The balloon has a lighter than air gas in it. It flies at 30 km above sea level. It is spherical, with a radius not exceeding five hundred meters. How long can it fly before a meteor pokes a hole in it?
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1$\begingroup$ Is your question about how often meteor entering the atmosphere reach 30km or does it include the size or energy carried by a meteor that can make a hole into a balloon (in which case the answer may only include big enough meteors)? $\endgroup$– Manu HJul 12, 2019 at 8:04
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$\begingroup$ questions about meteor flux in Earth's atmosphere have always been on-topic here, as have many questions about high altitude balloons. $\endgroup$– uhohJul 12, 2019 at 11:00
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1$\begingroup$ Welcome to Space! Do only want holes big enough to deflate the balloon and make it fall, or do you also want smaller holes? $\endgroup$– DrSheldonJul 12, 2019 at 17:34
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$\begingroup$ @Manu H Apart from dust I would have thought that most any meteor would puncture a high altitude balloon if it can reach it. The balloon may as well be about as fragile as a hat liner. $\endgroup$– Peter MartynJul 13, 2019 at 1:07
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2$\begingroup$ @Peter Martyn - the lighter than air gases tend to be small enough to permeate through any feasible balloon material, using thicker films with metal layers helps but makes thing heavier. The UV light is also pretty hostile, as are the day/night temperature swings. Long endurance for current balloons is measured in days and requires active buoyancy control in some form. $\endgroup$– GremlinWrangerJul 13, 2019 at 5:59
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1 Answer
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EDIT: As Peter Martyn commented, the paper gives another estimate, at the end of p. 875:
log N = 2.14 - 0.49 log m.
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Here's a rough estimate. From the curves at top left of the plot in figure 1 in this paper, we can expect on average, per year per million km2 of earth surface, 4.5 meteors, weighing 31 grams ("log m" -- base 10, not base e, which would mean 7 grams). Heavier ones are rarer.
Your 500 m diameter balloon's projected area is about 0.2 km2.
So the average duration between meteors hitting it is
1,000,000 / 0.2 / 4.5 = about a million years.
Even if I've horribly misinterpreted the plot, and even if meteors arrive in bursts (as they do), the balloon will very likely succumb to something else before any meteor hits it.
EDIT: As Peter Martyn commented, the paper gives another estimate, at the end of p. 875:
log N = 2.14 - 0.49 log m.
For m = 31 grams, this gives N = 48 instead of the plot's 4.5.
An order of magnitude more, but close enough for our purposes.
For m = 0.1 grams, still big enough to damage the balloon, N = 794.
Then the average duration between meteor hits is 1,000,000 / 0.2 / 794 = 6300 years.
answered Jul 14, 2019 at 23:36
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2$\begingroup$ Gee whiz, thanks very much for the link but the left hand margin of figure 1 seems to line up with a value of 1.5. Log M is 1.5 and therefore M is 31.623. Right? That is not 7 grams. <br/>Also I would have guessed that much smaller meteors would probably be dangerous and then I calculated it with the Halliday to Bland extrapolation on the lower right of page 875 to get M<sub>T=0.1 gm, log M<sub>T=-1, log N=(2.41-(-0.49)=2.9, N=794.328 incidents with M starts out greater than 0.1 grams per 10^6 km^2 per year. But there is something fishy about this. Am I doing it right? $\endgroup$ Jul 15, 2019 at 6:36
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2$\begingroup$ Right. The plot didn't specify the base of the logarithm. I guessed e. But from the paragraph above the plot, one can deduce that the base must in fact be 10. $\endgroup$ Jul 15, 2019 at 19:51
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$\begingroup$ So far your article is very confusing. Other authorities have MUCH MORE meteors. For example Lovell has thousands of tons of meteors PER DAY. He has 10^6 of them in the interval 0.01 to 0.1 grams, 4 X 10^5 in the interval 0.1 to 1 grams, 18 X 10^3 in the interval 1 to 10 grams and 2,500 in the interval 10 to 100 grams. That's for the whole earth. OK maybe about 510 X 10^6 km^2, right? My astronomy encyclopedia is more of the same. But Bland to Halliday on page 875? For example let M<sub>T > 10^-11 grams, N=6.309 X 10^7? Is that right? That isn't thousands of tons per day. $\endgroup$ Jul 16, 2019 at 6:06
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1$\begingroup$ I like this. It reminds me of the fermi estimation xkcd whatif. $\endgroup$ Jul 19, 2019 at 21:50
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$\begingroup$ @Camille On a second reading your Zolensky article looks more convincing than the MUCH MORE METEORS of some A.C.B. Lovell in D.R. Bates The Earth and Its Atmosphere in 1957 and it also felled an old Encyclopedia of Astronomy. Therefore the 6300 year figure would be my best guess for a 500 meter diameter balloon and what is much easier to tell is that it is very probably more than 194 years anyway, which fits an M<sub>T of 0.01 grams. Maybe DARPA has noticed and their very mysterious balloons are found at [Google] (darpa.mil/program/adaptable-lighter-than-air) . $\endgroup$ Jul 20, 2019 at 5:42