How far would I have to be from a nuclear detonation in space in order to survive it?

Question

Assume someone detonates a Hiroshima-sized nuclear bomb in space. Since in space there's no air, the bomb will behave differently than on Earth. In particular, there will not be an air pressure wave, and certainly no "mushroom" cloud — the energy will be sent in all directions equally, as kinetic energy of the bomb fragments, and as radiation (of all sorts). Therefore, the damage pattern on Earth probably is very different from the damage pattern in space.

Now the question is: How far do I have to be away from the bomb in order to survive it without injury? Let's assume that at the time of the explosion I'm in space with the thinnest space suit possible.

Answer 1

Nuclear bombs produce 3 effects on Earth

1. Thermal flash
2. Neutrons
3. Blast (caused by conversion of X-rays into heat)

In space, you need only concern yourself with the neutrons and X-rays.

Radiation Enhanced Bombs

According to Atomic Rockets: Radiation Flux:

A one megaton Enhanced-Radiation warhead (AKA "neutron bomb") will deliver a threshold fatal neutron dose to an unshielded human at 300 kilometers.

Normal Nuclear Weapons

A non-radiation enhanced bomb produces much less neutron radiation but more X-ray radiation. A 1 kton nuclear bomb is borderline survivable at a range of 30 km due to the X-ray flux.

The survivability range of nuclear bombs scales (roughly) linearly with bomb yield and as the inverse square of distance between bomb and victim. Meaning a 1 mton bomb would be borderline survivable at a range of ~900 km due to X-ray flux.

All numbers are for unshielded humans. Shielding can significantly alter these numbers.

Shielding

The effectiveness of X-Ray shielding is primarily determined by the amount of mass it contains (high atomic mass materials work slightly better than low atomic mass ones).

The effectiveness of neutron shielding is dependent upon the number of low atomic mass nuclei between the bomb and the victim. High atomic mass nuclei in your radiation shielding can make neutron radiation more difficult to manage.

Edit 10/09/2015:

I concur with Thucydides, anyone interested in this topic should go to Atomic Rockets and read all relevant sections. It includes a description of what a nuclear detonation would look like, what effects it'd have on spacecraft, etc.

As for survivability, my answer only considers a person wearing a minimal spacesuit for protection. The actual physical damage a 1 kton weapon would inflict on a body (human or otherwise) at a range of 30 km would be minimal. A person at that range would be hit with a lethal dose of radiation. Without medical care it might take them days or longer to die in an extremely unpleasant manner.

Edit 10/10/2015:

You should also realize that being outside the "deadly" zone listed above does not necessarily mean you will live. Radiation sickness is nasty and you'll require intense medical treatment in order to survive a large dose. Atomic Rockets has a Acute Radiation Syndrome Chart which tells you what symptoms you can expect from a given dosage. The chart gives you a probability of surviving any given dosage.

My numbers were for ~2.0+ Gray dosage - this gives you a survival probability of 35-40%.

Answer 2

About 100 miles (160 kilometers) for no injuries

Something cool that I found a while ago is NASA's report on Nuclear Weapon Effects in Space. First thing to keep in mind:

If a nuclear weapon is exploded in a vacuum-i. e., in space-the complexion of weapon effects changes drastically:

First, in the absence of an atmosphere, blast disappears completely.

Second, thermal radiation, as usually defined, also disappears. There is no longer any air for the blast wave to heat and much higher frequency radiation is emitted from the weapon itself.

The radiation is your only real problem in space. So with a nice radiation-proof spacesuit, you could survive a nuclear blast at a ridiculously close range.

So how far would you have to be in order to be safe from radiation, assuming essentially no radiation protection from your spacesuit? According to Wikipedia, a dose of 0.1 grays (10 rads) is enough to cause radiation sickness. Let's look at one of the charts NASA included:

This is for a 20-kiloton explosion. At sea level, you'd get 10 rads from being a mile or so away from the explosion. In space? It looks like we're at about 60 rads when you're 40 miles away. To reduce that by a factor of 6, we'll need to go $\sqrt{6}\approx 2.5$ times as far away, so about 100 miles away.

Of course, you'd still survive short-term if you're closer than that, but the closer you get the worse the radiation sickness will be.

Something else to remember is that in space 100 miles is not very far - the international space station goes that far in about 20 seconds.

Answer 3

The Atomic Rockets site has a pretty comprehensive section on nuclear weapons, and the answers there suggest that a nuclear weapon in space isn't as much of a threat outside of short distances due to the inverse square law (much of the radiation energy is dissipated into space) and the lack of a medium to transmit the energy to the target (the main thing you are going to be hit with is a blast of x-rays, which will spoil your day if you are too close).

The modifier is if the nuclear weapon is driving some sort of amplification device.

In the 1980's, it was postulated that the energy of an exploding nuclear bomb could be converted into a laser beam of x-rays if a sufficiently long and slender rod of the correct material was placed with one end on the bomb and the other end pointing at the target. As the material was converted into plasma by the exploding bomb, there would be a point where the long line of plasma should become a lasing cavity and emit a high energy x-ray beam, with a potential range of thousands of kilometres. This was the basis of the "Excalibur" device, which took the idea to "11" by envisioning a device which looked like a sea urchin carrying dozens to hundreds of "spines", each locking onto a different target. There were many practical reasons this never got off the ground (so to speak), but one of them was the efficiency of converting the bomb's energy to laser energy was very low. This might have been resolved since then.

The other idea would be to make the bomb drive a "shaped charge". Astounding as this sounds, evidently this was experimented with and some success was achieved, with a pre scored plate being converted into a shotgun charge with pellets moving at some astounding velocity at the target (@ 70 km/sec), while using various means to shape the plasma jet from the nuclear explosion can result in a narrow jet of hot plasma moving at something like .03*c*! This was evolved from the pulse units developed for the ORION nuclear pulse drive spacecraft, and known under the name "Casaba-Howitzer" Much of the information is still classified, but you would certainly be in grave danger even in a well armoured spaceship hundreds, if not thousands of kilometres from the blast.

Answer 4

Although there are a lot of if's hidden in your question, a sort of worst-case number can be determined.

First, a Hiroshima blast is about 15 kt. Since 1 Mt is $4\times10^{15}$J, a Hiroshima-sized blast releases about .015 times that, or $$E=.015\times 4\times10^{15} = 6\times10^{13}\text{ J}$$ For a fission bomb, about 35% of released energy is thermal, and about 3% radiation. The amount of thermal radiation required to breach a spacesuit is unknown, but let's say something on the order of 1 MW/m² for one second. After all, sunlight is about 1.5 $\times$10³ W/m², and a suit obviously won't have major problems with that. Assume a human body provides about 1 square meter of area (2 meters tall by 1/2 meter wide). Then the total thermal energy required will be 1 MJ. Since 35% of a bomb goes to thermal, we can write $$4\pi R^2 = .35 \times6\times10^{13} = 2.1\times10^{13}$$ and $$R = \sqrt{\frac{2.1\times10^{13}}{4\pi}} = 1.3\times10^6\text{ m}$$ 1300 km is much greater than is characteristic of terrestrial nukes but there's a good reason - the atmosphere absorbs most of it and produces blast.

Radiation is a different issue. First, about 1/10th as much energy goes into radiation as to thermal. However, since radiation will largely penetrate a suit, it might take less energy. But the fact that radiation will penetrate a suit means that some will simply pass through the body and produce no damage. Let's assume, purely as a fictional number, that 10% of radiation which hits a person will be absorbed. The unit of absorbed radiation is the Grey, which is 1 J/kg of tissue, and 5 Greys is a standard lethal dose for humans. For this set of assumptions,$$4\pi R^2 = 5\times 0.1\times .003 \times 6\times10^{13} = 9\times10^{10}$$ and $$R = \sqrt{\frac{9\times10^{10}}{4\pi}} = .84\times10^5 \text{ m}$$ So the two effects agree within less than a factor of 2, and 1000 km sounds like a nice round number for a survivable distance. Of course, that means that your suit didn't quite burn up, and you didn't necessarily die of radiation poisoning, so you might want to add a safety factor. I'd guess the 2,000 km is a much better number to use.

EDIT - In calculating radiation levels, I forgot to factor in body mass. Assuming 100 kg for mass gives a factor of 10 reduction in distance, to $$R = .84 \times 10^4 \text{m}$$