Idle Questions of the Nicoll Kind...

[seawasp]

... how far would you have to go between two stars in the galaxy (or, if that wouldn't suffice, the universe) to have a significant (say, >10%) chance of going through another star on the way (with "through" being "at some point you're within the photosphere")? Has anyone done this calculation (I'm sure SOMEONE has)? I suppose it's quite possible the answer is "go as far as you like, the chances will never exceed 1%" or something like that.

Comments

I'd guess 0

[mike giroux (from livejournal.com)]

If you consider how SMALL a star is compared to interstellar distances, the odds that 3 stars would be *precisely* on the same line seem really improbable.

0 seems like a reasonable guess. But if you really want to get a better estimate, I think a good place to start would be looking at stellar sizes and densities in globular clusters or galactic cores.

(Of course, I'm a computer programmer, not an astronomer, so this could be way off...)

[baronger.livejournal.com]

I've always seen this in SF, as a limiter to a magic interstellar drive too.

It has always seemed to me to be a small chance too. While stars are big, space is huge and stars are widely spaced out.

I sort of think its like the radiation experiments, where particles can go right through a solid object because they are unaffected by electron shells. And they will only be stopped by the nucleus of an atom which is really really unbelievably small compared to the overall atom.

Though I would have to ask, are we traveling toward the galactic center or away from it. Away from one it would seem that your risk would decrease, while traveling inward would be a greater risk with stars being closer together, and their being more of them.

[seawasp]

Also depends on how one defines the star. Above, I say "through the photosphere". If you say "through the gravity well greater than X", then you could have a MUCH larger target. Or "Through the corona", or "within the heliopause".

[baronger.livejournal.com]

Very true, especially if you consider how you might be effected. You might not be destroyed but you might have your course deflected ect.

Also to be considered of course it that where you see a star now isn't where it is now. That star 1,000 ly's away has had a 1000 years of movement.

Also since darkmatter affects how fast stars move in a galaxy that problem needs to be solved too. If I remember correctly star movement in galaxies, was one of the ways they confirmed its existence.

I can't wait for them to finish figuring out what is happening with the strange speed changes of the voyager spacecraft.

If you are going to include gravity effects remember the brown dwarfs which are difficult to detect, and the ones that are down right black.

[filkerdave.livejournal.com]

If it was TRULY a question of the Nicoll Kind, there would be some offhand reference to the interesting patters the radiation burns make on your skin

[gary-jordan.livejournal.com]

"...how far would you have to go between two stars in the galaxy..."

The answer is "100%," as defined by the way the question is stated. Gotta use a little more precision, there, Mr. Writer Sir. Maybe, "If I draw a straight line between Sol and a star 100,000,000 light years away, what are the chances that the line will intersect one or more stellar photospheres?"

The fun(nest) part is figuring out where a star 100,000,000 ly away "is."

[howardtayler.livejournal.com]

Somebody may have already crunched numbers you can use as they calculated the likelihood of stellar collisions during galactic mergers.

IIRC, even when there are millions (billions!) of objects massive enough to attract each other, and they're hurtling together in galactic clumps, stellar collisions are exceedingly rare. For a single spacecraft, your "less than 1%" guess is probably high by a few orders of magnitude.

[lexomatic.livejournal.com]

BOTEing it:

Assume a star is 10^6 km wide (it'll vary by a factor of ~100 either way, from red dwarfs to supergiants). Assume stars are separated by 10^13 km (1 Ly) (it'll vary between the halo, disc and core). The star occupies 10^-21 of that volume (more or less, depending how you share the volume between adjacent stars).

Assume shells of other stars around Star A, at 1 Ly intervals. (The answer probably varies by a sizeable factor if you assume a cubic or hexagonal packing.) Assume such an array is infinitely extended. We now hit Olbers' Paradox, which asks: why isn't the night sky uniformly bright? If you look far enough into infinite space, every point on the celestial sphere will have a star behind it. (The resolution, if you haven't guessed, involves a finite speed of light and universe of finite age.)

At radius R, there are N stars, each subtending angle S. At radius R*m, there are N*m^2 stars, since surface goes as square of the radius, but each subtends S*m^-1, since it's farther away.

Is this a converging or diverging series, and how quickly? Anybody here with a better grasp of calculus? Paging austin_dern, please.

[lexomatic.livejournal.com]

Wait, I think I have another formulation.

Shoot a ray from Star A. At each shell, there's a chance the ray will intersect another star. The chance depends on the fraction of the shell that is covered by stars; this is a constant (surface and number of stars both rise as the square of the radius). Let's call that chance P. P is the fraction of cis-stellar space subtended by the star, 10^-14 given my earlier numbers.

The chance of *not* hitting *any* star on a shell is (1-P). The chance of *missing* stars on two shells is (1-P)*(1-P), generalizable to (1-P)^N for N shells. Therefore the chance of *failing* to always miss, i.e., hitting at least once, is 1-((1-P)^N).

How many (N) shells do we have to traverse to have a chance F of hitting a star? Solve for 1-((1-P)^N) >= F. There's a logarithm in that process, I think. Where's a symbolic math package when you need one? Wolfram Alpha? Nope. Okay, let's try the iterative approach. At 100,000 radii your chance F is still about 10^-9. At 1 billion radii it's still 10^-5. At 1 trillion radii you finally hit F=10^-2 or 1%.