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The atmosphere of the earth protects us from cosmic rays and other kinds of space radiation. On the moon, there is little to no atmosphere, so anyone on the surface of the moon is directly exposed to space radiation. By digging an underground shelter it is possible to attain shielding from space radiation.

How deep would such a shelter need to be to provide the equivalent protection afforded by the Earth's atmosphere?

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    $\begingroup$ A couple meters will be fine. Earth's atmosphere is the equivalent of roughly 12m of water (8km effective thickness at normal conditions with approx. 1.5kg/m^3). Lunar soil density is probably around 3g/cm^3, so that would make it 4m, but we can live with a higher than normal level of radiation, anyway. $\endgroup$
    – CuriousOne
    Jan 15, 2016 at 20:01
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    $\begingroup$ The heavier elements in rocks (even Al and Si are heavier than H or O) will increase the stopping of gammas, so that helps you go thinner. Energetic particles from the solar wind will stop well before any gammas. Neutron production from energetic protons might also be an issue, but meters of soil will do the trick nicely. $\endgroup$
    – Jon Custer
    Jan 15, 2016 at 20:41
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    $\begingroup$ @JonCuster: Do you happen to know what happens to cosmic ray showers? There is an argument that one doesn't want to be at "just the right thickness of shielding to hit the shower max", since it would be so dense. A shower in air fans out over hundreds of meters, but the equivalent shower in rock might be more or less the cross section of a human, so even a single hit, no matter how unlikely, might be pretty bad. $\endgroup$
    – CuriousOne
    Jan 15, 2016 at 22:26
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    $\begingroup$ @CuriousOne - that is a good point that I had not considered. On the other hand, the folks up on the ISS don't even have meters of rock. $\endgroup$
    – Jon Custer
    Jan 15, 2016 at 22:42
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    $\begingroup$ @JonCuster: This may be one of the few case where less is more... a high energy cosmic ray will go right trough a person, but if it starts showering in the rock above one's head then it produces a lot of lower energy gammas and leptons that will deposit their energy right there... in the atmosphere the shower spreads out over hundreds of meters or even miles at its widest, but in dense material it deposits all of its energy within a few (ten?) cubic meters of volume. The probability to be hit by one is small, of course... but when it hits, it could be pretty bad. $\endgroup$
    – CuriousOne
    Jan 15, 2016 at 22:55

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On the surface of the Moon, the main source of radiation is energetic solar particles (mostly protons and electrons) and galactic cosmic rays (GCR). (The GCRs come out of the Solar system.) The gamma radiation (as a primary particle) is negligible. (The gamma flux in the space is very low...)

According to this article, most of the particle showers won't penetrate more than 0.5 m of lunar soil (with a density of 1.4 g/cm$^3$). (According to this presentation, the density of lunar soil ranges from about 1 g/cm$^3$ to 2 g/cm$^3$.) The showers have a sharp peak in the [energy deposit - penetration depth] relationship. After which the energy deposition usually drops to less than 10% of the peak value. (Only lightly ionizing particles remain.)

Although they couldn't study the contribution of neutrons (created in the particle showers), which can penetrate more rock than the charged secondary particles. (On current spacecrafts, 30-60% of the total equivalent dose might come from neutrons.)

Based on the article, about 0.5-1 m of soil might be sufficient.

Although the radiation level will be still higher than on the surface of Earth, it is hard to tell more without experiments or simulations. The problem is with the neutrons (and high energy muons). For these, the energy loss is not continuous, but characterized by discrete events. Thus they can often penetrate more material than expected by continuous energy deposit approximation. Thus also non-trivial if '8 km' of air can be substituted by 4 m of rock (as suggested by @CuriousOne). (Also partly because of the different composition of rock and air.)

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  • $\begingroup$ Why the down vote? $\endgroup$
    – fanyul
    Aug 26, 2020 at 8:33
  • $\begingroup$ Hi there! You neglected the gamma radiation. Hence -1. $\endgroup$ Aug 27, 2020 at 0:26
  • $\begingroup$ 0.5-1 meter isn't an answer. $\endgroup$ Aug 27, 2020 at 0:33
  • $\begingroup$ @descheleschilder Please show me any article, where they say that in ('open') space (outside the Earth's magnetosphere) the primary gamma radiation is important. (Compared to the other sources.) I didn't find any. $\endgroup$
    – fanyul
    Aug 27, 2020 at 0:34
  • $\begingroup$ That doesn't mean gamma radiation doesn't hit the moon's surface. It only takes one gamma photon... $\endgroup$ Aug 27, 2020 at 0:40
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Let's assume that the Cosmic radiation hitting the moon comes from either the Sun or any sources outside our solar system.

The gamma radiation component

In this article one can read:

It can pass through the skin, but it is absorbed by a few centimeters of body tissue or a few millimeters of aluminum. Gamma radiation is the most penetrating of the three forms of cosmic radiation. It can easily penetrate body tissue. It requires several centimeters of lead or about 1 meter of concrete to absorb it.

Now, the relative densities of the Moon's surface and that of concrete are about $3.4$ and $2.4$, respectively. This means the surface of the Moon absorbs the gamma radiation up to a depth of about $\frac{2.4}{3.4}=0.7$ times one meter which is obviously $0.7$ meter.

The electron and proton component

From the citation, we can infer that the electrons and protons penetrate less deep than the gamma photons do.

Conclusion

Hence, to be safe inside a station on the moon, it suffices to put it about $1.4$ meter below the moon's surface.

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    $\begingroup$ can you address the point brought up in the comments on the OP regarding cosmic ray showers? $\endgroup$
    – Mathew
    Aug 21, 2020 at 20:44
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    $\begingroup$ I don't think the lead is a good idea. The metre or so of Moon rock will be adequate protection from most of the stuff hitting the Moon. The problem with lead (or any heavy atom) is the secondary radiation created when it gets hit by extremely high energy stuff. (High energy gammas cause pair production when they pass near heavy nuclei, and of course those positrons make more gamma when they annihilate. Etc). Instead of lead, you could maybe use a metre or so of water. You're going to need a water reservoir anyway... $\endgroup$
    – PM 2Ring
    Aug 25, 2020 at 7:51
  • $\begingroup$ I'm suggesting not to use lead but moon-suface-material. This has about the same density as concrete. $\endgroup$ Aug 25, 2020 at 12:51
  • $\begingroup$ @PM2Ring Yeah! You would probably die of thirst. A thin layer of lead is indeed unnecessary. I deleted it from the answer. $\endgroup$ Aug 25, 2020 at 16:27
  • $\begingroup$ Why the downvote? Don't you like my answer? $\endgroup$ Aug 25, 2020 at 17:47

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