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I was wondering, when you have a "hypervelocity impact" e.g. a meteor or Space Debris hitting a body in orbit, why do you get a "flash" of light and how large would the flash be for a given impactor at a given speed?

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    $\begingroup$ Lots of energy released in a short time has many ways to make light. $\endgroup$
    – Jon Custer
    Dec 20, 2018 at 19:54
  • $\begingroup$ Yeah but, it there a specific - I don't want to say "formula" - but a means to predict the flash from a given collision? $\endgroup$ Dec 20, 2018 at 21:03
  • $\begingroup$ Think of it like this. Suppose you said two vehicles collided and asked for a formula of how big the repair bill would be. You can't really write one. The statement of what happened is too vague. There are too many ways things could break, too many variables affecting price. The way you would handle it is to take your collision to a mechanic and let him figure it out. $\endgroup$
    – mmesser314
    Dec 20, 2018 at 22:54
  • $\begingroup$ I expected that, but what if you had a general sense of how large the impactor was and how fast it was moving? A friend told me that the Thebit crater on the moon, at least the impact that created it, would be visible from Earth on a clear night, personally I'm skeptical of that, but I have no idea whether it's true or not. $\endgroup$ Dec 21, 2018 at 14:44

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An impactor of mass $m$ moving at speed $v$ will have kinetic energy $E_0=(1/2)mv^2$, which will be significant for hypervelocity impacts. When it hits something inelastically this gets converted into kinetic energy of ejected fragments, work in deforming the target, and through this heating. This heating will make the hot material radiate blackbody radiation - this is what produces the flash.

The problem is that the exact distribution of energy. Some of it will go into a hot spot or ball of plasma shining, but the amount is going to depend on how the impact happens.

If we just assume a fraction $\eta$ ends up as heating a plasma ball of radius $r$ it will have temperature $T=\eta E_0/(4\pi/3) r^3 C$ where $C$ is the volumetric heat capacity of the plasma. If it loses energy as blackbody radiation from a hemisphere as $E'=-(2\pi r^2)\sigma (E/(4\pi/3)r^3 C)^4 = -(27/128\pi^3 C^4) \sigma E^4 / r^{10}$, starting out as $E=\eta E_0$. The energy and brightness declines as $E\propto t^{-1/3}$. Note the extreme dependence on $r$; this is yet another reason it is hard to give a reasonable answer, since in practice $r$ (and $C$) will change fast over time.

To sum up, it all depends on complex deformation, fluid and plasma dynamics during the impact.

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Hypervelocity is defined as the velocity being above sound speed of the materials involved. That said, there is a phase during a hypervelocity impact where the projectile progresses faster than the materials involved can react. The contact line between the impactor and the target progresses so fast that the compressed material near the initial contact point is not able to escape. In other words, the material is trapped. It can only escape at a later stage, when the speed of the contact line between impactor and target decreases below sound speed of the materials involved.

This causes substantial heating to typically thousands of Kelvin. The energies involved are high enough to cause phase transitions of the materials up to ionization. What you see as flash is hot material being ejected (as soon as it is able to escape) and radiating like a black body as Andreas Sandberg wrote. Additional energy is being released by recombination of electrons and ions.

It's difficult to quantitatively estimate the brightness of the flash. However, some estimations can be done for the amount of ionized material and the duration of the impact. Of the impactor, a significant amount is ionized, should be roughly in the order of 10%. A similar amount (mass) of the target material also gets ionized. This gives you an estimation of the masses involved. Since the material was previously solid, the volume of the ionized material should be at least an order of magnitude above the volume of the initial impactor.

The impact process itself is characterized by the size and speed of the impactor. So the characteristic duration of the process is $d/v$ (with impactor diameter $d$ and velocity $v$). The typical impact velocity at 1 AU is around 20 km/s.

I don't know what impactor caused the Thebit crater (ca. 110 km in diameter). Given the size of the crater I would estimate it was probably large enough so that the amount of ionized material was visible from Earth, and the impact duration was also long enough to be seen. So yes, I would estimate the impact flash could have been seen from Earth, but only for a short time.

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