Speck of space dust + traveling at speed of light = Death?

Ok, supposing Challenger 2 is upgraded to travel at 9/10ths the speed of light, and the dudes are hauling a$$ towards Proxima centauri. Word on the street is that at near the speed of light, even a speck of dust would be like a Nuclear bomb hitting the spaceship.

So what are the chances that a speck of dust will hit the *Challenger 2 * while moving between our solar system and the next? Would the chance necessarily force the spaceship designes to put in some kind of force field to absorb such specks?

Naw, mass X speed = force A speck going really really fast still doesn’t have that much force.

Mass * velocity = momentum, not force. Force is mass * acceleration.

Kinetic energy OTOH is 0.5 * mass * (velocity)^2. A small bit of dust moving at very high speeds has a huge amount of kinetic energy and can indeed do a lot of damage.

Force = mass x acceleration (not speed).

Kinetic energy (which is what actually matters) is 1/2 x m x v[sup]2[/sup]. In other words, it varies as the SQUARE of velocity. And v is very large, so it could cause considerable damage.

Edit: Why does someone else always get there first?

90% of the speed of light is a long way away from 100% in terms of relativistic effects and the odds of hitting anything are pretty slim. (Heck, the Helios satellite is still in orbit after thirty years, with a peak velocity of 250,000 km/h or so. That’s a piddling fraction of a percent of light speed, but its orbit has a lot more debris than interstellar space).

So I think the need for a shield is probably a relative thing. You might only be completely annihilated by a speck of dust in every thousandth trip to a neighboring star (I’m pulling that number out of the air), but would you be comfortable just rolling the dice?

Example:

A .50cal Browning (heavy machinegun round) has a muzzle energy of about 18,000J.

A 0.5mg (milligram) grain of sand moving at 1000 kilometers per second (a tiny, tiny fraction of the speed of light) has a kinetic energy of 250,000J.

The grain of sand would probably disintegrate pretty fast upon impact at that kind of energy but it’ll certainly do some harm.

If a physical projectile moving near the speed of light hit something the amount of energy involved would be not terribly far from the amount of energy released if the projectile was a bit of antimatter.

It doesn’t matter whether it disintegrates on impact or not - it still carries all that energy, and that energy has got to go somewhere. It’ll go into damaging the ship just the same.

Well, let’s see.

mv = momentum, not force.

ma = force but in this scenario there is no acceleration

(1/2)mv[sup]2[/sup] is kinetic energy, the usual thing that is used to determine collision damage.

On review, I see others got to this point long before me…but read on…

(1/2)m[sub]speck[/sub]c[sup]2[/sup] is something like

(1/2)(1 x 10[sup]-9[/sup]kg)(3.00 x 10[sup]8[/sup] m/s)[sup]2[/sup] =
4.5 x 10[sup]7[/sup] joules

Although this is a lot of energy, there is an interesting question about what would actually happen on impact and how the energy would be dissipated. Would the speck punch a hole? Make a dent? Explode what it touched? Just burst into a splat of atoms and disperse?

I’ve posted about this before.This link may be of interest.

This is why the Enterprise has a deflector dish. :smiley:

Yes and no.

The energy essentially goes into breaking the atomic bonds in the nearby material. The more bonds broken within the grain of sand, the more energy is absorbed in doing so, and the less energy is transferred to the spaceship or whatever.

However, in reality, I suspect it doesn’t matter all that much, because the energy that would actually be absorbed by the sand grain is a small proportion of the entire available energy.

If it disintegrated on impact it would probably also look like a n-way elastic collision too, wouldn’t it? I mean, if the bonds broke that energy still needs to go to the constituent parts so they can do the actual dispersing instead of sitting there being bored all day. Granted if you have a 110^-9 kg grain of sand verses a 110^9 kg spaceship that’s a negligible amount of anyway, but hey, it’s there (right? I’m really not totally sure) so I’m counting it!

For relativistic velocities, this isn’t quite accurate. The true formula is

KE = mc[sup]2[/sup]*(1/sqrt(1 - v[sup]2[/sup]/c[sup]2[/sup]) - 1)

which works out to about 1.16x10[sup]8[/sup] Joules for a one-microgram particle going 90% the speed of light. This isn’t quite nuclear-bomb magnitude (according to Wiki, Little Boy’s yield was on the order of 10[sup]13[/sup] Joules), but it’s still significant — about the same as the kinetic energy of a small jet.

I won’t dispute your second point, but concerning the first one: note that if you used the 1/2 m v[sup]2[/sup] formula to calculate the kinetic energy you’d get an answer that was three or four times smaller. I’d call that a pretty significant effect.

Another thing to consider.

Space is REALLY empty (beside the planets and stars that is). Particularly intergalactic space.

We can look across BILLIONS of light years.

Now, think for a moment. How much dust/crap would have to be directly between you (your telescope) and a galaxy billions of light years away before it would totally block your view of the galaxy? A bucket full of sand? A truck load? A few of em? A bunch of em? Take your pick.

Now, distribute that sand along a cylinder a few meters wide and a few billion light years long.

That sand is going to be pretty thinly spread IMO.

If an honest working astronomer would like to chime in and tell us how thin or thick this stuff is spread I’d like to hear it !

But consider mars, a whole planet’s worth of space dust. Yet how much of the night sky does mars block when it’s out?

No, the Enterprise has a deflector dish so that they can reroute various forms of energy from their engines through the dish to solve otherwise insoluble problems. :smiley:

If its between you and the star you are looking at, all of it. Unless mars is closer to the star than it it is to you.

Maybe I’m not getting your point, or maybe your not getting mine.

Ahh…

I think I’ve got it Tao.

Its not a uniform cylinder the size of the telescope between the telescope and what your observing.

Its a cone that’s telescope sized at one end and say galaxy/whatever sized at the other end. Still, the dust has to be pretty thinly distributed to not cause alot of obscuration of the object of interest.

Setting aside the moral cost to a manned flight, this would depend on the value of the individual probe. If the cost of your interstellar mission were low and the redundancy were high–something like Freeman Dyson’s Astrochicken combined with some cheap means of effective interstellar propulsion–then you’d accept a 0.1% chance of annihilation as the cost of doing business, and just launch a few more probes to compensate for statistical launches. On the other hand, if each loss were equivalent to 10 years of GDP or more, you’d find those odds to be manifestly unfavorable, and you’d be willing to go to extreme measures to assure that even a fraction of a percent of a chance of mission failure can be averted. To place this in context, the generally accepted risk criteria for a low-cost, non-manned suborbital or sounding rocket launch is about 3 sigma, or that failure (of a critical subsystem) may occur about 0.3% of the time. A long duration or high value mission would be pushed to 6 sigma or higher as a required risk assessment, which is an untenable reliability figure for any conventional propulsion and controls technology over the duration of an interstellar transit; even if you don’t hit a grain of dust and come apart like a cheap gold watch, some other critical failure is likely to occur.

To place this in perspective of human lives, the US space program has a loss of about 1 person to every ten orbital flights, and while much outrage is evidenced every time loss of life occurs, the program continues on. Clearly, the cost here (aside from p.r.) isn’t lives, but opportunity cost expended. Interstellar missions, even unmanned, are not in the offing for the immediate future. And when they are, shielding from impact and radiation is definitely called for. Fortunately, space is full of material that makes for good shielding; water ice, readily available in mass quantities in the outsystem, makes for excellent ablative shield material.

Stranger

This concept fascinates me. What is it, besides a great potential band name?