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 '18 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? $\endgroup$ – user190684 Dec 20 '18 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 '18 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. $\endgroup$ – user190684 Dec 21 '18 at 14:44

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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