The Great Chinese Fireball of December 22, 2020

On December 22, 2020 at about 23h 23m 33s UTC a very bright fireball was seen in the sky of south-eastern China. The fireball lasted for several seconds and ended with an atmospheric explosion that was detected by US surveillance satellites. According to CNEOS's data, the fireball moved with a mean speed of 13.6 km/s and exploded at an altitude of about 35.5 km (Lat. $31.9^{\circ}$ N; Long. $96.2^{\circ} $ E). In this paper, using satellites data only, we estimate the atmospheric trajectory, the heliocentric orbit and the strewn fields for different mass/section ratio of the fragments. The trajectory was about from north to south and with low inclination with respect to the local surface. The explosion height appear consistent with a fragmented rocky body and the heliocentric orbit supports an asteroidal origin. The strewn field extend between two points with coordinates ($+31.3^\circ$ N; $96.3^\circ$ E) and ($+30.3^\circ$ N; $96.5^\circ$ E), for a total area of about 4000 $\textrm{km}^2$. However, given the unknown uncertainty of the satellites data, these results should be taken with caution.


Introduction
The Earth's atmosphere is constantly bombarded by macroscopic bodies belonging to the Solar System, in the meter or few meters class in diameter [4]. According to data made public by CNEOS (NASA-JPL Center for NEOs Studies) 1 , there were 851 bright fireballs reported by US government sensors, from April 15, 1988 to December 28, 2020. On average there is an event every two weeks anywhere on Earth. The satellites record the flare of the atmospheric explosions that occur when the body, stressed by the pressure and heat that develops during the fall, disintegrate itself. These events generally occurs at hypersonic speed, that is with a Mach number greater than about 5. The most intense atmospheric explosion ever detected was the Chelyabinsk event on February 15, 2013 [9].
On December 22, 2020 at 23:23:33 UT, a very bright fireball -which we will also call with the acronym "Country Code YYYYMMDD", i.e. CN20201222 -was seen from south China. At some point of its trajectory the fireball exploded even if, most likely, the major fragments continued the fall towards the ground. It was a Chelyabinsk-like event, albeit -fortunately -on a much smaller scale. In what follows, we want to reconstruct an identikit of the Chinese fireball based on the available satellite data. About orbit, dark flight and strewn field computation we have used the same process applied to two Italian fireballs, IT20170530 [2] and IT20200101, which led to recovery of the Cavezzo meteorite [7].

Data collection
We use satellites data from CNEOS that give fundamental information about main explosion location, height and pre-atmospheric speed vector (see Table 1). The IMO 2 website did not collect eyewitness accounts for this event and videos posted on YouTube are not very useful because, generally, they do not have data about the location from which they were recorded 3 . With a more in-depth investigation it will probably be possible to trace the locations. In general, CNEOS events agree in absolute time with independent records to within a few seconds and also locations Send offprint requests to: albino.carbognani@inaf.it 1 https://cneos.jpl.nasa.gov/fireballs/ accessed 2020 December 29 2 International Meteor Organization, www.imo.net 3 https://www.youtube.com/watch?v=N-npJtRt2TI  are correct in most cases [4]. The issue of speed accuracy is more delicate. It has been found that in some cases the error on the speed was of the order of 30%, while the radians have an accuracy of a couple of degrees. In general, only about 40% of the CNEOS events have an acceptable speed accuracy able to compute the orbit [4]. So, especially the results about the heliocentric orbit, should be taken with caution. In Table 1 we assumed that the uncertainty was about ±5 s on event time, ±0.1 • on the explosion coordinates, 0.5 km on the explosion height and about ±10% on the speed components.

Atmospheric trajectory and heliocentric orbit
Data from CNEOS give the values shown in Table 1 for the main fireball explosion. The velocity v is the pre-impact velocity in a geocentric Earth-fixed reference frame defined as follows: the z-axis is directed along the Earth's rotation axis towards the celestial north pole, the x-axis lies in the Earth's equatorial plane, directed towards the prime meridian, and the y-axis completes the right-handed coordinate system. In order to trace the atmospheric trajectory, with inclination angle and azimuth, we perform two rotation on v. The first rotation was made clockwise in the xy plane by an angle equal to the longitude of the explosion. The second also clockwise in the yz plane of an angle equal to colatitude. In this way we have the velocity vector seen from the explosion point, i.e. the trajectory inclination respect to the Earth's surface and the azimuth where the fireball came from (counted from north toward east). To estimate the uncertainty about trajectory angles we performed a Monte Carlo simulation using 5000 different scenarios compatible with the adopted uncertainties.
The results show that the fireball followed an atmospheric trajectory inclined by an angle of 5 • ± 2 • with respect to the horizontal plane, with an azimuth of 352 • ± 1 • (Fig. 1). The topocentric equatorial coordinates of the apparent Table 2. Data about the asteroid heliocentric orbit. The standard deviations are obtained with a Monte Carlo computation with 500 clones. The longitude of the ascending node has very low uncertainty because the value is determined by the time of the fireball fall only.

Quantity
Numerical value (J2000) Semi major axis (AU) The fireball traveled about from north to south and slowly entered the densest layers of the terrestrial atmosphere. The meteoroid could not withstand the pressure and intense heat that developed during the fall, and exploded at about 35.5 km above sea level. After the main explosion, the major fragments probably continued their fall towards the ground in dark flight phase. Assuming that the kinetic energy value is equal to the value of the estimated total impact energy T E , the equivalent meteoroid diameter D is given by: From Eq. 1, with T E ≈ 9.5 kt ≈ 4 · 10 13 J, v ≈ 13600 m/s and a bulk density ρ ≈ 2700 kg/m 3 (typical of an S-type asteroid [1]), it follows that the Chinese fireball was generated by a small asteroid with an equivalent diameter of about 7 meters. Usually the meteoroids fragmentation model assume that the fragmentation process starts when the aerodynamic pressure is equal to the mechanical strength S. According to the meteoroid height h e ≈ 35.5 km and speed v e ≈ 13.6 km/s in the main explosion, we can estimate a strength of about [5,6]: In Eq. 2, γ ≈ 3 is the ratio of specific heats and α ≈ 1 is the coefficient of ionization for plasma state; H ≈ 8 km is the atmospheric scale height and ρ sl ≈ 1.22 kg/m 3 is the atmospheric density at sea level. Considering that for a chondrite a strength S ≈ 10 7 Pascal could be expected [4,6], the estimated value tell us that, probably, the small asteroid of the Chinese fireball was a rocky body with some fractures or voids that decreased the strength [8]. Using the value of v ∞ = 13.6 ± 1 km/s as a pre-atmospheric value and correcting it for the Earth's rotation and gravity using "zenith attraction" method [2,3], the true geocentric speed result v g = 7.9 ± 2 km/s, while the heliocentric speed is v h = 37 ± 1 km/s. Taking into account the true distance and position of the Earth relative to the Sun, we found the heliocentric orbit whose elements are shown in Table 2. The orbit has a Tisserand invariant respect to Jupiter equal to T J = 3.6 ± 0.5, a typical asteroid value, and shows that -with a probability of about 90% -the fireball progenitor came from the Main Asteroid Belt (see Fig. 2).

Dark flight and strewn field
In order to model the dark flight phase it is important to know the atmospheric profile for the time and area closest to the meteoroid fall because the residual meteoroid trajectory, after the end of the luminous path, can be heavily influenced by the atmospheric conditions [2,3]. So we get atmospheric data about pressure, temperature, winds speed and directions by the GFS global atmospheric model 4 near the time and place of the fireball explosion (see Fig. 4). The vertical resolution of this model is height-dependent, from 100 m near the ground to about 7 km around 20 km height, but sufficient to a first raw estimate of the strewn field position with the same method used for the Cavezzo meteorite [7]. Table 3. Strewn field nominal centers for different mass/section ratio (spherical shape) and a mean meteorite density of about 3500 kg/m 3 . The motion of the residual meteoroids, starting from the observed terminal point of the luminous path, was described using Newton's Resistance law as in Ceplecha [3]. We assumed that the atmosphere had little effect on the small asteroid, as in Chelyabinsk case [9], and that the starting speed of the fragments -after the main explosionwas around the pre-atmospheric value, i.e. 13.6 ± 1. As a starting point for dark flight computation we have taken the main explosion coordinates given by CNEOS but with different mass/section ratio for the fragments. An average density ρ ≈ 3500 kg/m 3 -typical of a chondrite -has been assumed for the fragments, because it is reasonable to think that single meteorites have a higher density than the original asteroid. A dark flight example for M/S ≈ 600 kg/m 2 is shown in Fig. 3. In the final part of the dark flight the meteoroid was deflected towards East by wind, which distorted the final trajectory by about 2 km. As the mass/section ratio decreases, the wind influence is greater, so the strewn field location strictly depend from the assumed M/S ratio. The nominal coordinates of the impact points for meteorites with different mass/section ratio are given in Table 3. Considering the low trajectory inclination and the uncertainties of the explosion point, the strewn field orthogonal extension -with respect to the motion direction -is about ±20 km. The biggest meteorites, if any, are expected to be in a quite mountainous region, difficult to reach (see Fig. 1). However, given the uncertainties involved, any point between M/S ≈ 100 kg/m 2 and M/S ≈ 1000 kg/m 2 , is eligible for meteorites search. The strewn field total area can be estimated in about 4000 km 2 .

Conclusions
We give some results about the CN20201222 fireball, observed at about 23h 23m 33s UTC on December 22, 2020 and detected by the US surveillance satellites. The fireball was generated by the fall of a small asteroid of about 7 m in diameter. The explosion height is consistent with a fragmented rocky body and the computed heliocentric orbit supports an asteroidal origin. Fortunately, the potential fragments of the small asteroid did not fall in sea so, with an accurate search on the ground, it will be possible to find some interesting samples of the original body. The strewn field is approximately between two points with geographical coordinates (+31.3 • N; 96.3 • E) and (+30.3 • N; 96.5 • E), for a total surface area of about 4000 km 2 . However, given the unknown uncertainty of the satellites data (we have assumed reasonable values only), these results should be taken with caution.