITH ATTRACTIONAND DIURNAL ABERRATION Already knowing the point where the fireball begins and the initial velocity, it can be calculate the apparent radiant and the displacements due to the relative velocity between the bolide and the Earth.

Once the first time point is known (X1,Y1, Z1), that is, the beginning of the real atmospheric trajectory, and using any other point contained on the line (X2,Y2, Z2), the intersection of this line with the celestial sphere can be calculated, obtaining the radiant:

a (X X )2 (Y Y )2 (Z Z )2 R = 2 − 1 + 2 − 1 + 2 − 1 b 2 ¡(X X ) X (Y Y ) Y (Z Z ) Z ¢ R = · 2 − 1 · 1 + 2 − 1 · 1 + 2 − 1 · 1 c X 2 Y 2 Z 2 R2 R = 1 + 1 + 1 − sk y q b b2 4 a c − R − R − · R · R (3.76) tR = 2aR X X t (X X ) R = 1 + R · 2 − 1 Y Y t (Y Y ) R = 1 + R · 2 − 1 Z Z t (Z Z ) R = 1 + R · 2 − 1

for the calculation of tR is chosen the negative root since it is the closest to point (X1,Y1, Z1), and this is precisely what is of interest, since it has to be done the backward projection from first point to find the radi- ant. The (XR ,YR , ZR ) calculated coordinates will be at a distance Rsk y , which should tend to infinity. Only the Equation 3.41 would remain to obtain the apparent right ascension and declination of the radiant.

Finally, the calculations performed are checked graphically. The two great circles defined by the apparent trajectory must intersect in the radiant.

The presence of the Earth not only disturbs the velocity of the meteoroid but also modifies its velocity vector. This causes a shift of the radiant towards the zenith. The lower the meteor velocity, the greater the zenith attraction will suffer. It was proposed by [Andreev, 1991] a valid formula for slow and fast meteors: · µ ¶¸ Vg V z∗ ∆z 2arctan − ∞ tan (3.77) = Vg V · 2 + ∞ where ∆z z z0, z is the true zenith distance of the radiant, z0 the zenith distance of the radiant from the = − observation point and z∗ the zenith distance of the radiant where the meteor would have been seen in the zenith.

It can be related z∗ to the horizontal or topocentric coordinates a0 and z0 of the radiant from the observa- tion point by:

¡ ¢ z∗ arccos cosz0 cosγ sinz0 sinγcos(a∗ a0) (3.78) = + − where a0 the azimuth of the radiant from the observation point, a∗ the azimuth of the radiant where the meteor would have been seen in the zenith and γ the geocentric angle between the observation point and the point where the meteor would have been seen in the zenith. It can be expressed γ as:

µ R ¶ γ ψ arcsin ⊕ sinψ (3.79) = − R hi · ⊕ + being hi the initial height of the meteor, ψ the angular distance between observation point’s zenith and the beginning of the meteor, R the radius of the Earth. ⊕ To compute the arc ψ, that is, the shortest distance between two points on the surface of a sphere, also know as orthodromic distance or great-circle distance, the Vincenty formula [Vincenty, 1975] is used:

à p 2 2 ! (cosδ2 sin(α2 α1)) (cosδ1 sinδ2 sinδ1 cosδ2 cos(α2 α1)) ψ arctan − + − − (3.80) = sinδ sinδ cosδ cosδ cos(α α ) 1 2 + 1 2 2 − 1 36 3.A UTOMATIC DETECTIONAND ANALYSIS OF METEORS

where α and β are the right ascension and the declination respectively. The observation point from where the meteor appears in the zenith is computed in an equivalent way to 3.76, that is the collision of the vector that joins the center of the Earth and the first point of the meteor with the Earth’s surface. The azimuth and zenith distance are obtained in the following way:

¡ ¢ z0 arccos sinϕsinδ cosϕcosδcos(LST α) = + − µ sin(LST α) ¶ (3.81) a0 arctan − = cosϕtanδ sinϕcos(LST α) − − where LST is the local sidereal time and ϕ is the latitude of the observing point.

By applying 3.81 is obtained z0, a0, a∗, and having ψ from 3.80 and γ from 3.79, it can be computed ∆z from 3.77. Therefor, the real zenith distance z is known. To compute the real azimuth of the radiant a it has to be applied the following formula:

µ cosδsin(LST α) ¶ a arcsin − (3.82) = sinz0 With this data the radiant position in equatorial coordinates can be recovered taking into account the zenith attraction:

δ arcsin¡sin(π/2 z)sinϕ cos(π/2 z)cosa¢ = − + − µ sin(π/2 z) sinδsinϕ ¶ (3.83) α LST arccos − − = − cosδcosϕ

Finally, diurnal aberration has to be taken into account. Since the Earth rotates around its axis, the posi- tion of the radiant moves in ∆α and ∆δ. The diurnal aberration is caused by the velocity of the observation point on the rotating surface of the Earth. Therefore, it depends not only on the moment at which the obser- vation is made, but also on the latitude and longitude of the observer. It is an effect similar to the aberration of light 3.2.3. It is used the approximation proposed by [Bellot-Rubio, 1992]:

26.62◦ ∆δ cosϕsinδcos(LST α) = − Vg − (3.84) 26.62◦ ∆α cosϕsecδcos(LST α) = − Vg −

To allow a better correlation of the computed radiant with the already known meteor showers, both es- tablished and under study radiant have been implemented from data sources provided by IAU’s Meteor Data Center [Tadeusz Jan Jopek and Zuzana Kavuchova, 2017].

3.4. CALCULATION OF ERRORSIN RADIANT DETERMINATION The error calculation process requires more computing time since require to study how the uncertainty af- fects the results. From the simplex method, which transforms the pixel positions into real coordinates, an average error is obtained for both right ascension and declination of each meteor. The calculation of errors is based on assuming the worst scenario, that is, that each computed point of the apparent trajectory presents just the error for each component of the trajectory that maximizes the total error. This will produce the great- est deviation of the trajectory. The cases of maximum deviation will occur when the trajectory rotates as much as possible, it happens with some of the error’s combinations assuming a gradient from the beginning of the trajectory with the maximum positive error, to the end of the trajectory with the maximum negative er- ror and vice versa for each component. As Figure 3.17 shows this will produce 4 deviations for each trajectory, which generates 16 candidate deviations to delimit the maximum possible radiant errors. The possibilities that produce a larger absolute error were chosen in order to constrain the error in radiant determination. This is key point to calculate the orbital elements of the meteoroid. 3.4.C ALCULATION OF ERRORSIN RADIANT DETERMINATION 37

Figure 3.17: Schematic diagram for radiant error computation. On the left, the two largest possible deviations for each apparent trajec- tory are shown, which delimits the margin of error of the calculated radiant. On the right, the four possibilities of deviation assuming the worst case.

Equivalently, all possibilities will be checked for the greatest variations in the initial height ∆hi , terminal height ∆h f and distances covered ∆d by the meteor.

Taking into account that the time’s precision of the SPMN network cameras is ∆t 0.001s, and together = with the estimated distance error previously computed, the initial and terminal velocities error are obtained by basic propagation of uncertainty: s µ ∆d ¶2 µ ∆t ¶2 ∆V V (3.85) = · d + t However, the error associated with the time measures is so small that it does not affect the final calcula- tion and can be neglected. From experience it is known that the variations of the magnitude estimated by photometry are usually about 0.5 magnitudes due that is also depends on the geometry of the trajectory ± and the position of the station. This seems to be consequence of the heterogeneous ablation of the mete- oroid that usually rotates and produce luminosity charges accordingly to [Trigo-Rodriguez et al., 2013].

It is necessary to highlight some errors assumed when estimating the trajectory of the bolide. For exam- ple, the irregular nature of the glare means that the estimation of the mass center in the detected area does not correspond to the center of mass of the object. Many times, due to the fragmentation of the fireball, the flash spreads as if it were a wake, while the object itself remains close to the shock front. This is one of the reasons why the estimation of velocities is not entirely reliable and requires prior treatment.

Another example of error that is difficult to estimate is that are associated with the meteor photometry. Some events occur with partly cloudy skies or light pollution. This may cause inconsistencies on the pixel counts of the reference stars used to estimate the magnitude.

Even with all the observational difficulties, with the appropriate treatments of meteor data it is possible to obtain more than acceptable results, and the radiant and orbital data match those available from meteoroid streams.

4 STUDY CASES

4.1. TAURID FIREBALL: SPMN251019B The first case study is the SPMN251019 event (see Table 2.1) that occurred on October 25th, 2019. Thanks to the SPMN network facilities it was videotaped by three stations: Astronomical observatory at Puig des Molins (Eivissa), Montseny Astronomical Observatory (Montseny) and cameras from Folgueroles station. Both the Montseny and Folgueroles stations have wide-field cameras while the Eivissa station is equipped with an all- sky camera. The bolide practically flew over the zenith of Folgueroles and Montseny, and on the contrary, it was captured from a considerable distance and a low latitude from Eivissa. For these reasons, the astrometric results from the Folgueroles and Montseny stations have lower uncertainty.

Bright fireballs recorded on October and November are often belonging to one of the Taurid streams (Northern or Southern). The Taurid complex is, in fact, relevant for the study of impact hazard associated with large meteoroids due to the frequency and size of the bodies reaching the top of the atmosphere or the Earth. The Taurid swarm is a potential source of risk related to possible impacts by cosmic objects. It was proposed that Tunguska event was the result of some meteoroid belonging to this Taurid stream [Sekan- ina, 1998]. Several studies point to the relationship between the Taurid complex and the disruption of the 2P/Encke comet [Blanch, 2017]. Very bright fireballs reinforce the evidence that evolved comets can produce meter-sized meteoroids. Several Near Earth Objects (NEOs) have been dynamically associated with the Tau- rid complex clearly suggesting that the progressive disruption of a larger cometary progenitor is the source of this complex of bodies [Babadzhanov et al., 2008].

One of the complications of this case results in that the two closest stations recorded the beginning and the end of the meteor, but not the intermediate part, which was only been filmed from Eivissa. From the as- trometric measurements of the video frames it has been obtaining a magnitude of 13.5 0.5. The fireball was − ± first detected at a height of 80.0 0.1km and the end ocurred at 58.3 0.1km, which indicates the low possi- ± ± bility of being a meteorite-dropper since its terminal height was too high. Table 4.1 shows the SAO number of each reference star selected to perform the astrometry, the plate coordinates measured over the image (x, y), the standard coordinates computed (ξ,η), the right ascension and declination of each star and the respective error. It can be seen how the error is smaller for the video from Folgueroles (b) since a less reference star has been used, which can give a false sense of precision that will have to be checked by analyzing the geometric coherence. In the Figure 4.1 is depicted the three apparent trajectories corresponding for each station and the result of the reduction. The obtained result is very consistent with the identified constellations and the fireball direction.

Thanks to the apparent trajectories, the observed radiant is found at the point of intersection between them on the celestial sphere. As shown in Figure 4.2 the three astrometries point to the same radiant, the small variations are due to as Eivissa station has wider field that exhibits much higher distortion and pro- duces a larger uncertainty. At the same time the observation point is much more distant, so that the accuracy of both the coordinates of the bolide and the reference stars is lower. Still, the results are very similar. The associated errors have also been plotted by using the method explained in Section 3.4. The results of the

39 40 4.S TUDY CASES computed radiant are shown in the Table 4.2, both the observed, geocentric and the heliocentric one. The initial velocity of the fireball, that is, its pre-atmospheric velocity, was found from the velocity measured at the earliest part of the meteor trajectory. It has been estimated to be 28.0 0.2km/s, which is around the typ- ± ical velocity of Taurid meteor stream. The results, the radiant and the pre-atmospheric velocity, are in good agreement with the established southern Taurid shower [Jenniskens et al., 2016] but to demostrate its origin it has to be computed the heliocentric orbit (see 4.3.

Station Ref SAO x (px) y (px) ξ η RA (◦) DE (◦) err. RA (%) err. DE (%) 1a 30631 457.2 497.85 0.09 0.54 268.302 57.01 0.009 0.009 2a 17074 538.1 390.8 0.31 0.73 245.92 61.57 0.018 0.053 3a 17365 493.6 390.2 0.18 0.78 257.125 65.769 0.067 0.06 4a 18222 409.2 404.0 -0.09 0.81 287.974 67.721 0.023 0.04 Eivissa 5a 8220 511.9 305.0 0.35 1.13 230.092 71.859 0.032 0.032 6a 8102 504.7 282.2 0.37 1.27 222.576 74.174 0.017 0.023 7a 19019 333.85 432.5 -0.34 0.76 310.523 61.908 0.03 0.094 8a 34137 257.6 411.3 -0.65 0.9 332.736 58.253 0.049 0.01 9a 19302 311.65 414.0 -0.43 0.85 319.53 62.642 0.116 0.061 10a 20268 276.5 345.85 -0.62 1.23 342.449 66.23 0.009 0.012 1b 60198 393.05 45.75 0.57 -0.1 113.477 31.89 0.034 0.076 2b 79666 405.2 91.35 0.56 -0.18 116.042 28.03 0.037 0.078 3b 95895 614.1 48.65 1.16 -0.35 99.092 15.758 0.004 <0.001 Folgueroles 4b 115456 575.5 210.75 0.9 -0.64 111.678 8.299 0.029 0.024 5b 115756 574.55 258.85 0.85 -0.75 114.641 5.236 0.024 0.026 6b 61414 210.5 185.1 0.13 -0.14 140.163 34.395 0.012 0.063 7b 81064 201.95 302.25 0.02 -0.31 148.141 26.014 0.038 <0.001 8b 81004 226.85 313.9 0.04 -0.35 146.409 23.782 0.066 0.103 9b 98967 241.15 442.5 -0.06 -0.6 152.053 11.981 0.012 0.037 1c 94027 386.1 234.85 0.15 -0.24 68.982 16.52 0.014 0.062 2c 77168 363.4 420.8 -0.06 -0.01 81.566 28.612 0.078 0.453 3c 39955 261.9 466.0 0.02 0.23 75.488 43.823 0.086 0.285 4c 40186 262.5 496.7 -0.02 0.28 79.165 45.996 0.02 0.136 Montseny 5c 58636 363.8 510.75 -0.18 0.12 89.914 37.213 0.06 0.455 6c 40750 308.25 547.6 -0.16 0.28 89.864 44.945 0.021 0.101 7c 40756 299.9 553.75 -0.15 0.3 89.965 45.934 0.042 0.306 8c 39053 154.8 400.15 0.28 0.36 55.739 47.789 0.028 0.037 9c 38787 124.0 397.95 0.33 0.42 51.091 49.863 0.038 0.09 10c 23789 87.95 410.15 0.37 0.52 46.212 53.509 0.033 0.052

Table 4.1: SPMN251019B data reduction for the station Eivissa, Folgueroles and Montseny. SAO number, plate coordinates in pixels (x, y), standard coordinates (ξ, η), right ascension and declination and their respective errors are shown.

Radiant Data Observed Geocentric Heliocentric

RA (◦) 42.7 0.2 40.2 0.1 346.5 0.2 ± ± ± DE (◦) 11.3 0.1 9.3 0.1 -4.2 0.2 ± ± ± V (km/s) 28.0 0.2 25.1 0.2 36.7 0.2 ± ± ±

Table 4.2: SPMN251019B observed, geocentric and heliocentric computed radiant and the velocity, with their corresponding errors. 4.1.T AURID FIREBALL: SPMN251019B 41 Figure 4.1: SPMN251019B apparent trajectory recorded and reduced from Eivissa (a), Folgueroles (b) and Montseny (c). Reference stars and constellation are pointed out. 42 4.S TUDY CASES Figure 4.2: SPMN251019B apparent radiant basedplane on and the the records nearby from constellations Eivissa of (orange), the Folgueroles Northern (red) hemisphere and are Montseny show. (green) plotted into the celestial sphere with propagation errors. Ecliptic, equatorial 4.1.T AURID FIREBALL: SPMN251019B 43 Figure 4.3: SPMN251019B atmospheric trajectory based on the records from Eivissa (orange), Folgueroles (red) and Montseny (green). Vertical projection (white) and observation range are shown. 44 4.S TUDY CASES

Once the atmospheric trajectory of the bolide has been reconstructed, it is observed how in the recording from Eivissa in Figure 4.1 the fireball luminous path is fainter due to the distance to the recording station (about 340 km). The trajectory reconstruction shows in Figure 4.3 fits perfectly with the direction and visual field of the stations. The height of the starting point has been determined using the Montseny station (red) and the terminal height thanks to Folgueroles station (green).

Using the starting and ending points of the atmospheric flight the radiant was computed, so together with the velocity, the following orbital parameters were computed: the semi-major axis a, the orbital eccentricity e, the inclination i,the argument of perihelion ω, the longitude of the ascending node Ω and the perihelion distance q. These parameters finally confirm that the SPMN251019B event belongs to Southern Taurid me- teoroid stream. The orbital parameters are shown in Table 4.3.

Orbital Parameter

a (AU) e q ω(◦) Ω(◦) i (◦) 4 2.91 0.02 0.794 0.005 0.415 0.005 108.5 0.5 31.196 10− 1.8 0,5 ± ± ± ± ± ±

Table 4.3: SPMN251019B computed orbital parameters and their errors.

Assuming that the typical bulk density of Taurid meteoroids is of about 1.6 g/cm3 [Babadzhanov and Kokhirova, 2008] and using the method explained in Section 3.2.5, the calculation yields 4.7 0.1kg for the ± initial (photometric) mass and 17.8 0.3 cm for the initial size of the meteoroid. However, these results will ± be taken with caution and will be compared with those obtained by characterizing the flight as discussed in Section 3.3.7.

To characterize the atmospheric flight it has been computed the parameters α (ballistic coefficient) and β (mass loss ratio) were computed. Such approach provides information on the meteoroid properties and will be used to estimate whether the fireball is likely meteorite candidate by applying α β criterion. In order to − validate the approximation of the observational data, the normalised observation has been scatter over the α β fitted curve in Figure 4.4, showing good agreement. In view of these results, a high degree of confidence − can be expected in the conclusions obtained following the characterization of atmospheric flight, such as the initial mass or the possibility of creating meteorites.

16 alised observation 15

14

13

12

11 Normalised height Normalised

10

9

8 0.2 0.4 0.6 0.8 1.0 Nnormalised velocity

Figure 4.4: Plot of observational data with velocity normalized to entry velocity and height normalized to the atmospheric scale height for the SPMN251019B event. 4.2.S PORADIC SUPERBOLIDE: SPMN160819 45

Now defining a 50 g terminal mass as meteorite dropping event, and taking into account the bolide tra- jectory angle to the local horizon γ, which is for this event 28.59◦, it can be graphically inferred if some frag- ment has survived, just by assuming the two extremes of shape change coefficient. Figure 4.5 shows that the SPMN251019B (red dot) is not event in the likely fall area. Assuming a typical meteoroid, that is, a rounded brick body, it is computed an almost null terminal mass, as expected given the high altitude of the event. On the other hand, the estimated pre-atmospheric mass is 43.1g having an initial size of 0.4cm. The results are far from the 4700g computed with the photometric mass and more consistent with the typical cm-sized me- teoroids forming a cometary stream (see e.g. [Trigo-Rodriguez and Blanch, 2017]). However, these differences should not be so alarming given the inaccuracy of photometry, it can even be considered that due to all the assumptions made they are in an acceptable order of magnitude.

ble fall

−

Figure 4.5: The bounding line for a 50 g meteorite is shown in black for the case where there is no spin (µ 0) and in gray where spin = allows uniform ablation over the entire surface (µ 2/3). =

The most relevant computed values of the SPMN251019B event are presented compiled in Table 4.4.

SPMN251019B

Mag hi (km) hf (km)V (km/s)Vf (km/s)Me (g)Mf (g) ∞ -13.5 0.5 80.0 0.1 58.3 0.1 28.0 0.2 17.59 0.2 43.1 0.003 ± ± ± ± ±

Table 4.4: SPMN251019B computed trajectory, velocity and mass data obtained from the observations

This work was published in the 51st Lunar and Planetary Science Conference [Peña-Asensio et al., 2020]. The abstract can be found online through this link: https://www.hou.usra.edu/meetings/lpsc2020/ pdf/2742.pdf.

4.2. SPORADIC SUPERBOLIDE: SPMN160819 In practice bolides brighter than 16 magnitude, called superbolide, are often recorded from very far away − cameras (sometimes security patrol sensors or dashcams) so the image are interfered by the Earth atmo- sphere and the videos do not have the desired quality, especially at the beginning of the light phase since it often appears very far away with significant extinction. It is precisely this initial part that is most relevant to estimate the heliocentric orbit because it provides the initial (pre-atmospheric) velocity. For this reason the interest in spaceborne fireball observation has been growing. Thanks to the large number of satellites ded- icated to Earth-observation, it is possible to use data collected from space to complement or verify meteor event analyses. 46 4.S TUDY CASES

The best documented case of satellite data use was the Chelyabinsk event due to its enormous dimen- sions. An example of this is [Miller et al., 2013], where the atmospheric trajectory was estimated through the parallax-displaced of the debris trail. There are also examples of the orbit reconstruction by using multiple wavelengths [Proud, 2013], however given the high exposure time of the images it was required to use an es- timated velocity. Not only can cameras provide information about bolides, there are different instruments equipped with sensors capable of measuring peak brightness and radiated energy. This can be used to verify the absolute astronomical magnitude computed from Earth’s observations, as well as relevant information on the position of the brightest point. In this way it was possible to verify with U.S. Department od Defense (DoD) satellite instruments that the equivalent energy of the Chelyabinsk event was 530 kt of TNT [Brown et al., 2013]. These cases mentioned demonstrate the ability of Earth-observation satellites to provide valu- able insight on trajectory reconstruction in the more likely scenario of absence of ground observations.

On August 16, 2019, a very bright superbolide catalogued as SPMN160819 event occurred (see Table 2.1). It was an event of considerable importance due to its magnitude that, unfortunately, was only partially recorded from the Eivissa station of the SPMN network. However, thanks to citizen collaboration, access to two more records was obtained: an image from Costa Brava and a video from Sardinia (see Table 2.1, which despite their low resolution, were used in the superbolide analysis.

Given that in casual recordigns often is impossible to identify enough reference stars to perform the as- trometry, data obtained by satellites can played a crucial role in the reconstruction of the trajectory. As an example, it has been used the peak brightness coordinates measured by the Center for Near Earth Object Studies of NASA1 and the SPMN recordings to reconstruct the real atmospheric trajectory of this superbolide.

First, the point of maximum brightness measured by U.S. DoD satellites has been used to establish a point through which the apparent trajectory must necessarily pass. That is, the point of maximum energy as seen from each observation point has been projected on the celestial sphere. In Figure 4.8, that point is repre- sented in red, also in red its projections appear in Figure 4.7.

The recording from Eivissa is the only one that allows to perform a complete astrometry thanks to the number of stars registered. Once a point is known, the astrometry is adjusted so that the result is consistent. In this case, since from Eivissa only the first part of the fireball path was recorded and the point of maximum brightness occurs in the second half of the light trace, the estimated apparent trajectory (in yellow) must have greater declination given its direction of appearance while the great circle it defines must contain the projection of the point. Table 4.1 shows the astrometry result for Eivissa station.

Ref SAO x (px) y (px) ξ η RA (◦) DE (◦) err. RA (%) err. DE (%) 1 91781 339.0 424.8 -0.54 -0.32 3.309 15.184 0.461 0.234 2 108378 400.05 349.75 -0.26 -0.36 346.19 15.205 0.346 0.205 3 54471 175.55 413.15 -0.69 0.17 17.433 35.621 0.13 0.02 4 54058 228.2 406.25 -0.62 0.03 9.832 30.861 0.249 0.143 5 73765 266.35 379.4 -0.5 -0.04 2.097 29.09 0.536 0.059 6 90734 329.2 262.85 -0.12 -0.06 340.751 30.221 0.144 0.669 7 90238 399.05 229.1 0.06 -0.21 331.753 25.345 0.591 0.949 8 22268 62.45 272.6 -0.45 0.65 21.454 60.235 0.66 0.071 9 21133 116.65 230.6 -0.3 0.53 2.295 59.15 0.313 0.425 10 125122 557.9 48.2 0.75 -0.43 297.696 8.868 0.045 0.591 11 105223 547.6 36.1 0.76 -0.4 296.565 10.613 0.112 0.217 12 105500 482.4 38.6 0.65 -0.26 299.689 19.492 0.189 1.083 13 20268 118.45 142.55 -0.09 0.58 342.42 66.2 0.392 0.646 14 34137 168.25 129.25 -0.0 0.46 332.714 58.201 0.137 0.906

Table 4.5: SPMN160819 data reduction for the station Eivissa. SAO number, plate coordinates in pixels (x, y), standard coordinates (ξ, η), right ascension and declination and their respective errors are shown.

Now it is estimated the intersection of the planes containing the apparent trajectories that are consistent

1https://cneos.jpl.nasa.gov/fireballs/. 4.2.S PORADIC SUPERBOLIDE: SPMN160819 47 with the previously computed values and with the references of the recordings from Sardinia, in which is seen Jupiter, and Costa Brava, in which the moon appears.

In order to compute the total distance of atmospheric flight, the pixels of the persistent wake captured from Costa Brava have been measured, as well as the distance from the beginning to the moon, obtaining an estimate of the total distance traveled by the superbolide (the cyan blue color denotes the part added with the measurement from Costa Brava).

From the recording from Eivissa, which the Moon appears at a similar altitude, the superbolide was clearly more luminous than the Moon. It has been estimated to exhibit an absolute magnitude of 16.5 0.5. The − ± superbolide was first detected at a height of 48.0km and ended at 28.5km. Obviously, the event appeared so far away from the SPMN station that the first detection happened when the luminous phase involved already strong meteoroid fragmentation and is not representative of the real beginning.

Since from Sardinia the meteor was recorded from the beginning to the end, it can be obtained the ve- locity curve to parameterize the atmospheric flight. To do this, using the temporary first marks from Eivissa and the velocity at the point of maximum brightness from satellite data, it has been possible to approximate a conversion between pixels and real distance consistent with the data. The result for the pre-atmospheric ve- locity has been 16.6km/s and the terminal velocity 11.8km/s. The results of the computed radiant are shown in the Table 4.6, both the observed, geocentric and the heliocentric one.

Radiant Data Observed Geocentric Heliocentric

RA (◦) 206.9 194.0 221.2 DE (◦) 56.9 52.8 17.1 V (km/s) 16.6 12.6 34.0

Table 4.6: SPMN160819 observed, geocentric and heliocentric computed radiant and the velocity, with their corresponding errors.

By applying the software mentioned in Section2, the orbital parameter has been computed. Because the superbolide was only recorded by one station and also partially, and that the recording from Sardinia there are not enough reference stars, it has not been possible to estimate the errors rigorously. Table 4.3 shows the approximate orbital parameters for the SPMN160819 event. It was of sporadic origin.

Orbital Parameter

a (AU) e q ω(◦) Ω(◦) i (◦) 1.46 0.367 0.923 134.00 143.658 17.51

Table 4.7: SPMN160819 computed orbital parameters. 48 4.S TUDY CASES Figure 4.6: SPMN160819 apparent trajectory recorded and reduced from Eivissa (a), Sardinia (b) and Costa Brava (c). Reference stars and constellation are pointed out. 4.2.S PORADIC SUPERBOLIDE: SPMN160819 49 Figure 4.7: SPMN160819 apparent radiant basedplane on and the the records nearby from constellations Eivissa of (orange), the Sardinia Northern (green) hemisphere and are Costa shown. Brava (purple) plotted into the celestial sphere with propagation errors. Ecliptic, equatorial 50 4.S TUDY CASES Figure 4.8: SPMN160819 atmospheric trajectory based on the records from (orange), Sardinia (green) and Costa Brava (purple). Vertical projection (white) and observation range are shown. 4.2.S PORADIC SUPERBOLIDE: SPMN160819 51

The slope between the trajectory and the local horizon is one of the key parameters that define the fate of the meteoroid. In this case the slope was estimated to be 37◦. After performing the fitting of the normalised velocity and the normalised height in order to parametrize the atmospheric flight (see 4.9) and assuming a mean value of ordinary chondrite’s density of 2.7g/cm3 [Consolmagno and Britt, 1998], the α β criterion − shows that it will probably produce meteorite, as it is depicted in Figure 4.10. The initial mass of the meteoroid has been estimated to be 1121kg with an initial size of 93cm. The terminal mass computed is 1.3kg, which is in good agreements with previously study of bolides with these characteristics. In the case of Villalbeto de la Peña fall, for example, the meteoroid had 70cm and a pre-atmospheric mass of 760 150kg [Llorca et al., ± 2005, Trigo-Rodriguez et al., 2006].

12 bservation 11

10

9

8

7

Normalised height Normalised 6

5

4

0.2 0.4 0.6 0.8 1.0 Normalised velocity

Figure 4.9: Plot of observational data with velocity normalized to entry velocity and height normalized to the atmospheric scale height for the SPMN160819 event.

ble fall

−

Figure 4.10: SPMN160819 flight parametrization. The bounding line for a 50 g meteorite is shown in black for the case where there is no spin (µ 0) and in gray where spin allows uniform ablation over the entire surface (µ 2/3). = =

In summary, it has been possible to reconstruct the trajectory of this superbolide thanks to the synergy between satellite data, a SPMN station and a random picture of the superbolide persistent trail. Using these 52 4.S TUDY CASES records, it has been possible to characterize the atmospheric flight and estimate the terminal mass, being a clear example of meteorite-dropper candidate. Unfortunately, given its coordinates, it may not be possible to collect any meteorite as they probably fell into the Mediterranean Sea. Table 4.8 compiles the most relevant computed values of the SPMN160819 event.

SPMN160819

Mag hi (km) hf (km)V (km/s)Vf (km/s)Me (kg)Mf (kg) ∞ -16.5 48.0 28.5 16.6 11.8 1121 1.3

Table 4.8: SPMN160819 computed trajectory, velocity and mass data obtained from the observations. 5 DISCUSSION:IMPLICATIONFOR IMPACT HAZARD

This work exemplifies how ground-based recording of large bolides increases our statistics on large mete- oroids reaching the Earth’s orbit. Here the relevance of studying these meteoroids are put in context, even when some are quite small and are not directly hazardous. Despite of this, the meteoroid streams from which these rocks are coming could contain hazardous meter-sized projectiles.

It is used to talk about catastrophic impacts that occur in timescales of millions of years, but it only can be studied the environmental effects caused by them, sometimes highly biased by geologic activity. Statis- tically, bodies few meters to tens of meter in diameter are the most frequent to collide with our planet, so it is important to quantify how they can contribute with direct hazard to humans. To do so it is needed to understand the behavior of stony bodies decelerating in the terrestrial atmosphere, using new perspectives [Moreno-Ibáñez et al., 2015, Moreno-Ibáñez et al., 2018, Moreno-Ibáñez et al., 2020].

The need of quantifying the magnitude and nature of asteroid impacts has been emphasized previously [Chapman et al., 1982, Chapman et al., 1989]. A 1996 Resolution of the Council of Europe promoted the de- velopment of detection programs to search, characterize and catalogue Near Earth Objects (NEOs), and the subgroup of Near Earth Asteroids (NEAs). The European Union interest promoted the Horizon 2020 program Protec-2-2014: “PROTECTION OF EUROPEAN ASSETS IN AND FROM SPACE-2014-LEIT SPACE”, which em- phasizes the relevance to find and monitor hazardous asteroids.

NEAs have orbits with perihelion distance q 1.3 astronomical units (AU) and aphelion distance Q < > 0.983AU (see the different types in Table 5.1). Asteroids dominate the near-Earth region because represent a population of thousands of bodies compared with about one hundred dark cometary objects that share dy- namic and physical properties of being dormant comets [Jenniskens, 2007]. Many asteroids are rubble piles produced by re-aggregation after catastrophic impacts [Michel, 2001, Michel et al., 2002, Davis et al., 2002].

The lack of completeness of asteroid catalogues is exemplified with the close approach of the 30-meter in diameter NEA 2012 DA14 “Duende” during 2013. It passed within 27,700 km of the Earth’s surface. Para- doxically, the very same day an 18-m in diameter unnoticed asteroid broke apart in the city of Chelyabinsk (Russia).

The possibility that meteorite-dropping bolide complexes associated with asteroids could exist was first proposed by [Halliday, 1987].[Trigo-Rodriguez and Llorca, 2007] also found dynamic associations between large meteoroids and Near Earth Objects (NEOs). Many asteroids are rubble piles and so probably do not re- quire a collision in order to be disrupted, but only tidal fracturing caused by close encounters with planets and fast rotation [Trigo-Rodriguez et al., 2007, Trigo-Rodriguez et al., 2008]. Meteoroids ejected by a fast rotator could have quite low de-coherence timescales if it is considered the YORP effect. Alternatively, a catastrophic disruption produces fragments in which typically the escape velocity is considerably smaller than the orbital

53 54 5.D ISCUSSION:IMPLICATION FOR IMPACT HAZARD

Group Description Orbital Definition NECs Near-Earth Comets q<1.3 AU, P>200 y NEAs Near-Earth Asteroid q<1.3 AU Atiras NEAs named after asteroid Orbits are contained entirely 163693 Atira with the orbit of the Earth a <1.0 AU, Q <0.983 AU Atens NEAs named after asteroid Earth-crossing NEAs with 2062 Aten. semi-major axes smaller than Earth’s a <1.0 AU, Q >0.983 AU Apollos NEAs named after asteroid Earth-crossing NEAs with 1862 Apollo semi-major axes larger than Earth’s a >1.0 AU, q <1.017 AU Amors NEAs named after asteroid Earth-approaching NEAs with 1221 Amor orbits exterior to Earth’s but in- terior to Mars’, accomplishing a>1.0 AU, 1.017

Table 5.1: Orbital definitions of the Near Earth Object groups and their respective acronyms (Adapted from NEO JPL). velocity, so a large amount of the mass is ejected away at escape velocity [Trigo-Rodríguez et al., 2015]. Con- sequently, these physical processes occurring in or close to the near-Earth space could produce meter-sized rocks forming a stream of asteroidal fragments moving on nearly identical orbits [Williams, 2011, Jenniskens, 1998, Trigo-Rodriguez et al., 2007]. This is a likely source of meteorites to Earth but is more probable that the delivery from NEOs is dominated by low compressive strength materials: well fractured ordinary chondrites or well fragile carbonaceous chondrites [Trigo-Rodriguez and Williams, 2017].

The study of Cosmic Ray Exposure Ages (CREAs) in meteorites is particularly important and informative by the solar wind noble gases implanted in them during the movement around the Sun of the meter-sized progenitor meteoroids. It is well accepted that the inferred CREAs corroborate that most meteorites reach the Earth after timescales of tens of Ma, so most of them are delivered from the main belt by resonances[Marti and Graf, 1992, Morbidelli and Nesvorný, 1999]. Such timescales are consistent with meteorites delivered from the main asteroid belt (MB) through dynamic resonances. A more exhaustive and recent review by [Eu- gster et al., 2006] identified some chondrites exhibiting smaller CREAs (see Figure 5.1).

A parameter that inform about the ability of meteoroids to penetrate into the atmosphere and constitute source of hazards to human beings is the ablation coefficient. It is a factor that determines how the bolide lose mass as it interacts with the atmosphere. A low ablation coefficient will effect on the meteoroid with a more efficient loss of mass and vice versa.

2 2 The ablation coefficient is normally given in units of s km− . The value of the ablation coefficient will depend on the meteoroid composition, density and body shape. In general, the ablation coefficient range 2 2 is between 0.01 and 0.3s km− . In order to exemplify this, Figure 5.2 shows a simulation for a bolide with a pre-atmospheric velocity of 25 km/s and a zenith angle of 45◦ starting to decelerate at an altitude of 100km with an initial mass of 1g.

As it is seen for the same initial conditions the larger the ablation coefficient is, the faster the body de- celerates. As the mass of the body decreases due to the ablation coefficient, the drag force caused by the atmosphere causes more influence. 55

Figure 5.1: Typical CREAs for chondritic meteorites. Adapted from [Eugster et al., 2006].

Figure 5.2: Comparison of bolides with the same initial conditions but different ablation coefficients. 56 5.D ISCUSSION:IMPLICATION FOR IMPACT HAZARD

Even when the atmosphere can be considered a good shield for meter-sized asteroids, recent meteorite- dropping events suggest that small asteroids produce shock waves and heat with potential to damage hu- mans [Brown et al., 2013]. In fact, the atmospheric behavior of high-strength meteoroids makes also possible to have meter-sized projectiles reaching the ground and excavating a crater. A good example of it was the crater generated in Carancas (Perú) by a relatively small meteoroid [Tancredi et al., 2009].

There is evidence about the existence of meter-sized projectiles forming streams. [Wolf and Lipschutz, 1995] and [Lipschutz et al., 1997] argued that there is evidence from meteorite falls statistics for the existence of such streams. In fact, a plausible association between the NEO 2002NY40 and several bolides recorded over Spain and Finland was found [Trigo-Rodriguez and Williams, 2017]. [Babadzhanov et al., 2008] also found meteor showers dynamically associated with 2003 EH1. In addition, two meteorite-dropping bolides were linked with the Potentially Hazardous Asteroid (PHA) 2007LQ19 [Madiedo et al., 2014]. It was also found a dynamic link between Annama chondrite and PHA 2014UR116 [Trigo-Rodríguez et al., 2015]. Finally, an- other dynamic link between comet 2P/Encke, the Taurid complex NEOs and the Maribo and Sutter’s Mill meteorites has been proposed by [Tubiana et al., 2015].

Finally, the successive encounters of periodic comets with the Sun makes them to disrupt as a conse- quence of aging [Napier et al., 2015]. This process is source of a significant number of extinct comet frag- ments, some of them transformed in dark asteroidal projectiles (Figure 5.3). A good example of the outcome of this process is the challenging Apollo asteroid 2015 TB145. This 650m in diameter asteroid was discovered in Oct. 2015, with only three weeks of margin, and should not leave us indifferent.

The hazard associated with these dormant comets is exemplified by their capacity to deposit energy. Given its size, and the encounter velocity of 35km/s, 2015 TB145 could exemplify the serious risk that similar asteroids could pose to Humanity. The low reflectivity of these objects also made that it is underestimated their devastating potential. As an example, the original 400 m in diameter estimate assuming an ordinary chondrite albedo, was reassessed into 650 m from the study of radar images obtained from Arecibo and Gold- stone (5.3). These objects are extremely dark and difficult to find, so their discovery requires systematic stud- ies performed from space-based IR telescopes. Recent progress in the study of these objects has been made by OSIRIS-REx mission [Lauretta et al., 2014].

Figure 5.3: The radar appearance of recently discovered extinct comet 2015 TB145 (NAIC-Arecibo/NSF). 6 CONCLUSIONSAND FUTUREWORK

The work carried out contributes with a software tool for the detection and reconstruction of meteor trajec- tories, increasing the capacity to quantify its ability to penetrate into the atmosphere and suppose hazard to humans. Thanks to the application of new techniques, the analysis of the atmospheric deceleration of cm to m-sized bodies flight is facilitated through, providing relevant information about the survival of meteorites, the nature and origin of these meteoroids and the characteristics of the atmospheric.

In summary, the main contributions and conclusions of this master thesis are:

• Novel computer vision techniques, image processing and motion detection methods have been ap- plied for automatic extraction of the meteor position throughout the recording. To avoid false positives produced by glares during the ablation process, a Kalman filter has been implemented to predict the motion of the bolide. In addition, a post-processing treatment has also been developed using clustering algorithms to discard incorrect points.

• To transform the fireball’s motion from pixels to apparent trajectory, it is necessary to identify stars as a reference for the reduction. After automatically overlap frames without detection to highlight faint stars, a corner algorithm is applied to identify such stars. A subsequent treatment is performed to avoid possible false positives due to objects such as trees or buildings.

• Corrections of the atmospheric extinction and refraction, as well as light aberration due to the Earth’s motion has been implemented in order to improve the photometry. This allows to estimate the bright- ness and photometric mass of the bolide to get information about its mass and possible size.

• The atmospheric trajectory reconstruction of fireballs has been implemented using a routine based on multi-station records. This technique uses principles of stereoscopy, spherical geometry and sim- plex algorithm to minimize errors. It also includes a model to approximate the distortion of the lens produced by wide-field and all-sky cameras. This has been tested successfully with two study cases.

• A realistic model for representing the atmospheric trajectory of the bolide in 3D and in real scale has been developed. To check the results of the astrometry, a stellarium has been built showing the con- stellations. This graphic model serves as a generator of valuable multimedia content for scientific dis- semination and outreach.

• It has been implemented a characterization of bolide’s atmospheric flight allowing to compute the pre- atmospheric mass and to identify probable meteorite-dropper bolide by using the α β criterion. − • The event studied SPMN251019B exemplifies the dominant class of cm-sized meteoroids and adds in- formation on the bolides associated with the Taurid complex and the origin and evolution of hazardous short period comets as 2P/Encke.

• The superbolide studied SPMN160819 demonstrates the ability to use Earth-observation satellite data by using the peak brightness coordinate measured from space.

57 58 6.C ONCLUSIONSAND FUTUREWORK

• Chelyabinsk or Carancas events have exemplified that the risk associated to meteoric phenomena is real. Fortunately, the atmosphere produces the fracture of small asteroids before crater excavation. However, superbolides can produce strong shock waves that can break windows and even tear down weak buildings. Also the energy radiated by a superbolide could cause severe burns in humans and animals located near the event as was well exemplified by Chelyabinsk.

• The software developed SPMN 3D Fireball Trajectory and Orbital Calculator (3D-FireTOC) has demon- strated its ability and potential to quantify the impact hazard associated with m-sized asteroids by re- constructing the trajectories.

• The automatic meteor detection and analysis opens the possibility of providing early warnings associ- ated with massive meteorite and shock waves arrival to the ground.

This master thesis has been carried out with a view to its extension to a doctorate. This work has been made in the framework of the data obtained in the project [Trigo-Rodriguez, 2018]. It is therefore framed in a medium-long research project, the intention being to deepen the issues addressed and apply the tools devel- oped in future research. Therefore, both ideas for improving the software and new applications connected to this work are proposed:

• Implement a more complex model for fish-eye distorsion correction, e.g.: [Borovicka et al., 1995].

• Develop of a model to characterize the dark flight [Pecina and Ceplecha, 1983], improving the strewn- field by including wind profiles.

• Build an user interface for 3D-FireTOC.

• Research on meteoric impact flux distribution for planetary evolution [Opik, 1963] and minor body orbit study [Lefeuvre and Wieczorek, 2008].

• Automatic analysis of monitoring meteors from space.

• Create a gimbal type device to track and zoom the fireball in real time.

• Intelligent light spectra analysis emitted by bolide to study the ionization process [Trigo-Rodriguez and Llorca, 2007] and chemical abundances [Trigo-Rodriguez et al., 2003].

• Application of novel nanoindentation technique to characterize mechanical properties of cometary or asteroid proxies [Moyano-Cambero et al., 2016]. REFERENCES 59

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