In relativistic interstellar travel, would a speck of dust = total destruction?

[Fanghur]

Let's say that we eventually progress to the point where we are able to (somehow) produce huge amounts of antimatter, at least by today's standards, and we build an interstellar spacecraft to travel to Proxima Centauri. Let's say that using antimatter propulsion, along with several other propulsion types, we are able to propel the spacecraft up to a significant percent of the speed of light, say 50%. If I'm not mistaken, at those speeds it would take approximately 9 years for the ship to travel to Alpha Centauri from the point of view of those left on Earth, and ~2.5 years from the perspective of those inside the ship travelling at 50% the speed of light due to the time dilation effect. *Note that these numbers are not taking into account the deceleration period.

 

Would I be correct in saying that when travelling at such speeds, hitting anything along the way, even something as tiny as a speck of dust smaller than the width of a human hair, would spell disaster for the entire ship? I'm not certain of the mathematics involved, but I would imagine that at those speeds the relativistic mass of that speck of dust, and its resulting kinetic energy, would dwarf any atomic bomb we have ever created.

 

Would that be a fair assessment?

Edited May 2, 2013 by Fanghur

[swansont]

At 0.5c, gamma is about 1.15, so the kinetic energy of any piece of matter is going to be about 15% of its rest mass energy, as measured in the craft's frame. That won't dwarf bombs that have been detonated.

 

A kiloton TNT equivalent is 4.184 x10^12 Joules, which corresponds to ~46 milligrams of rest mass energy. Thus a megaton bomb is ~46 grams. A speck of interstellar "dust" would have to be 300 grams to have this much kinetic energy. Still, these collision would be a problem even if they don't reach nuke proportions.

[Dekan]

This is a good question. And the answer is found, by looking at it from the viewpoint of the speck of dust.

 

The dust-speck is not moving, relative to anything in its close-by environment. It's just floating in space, calmly. It has a natural rest-mass. Which is not increasing, or doing anything, except staying the same mass always, peacefully.

 

The puny speck doesn't know about an approaching interstellar spacecraft, such as Fanghur's inspiring AM-powered Centauri Ship. This ship, travelling at 0.5c, will have gained huge relativistic mass. Which will enable it to smash a mere dust particle aside! Like a rolled-up New York Times swatting a fly on the wall.

 

So small specks of interstellar dust won't present any problems to future starships.

Edited May 2, 2013 by Dekan

[krash661]

Interesting.

as i read about interstellar travel, the question i receive is,

how do you travel so fast and not hit anything.

 

but there's probably info i'm missing somewhere,

i'm not sure.

[michel123456]

There will be no politicians floating in space, hopefully

[Delta1212]

This is a good question. And the answer is found, by looking at it from the viewpoint of the speck of dust.

 

The dust-speck is not moving, relative to anything in its close-by environment. It's just floating in space, calmly. It has a natural rest-mass. Which is not increasing, or doing anything, except staying the same mass always, peacefully.

 

The puny speck doesn't know about an approaching interstellar spacecraft, such as Fanghur's inspiring AM-powered Centauri Ship. This ship, travelling at 0.5c, will have gained huge relativistic mass. Which will enable it to smash a mere dust particle aside! Like a rolled-up New York Times swatting a fly on the wall.

 

So small specks of interstellar dust won't present any problems to future starships.

From the perspective of a bullet, it's falling to the ground when out of nowhere someone comes hurtling at it at 1,000 miles per hour... easily knocking it aside, and harming no one. Right?

[Dekan]

Delta not right - the bullet got shot out of a gun. The gun gave it an impetus, which made it fly through the air.

 

The specks of interstellar dust haven't been shot from anything, unless it's the Big Bang, but that's another fable.

 

 

[Delta1212]

Delta not right - the bullet got shot out of a gun. The gun gave it an impetus, which made it fly through the air.The specks of interstellar dust haven't been shot from anything, unless it's the Big Bang, but that's another fable.

From the perspective of the spaceship, the dust is hitting it at a significant fraction of the speed of light. From the perspective of the dust, the spaceship is hitting it at a significant fraction of the speed of light. From the perspective of the person, the bullet is hitting them at a thousand miles per hour. From the perspective of the bullet, the person is hitting it at a thousand miles per hour.

 

If you think it makes a difference, try launching someone at a thousand miles per hour into a stationary bullet and see what happens.

[swansont]

Delta not right - the bullet got shot out of a gun. The gun gave it an impetus, which made it fly through the air. The specks of interstellar dust haven't been shot from anything, unless it's the Big Bang, but that's another fable.

 

Physics works in more than one reference frame.

[John Cuthber]

Just a thought. Nuclear bunkers don't normally fly.

The shielding needed would be prohibitively heavy.

I suspect that 46 g of TNT would punch a hole in the skin of an aircraft.

And there would be more than 1 speck of dust.

 

(BTW, I'm amused by Dekan's failure to accept relativity on a thread about relativity.

Edited May 3, 2013 by John Cuthber

[krash661]

Just a thought. Nuclear bunkers don't normally fly.

The shielding needed would be prohibitively heavy.

I suspect that 46 g of TNT would punch a hole in the skin of an aircraft.

And there would be more than 1 speck of dust.

from what i understand,if i remember correctly, this is not a problem,(shielding)(but i could be wrong).

one of the main problems is,

how to stop people from going insane from the long distances and boredom.

human element is the problem.

[Phi for All]

one of the main problems is,

how to stop people from going insane from the long distances and boredom.

human element is the problem.

 

!

Moderator Note

Let's discuss this in a different thread if you like, but not in this one.

[krash661]

yeah no problem at all

[imatfaal]

I don't know what levels of shielding would be proposed or feasible - but, after reading John's post above, I googled "50 grams of TNT" and (apart from a very bad youtube video) I did find out that a significant number of anti-personnel mines have less than 50 grams of TNT and that anti-tank mines can have only ten times that figure. Whilst impacting interstellar dust is not designed to penetrate armour it will be continuous and personnel must be protected. Due to recent tragic events I know that the best (although not good enough) vehicular wheeled protection against mines in use at the moment is the Cougar/Mastiff - it is smaller than any envisaged life capsules and is proof against most anti-personnel IEDs; but it weighs in at 14 tonnes.

[swansont]

Keep in mind that the 46 grams I quoted (if that's the source for the later value) of material equates to a Megaton of TNT, if converted.

 

300 micrograms of material would have the impact kinetic energy of a ton of TNT, if moving at 0.5c

[imatfaal]

Keep in mind that the 46 grams I quoted (if that's the source for the later value) of material equates to a Megaton of TNT, if converted.

 

300 micrograms of material would have the impact kinetic energy of a ton of TNT, if moving at 0.5c

Ah yes...going back to read your post #2.

[Mr Monkeybat]

There are speculative solutions to the space dust problem, like vaporizing the dust ahead with lasers, or ionizing them so they can be deflected with magnetic fields. But the faster you go the harder it gets.

[Dekan]

I can't understand this "space dust" problem. The tiny particles of dust aren't accelerating - relative to the general background of the galaxy and the universe. So they aren't acquiring any extra mass.

 

The only thing accelerating, is the starship. This is accelerating relative to the universal background. And the acceleration results in the ship gaining more speed. Which endows the ship with more mass, according to the well-known equation.

 

Therefore a starship travelling at a huge speed, such as 0.9999999c, will have a correspondingly huge mass. The mass of a planet, perhaps. Such a planet-sized mass can easily brush dust-particles aside.

 

I mean, is our planet Earth seriously affected by dust-particles. Obviously not - so how can they affect a starship with a mass equal to Earth?

Edited May 4, 2013 by Dekan

[John Cuthber]

The earth is buffered by the atmosphere. If it hits dust, or even small rocks they get trashed in the atmosphere.

What you seem to to realise is that relativity works with velocities.

There is no preferred frame of reference with respect to which the dust is stationary and the ship is moving.

It is equally valid to say the ship is stationary and the dust is travelling at near the speed of light.

So the ship gets hit by fast moving stuff and that damages it.

[Janus]

I can't understand this "space dust" problem. The tiny particles of dust aren't accelerating - relative to the general background of the galaxy and the universe. So they aren't acquiring any extra mass.

 

The only thing accelerating, is the starship. This is accelerating relative to the universal background. And the acceleration results in the ship gaining more speed. Which endows the ship with more mass, according to the well-known equation.

 

Therefore a starship travelling at a huge speed, such as 0.9999999c, will have a correspondingly huge mass. The mass of a planet, perhaps. Such a planet-sized mass can easily brush dust-particles aside.

 

I mean, is our planet Earth seriously affected by dust-particles. Obviously not - so how can they affect a starship with a mass equal to Earth?

To "brush" those particles aside, the ship has to accelerate them, and that means the ship has to transfer energy to the particle.

 

It's basically the same as you were tossing small rocks up into the air and hitting them with a wooden bat. The bat is much more massive than the rocks and the rocks are just hanging there in the air when it hits them, but you are still going to end up with some nasty dents in the bat.

 

All that counts is the relative velocity between dust particle and ship.

 

The apparent increase of relativistic mass of the ship doesn't really matter. You also would have to take into account that the ship would be length contracted. At 0.9999999c, a 10cm thick bulkhead would only be 0.45 mm thick according to the "stationary" dust particle.

[Dekan]

Thanks, but is the situation as symmetrical as you make out.

 

A starship can accelerate, because it has engines on board, which make it go faster. Whereas the dust particles haven't got engines, so they can't accelerate. They just float, powerless.

 

By contrast, the powered starship goes ever faster, pushed on by its engines, which give it more speed and mass, until eventually the ship's mass gets so great, that it becomes like a planet.

 

Then, even if it isn't buffered by an atmosphere, as you suggest, won't the ship's sheer naked mass, enable it to brush tiny dust particles aside. Couldn't such a ship travel through space, like the Earth travels round the Sun, without being bothered by dust particles?

Edited May 4, 2013 by Dekan

[krash661]

which give it more speed and mass, until eventually the ship's mass gets so great, that it becomes like a planet.

can you show the math on this please.

[Dekan]

I refer you to Einstein, my predecessor.

[John Cuthber]

I refer you to Einstein, my predecessor.

Who was the first to point out that there is no preferred frame.

And, with no preferred frame, there's no way you are right.

 

The point also remains that, from the point of view of those on the ship, it weighs exactly the same as it always did.

[Janus]

Thanks, but is the situation as symmetrical as you make out.

 

A starship can accelerate, because it has engines on board, which make it go faster. Whereas the dust particles haven't got engines, so they can't accelerate. They just float, powerless.

 

By contrast, the powered starship goes ever faster, pushed on by its engines, which give it more speed and mass, until eventually the ship's mass gets so great, that it becomes like a planet.

 

Then, even if it isn't buffered by an atmosphere, as you suggest, won't the ship's sheer naked mass, enable it to brush tiny dust particles aside. Couldn't such a ship travel through space, like the Earth travels round the Sun, without being bothered by dust particles?

 

For one, your spaceship moving at 0.9999999c, would only experience a "mass increase" of 223 times its rest mass; nowhere near that of a planet. Secondly, the Earth's orbital speed is only 30 km/sec. The kinetic energy of a dust particle with that relative speed is many factors smaller. If the Earth were to collide with a 10 mg particle at orbital speed, the impact would release 4.5 million joules of energy. IT does not matter whether we consider the partical as moving or the Earth. With the Earth, this energy is released traveling through the atmosphere and you see a meteor. Many of them are no bigger than a grain of sand, but release enough energy to be seen for miles.

 

If the Earth collided with a 10 mg one without the buffering effect of the atmosphere, it would realease the energy on impact, which would be the equivalent of setting off 1 kg of TNT. (So, just like the bat in my prior example, the Earth would end up with a ding.)

 

So even at the orbital speed of the Earth, collsision with a small particle involves no small amount of energy.

 

Now, this is a small amount of energy when it comes to the kinectic energy of the Earth, which means the Earth's orbital speed will change only by an insignificant amount in t collision. However, this does not mean that the Earth would come away unscathed.

 

With our spaceship, a collision won't decrease the total velocity of the Ship measureably, but this does not mean that the point of impact will not receive considerable damage. It doesn't matter if our ship reaches its destination in the most part unabated if it is a molten slag due to all the high energy collision that it absorbed along the way.