I have this idea. It involves a particular assassin of our acquaintance taking a job on a space station, probably an asteroid-mining operation owned by a big evil mega-corporation.
Awhile back I was daydreaming about artificial gravity systems with my limited knowledge of astrophysics, and I thought, Hey, they've simulated black holes in labs in the last 5 years....what if the space station engineers created a "hypermass" artificial gravity system made from a sort of controlled super-heavy black hole at the center of the station (I guess some other authors have already considered this, but I don't read much hard SF so I don't know of any examples).
I cribbed the word "hypermass" for use in a story and never explored how the thing might work.
Today, I was daydreaming about what might happen if the thing went wrong, because as you know, Bob . . . Bad Things tend to happen in my stories.
So I'm envisioning Quinn being stuck in this mining station, which is gradually collapsing in the middle, trying to kill the guy she's been contracted to kill while trying to get out herself--kind of like the Poseidon Adventure. But the collapse would have to occur at a fairly steady or slowly accelerating rate (ideally), or the station would just cease to exist. I think it would create a great atmosphere of claustrophobia if it happened slowly, but I don't know if that's possible.
Thoughts? Any way I can make this work?
36 comments:
Hm!!!??? The March issue of "Astronomy" has articles about extreme stars. The collapse of such stars into black holes may occur in a matter of milliseconds. Now, die-hard hard science nit-picking critics may squawk at your notion of gradual collapse, but you would hear no complaint from me. After all, your stories are fiction. It's a "what if" scenario. The hypermass could be accumulating matter from the station gradually until it reached some limit, then "WHAHM," the big crunch!!!!
If Quinn has a streak of mean, and I don't get the impression that she does, she would incapacitate her target and leave him to sweat the final moments. Tie him to the railroad tracks, so to speak.
If SF writers were paranoid about hard science criticism, not a word about FTL space travel would ever be written, and the genre would be much the poorer for it.
SG
I guess the "containment field" around the hypermass could have a leak. In theory, the hypermass "mass" wouldn't attract any futher "mass" unless said "mass" crossed the event horizon--so something would have to happen to either move the 'mass or toss something into its field of gravity (even dust would accumulate over time). Once the hypermass started accumulating more mass, however, it would grow, thereby expanding the event horizon, after which the implosion would accelerate exponentially. That's my best rubber-guess, anyway. It wouldn't stop the hard SF-physicist types from lamblasting my premise.
Quinn's not sadistic per se, but she does have a certain pragmatism, and the railroad tracks scenario did occur to me. I don't know if it's as dramatic as I want, but oh well! Scenerios envisioned in the early planning stages of a story rarely make it to the final cut.
Another thing, though--I could have some kind of small leak in the body structure of the station so it gradually collapses in on itself, but that's not as interesting or dramatic as a black hole.
I think my problem here is having anybody get out alive.
I don't know if you've read much of Larry Niven. I haven't, for many years. In one story, a character happened to get too close to a neutron star. The tidal forces ripped him apart. In a continual series of his, he had one starfaring race fleeing the galaxy, because of the expanding black hole at the center of it.
There was the movie, "The Black Hole," which came out in 1979. It had a most confusing, unsatisfactory ending.
I'll get back to you as I learn or relearn this subject. Shee!!! For somebody that's been interested in astronomy for over fifty years, I really don't know very much.
SG
Based on the preliminary reading I did yesterday, it doesn't seem that anyone knows very much, so don't let it bother you.
Yeah!!! One thing I have learned in my several decades of going to and fro upon the earth(Job 1:7) is that I really don't know very much about anything. My one consolation: neither does anybody else.
The beauty of studying things one has forgotten is that it's fun to relearn them.
SG
I'd say you can almost certainly make the concept credible enough... Notwitstanding that the Comic Book Guy from the Simpsons (or one of his real-life analogues) will almost certainly find some excuse or another to quibble...
The only real physical difficulties are i) how you get a black hole in the first place, and ii) how you get one small enough to be useful... the smallest ones we know about are the mass of biggish stars (Google the Tolman-Oppenheimer-Volkoff limit, if you haven't already... this is the mass at which you start getting them after stars collapse)... But actually, theroetically, there's no phyical reason you can't have one smaller. Just gotta get the matter compressed enough in the first place somehow.
As to your 'how could it happen slowly' question, actually, it would seem to me if you went to the trouble of building something around a smallish black hole in the first place, you'd probably build it pretty @#$^ing solid... but you know... just 'cos you built it so nothing can go wrong doesn't mean your crazy overengineered lattice of wonderfully stiff alloys and composites can't start to collapse... due to sabotage... or some unforseen exotic decay...
Depending on how big we're talking, here (both bits... the hole and the station), and how far apart they are (matters, actually ... see F = Gm1m2d^2), it might actually do very little when the bits and pieces of the station drop into the hole... since the black hole's mass would probably be a fair bit greater than that of the structure... but still, you can have slow collapse, with the drama of it all eventually disappearing into the event horizon at the end...
As to how anyone gets out, again, not a huge problem. The thing that's been constructed was put together in such a fashion that the actual acceleration due to the hole's gravity is around 9.8 m/s^2 at the place where people are walking around... Stuff falls off at the usual rate (but as it gets a bit closer to the hole, it accelerates faster, due to greater proximity ... see F=Gm1m2d^2 again ...) so any vessel capable of getting away from Earth's gravity has no great difficulty getting away from this thing... provided it doesn't get closer to the centre than anything is supposed to do.
So yeah, it's reasonable enough, I think. Would imagine we're talking about some pretty hefty engineering, but it's possible.
Other thought... say stablizing the thing is really about keeping it balanced at that safe distance... you've got some crazy system of thrusters or big whirling massive gryoscopic thingies to balance it when say, something big lands on one side, throws off the centre of mass, pulls the hole that little bit closer to one side than it's supposed to be...
And someone breaks that, badly. Or there's a big explosion, drops some sizeable chunk of the structure into the hole, and the thing starts whirling and groaning like a limping bird around the hole, all its systems trying to keep it from going the rest of the way, oscillating unstably, bits coming too close, dropping off, the whole thing gradually breaking down, falling apart, and no one quite knows when the last of the whole damned thing is gonna go down like an ocean liner into the event horizon.
say stablizing the thing is really about keeping it balanced at that safe distance... you've got some crazy system of thrusters or big whirling massive gryoscopic thingies to balance it when say, something big lands on one side, throws off the centre of mass
Yeah... we're on the same page. I was visualizing (texturalizing?) the same sort of thing, but I was worried I had seen too many Star Trek episodes.
Here's a link to a simple explanation of the Newtonian Laws of gravity, for my own convenience. I remember learning all of this long, long ago.
http://www.astronomy.ohio-state.edu/~pogge/Ast161/Unit4/gravity.html
And you're right, SG, it is fun to relearn this stuff. I swear that's the 2nd best part of being a writer.
Ok, bear with me here....
I was just reading Astrophysics 161, about Forces coming in pairs (Newton's Third Law)...
"If I set an apple on this table, it pushes down on the table with a force equal to its mass times the acceleration due to gravity.
To hold it stationary (unmoving), the table must be exerting an equal and opposite upward force."
...and taking into account that the moon stays in orbit around the earth because it is constantly falling in a circular direction....
would not a space station built in a ring/sphere around a speck of hypermass, by default remain rotating equidistant at all points from that speck of mass, because of the equal gravitational pull on all sides? Unless of course something threw it out of whack? (Restating what AJ said but with a different design in mind, and the speck outside of the station.) The problem then becomes building an electromagnetic shield around the speck, to keep out space dust, etc.
Ugh. Arrgh! I don't have the math for this.
Yup, it seems to me that AJ has the straight of it here.
Although the planet Jupiter has 318 times the mass of Terra, gravitational force at its "surface" is just 2.64 times that of Terra at its own surface becouse of the good ol' inverse square law. There is no law that the gravitational field at the mining satellite be one standard gravity. It could be set at whatever level that may inhibit loss of bone mass. Even so, as AJ points out, the hypermass would need to be small enough so that one wouldn't need to be billions of miles from it to experience one gravity. As things now stand in the natural universe, black holes are indeed several solar masses. With futuristic engineering, the size may be whittled down.
In the classics, "Star Trek," and "Star Wars," artificial gravity, force screens, FTL, are all assumed, not explained. It's the interplay among sentient beings that is of major importance. But in your story, it's the failure of the artificial gravity that is pivotal, so some explanation is called for. The fantasy nuts among us may not mind a hokey display of pseudoscience, but the hard science folks will squawk.
SG
Hey, while I was composing this, you posted a reply or two of your own. I was contemplating that the containment field would not be magnetic, since a black hole has no free electrons whose movement would generate a magnetic field, but such a field to keep other things out makes sense.
I think, actually, keeping dust out wouldn't be that major a concern. Bear in mind that it's the mass of the Earth that keeps us in place, and the Earth is constantly getting rained on by cosmic dust due to its mass pulling it in, and it's not like we're noticing much difference real quickly. The actual mass of the hole would be big enough that a bit of scruff getting sucked into it--even a fairly constant rain of the normal sort of material that might be floating near a space station--wouldn't have an appreciable effect. You could probably drop a coupla Saturn V's into it, no big deal, apart from the (theoretical) flash (no, black holes aren't quite always black... it's believed they can flare in odd ways due to effects at the even horizon as stuff is captured). And the slightly higher mass wouldn't really effect stability, either, of something with the hole at its centre, as the slightly greater attraction would be equal around the whole structure... slightly greater stresses depending on how much mass we're talking, but years of space dust wouldn't even rate.
The 'off-balance' problem, I think, actually is the much bigger one. Something big landing on one side, the hole gets pulled a little closer at the same time the something big does... attraction increases with the distance, and, potentially a very dangerous positive feedback sets in. What I'd think you'd want is something dynamic to offset that... Say big masses you can move around the ring at will to the far side, to balance the forces. Mebbe a real smart computer with sensors all over the place to figure out when things get thrown slightly off, and compensate.
Thinking about it, actually, you might need something like that even to compensate for relatively small mass shifts... people walking, vehicles, whatever (don't know how big you're thinking here), all of that could cause trouble of the 'off balance' sort. I'd think you'd need a way to compensate.
Seems to be a case in which size definitely matters.
That's why I said I don't have the math. I need to find some geek to compute the minimum size I can make this station and still have it viable. I wonder if in all of Silverberg's essays he had something applicable....
Here's a sort-of answer...
According to the Wiki article about the Schwartzchild radius, the size at which the earth collapses into a gravitational singularity is about 9 milimeters.
So in order to imbue my fictitious station with Earth-gravity (1-G) my speck of hypermatter could be as small as this: [ ]
You'd think it'd be easy to lose that way.
You'd probably need it substantially smaller for it to be practical.
To use an object the mass of the Earth, and to get Earthlike gravity, you'd have to be about as far from the singularity as we are from the centre of mass of the Earth... so the station would have to be about the circumference of the Earth... and with that much matter anyway, why make a space station...
When you could just as easily make a planet?
A substantially less massive blob of matter (but still pretty freakin' massive in engineering terms), much closer, you'd still get Earthlike gravity... Another nice effect would be that the gravitational well would be 'steeper'... that's to say it would fall off more rapidly as you get away from the object... So while you'd get Earthlike gravitational acceleration at the point you've got people walking around, and you'd need vessels that could counteract that to get away, they'd actually benefit from the fact that the falloff in the attractive force would be more rapid than it is pulling out of the Earth's well...
Hold on... I'll do a bit of math... give you some proportions...
Thinking it through, it's pretty simple.
F=ma. We want acceleration same as we get with Earth's mass and distance to the centre, at 9.8 m/s^2. F=Gm1m2/d^2, so for constant a, m/d^2 is constant... whether it's the mass of the Earth and it's radius in the figure or our hypothetical station and singularity... ergo...
The mass of the object you want is the Earth's mass times the square of the distance to the singularity expressed as a proportion of the radius of the Earth...
Or, for a distance of 1/10th the radius of the Earth, you can make do with a singularity that's 1/100th the mass of the Earth. For 1/1000th, you'll get away with a mass of 1/10^6 Earths...
Or, at 6km from a singularity weighing about 6*10^18 kg, you've got Earth normal gravity, more or less.
You want smaller? Mebbe 600m from a singularity of 6*10^16 kg. Still one heavy, heavy pile of stuff, I guess. And seems a bit close for my comfort. But you get the general idea.
Dude. You are such a geek.
I mean that in the best possible way, of course.
I'll digest this for a day or two and get back to you. I'm having to exhume entire lobes of math and physics that haven't been touched in 15 years.
Sad...
Yup, AJ does have the straight of it. If the acceleration caused by gravity is considered a constant, then the mass of the desired object varies directly as the square of the distance. Halve the distance, and the mass required is one quarter of the original. Halve distance again, the mass needed is one quarter of that, or a sixteenth of the original, and so on.
Radius of earth is about 4000 miles,or 6400 kilometers. If the space station is one four-thousandth of that, one mile in radius, the mass required is one sixteen-millionth that of the earth.
Such a mass, if it were the same density as earth, is nearly sixteen miles in radius.
We don't want that.
To become a black hole, an object, a star, must have at least three solar masses; to become a neutron star, at least 1.4 solar masses. These fractional earth masses don't make the grade.
But what about the superdense material of white dwarves, the sort of stellar object our sun will become in a few billion years? Suppose the evil megacorporation pried an appropriate mass from one of them, toted it to the asteroid belt, and built a Dyson sphere about it. If the object remained at its density, it may be of a size to keep track of. The main hangup here is that, once freed of the crushing gravity of its parent star, the material is most likely to return to the proton-neutron-electron mode of lesser density and pressure. In short, BLOOEY!!! at the instant of its removal from its mother star. No need to spank it, it will blow of its own accord at being wrested from its womb.
Houston, we have a problem.
SG
To become a black hole, an object, a star, must have at least three solar masses; to become a neutron star, at least 1.4 solar masses...
... quite true, for black holes that form from stars (as already noted above... see again the Oppenheimer-Volkoff limit). But that's because the mechanism by which the required density is initially achieved is gravitational collapse, and that's how much mass you need to force such densities.
However, theoretically, nothing prevents smaller holes from existing. And they'd be quite stable, according to the physicists I'm reading. Indeed, there may be lots of those around now (they're actually a dark matter candidate)... though we haven't seen direct eveidence of any such thing yet, they'd be difficult to detect by nature... Google 'primordial black hole', for papers on the subject.
So you've still got two plausible possibilities: 1. Find a surviving primordial black hole (one theory says they should have evaporated by now, another says there are ways they could have survived), and tug it to where you need it, (difficult, but actually not impossible... you can deflect them the same way you can any object in space with gravitational slingshot tricks, which wouldn't actually require you to get inside their horizon), or 2. Make one, by some sci-fi-ish technology involving either a). speeding the evaporation of a stellar mass hole, or b) collapsing normal matter with insane amounts of force.
...a black hole with the mass of the earth and corresponding Schwartzchild radius would create the same gravitational potential as the earth for distances greater than the earth's radius...
Quite... two objects of the same mass create the same gravitational potential energy on another object of a given mass at a given distance regardless of the first object's density... and that's for all distances from the centre of mass, less than and greater, from infinitesimal to infinite (tho', of course, for a more dense object of the same mass, you can obviously get a lot closer to the centre of mass, and thus experience a much more intense gravitational field, which is the advantage of a singularity, here).
Nonetheless, just for clarification, the radius of the space station around mass equivalent to one Earth (regardless of the density of the mass) would still have to be the radius of the Earth to get the same gravitational acceleration as we experience on the surface of the Earth. Working with the Gauss' law notion above, visualizing it through the 'flux lines' concept often used for visualizing force effects as distances increase, you can think of it as being a function of the surface of the enclosing sphere, which increases as the square of the distance from the centre of mass. Double the distance, quadruple the area of the enclosing sphere, quarter the intensity of the flux lines. If you're closer in, the flux is more intense, and you experience a higher gravitational field. Further out, you get less.
Also, again, as I stated earlier: smaller masses would be different. Steeper gradient, more rapid falloff in gravitational potential energy for the same distances.
Ummmm... as respectfully, I'm not even sure quite what you're dissenting from. But you might just try it with the equation for the law of univeral gravitation and see what you get.
Again, that's F = Gm1m2/d^2. Try substituting with F=ma where m is the test mass, m1 is the test mass m2 is the mass of the singularity, and you'll see what I mean, I think. Or I hope.
And for clarification, by 'gradient' I mean the change in the gravitational force with distance. So think of it this way: you actually get the same force twice as close to a mass 1/4 the size... but moving a metre from the latter mass is much larger proportional change in distance tham moving a metre from the former, so it makes a bigger difference in terms of the force felt after you move that distance.
Again, try it with the equations, I expect you'll find it works.
I'm very glad that Holly has you uber-geeks (said with the utmost respect for your abilities to comprehend and explain physics and math concepts). Just reading what you folks have written has my mind considering turning into a hypermass itself. As such, it should certainly be small enough for Holly's station engineers to manage! I felt bad when she proposed something about which I could come up with nothing intelligent or substative to say. I'll stick with talking about the plebian matter of turning wool into clothing. This is what will keep me alive after life as we know it ceases. I will be able to barter this skill for other stuff. No, not hoping for or dreading such. Just justifying why I spend my time learning this stuff. The only other reason is that I'm just weird. (I heard that thinking!)
SG here.
Let's cut to the chase, chillun.
Yup, if we have an earth mass in that chunk of degenerate matter, be it black hole, neutron star, or white dwarf, we'd need a station with earth radius for the same gravitational effect.
Why not make a planet?
Unlikely!!! Ee-ville megacorporation has a habit of carving up planets and carting the mineral resources elsewhere to sell for obscene profits. Yeah, the company might build a Dyson sphere of Terran dimensions for luxury condos for its CEO's, but it's doubtful that it would park it next to an asteroid belt as a bullseye for any and all objects with suicidal tendencies.
Nope, for mining operations we don't need no steenkeeng earth mass nor earth size station. A structure a couple miles across with the appropriate mass in the middle is sufficient. Nor do we need esoteric tractor beams or pressor beams to hold the mass in place. Just put spin on the station so that it orbits the mass. A containment field of some kind may be necessary for the degenerate matter.
Gentle Readers of Holly's stories ain't looking for doctoral dissertations on astrophysics. They want to know how Quinn does her job and gets her young self outta there without becoming a smear on the surface of the degeneracy. One problem she may have is that she will need to bring some proof that she has performed her task; haul the body of her victim with her!!! Naw!!! The head will do.
SG
Yo, Captain Anonymous---post your name, and cite some sources for your speculations, or be deleted. You have 24 hours. Maybe less.
Take it easy, SG, all of this stuff is food for fodder, whether it makes it into the story or not. Who was it said, only about 10% of your research should actually make it into the story?
Shirley, this is turning my brain to pudding, too, but it's fascinating! You and me will just sit and be fiber-y while the boys hash it out.... then I'll wade in, pick up the pieces I need, slap off the dust and write my story.
Thanks again, AJ. My most knowledgeable SF-geek mentor-writer-friend, Rob, is echoing much of what you've told me, plus a few other interesting tidbits. I'll send it to you, if you like.
Shirley is not weird. A couple centuries back, a year or two before my time, the ability to spin thread was a requirement for the ordinary housewife.
SG
Believe you mean 'agreeing'... as I'm not known for consenting to much.
As to the statement on acceleration being misleading, note that that it specifically describes gravitational acceleration (see... it's right there in the sentence you quoted). That would be the acceleration due to the gravitational field of the attracting mass... Centripetal forces aren't gravitational forces... tho' yes, you certainly could introduce them to offset a gravitational force, but that's quite beside the point I was trying to address.
As to the gradient, look: here's the math.
SG again.
Putting a spin on the hoop, which has no material connection to the mass providing the gravitational effect, would contribute counteracting forces to that of the degeneracy. The super-engineers of the far future would have figured out how to balance the two.
Again, it isn't necessary to maintain one earth gravity on the station, just enough to counteract loss of bone mass. And Ee-ville megacorporation may not give any part of a rat considering the comfort of its employees. The Spanish didn't care much about the conditions of the natives in the silver mines in Mexico. Let 'em die and reduce the surplus population. They'll make good fertilizer 'n' there's plenty more like 'em.
SG
... oh. And you're very welcome, Holly. Was a bit of entertainment, thinking it through.
I'm pretty sure, now, too, that the smaller holes would spark fusion in infalling matter for which any remaining feasible fusion reaction remains, same as you get in the accretion disks around the bigger ones. And yeah, there'd be x-ray emissions, all the fun stuff you get with bigger holes, due to matter spiralling in... So while my previous statement still holds re dropping a Saturn V into one not wildly affecting the gravitational field it emits, such a fumble-fingered moment would make for a fair bit of radiation.
Hmmm... typo in that paper (no, not to worry, the OCD is really quite mild, honest)...
'a fifth (as opposed to a five hundredth...' right at the end, should read 'a fiftieth (as opposed to a five thousandth...
...tho', actually, the point comes out the same. But I'll fix it.
Don't flatter yourself, wiseguy, you're one of about four morons I can name off the top of my head.
Go squat somewhere else. And learn to read for content before jumping into a conversation in progress.
SG here.
Doggone it!
The more I think about this, the more it seems like a Rube Goldberg device. Ee-ville magacorporation is into making profits. The expense of obtaining a degenerate mass, "machining" it to fit specifications, and hauling it to a parking orbit would generate some humongous cost overruns, cutting deeply into the obscenely bloated salaries of the CEO's. The easiest way to create "artificial" gravity is to put spin on the station. Ee-ville, with its eye ever on the bottom line, would probably go that route.
Oops, it just occurred to me. The degeneracy could be used as an energy source as well as a gravity source. White dwarves shine for millions of years after their nuclear fires are spent. The Solar System's asteroid belt is out there in the too-damn-cold zone, so too could that of another system be. Nothing like pulling your chair up close to a cozy white dwarf.
A problem arises in that a small chunk of degenerate matter will lose its heat at a much faster rate than would a solar mass.
It seemed for a while that the whole idea should just be junked, but now I see that it is salvageable. Lay on, MacHolly, and cursed be he who cries, "Hold, enough!"
SG
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