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If a spacecraft travels at 10% the speed of light will it be destroyed by collisions with interstellar dust and particles?

The spacecraft will be traveling to nearby stars, not going through a nebula.

uhoh
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sno
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  • Why specifically 0.1xc? Or is it simply: Is there a practical limit on the speed of a space journey imposed by potential, but inevitable, collisions with interstellar dust and particles? – Ng Ph Jun 30 '21 at 14:07
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    It's from a comment by Zubrin that fusion rockets could reach 0.1c – sno Jun 30 '21 at 16:17
  • Thx! I didn't know this. Your question makes sense. – Ng Ph Jun 30 '21 at 17:11
  • I think the answer depends on how much armor is on the front. Keep in mind that accelerating a spacecraft to even 1% c is very speculative. – ikrase Jun 30 '21 at 19:58
  • VERY hard to say, as density of interstellar medium varies over TEN magnitudes... But any actual dust, even microscopic, will carry a real big wallop. A grain of sand 1 milligram in mass will impart the energy of 450 sticks of dynamite. – CuteKItty_pleaseStopBArking Jul 01 '21 at 07:20
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    Given the huge ten orders of magnitudes of variations in density, it would help if you would clarify your question. Are you interested in sending a spacecraft to a nearby star. At 10% c, a one-way journey to the closest would take over 40 years. Are you interested in sending a spacecraft through the heart of the Orion Nebula at 10% c? That would be a one-way journey lasting 13400 years. Note well: In 13400 years, humanity (if it survives that long) will probably have slightly improved technology. – David Hammen Jul 01 '21 at 21:07
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    You mentioned Zubrin in a comment. He has said, multiple times, that if we are planning something in space that would take over 50 years to accomplish it would be best not to undertake that venture because technology will overtake in 50 years. That means once we can make a vehicle that can go at 10% c, we should only think of sending it to the nearest stars -- and that means having to plow through a interstellar medium with a rather low density of 0.3 atoms/cc as opposed to a million atoms/cc as in the current answer. – David Hammen Jul 01 '21 at 21:26
  • @David Hammen Yes I was thinking of travel to nearby stars, not going through a nebula. – sno Jul 03 '21 at 03:44

1 Answers1

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Based on this answer:

$$E \approx \frac{1}{2} m v^2 = \frac{1}{2} m c^2 \left(\frac{v}{c}\right)^2$$

The mass of a proton $m_P c^2$ is about 938 MeV, so if an innocent atom of hydrogen or bare proton in space were hit by a spacecraft at 0.1 c, in the spacecraft's frame it would look like a speedy proton. Of what energy?

$$E = \frac{938}{2} 0.1^2 = 4.7 \text{ MeV}$$

From here I clicked proton projected range and found out it will be about $1 \times 10^{-2}$ g/cm$^3$, or about 5-10 microns in some low-density material.

Cold interstellar medium is about $1 \times 10^{12}$ protons/m$^3$ or $1 \times 10^{6}$ protons/cm$^3$, but comments below indicate that typical values are way lower, only 0.05 to 0.3 protons/cm$^3$. So I will use 0.1 /cm$^3$ ($1 \times 10^{5}$ /m$^3$) going forward.

At 0.1 c each square meter of spacecraft intercepts $3 \times 10^{7}$ m$^3$/s or $1 \times 10^{12}$ protons/sec.

This is not a lot of heat

The power deposited in the 10 micron thick layer can be gotten from multiplying 4.7 million volts by $1.5 \times 10^{-7}$ amps (coulombs/second) per square meter, or 0.7 watts. In order to calculate what temperature can re-radiate that power use the Stefan–Boltzmann law with $\sigma = 5.67 \times 10^{-8}$:

$$P = \sigma T^4$$

which gives us a skin temperature of about 60 Kelvin, not even enough to keep standard electronics working.

Sputtering is not a problem

Our 10 micron thick square meter has of order 0.1 mole or about $10^{23}$ of atoms.

From random links 1, 2, and Figure 1 in 3 I will ballpark the sputter rate at $10^{-4}$ atom/atom which is conservative.

So at $10^{12}$ protons per second we'll sputter $10^{8}$ per second, meaning we'll loose 10 microns every 30 million years.

Note that the sputter rate may be a few orders of magnitude faster because my estimate was conservative and at 3300 K the atoms are already pretty energetic and predisposed to leave.

But what about things bigger than protons, like cosmic dust?

Damage by things bigger than a proton is going to be a big problem, but I don't know how big. I will leave that aspect to another answer

projected range of a 4.7 MeV proton

uhoh
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  • "Shields up, Scotty!" problem solved :-). Certainly doing what you can by way of shaping the spacecraft so impacts are at a shallow angle will help a very little bit, too. – Carl Witthoft Jul 01 '21 at 13:57
  • Downvoted because you used 10^6 atoms per cm^3, the upper density of a molecular gas cloud. That's a protostar. A better value is 0.3 atoms per cm^3, the density of the Local Interstellar Cloud. – David Hammen Jul 01 '21 at 14:06
  • @DavidHammen The link I cite says "In cool, dense regions of the ISM, matter is primarily in molecular form, and reaches number densities of 10^6 molecules per cm3" (1 million molecules per cm3)." If your argument is with the Wikipedia article, please cite a better source. – uhoh Jul 01 '21 at 14:13
  • @uhoh You wrote this answer as if that very high density is the density of the interstellar medium. That very high density is the density of a very tiny fraction of one percent of the interstellar medium. The solution is simple: Don't go there. Besides, the nearest molecular cloud / protostar with that density is 1000 light years away -- a 10000 year trip at 0.1 c. The Local Interstellar Cloud has a density of ~0.3 atoms per cc. – David Hammen Jul 01 '21 at 20:58
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    The Local Interstellar Cloud, and the nearby G Cloud (with a similar density) extend to several nearby stars. The Local Bubble, in which the Local Interstellar Cloud is embedded, has an even lower density of 0.05 atoms per cc, and extends for over a hundred light years. A better answer would address these local densities that are over six orders of magnitude smaller than the value you used. – David Hammen Jul 01 '21 at 21:02
  • @DavidHammen Okay now these are helpful! Once my morning coffee kicks in I'll update. I'll choose maybe 1/cc to be a little conservative, and the temperature will drop substantially; by perhaps order of $10^{6/4}$ and the sputtering is probably no longer such a concern. – uhoh Jul 01 '21 at 22:04
  • @PM2Ring yes I said I would and then it seems I've lost track of my tasks. I thought of this after seeing a similar new question but couldn't remember where this is, so your ping is both timely and helpful! As soon as I get to a real computer I'll get this done and ping you back. Thanks! – uhoh Jul 26 '21 at 04:59
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    @DavidHammen should be much happier with this version. :) – PM 2Ring Jul 26 '21 at 14:00
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    @PM2Ring Much happier. – David Hammen Jul 26 '21 at 14:51