The interaction of small asteroids in the Earth's atmosphere

Our Earth. A little planet in a huge space. It seems very unlikely that Earth could be hit by another cosmic body, such as a comet, an asteroid, or a meteoroid. However, the Earth is continuously hit by meteoroids and sometime also by an asteroid or a comet.

What is a meteoroid? What is a meteor? What is a meteorite?
According to the International Astronomical Union, a meteoroid is an interplanetary body, deriving from asteroids or comets, with a mass range from one thousand millionth of kg and ten million of kg. In other words, it is a body larger than a molecule, but smaller than an asteroid.
As a meteoroid enters the Earth's atmosphere, it collides with air molecules. At the heights where most meteors ablate, the mean free path of the air molecules is about 0.1-1 m. On the other hand, common meteoroid dimensions are of the order of 0.1-1 cm. This means that there is no hydrodynamic flow around the meteoroid and single air molecules impact on the body. If we consider a meteoroid a typical geocentric speed of 40 km/s, it can be found that air molecules impinge on the body with the same speed. The kinetic energy is about 8 eV per nucleon: a nitrogen molecule then has an energy of about 230 eV. The impact energy is readily transformed into heat, which makes atoms evaporate from the meteoroid. The collisions between free atoms and air molecules produce heat, light and ionization, i.e. a meteor. Since this transformation occurs throughout the flight, the meteoroid atoms are dispersed in a cylindrical channel along the path.
According to its dimensions, material strength, and atmospheric trajectory, a meteoroid can reach different zones of the atmosphere. Generally, the bodies that can reach the stratosphere are large enough to produce a bright meteor. If the magnitude is less than -4 we have a bolide. When the originary meteoroid is very large, on the borderline with asteroids, it can reach the troposphere. Generally these bodies exploded in the atmosphere (airburst). If a meteoroid survives to the interaction with air molecules and reach the soil, the remnant of the originary meteoroid is called meteorite.

The nomenclature is summarized in this FIGURE (image credit: R. Baldini).

Bolides and airbursts
The atmospheric interaction of large meteoroids provides our primary tool to characterize their population, physical and chemical properties, and dynamical evolution. In turn, this can lead to a better understanding of the diverse populations of small bodies of the Solar System. Currently, our knowledge is still quite limited, although, especially after the impact of comet D/Shoemaker-Levy 9 on Jupiter, the research efforts in this field have been intensified. In particular, in 1994 the US Department of Defense made of public domain its records on energetic bolides over a time span of about twenty years. These data indicate that, from 1975 to 1992, there were 136 airbursts of energy greater than 1 kton, but the real number was probably at least 10 times higher, because the satellite system does not cover the entire Earth surface. One of the most important question, today still open, is to understand why meteoroids break up at dynamical pressures lower than their mechanical strength. This is of paramount importance, because it allow to know whether or not a meteoroid might reach the soil. Therefore, it allows to establish a reliable criterium to assess the impact hazard.

We can however set up a reliable phenomenological model, even though we have not an efficient and quantitative theory. Specifically, as noted by Zdenek Ceplecha, it is still unknown why large meteoroids/small asteroids break up at dynamical pressures lower than their mechanical strength. For example, the Peekskill meteorite has an estimated strength close to 30 MPa, but it was found that the maximum value of fragmentation pressure was about 0.7-1.0 MPa. Why? One possible answer was recently given by Luigi Foschini, who proposed a model based on the interaction of shock waves and turbulence under unsteady conditions (see L. Foschini: "On the atmospheric fragmentation of small asteroids" Astronomy and Astrophysics 365, 2001, 612), but this is only a conceptual outline, and numerical models are necessary.

When a large meteoroid enters the Earth's atmosphere, it has a speed in the range 12-72 km/s, hence it moves at hypersonic speed (that is, with Mach number greater than about 5). Since here we are interested in the dynamics of a meteoroid large enough to reach the lower atmosphere, the fluid can be treated as a continuum. Thus, we can use current knowledge about hypersonic aerodynamics in order to understand meteoroid airbursts.
It is important to note that for large Mach numbers the linearized equations for the speed potential are not valid, so we cannot use laws holding for supersonic speeds. In hypersonic flow, Mach waves and oblique shock waves are emitted at small angles with the direction of the flow, of the order of the ratio between body thickness and length, and thus tend to follow the surface of the body. Under these conditions, the atmospheric path of a large meteoroid can be seen as a long cylinder, generating pressure waves that can detected in different ways (barographs, seismographs).
Under steady state, the small angle of Mach and oblique shock waves gives also rise to the concept of hypersonic boundary layer near the surface. In front of the meteoroid there is a bow shock, that envelopes the body. The shock is stronger on the symmetry axis, because at this point it is normal to the stream. Then, we find a zone where molecular dissociation is the main process and even closer to the body surface, we find the boundary layer, where viscous effects are dominant. As the air flows toward the rear of the meteoroid, it is reattracted to the axis, just like in a Prandtl-Meyer expansion. As a consequence, there is a rotation of the stream in the sense opposite to that of the motion (rectification); this creates an oblique shock wave, which is called wake shock. Since the pressure rise across the bow shock is huge when compared to the pressure decrease across the Prandtl-Meyer expansion, one can assume, as a reasonable approximation, that there is a vacuum in the rear of the meteoroid.


(image credit: R. Baldini)

The fluid temperature increases in the boundary layer, because the speed must decrease to zero at the meteoroid surface; moreover there are heating effects due to viscous dissipation. There are also regions (like in the Prandtl-Meyer expansion) in which the presence of vacuum or near-vacuum strongly reduces heat transfer, and this contributes to the increasing body temperature. If the generation of heat increases so quickly that the loss of heat may be inadequate to achieve an equilibrium state, we may have a thermal explosion. This explosion generates pressure waves that can be detected on the ground by seismographs or barographs. It is very interesting the paper by A. Ben-Menahem: "Source parameters of the Siberian explosion on June 30, 1908 from analysis and synthesis of seismic signals at four stations" (Physics of the Earth and Planetary Interiors 11, 1975, 1), where the scientists analysed seismic and infrasound data from the Tunguska event of 1908 (see below). Note that after the Tunguska event no meteorite was recovered, so the argument the meteorites are usually cold immediately after landing does not rule out this kind of thermal explosion in this case.
It is worth noting that this picture does not take into account how does the ablation modify the hypersonic flow. This is still unknown.

For italian readers, other informations about these arguments are available on a popular astronomy book:
A. Carbognani, L. Foschini: Meteore - Dalle stelle cadenti alla catastrofe di Tunguska. CUEN, Napoli (1999).

The TUNGUSKA event (June 30, 1908)

On June 30th, 1908, something exploded over Tunguska, in central Siberia. Among many different effects, the Tunguska explosion produced shock waves, which were recorded by seismographs at several sites. A. Ben-Menahem (1975) made a detailed analysis of these seismic records and derived an explosive energy of 12.5 Mton. Other analyses suggested an energy value in the range 10-20 Mton. Ben-Menahem also concluded that the data on the energy source are consistent with an airburst at a height of about 8.5 km.
The explosion occurred at 0h 14' 28'' UT and devastated about 2,150 square kilometers of Siberian taigà, felling more than 60 million trees. The explosion epicenter has been localized at 60 53' 09'' N and 101 53' 40'' E, near the river Stony Tunguska.
Over the last ninety years this catastrophic event has inspired a plethora of scientific investigations. Despite many interesting findings, there are still substantial open questions and inconsistencies among the theories and the available data.
On July 20 - August 1, 1991, the first italian expedition, composed by M. Galli, G. Longo, S. Cecchini and R. Serra, went in Siberia. The italian researchers found several microspherules in trees, that are remnants of the Tunguska Cosmic Body (TCB). After an analysis with scanning electron microscopy (SEM), they found some chemical elements that strengthen the hypotesis of the asteroidal origin of the TCB.
On July 14-30, 1999, a second italian expedition went in Siberia in order to find scientific data, which allow to give a reasonable certainty about this event.

References:

Some other special episodes

PEEKSKILL (October 9, 1992)
On October 9, 1992 a fireball brigh like the full moon (-12) was observed in Northern America. The cosmic body ended its flight on a car in Peekskill (NY, USA) and a meteorite (H6) of 12.4 kg was recovered. The event was recorded by 16 video cameras and this allowed to infer the orbit of the parent body. More details and photos in the Peekskill Meteorite and Fireball web site.

LUGO (January 19, 1993)
On January 19, 1993, a very bright bolide (peak magnitude -23) crossed the sky of Northern Italy, ending with an explosion approximately over the town of Lugo (Emilia Romagna, Italy). The explosion (14 kton of energy) generated shock waves which were recorded by six local seismic stations.
We can summarize some features of the Lugo bolide: it had a grazing trajectory in the atmosphere, it was probably a carbonaceous chondrite, but it exploded at a height higher than usual and with a single airburst, without fragmentations. The recent discovery by the NEAR probe of a carbonaceous asteroid (253 Mathilde) with a very low density (about 1300 kg/m^3) suggests the existence of porous bodies (i.e. bodies with internal cavities) among asteroids.
If we assume that the Lugo bolide was a porous carbonaceous chondrite, we have a body which was probably stronger than a cometary fragment, but which could explode at a higher altitude than those typical for stony objects, because of its porosity. It is very likely that porosity increases the burst efficiency: when ablation removes the surface of the body, cavities may appear which increase the aerobraking and generate a sudden deceleration. The kinetic energy then is rapidly transformed into heat, so that the body bursts within a scale height (FIGURE; image credit: R. Baldini).
Reference: L. Foschini: On the airburst of large meteoroids in the Earth's atmosphere - The Lugo bolide: reanalysis of a case study. Astronomy and Astrophysics 337, (1998), L5.



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