Re: Take One Magical Spacedrive

sigidunum@xxxxxxxxx wrote:

On Jun 25, 9:24 am, Hop David <h...@xxxxxxxxxxx> wrote:



Well, according to http://www-ssg.sr.unh.edu/ism/what1.html
the interstellar medium has about 1 atom per cubic centimeter, 3 out of
4 atoms H, the 4th He.


It varies by about an order of magnitude, even in "normal"
interstellar space. So, in the immediate region of the Sun it's about
0.2 atoms/cc (because we're in the "local bubble").

To be honest, I have no idea how accurate the guestimate I cited is.


So each cubic centimeter would have 1.75 protons
or neutrons per cm^3 or about 3E-27 kg/cm^3

The cubic centimeters it'd pass through in a second would be velocity
(in cm/sec) * cross section of space craft (in cm^2)

I would guess kinetic energy is 1/2 * sqrt(1/(1-(v/c)^2)) * m * v^2.


A classical calculation gives a hydrogen atom at lightspeed a kinetic
energy of about 1.6E-27 kg * (3*10^8 m/s)^2 = ~1.4E-10 joules.

You're using E = mc^2 evidently. Which is probably right.

I was using KE = 1/2 mv^2
and multiplying mass by gamma to correct for relativistic speeds.

However at light speed gamma (sqrt(1/(1-(v/c)^2))) becomes
sqrt(1/0). This would give a hydrogen atom traveling at light speed infinite mass.

I recall making some progress trying to plow though special relativity. But that was a few years back. And I made no progress with general relativity. I used the words "I would guess . . ." because I'm not sure.

Two books to get my next trip to the city: A book on linear algebra (for another thread) and a book on relativity.


That's not much, but -- you're going to sweep through a lot of
hydrogen atoms as you zip along. You're moving at 30 billion
centimeters/second. So, 3 x 10^10 impacts/second gives a power input
of 4.2 watts/square centimeter, or 42,000 watts/square meter.

If that's right, then the leading edge of your ship is going to glow.
Brightly.

Relativistic correction: if you're traveling at 0.99c, then the
classical calculation drops the power output by 0.99^3 (because the
kinetic energy drops as the square of the velocity, and the collisions/
second drop too). But the atoms will seem to be about 7 times as
massive, and so will produce 7 times as much energy. Yikes.

Note that dropping your speed a little helps a lot. At 0.9c the power
input is down to about 3 watts/cm^2, even with relativity. At 0.5c
it's a mere ~half-watt/cm^2.

That still seems high, so I'd be happy if someone checked my
calculations.


Doug M.




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Relevant Pages

  • Re: Take One Magical Spacedrive
    ... James Nicoll wrote: ... the interstellar medium has about 1 atom per cubic centimeter, 3 out of 4 atoms H, the 4th He. ...
    (rec.arts.sf.science)
  • Re: Aether Displacement II
    ... the aether may consist of movable particles, ... with an average density of about 1 atom ... I'm not talking about 1 atom per cubic centimeter. ... what occupies the rest of the cubic centimeter, the aether. ...
    (sci.physics.relativity)
  • Re: Aether Displacement II
    ... the aether may consist of movable particles, ... with an average density of about 1 atom ... I'm not talking about 1 atom per cubic centimeter. ... what occupies the rest of the cubic centimeter, the aether. ...
    (sci.physics.relativity)
  • Re: Is the Local fluff (LOCAL INTERSTELLAR CLOUD) composed of ionized hydrogen or rather neutral one
    ... hydrogen atom per cubic centimeter of space we get that we are ... compelled to put some 3 microjoule per square cm to get 13.6 ... If the photons are not absorbed to ionize that particular atom, ...
    (rec.arts.sf.science)
  • Re: GR "Spaghetification"
    ... issue that it is a physical fact the atom gets ripped apart at some point, even if never seen by anyone. ... I explicitly said I was discussing General Relativity, ... We do know that in GR any atom approaching the singularity of a black hole will be ripped apart, because any object of finite size will be ripped apart. ... It is generally expected that when we ultimately understand this, the quantum details will have modified the GR description so there is no actual singularity; that is merely an expectation, not a conclusion. ...
    (sci.physics.relativity)