In the 3/20/09 column under the “Questions we’re still thinking about” section, as much as it’s played for laughs in the column, I think the general idea about a grapefruit-sized sun is actually an intriguing question that I’d be interested in (once you remove the hyperbole from it)
Any SDSABers wanna take up the challenge 
? Or maybe any staffers talk Unca Ceese into actually answering the question?
Is the entity of the same composition as the Sun, but with less proportionate mass? It would just explode/dissipate and might do some damage to whatever room/building it’s in (the Sun’s not very dense so it would be like a futuristic plasma weapon :))
Or is it an entity of the same mass as the Sun, but squeezed into a grapefruit sized sphere? I still think it would explode, as it has not reached critical density for a black hole (which is around a quarter rather than a grapefruit). In fact the only thing I don’t know right now is the nature and aftereffects of such an explosion.
I assumed it was a “magic” sun with the exact same properties as our sun but smaller AND would not dissipate. This will be an interesting read when the experts take over.
I took it to be a sphere that radiates the same amount of light (per surface area, not total) as the Sun. Then, if it was about 50 feet away, it would look just like the Sun. If it truly radiated all the UV and higher frequencies, you’d get pretty nasty radiation with only 50 feet of atmosphere between you and it.
If it only radiated the light that actually passes through the atmosphere (at, say, high noon with the Sun directly overhead), you could light and heat a pretty big area. If you have some way to hang it from the rafters of a large warehouse-type building.
Just don’t put it on a treadmill, please…
Hmmmm… What if it were on a solar powered treadmill…
But could it then take off?
You’re thinking of a planetary mass. The Sun’s Schwartzschild radius is about 3 kilometers, so anything smaller than that goes black (and once you go black, you never go back).
‘Grapefruit-sized sun’ is just another way of saying ‘H-Bomb’, isn’t it?
My amateur astronomy training tells me that if a grapefruit magically turned into a real star with appropriate density fissioning core and shell layers, and so on, it would just explode. I doubt it’d wipe out the whole planet, but might do a fine job of wiping out London, UK and most of West Europe. It’d easily be the most radioactive bomb ever, in any case.
In the other case when even a small star magically shrinks into a grapefruit, it’d instantly both snuff itself out and become a black hole. That wouldn’t necessarily be instantly Earth destroying either, as some anti-LHC zealots believe to my endless amusement.
Without fancy maths that I’m not familiar enough with to do for you, it gets hard to say, here. One thing is for sure - it would completely wreck Earths current orbit, which would eventually result in it’s demise.
Why not ask here?:
http://curious.astro.cornell.edu/
for a more graphical (and accurate) explanation of what would happen. I’m sure they’d love that question.
My amateur astronomy training tells me that if a grapefruit magically turned into a real star with appropriate density fissioning core and shell layers, and so on, it would just explode. I doubt it’d wipe out the whole planet, but might do a fine job of wiping out London, UK and most of West Europe. It’d easily be the most radioactive bomb ever, in any case.
In the other case when even a small star magically shrinks into a grapefruit, it’d instantly both snuff itself out and become a black hole. That wouldn’t necessarily be instantly Earth destroying either, as some anti-LHC zealots believe to my endless amusement.
Without fancy maths that I’m not familiar enough with to do for you, it gets hard to say, here. One thing is for sure - it would completely wreck Earths current orbit, which would eventually result in it’s demise.
Why not ask here?:
http://curious.astro.cornell.edu/
for a more graphical (and accurate) explanation of what would happen. I’m sure they’d love that question.
Whoops, I meant fusioning core of course… before any arguments start.
I don’t think it would be that large of an explosion. Here’s my reasoning:
From the Sun’s volume and mass, its average density is about 1.4 g / cm^3. Taking a grapefruit to be 1 liter, that’s 1.4 kg of (mostly) Hydrogen, or 1400 moles. At STP, one mole of gas has a volume of 22.4 liters, so 1400 moles would have a volume of about 31 cubic meters, or a cube about 3 meters on a side. I haven’t accounted for the temperature yet, so the pressure would be higher by a factor of Tsun / 300K. The Sun’s surface temperature is about 5800K, so if the gas expanded until it had a volume of a cube 8.4 meters on a side, its pressure would be 1 atmosphere. Of course, it’s displaced that much air also, but that seems like enough to destroy a house, and maybe the ones next door. The hydrogen would burn, but I would expect that to be more of an added fireball than an explosion.
Now the core is about 16 million K, so if the grapefruit Sun were at that temperature, the gas would have to expand to a cube about 120 meters on a side to have a pressure of 1 atmosphere. This seems to me like it could destroy a few city blocks, but not even a whole city, let alone a whole country.
There’s probably an easier way to estimate the size of the explosion, but I don’t see how it’s going to be large enough to destroy a city.
This is all well and good, but I’d like to see some numbers on a Sun-sized grapefruit.
Mass? Juice content? Thickness of rind? How long could it feed the Earth, one half-normal-grapefruit size portion per person per day? How fast would it spoil?
If you dropped it into the ocean, would it boil all the oceans away? How long would that take? Would it burn through the bottom of the ocean and into the mantle?
It’d have about 70 percent of the mass of the Sun, but its mass would be mostly from Carbon and Oxygen, so I’d WAG it wouldn’t support much fusion. It’d probably just collapse directly into a white dwarf (and well before it had a chance to spoil).
Well, you haven’t really accounted for the whole fusion-thing, which it seems to me would be a bigger contribution to the explosive yield than just the expansion of compressed hydrogen gas… (And if it’s not fusioning, it isn’t really a sun.)
On the other hand, we’d be too dead to care I’d think; a stellar mass black hole that fell into the Earth would have more than enough gravity to squash us flat. And that’s ignoring whatever tidal forces and the effects of the hole’s rotation would be. It might or might not not be “instantly Earth destroying” in the sense of sucking it in, but I expect Earth would rapidly be shredded into an accretion disc.
And unlike the supposed LHC holes, such a black hole would be big and stable enough to eat the planet, eventually.
As for what would happen with a grapefruit sized “star”; either it would explode immediately or rapidly run out of fusion fuel and die, as others have said. What would happen if magically self sustaining I’m not sure; it might burn it’s way down to the center of the earth and add to the Earth’s internal heat. I don’t know if that would be significant for something on the Earth’s scale, but I doubt that the burning-a-hole-to-the-core process would be healthy to be anywhere near.
On the other hand, it may be hot but not dense; in that case, it would stay on the surface. I doubt that having a continuous fusion reaction on the Earth’s surface would do it’s habitability any good.
It’ll either explode or it will continue fusioning, but it won’t do both.
Anyway, the contribution due to a grapefruit sized volume of the Sun fusioning is completely negligible. The Sun has about 1.4 10[sup]30[/sup] time the volume of a grapefruit, and radiates 3.8 10[sup]26[/sup] Watts, so an average grapefruit sized volume generates less than a milliwatt. It takes a cone of the Sun with a base as big as the area of the grapefruit, but as tall as the radius of the Sun to produce the energy that radiates from a grapefruit-sized spot of the Sun.
Well, turns out you’re right! Even taking solar core conditions (as was going to be my rebuttal based on the fact that a ‘shrunken’ sun wouldn’t really do anything at all in the way of fusion, lacking the necessary gravitational pressure), you only get fairly negligible power output due to fusion. Who’d have thought the Sun’s such a slacker when it comes to fusioning!