(Very) small world with decent gravity

[rancke]

The webcomic Escape from Terra currently features a small asteroid with enough gravity to retain an atmosphere. The explanation starts here:

http://www.bigheadpress.com/eft?page=215

I wonder if any of our resident astronomy savants can tell us if the explanation actually works (or is plausible enough for RPG purposes ). If it does, I'm so going to use it for one of the odd worlds in the OTU.

Obviously, even if it works, it'll be a 'once in the lifetime of the galaxy' sort of explanation, but one out of umpteen explained is better than none, right?


Hans

 

[aramis]

It would have to be a naked singularity, and it being inside the asteroid indicates a sophontological origin. It staying centered without collapse and growth also makes it implausible.

 

[Icosahedron]

It's not what I'd describe as a plausible explanation.

I'm not sure that such a hole would have to be a naked singularity, though I think the one described is too small to do the job. But the chances of it accidentally hitting and coming to rest inside an asteroid make the explanation as unlikely as anything else you could come up with.

And then you have the question of where the atmosphere came from, since it couldn't have been there before the black hole arrived.

And even if you had the incredibly slight chance of a black hole lodging in the asteroid during its atmospheric formation stage, the atmosphere wouldn't become breathable without eons of terraforming by plant and animal life, or centuries of artificial terraforming.

And during all this time the black hole doesn't consume the planet.

And if you're going to artificially terraform, you might as well add artificial gravity...

Shall I stop there?

 

[rancke]

It's not what I'd describe as a plausible explanation.

Awwwww...

I'm not sure that such a hole would have to be a naked singularity, though I think the one described is too small to do the job. But the chances of it accidentally hitting and coming to rest inside an asteroid make the explanation as unlikely as anything else you could come up with.

"Once in the lifetime of the universe"?

And then you have the question of where the atmosphere came from, since it couldn't have been there before the black hole arrived.

I assume the billionaire terraformed the asteroid.

And if you're going to artificially terraform, you might as well add artificial gravity...

If you have artificial gravity. Could be a TL 8 system.

Also, I was contemplating using this dodge for a size 1 world with breathable atmosphere. Providing a size 1 world with atmosphere (by bombarding it with ice asteroids) would be much much less of an engineering task than providing it with artificial gravity.


Hans

 

[aramis]

That bombardment would also dislodge the singularity, resulting in accretion.

Keep in mind that, with a singularity, it WILL hollow out a cavity. presuming a solid iron asteroid, we can presume it can handle some 20G stress. at the 20G threshold, that's where the cavity begins.

The tidal stress, however, is much more severe than would be true of a uniform gravity; you've got most of the mass of an earth sized planet down to the size of a grain of sand or less. And hundreds of G's at it's surface, and out to several MILES.

Displace the asteroid some 20 feet, and you have just pulled it out of center, and the cavity gets to grow, plus you accellerate the planet the direction displaced due to tidal difference, and PTOOEYY!!! out it comes.

 

[rancke]

That bombardment would also dislodge the singularity, resulting in accretion.

Unless someone calculated the effect of multiple simultaneous meteor strikes to cancel each other out.

Keep in mind that, with a singularity, it WILL hollow out a cavity. presuming a solid iron asteroid, we can presume it can handle some 20G stress. at the 20G threshold, that's where the cavity begins.

I'm afraid you're losing me here. BTW, What about the "transient neutronium, degenerate matter, etc." that the billionaire is talking about? Is that the result of the black hole squeezing a much bigger body down to a 10 km diameter?

Displace the asteroid some 20 feet, and you have just pulled it out of center, and the cavity gets to grow, plus you accellerate the planet the direction displaced due to tidal difference, and PTOOEYY!!! out it comes.

And if the world is 1000 miles in diameter? With the abovementioned exquisitively calculated simultaneous meteor strikes?


Hans

 

[robject]

The tidal stress, however, is much more severe than would be true of a uniform gravity; you've got most of the mass of an earth sized planet down to the size of a grain of sand or less. And hundreds of G's at it's surface, and out to several MILES.

I think the tidal forces would be truly ghastly. I mean it's impossible to have any sort of "useful" gravity there; remember Niven's short story about the Neutron Star?

 

[aramis]

I think the tidal forces would be truly ghastly. I mean it's impossible to have any sort of "useful" gravity there; remember Niven's short story about the Neutron Star?

I've not read that one. However, I've seen the maths.

Hans: if the singularity is generating .5G's at planetoid surface, at 500 miles radius... Chart shows Y G's at X miles from center of singularity, based upon inverse square law, and ignoring the fractional G's of the asteroidal shell.

Miles G's
500 0.5
450 0.62
400 0.78
350 1.02
300 1.39
250 2
225 2.47
200 3.13
175 4.08
150 5.56
125 8
100 12.5
75 22.22
50 50
40 78.13
30 138.89
20 312.5
15 555.56
10 1250
5 5000
4 7812.5
3 13888.89
2 31250
1 125000

Somewhere around 50 miles, rock fails.

The impacts required to land the comets will, at the very least, stress the interior. The natural consequence is that the interior will get LESS dense, not more, as it approaches the failure point.

The "neutronium" is pure USBS... it would have to have been manufactured and placed, not formed naturally, since the inner shell's pressure is forcing the shell to cross its own failure point on tensile strength.

 

[Icosahedron]

Hans, keeping the black hole at the centre of the asteroid would be like balancing a pencil on its point. The slightest movement would bring it into contact with the rock, which it would then devour.

It attracts and is attracted to the surrounding rock by gravity and a thought experiment will show what happens:

Forgetting its initial entry and associated movement complications, including how it came to rest, let's assume the hole begins stationary in the exact centre of a spherical planetoid. All the rock around it is crushed and absorbed - out to the 20G radius (using Aramis' figures). As the rock is pulled toward the hole, the hole is pulled toward the rock. Flaws in the rock will ensure that rock in one direction is broken away and absorbed quicker than another direction, so the hole will tend to bounce around in an ever-growing irregular cavity within the planetoid, devouring rock as it goes. Whilst it remains in the cavity it will provide an erratic gravitational field, but it won't stay inside for long. I'm not sure how long without doing more maths than I care to, but the hole's appetite will increase as it grows, and I suspect that it will soon burst out of the planetoid and then burrow back in again, repeating this numerous times in an erratic gravitational dance with the remnants of the planetoid. Not the sort of place I'd build a mansion...

Sorry Hans, you can have what you want IYTU, but in reality it won't explain that extra gravity. (Also, in reality, as opposed to Traveller, a Size 1 world won't support a breathable atmospheric pressure either, but even I turn a blind eye to that).

Black holes are out since they have an insatiable appetite, but I'm not sure whether 'neutronium' is unstable and reverts once the gravity that formed it is removed, and likewise I'm not sure about the stability of white dwarf material - maybe someone else could clarify?
I gather that WD material is thought to crystallize as it cools, but I dunno whether the crystal structure is something that would hold it together if high gravity conditions were removed.

If white dwarf material is stable in zero-G, you could have your vanishingly rare event as a stellar collision that shatters a white dwarf. The pieces cool much quicker than a whole star and have long-since cooled to black dwarf material. A piece has entered a starsystem as a captured body and has accreted local material (including gases) to form a planetoid around the black dwarf core.

Depends on the stability of WD material, but perhaps makes a more plausible core than the black hole. You'll need a better armchair astrophysicist than me to be sure.

Hope that helps.

PS. Somewhere not a million light-years from that planetoid, there are some black dwarf remnants that would make extremely well-armoured planetoid ships for players with munchkin tendencies...

 

[rancke]

Hans, keeping the black hole at the centre of the asteroid would be like balancing a pencil on its point. The slightest movement would bring it into contact with the rock, which it would then devour.

Did you read the explanation? The black hole is supposedly very small. So while it will, indeed, devour the rock, it'll take time. Lots of time.


Hans

 

[rancke]

Hope that helps.

You and Wil are no fun at all, you know that, right?


Hans

 

[aramis]

You and Wil are no fun at all, you know that, right?


Hans

Sadly, it's one of those "Nifty ideas" that, on first blush, looks reasonable, but if you do any of the math at all, suddenly gets REALLY unpleasantly improbable.

It would require, absolutely require, some form of gravity manipulation to keep it centered.
Given that the mass required is about 200x that of the asteroid... and once you move even a couple centimeters off center, you have a discrepancy on the opposite sides of several G's, and that being weaker on the further side, it just snowballs.

In very short order (a matter of seconds) it will be moving a couple KPH towards the near side. Actually, it will mostly pull the planetoid... but net effect is the same... and as it closes, the gravity and acceleration accretes RAPIDLY... the shell is slung outward, and possibly escapes for several days.

It's going to look much like the destruction of Vulcan in ST XI...

 

[coliver988]

Did you read the explanation? The black hole is supposedly very small. So while it will, indeed, devour the rock, it'll take time. Lots of time.


Hans

actually, now they think black holes do go away, even the big ones. Hawkings has decided that information CAN come back out. So the smaller the black hole, the more rapidly it actually evaporates (if I read that article correctly and actually remembered that and just did not make things up [there was another article about how memory is changed when you recall it, and yet another about wandering thoughts...]).

I suppose you could keep feeding it. Not sure. Somewhere else there's a discussion of Star Trek & Traveller, and the guess was the TL was 16 or 17. The Romulans use a singularity to power their big warbirds (uh-huh, so the mass of the ship is about the same of a planet?! mighty big M-drives!).

The other option is huge grav plates all over your small world, buried underground. Lots of them...

 

[aramis]

The Romulan drives also use massive gravitics to hold it in place.

 

[Icosahedron]

Did you read the explanation? The black hole is supposedly very small. So while it will, indeed, devour the rock, it'll take time. Lots of time.


Hans

Yes, I read the explanation - did you read my reply where I said that I doubted if a hole that small would supply the necessary gravity, and I also said that I didn't know how long it would take without doing more maths than I care to, but probably not too long?

You and Wil are no fun at all, you know that, right?

Well at least I provided an alternative.

 

[Icosahedron]

In very short order (a matter of seconds) it will be moving a couple KPH towards the near side. Actually, it will mostly pull the planetoid... but net effect is the same... and as it closes, the gravity and acceleration accretes RAPIDLY... the shell is slung outward, and possibly escapes for several days.

It's going to look much like the destruction of Vulcan in ST XI...

I'm not sure it would move quite that fast, Aramis. You're assuming (and so was I) that there is no resistance to the hole's consumption of material, but I believe it will have a maximum accretion rate proportional to its size (probably to its surface area). As the hole absorbs rock the accretion zone will rise in temperature (and pressure) and the pressure exerted by the heated plasma may serve to slow the motion of the hole.

Thinking about it, instead of a dark collapse like Vulcan, or looking like a Swiss cheese after playing ping-pong with the black hole, it may be that the whole planetoid would first flare up into a mini star with a nova eruption long before it vanished up its own black hole.

...Not that that improves the survival chances of its surface dwellers.

 

[Icosahedron]

actually, now they think black holes do go away, even the big ones. Hawkings has decided that information CAN come back out. So the smaller the black hole, the more rapidly it actually evaporates (if I read that article correctly and actually remembered that and just did not make things up [there was another article about how memory is changed when you recall it, and yet another about wandering thoughts...]).

Black holes will evaporate eventually, if they're starved, but a hole at the centre of a world will not be starved, and anyway a hole big enough to provide the required surface gravity won't evaporate 'anytime soon'.

I suppose you could keep feeding it. Not sure. Somewhere else there's a discussion of Star Trek & Traveller, and the guess was the TL was 16 or 17. The Romulans use a singularity to power their big warbirds (uh-huh, so the mass of the ship is about the same of a planet?! mighty big M-drives!).

Yeah, well that's Trek Tech for you...

The other option is huge grav plates all over your small world, buried underground. Lots of them...

I think Hans wanted to avoid technology. Check out whether WD material is stable, Hans - or rule that it is, and previous theories to the contary were wrong...

 

[aramis]

The Roche limit is going to be an issue, and the spaghettification point will be several dozen miles. Once you hit a g difference per CM, you're going to be ripping molecules from each other... yeah, you'll be radiating Gamma- and X-rays... but that's part of ANY feeding singularity. Which may or may not actually be a true mathematical singularity, anyway...

Nasa put neutron star densities at 3E26 kg/km³... or 3E17 Tm/m³. (http://heasarc.gsfc.nasa.gov/docs/xte/learning_center/ASM/ns.html)

An earth mass is 5.9742 E24 kg, or about 5.9E21 Tm... a neutron star of earth mas would be roughly 19 cubic kilometers. But we don't need earth mass. we need 1/64th of it to get the 1G at 1000km or about 9.2E19 Tm. This is below the 3.2E20 Tons of mercury, so it will be shedding mass. our needed mass as a neutron star will be in roughly 300 cubic meters...

At quark star densities (about 9E2 higher), we get an object under a meter.

A coupe recent articles suggest that black holes do have a maximum density, and that the singularity doesn't actually occur, it just is close enough to be negligible.. these produce "naked singularities"... even so, we should be looking at, IIRC, an object about a liter with about 1% of the mass inside the event horizon...

 

[G. Fieendish]

actually, now they think black holes do go away, even the big ones. Hawkings has decided that information CAN come back out. So the smaller the black hole, the more rapidly it actually evaporates (if I read that article correctly and actually remembered that and just did not make things up [there was another article about how memory is changed when you recall it, and yet another about wandering thoughts...]).

I suppose you could keep feeding it. Not sure. Somewhere else there's a discussion of Star Trek & Traveller, and the guess was the TL was 16 or 17. The Romulans use a singularity to power their big warbirds (uh-huh, so the mass of the ship is about the same of a planet?! mighty big M-drives!).

The other option is huge grav plates all over your small world, buried underground. Lots of them...

Re: Romulan Power Plants...
Romulan Warbirds are powered, at least in the Next Generation, by artificially created Quantum Singularities, which technically are different, from the singularity found at the centre of a Black Hole, as they don't have event horizons cloaking them...