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The Tunguska Event occurred over 100 years ago in 1908, over the Eastern Siberian taiga. A large explosion engulfed the sky and destroyed a large 2000 $\text{km}^2$ of forested area underneath. People who witnessed it from afar, reported a bright flash that filled the sky, nearing solar brightness. No crater was found at ground zero, but the blackened trees where all knocked down in a radial pattern from the epicenter of the explosion. There is still debate within the scientific community whether this was an icy comet body or a rocky asteroid. Both scenarios are plausible according to modelling done by Robertson and Mathias (2019) where they used computer simulations to model the airbursts of different body types, taking into account wind speed resistance of the trees ( 40 - 50 $\text{ms}^{-1}$), comparing with nuclear explosion tree stand tests done in the 20th century. They found the explosion energy most likely to be around 10 Mt of TNT equivalent, but due to the nature of the lack of data of the incident a wide range of 3 Mt to 30 Mt is accepted, along with uncertainties in the airburst height. Other analyses have also suggested the icy comet hypothesis, but it is generally accepted that it was a rocky asteroid that airburst exploded after hitting denser parts of the lower Earth atmosphere.

Indeed this happened relatively recently - on the 13th of February 2013, the Chelyabinsk asteroid exploded in the atmosphere blowing out glass and collapsing roofing of surrounding city's buildings, causing injuries to $\sim$ 1000 people. Some where hospitalized from the direct shockwave of the explosion. It was around 20 meters in diameter before the airburst. Although rare, these incidents show the importance of keeping a look out for space bodies in our solar system, and the precarious nature of the life on this planet. It is why dedicated government departments such as the USA's NASA (Planetary Defence Coordination Office) have teams that track and monitor space objects that could collide with Earth, along with many observational astronomers around the globe.

This is a short article that gives a rough estimation of the mass and radius of the Tunguska asteroid body before it exploded assuming density, the final velocity is equal to the escape velocity of Earth and a homogenous spherical morphology, with perfect kinetic energy conversion to the fireball. A good ball park figure for the density of a rocky asteroid would be $\rho$ = 2 g/cc or 2000 $\text{kg m}^{-3}$. The escape velocity of Earth is $v_{earth} = \sqrt{2GM/r} = 11.2 \ \ \text{km s}^{-1}$. Where $G$ is the universal gravitational constant, $M$ is the mass of the Earth and $r$ is Earth's radius. Now, $E_{exp} = 10 \ \ \text{Mt} \approx 4 \times 10^{16}$ J, thus we can figure out the mass from the assumed perfect kinetic energy conversion:

$\begin{aligned} E_{exp} &= KE ,\\ E_{exp}&= \frac{1}{2}mv^2,\\ m &= \frac{2E_{exp}}{v^2},\\ m &= \frac{2(4 \times 10^{16} \ \text{J})}{(11200 \ \text{m s}^{-1})^2},\\ m &= 6.4 \times 10^{8} \ \text{ kg}. \end{aligned}$ This is no light object, now using the fact that we assume a spherical body, $V = (4/3)\pi r^3$, $\begin{aligned} \rho &= \frac{m}{V}, \\ \rho V &= m, \\ \rho (\frac{4}{3} \pi r^3) &= m, \\ r &= \left[ \frac{3m}{4\pi \rho} \right]^{1/3},\\ r &= \left[ \frac{3(6.4 \times 10^{8} \ \text{ kg})}{4\pi (2000 \ \text{kg m}^{-3})} \right]^{1/3},\\ r &= 42 \ \text{m}.\end{aligned}$

Thus we get an asteroid with a diameter of around 80 meters in size. Take note that the asteroid would of had a higher initial velocity than the escape velocity of Earth due to its initial orbit around the Sun; this is a quick calculation that still puts it in the literatures diameter range. Robertson and Mathias (2019) states possible ranges between 50 m and 100 m in diameter for the power of the explosion that occurred. It gives an understanding of the size and mass of such an object using basic mechanics. Consider the Fat Man nuke that was dropped on Nagasaki in 1945, which had a $\sim$ 20 Kt explosion. Therefore the Tunguska asteroid airburst explosion was around 500 times more energetic. This, was evidenced by the absolute destruction of the forested area along with it's wildlife. Jenniskens et al. (2019) stated it possibly killed atleast 3 people and injured and rendered unconscious many others, according to first hand accounts from the indigenous Evenki, who lived throughout the region. Its a cold, dark and indifferent Universe out there - international cooperation is what is needed to fight off using horrific man-made explosions against each other, as with the need to prepare and mitigate some things the Universe may throw at us.

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Bibliography

Peter Jenniskens, Olga P Popova, Dmitry O Glazachev, Elena D Podobnaya, and Anna P Kartashova. Tunguska eyewitness accounts, injuries, and casualties. Icarus, 327:4–18, 2019. URL: https://www.sciencedirect.com/science/article/pii/S0019103518305104, doi:https://doi.org/10.1016/j.icarus.2019.01.001. ↩

Darrel K. Robertson and Donovan L. Mathias. Hydrocode simulations of asteroid airbursts and constraints for tunguska. Icarus, 327:36–47, 2019. Tunguska. URL: https://www.sciencedirect.com/science/article/pii/S0019103518304202, doi:https://doi.org/10.1016/j.icarus.2018.10.017. ↩ ^{1 2}