New methodology to determine the terminal height of a fireball
Graphical abstract
Introduction
Deriving the meteoroid trajectories in the atmosphere is of particular interest to researchers. On the one hand, orbital parameters can be derived based on the time of appearance, meteor position and initial velocity, allowing us to estimate their parental relationship with parent bodies – asteroids and comets. On the other hand, a knowledge of physical parameters such as mass, velocity, deceleration, height, at different points of its trajectory turns out to be very useful so as to predict the energy of a possible surface impact, locate meteorite fall and/or understand the ablation and other mass loss mechanisms occurring along the flight.
Various photographic and video techniques have been developed to obtain the most accurate and systematic observations of meteors. Whipple and Jacchie (1957) (later modified by McCrosky and Posen, 1968, Pecina and Ceplecha, 1983, Ceplecha et al., 1993) derived a methodology by considering the separate meteor trails obtained when shuttering the video image. This technique allowed them to study the problem at shorter flight intervals. This analysis was dependent on the body properties’ average values provided by the bibliography. However, a reliable theoretical flight model is still to be developed. The accuracy of theoretical results usually requires a very good precision in observation techniques. For example, Ceplecha et al. (1993) developed a theoretical model which included meteor fragmentation, but it needs very precise fireball records. Along the years different methods have been developed in order to increase the accuracy of the theoretical models.
One of the first theoretical models for meteors (known as Single Body Theory) was developed by Hoppe (1937). It was an extensive study of the flight mechanics and thermodynamics processes. Levin, 1956, Levin, 1961 studied the meteoroids’ atmospheric entry with account for fragmentation and deceleration. He concluded that the mass of the body is related to its middle section by means of a parameter that characterizes the rotation of the fireball.
Later on, Ceplecha and McCrosky (1976) explored which fireballs of the Prairie Network were ordinary chondrites. The authors considered the fireball terminal height as a main characteristic factor. It was concluded that carbonaceous material shall ablate more readily and, consequently, these bodies may have shorter trajectories. The authors derived an empirical criterion (Eq. (1)) that established a weighted relation between the fireball terminal height and other flight properties of the fireball (namely, air density at terminal height, , the preatmospheric mass, [g], preatmospheric velocity, [km/s], and the zenith distance of the meteor radiant, [degrees]).This expression also has a theoretical meaning based on the single body theory, as explained in their work. Coefficients A, B and C are obtained by using a least squares fit to 156 fireballs of the Prairie Network (McCrosky and Boeschenstein, 1965). Owing to this criterion (Eq. (1)), Ceplecha and McCrosky (1976) classified the Prairie Network fireballs into four different groups. In their discussion they suggested that ordinary chondrites should all belong to the same range of PE values ().
Besides, Ceplecha and McCrosky (1976) took advantage of the fireballs’ observed properties in order to shed more light in the validity of the previous criterion (Eq. (1)). Two parameters were used: K (the shape–density coefficient) and σ (ablation coefficient) . The average values (for all the observational measurements) are used to define a new parameter, SD:The average numbers, and , are weighted by the ratio of the deceleration to its formal rms error. Then, SD is a parameter that has little influence from observational errors. As Ceplecha and McCrosky (1976) stated, SD depends on the second derivative of the observational measurements via these two refined numbers, whereas PE is chosen as the simplest possible empirical expression. Therefore, SD is a new criterion which can be compared against the PE criterion. These two parameters (1), (2) turned out to be related when the meteor initial mass could be considered small or the ablation was large.
Slightly different methodology was suggested by Wetherill and Revelle (1981). They included four meteorite selection criteria to build up their classification. Wetherill and Revelle (1981), gave more importance to the dynamic mass than to the photometric mass; besides, they also took into account the deceleration of the body and the light curves to identify the survived meteorites among the fireballs registered by the Prairie Network. The authors highlighted the importance of the observed terminal height concluding that for meteorite-producing fireballs its value should agree with the theoretical value, calculated using dynamic mass, as well as with that of Lost City fireball to within 1.5 km, when scaled for mass, velocity, and entry angle in accordance with classical single body meteor theory.
In Revelle (1979), the study of the interaction between large meteoroids and the atmosphere is done via a quasi-simple ablation model. The results are compared to photographically recorded meteorite falls as well. Later publications have gathered and expanded the physical problem of the deceleration of meteoroids in the atmosphere (e.g. Bronshten, 1983).
Halliday et al., 1989a, Halliday et al., 1989b studied observed fireball properties to derive the presence of correlations. They used 44 MORP recorded fireballs to classify as strong, moderate, weak or not having any correlation the observed data (i.e. initial velocity, total light emitted by the fireball, initial and end masses, initial and end heights, orbital elements, etc.). Despite of the observational errors (cameras not able to film all the trajectory, not clear sky, etc.), they found some strong correlations: mass lost by ablation versus the peak brightness, and duration of luminosity recorded by MORP versus zenith distance of the radiant.
Stulov et al., 1995, Stulov, 1997, Gritsevich, 2007 proposed a new methodology. Instead of using the average values as input parameters, they gather all the unknown values into two new variables α (ballistic coefficient) and β (mass loss parameter), mathematically introducing similar idea with scaling of parameters as suggested by Wetherill and Revelle (1981). Adjusting the resulting equation to the trajectory observed, these new variables can be derived for each meteoroid. The resulting values allow to describe in details the meteoroid trajectory in the atmosphere and invent new classification scale for possible impacts (Gritsevich et al., 2011, Gritsevich et al., 2012). This allows to determine other important parameters, such as preatmospheric and terminal mass values, ablation and shape change coefficients, as well as terminal height. The methodology to determine terminal height has been implemented for fully ablated fireballs by Gritsevich and Popelenskaya (2008). In the present study we significantly specify and expand the applicability range of this methodology by testing it on larger data set.
In the following sections we present the results of applying this last methodology to a large number of MORP fireballs, including suspected meteorite-producing events included in the table 6 by Halliday et al. (1996). Alternatively, we suggest a more accurate method of calculation. Section 2 takes a look on previous and present terminal height determinations. We then compare observed values to our derived values in Section 3. Section 4 contains our discussion. Finally the conclusions and suggestions for future research are presented in Section 5.
Section snippets
Theory
The equations of motion for a meteoroid entering the atmosphere projected onto the tangent and to the normal to the trajectory are well known. Once we consider some simplifications (see Gritsevich, 2010) we have:
M is the body mass, V is its velocity, t is the time, h is the height above the planetary surface, γ is the local angle between the trajectory and the horizon, S is the area of the middle section of the body, is the atmospheric density and is the drag
Results
We have derived terminal heights by means of the previous development. In order to do so, we have used the α and β values which have been previously derived using the methodology described above by Gritsevich (2009) for the MORP fireballs. These heights are compared to the fireballs observed terminal height values; Halliday et al. (1996) collected them along with other fireball parameters such as: brightness, beginning and ending velocity, beginning height above sea.
The results of the following
Discussion
As explained in Section 2, Eq. (20) should lead to good results when β values are high. In Fig. 4 we notice that for the differences between derived and observed terminal heights are small. However, this equation did not take into account the decrease in velocity close to the terminal point of the trajectory. Given that the amount of fireballs studied is large, we continued our analysis considering this fact (see Eq. (21)).
Formula (21) seemed to provide accurate results with regard to the
Conclusions
Previous work has been done to estimate the terminal height of fireballs (see Section 1). In this paper, we have derived the terminal heights for MORP fireballs using newly developed as well as previously suggested methodology. This methodology had only been tested on several fully ablated fireballs with large β values by Gritsevich and Popelenskaya (2008). We were particularly interested in determining whether this new mathematical approach works equally accurately with fully ablated fireballs
Acknowledgments
We thank support from the Spanish Ministry of Science and Innovation (Project AYA2011-26522), the Academy of Finland (Project 260027) and the Finnish Geodetic Institute. The concept of the methodology and calculations were made by Manuel Moreno-Ibáñez and Maria Gritsevich, the later while she was hosted in MIIGAiK as invited expert in the Project No. 14-22-00197 ”Studies of Fundamental Geodetic Parameters and Topography of Planets and Satellites” supported by the Russian Science Foundation.
References (37)
- et al.
Atmospheric deceleration and light curves of Draconid meteors and implications for the structure of cometary dust
Astron. Astrophys.
(2007) Simulation of the capabilities of an orbiter for monitoring the entry of interplanetary matter into the terrestrial atmosphere
Planet. Space Sci.
(2014)Physics of Meteoric Phenomena
(1983)- et al.
Fireball end heights – A diagnostic for the structure of meteoric material
J. Geophys. Res.
(1976) - et al.
Atmospheric fragmentation of meteoriods
Astron. Astrophys.
(1993) - et al.
Constraining the luminous efficiency of meteors
Icarus
(2011) - et al.
Consequences of collisions of natural cosmic bodies with the Earth’s atmosphere and surface
Cosmic Res.
(2012) Approximation of the observed motion of bolides by the analytical solution of the equations of meteor physics
Solar Syst. Res.
(2007)Estimating the terminal mass of large meteoroids
Doklady Phys.
(2008)Identification of fireball dynamic parameters
Moscow Univ. Mech. Bullet.
(2008)
The Pribram, Lost City, Innisfree, and Neuschwanstein falls: An analysis of the atmospheric trajectories
Solar Syst. Res.
Determination of parameters of meteor bodies based on flight observational data
Adv. Space Res.
On a formulation of meteor physics problems
Moscow Univ. Mech. Bullet.
Meteor and fireball trajectories for high values of the mass loss parameter
Doklady Phys.
Approksimatsiya resheniya uravneniy meteornoy fiziki elementarnymi funktsiyami Elementary functions approximation for the solution of meteor physics equations
Mat. Model.
Standards for crater formation and meteorite fallout by the light sector of an atmospheric trajectory
Doklady Phys.
Detailed records of many unrecovered meteorites in western Canada for which further searches are recommended
J. R. Astron. Soc. Can.
The typical meteorite event, based on photographic records of 44 fireballs
Meteoritics
Cited by (28)
Ultra high energy cosmic rays The intersection of the Cosmic and Energy Frontiers
2023, Astroparticle PhysicsCitation Excerpt :Meteors are generated by the interaction of a cosmic body with the Earth’s atmosphere. The physical characteristics of the interacting body, as well as the entry angle, determine the magnitude and duration of these phenomena [1038–1041]. Estimates suggest that, on average, meteoroids cumulatively deposit 5 to 300 t of extraterrestrial material every day, mostly into the Earth’s atmosphere [1042–1044].
The January 7, 2015, superbolide over Romania and structural diversity of meter-sized asteroids
2017, Planetary and Space ScienceCitation Excerpt :Ceplecha (1994) used the old luminous efficiency and overestimated the masses and sizes of the studied meteoroids. Bolide end heights were recently discussed also by Moreno-Ibáñez et al. (2015). Their methodology, however, relies on observed deceleration along the trajectory and does not take into account bolide luminosity, and is therefore not suitable in the present cases.
Implications of the atmospheric density profile in the processing of fireball observations
2016, Planetary and Space ScienceCitation Excerpt :When a large meteoroid enters Earth׳s atmosphere it generates a visual fireball that can be recorded by cameras. The object causing the fireball can penetrate the atmosphere down to the height of around 20 km in its luminous phase, and in exceptional cases, even lower (Moreno-Ibáñez et al., 2015). In other words, the lower portion of the visual flight occurs within the stratosphere.
Simultaneous optical and radar observations of meteor head-echoes utilizing SAAMER
2015, Planetary and Space ScienceCitation Excerpt :It is from these fairly limited measurements that other parameters, such as mass can be estimated with less accuracy. The study of meteors and their interactions with planetary atmospheres involve many aspects, including theory and modeling, such as described in McNeil (1999), Oppenheim et al. (2000), Dyrud et al. (2007), Close et al. (2002) and more recently the techniques described in Gritsevich (2009), Bouquet et al. (2014), Moreno-Ibánez et al. (2015) to name a few representative examples. In addition, there have been many observational studies which use radars (Reddi and Nair, 1998; Janches et al., 2003, lidars (Grime et al., 1999; von Zahn, 2001), and spectroscopy and imaging (Shamir, 2005; Kaiser et al., 2004).
On the Effect of COVID-19 Lockdown on Seismic Detection Capability
2024, Advances in Science, Technology and Innovation