Launch Spacecraft to Near c Speeds: Is it Possible?

[kolleamm]

Is it possible to spin a tiny spacecraft to near c speeds, and then have it eject from the object it's spinning on into space?

I came with this idea after seeing the Starshot project that involved lasers and thought there might be a better way. What are your thoughts on this?

Thanks

 

[berkeman]

Is it possible to spin a tiny spacecraft to near c speeds, and then have it eject from the object it's spinning on into space?

Not through an atmosphere. If you have a particle accelerator in orbit or on the Moon, you could launch protons or electrons in a beam...

 

[kolleamm]

Not through an atmosphere. If you have a particle accelerator in orbit or on the Moon, you could launch protons or electrons in a beam...

What about bigger things like 0.5grams?

 

[Ibix]

The centripetal force requirements will be impressive - $\gamma^2mv^2/r$, if I'm not mistaken.

Edit: I make it 1.5×10⁹N for your 0.5g craft on a 10km ring at 0.5c - comparable to the weight of the larger aircraft carriers.

 

[kolleamm]

The centripetal force requirements will be impressive - $\gamma^2mv^2/r$, if I'm not mistaken.

Edit: I make it 1.5×10⁹N for your 0.5g craft on a 10km ring at 0.5c - comparable to the weight of the larger aircraft carriers.

If the thrust of the Saturn V rocket was 10^7 N at liftoff, would these numbers you gave me make the idea practical? It's only about a factor of 100 off.

Edit - I take that back if we consider the 1.5

 

[berkeman]

What about bigger things like 0.5grams?

I'm only aware of one such test. The results were impressive!

https://upload.wikimedia.org/wikipedia/commons/0/09/Operation_Crossroads_Baker_Edit.jpg

 

[Ibix]

If the thrust of the Saturn V rocket was 10^7 N at liftoff, would these numbers you gave me make the idea practical? It's only about a factor of 100 off.

Only a factor of 100? Where are you going to get a hundred Saturn Vs from? Also note you need to be able to provide that at all points around a 10km radius ring, not at one point as in a rocket.

Note also that this is merely the centripetal force. I have said nothing about the force that increases the speed..

I have never looked into this, but do note that the accelerator at CERN is an incredible achievement, and it spins a handful of particles around. On that bases, I very much doubt a ring accelerator for a macroscopic object is practical.

 

[Stavros Kiri]

Is it possible to spin a tiny spacecraft to near c speeds, and then have it eject from the object it's spinning on into space?

Also note you need to be able to provide that at all points around a 10km radius ring, not at one point as in a rocket.

Note also that this is merely the centripetal force. I have said nothing about the force that increases the speed..

I have never looked into this, but do note that the accelerator at CERN is an incredible achievement, and it spins a handful of particles around. On that bases, I very much doubt a ring accelerator for a macroscopic object is practical.

I agree with Ibix. It doesn't seem a very practical idea, since, considering the range and scale of the force and things, it's probably easier or we might as well use the same force to pull it and linearly accelerate it, instead of having it spin! ...
(depends on the set-up though ...)

 

[pervect]

Is it possible to spin a tiny spacecraft to near c speeds, and then have it eject from the object it's spinning on into space?

I came with this idea after seeing the Starshot project that involved lasers and thought there might be a better way. What are your thoughts on this?

Thanks

The idea of spinning things as a means of launching spacecraft has real life grounding in the idea of space tethers. See for instance <<wiki>>. Actual implementations aren't "tiny", and they don't move at half the speed of light. But one can use some of the design equations to see what would happen if one tried to make them smaller and faster. There will be some modest relativistic corrections from the wiki formula (which are classical). I believe these corrections will tend to make things worse for your idea, rather than better, so we are being optimistic by ignoring them. However, I believe at .5c these relativistic corrections should be much less 2:1, the gamma factor is only about 1.15.

Using some of the math of actual space tethers one can evaluate how far the idea can be pushed. See the section

There are design equations for certain applications that can identify typical quantities that drive material selection.
...
For rotating tethers (rotovators) the value used is the material’s ‘characteristic velocity’ which is the maximum tip velocity a rotating untapered cable can attain without breaking,
$$V_c = \sqrt{\frac{2 \sigma}{\rho}}$$

Here σ is the stress limit (in pressure units), i.e. the maximum force/unit area, and ρ is the density of the material.

The rotovator is one of the "best-case", it's faster than the circular hoop, but at this point can use either formula to get some idea of the numbers.

Next one looks at at this section on known materials that calculate the characteristic velocities of various materials. The theoretical value for carbon nanotubes (which may or may not be realizable) is, at 6 km/sec, very, very smallert than .5c.

So the basic conclusion is that even theoretically, the strongest known material (carbon nanotubes) won't reach your goal of .5c. One cannot "spin up" a cable made of carbon nanotubes to that sort of speed and expect it to hold together. Steel would be much worse.

So in order to do what you want, one would need to postulate the existence of materials that are much, much stronger than carbon nanotubes on a strength/weight basis.

 

[Sorcerer]

The idea of spinning things as a means of launching spacecraft has real life grounding in the idea of space tethers. See for instance <<wiki>>. Actual implementations aren't "tiny", and they don't move at half the speed of light. But one can use some of the design equations to see what would happen if one tried to make them smaller and faster. There will be some modest relativistic corrections from the wiki formula (which are classical). I believe these corrections will tend to make things worse for your idea, rather than better, so we are being optimistic by ignoring them. However, I believe at .5c these relativistic corrections should be much less 2:1, the gamma factor is only about 1.15.

Using some of the math of actual space tethers one can evaluate how far the idea can be pushed. See the sectionHere σ is the stress limit (in pressure units), i.e. the maximum force/unit area, and ρ is the density of the material.

The rotovator is one of the "best-case", it's faster than the circular hoop, but at this point can use either formula to get some idea of the numbers.

Next one looks at at this section on known materials that calculate the characteristic velocities of various materials. The theoretical value for carbon nanotubes (which may or may not be realizable) is, at 6 km/sec, very, very smallert than .5c.

So the basic conclusion is that even theoretically, the strongest known material (carbon nanotubes) won't reach your goal of .5c. One cannot "spin up" a cable made of carbon nanotubes to that sort of speed and expect it to hold together. Steel would be much worse.

So in order to do what you want, one would need to postulate the existence of materials that are much, much stronger than carbon nanotubes on a strength/weight basis.

Perhaps Adamantium would do the trick?

 

[jocarren]

Perhaps Adamantium would do the trick?

Is Adamantium massless? Otherwise: no.

 

[Sorcerer]

Is Adamantium massless? Otherwise: no.

Why does it need to be massless? I thought we were just discussing the material for the device to accelerate the projectile.

 

[jocarren]

Why does it need to be massless? I thought we were just discussing the material for the device to accelerate the projectile.

The problem is that any massive proyectile would require A LOT of energy to accelerate near c, adding a massive bar to exert centripetal force on the proyectile would only increase the energy requirement.

That's (part of) why the guys at the LHC don't use a slingshot to accelerate particles, they use electromagnetic fields instead (though, I'm not sure if that method would be any more energy efficient than use a macroscopic device to hold a macroscopic proyectile spinning at relativistic speed).

Maybe if we spin the thing around a black hole or neutron star, lowering the orbit as it comes closer to c. That's the only way I can think for it to be "feasable".

 

[pervect]

Perhaps Adamantium would do the trick?

The strength/weight ratio of a substance is closely related to the speed of sound in that substance. Adamantium as a comic book material doesn't have to obey the laws of physics. Materials consistent with the laws of physics (in this case, the laws of special relativity) need to have a speed of sound in the material that's less than the speed of light. This does put a fundamental limit on the strength/weight ratio.

There isn't any really well developed theory for materials that would have a speed of sound an that is appreciable fraction of "c", and we don't know of any actual materials with such a high speed of sound we could measure or experiment with. All known existing materials have a speed of sound that's much much lower than "c".

 

[PeterDonis]

Maybe if we spin the thing around a black hole or neutron star, lowering the orbit as it comes closer to c.

This won't help. The orbital speed might approach $c$ as measured by local observers, but the actual energy at infinity of the object is decreasing as the orbit gets closer, which means that when you launch it, it will end up moving more slowly as seen by observers far away, and take longer to get to some distant point. Heuristically, the increased orbital speed in a lower orbit is more than outweighed by the fact that, once you launch it, the object has to climb farther to get out of the gravity well; it ends up losing more speed in the climb than it gained from the increased orbital speed.

 

[jocarren]

This won't help. The orbital speed might approach $c$ as measured by local observers, but the actual energy at infinity of the object is decreasing as the orbit gets closer, which means that when you launch it, it will end up moving more slowly as seen by observers far away, and take longer to get to some distant point. Heuristically, the increased orbital speed in a lower orbit is more than outweighed by the fact that, once you launch it, the object has to climb farther to get out of the gravity well; it ends up losing more speed in the climb than it gained from the increased orbital speed.

Yes, I forgot to account for the big big mass. "It won't help" should be the title of this thread.