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Is there truth about a pinhead size of the core of the Sun? 
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#1
Jun314, 07:31 AM

P: 24

Is it true that a pinhead size if the Sun's core if materialised on the earth would be too dangerous to go within 90 miles of it?
I read from Wikipedia that the energy produced in the Sun's core is about 270 watts/m3. About the same as an active compost heap. I know the pinhead of core matter would be 15 million degrees but be only be around a cube around 1mm. 


#2
Jun314, 01:04 PM

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P: 2,853

A pinhead sized piece of the Sun's core would quickly blow apart if removed from the Sun (assuming it kept its temperature, as I'm guessing is the case in your scenario). It's far too hot for the small amount of gravitational force to keep together. But apart from it's temperature, there's nothing super exotic about the Sun's core, unlike, for example, white dwarf material or neutron star material.
We can estimate the energy contained in a 1mm cube of the Sun's core, to see how big of an explosion it would make. The Sun's core is at ~15 million Kelvin, and a density of ~100g/cm^3. Given that the average thermal energy is ~1.5NkT, then: $$E\approx\frac{3}{2}N_Ak(15,000,000K)(100g/cm^3)(1mm^3)\approx 19,000 J$$ Which is not much. It's equivalent to about 5 grams of TNT. I expect this tiny amount of material to basically make a pop and just fizzle up in the air. Safe distance is maybe 10 meters or maybe 100 meters just to be extra safe...probably not the 90 miles though... 


#3
Jun314, 04:52 PM

P: 24




#4
Jun314, 05:05 PM

Mentor
P: 11,904

Is there truth about a pinhead size of the core of the Sun?



#5
Jun414, 12:39 PM

P: 24

What I want really from this question is accurate explanation in physics to debunk this "urban legend" that has been going around as fact in several publications. 


#6
Jun414, 12:59 PM

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P: 11,904




#7
Jun414, 01:23 PM

Sci Advisor
P: 2,853

##m=\rho(1mm^3)\approx 10^8 kg## That's 100,000 tons of material! Let's look at the energy content of this material. A neutron star is entirely degenerate matter at a temperature of ~1 million Kelvin or higher. Because the neutron star is totally degenerate, it's actual energy content will NOT be ##3/2NkT## but will be ##3/2NkT_F## where ##T_F## is the "Fermi temperature" (rather than the actual temperature). But, we know that ##T_F>>T## for highly degenerate matter, so we can use ~1 million Kelvin as a LOWER BOUND for the energy calculation. Assuming Neutron star matter is made entirely of neutrons, then the lower bound energy contained in 1 cubic mm of neutron star matter would be: ##E>\frac{3}{2}k(1,000,000K)(\frac{10^8 kg}{1 amu})\approx 1.3\cdot10^{18}J## This gave us a LOWER BOUND of the energy (probably several orders of magnitude lower!) contained within this pin drop sized piece of neutron star matter to be 10^18 Joules! That's equivalent to 240 MEGATONS of TNT! This LOWER BOUND is 5 times bigger than the Tsar Bomba's (largest fusion bomb ever created) yield. I would expect the ACTUAL energy to be at least 10 times higher. THAT's devastation right there! 


#8
Jun414, 02:24 PM

P: 24

Studying the responses of Matterwave and Drakkith has brought together what I wanted overall. I understand that the Sun's core itself would by a pinhead size worth on earth not cause much damage but by Matterwave's contribution about exotic matter densities would be more disastrous, I can accept a neutron star is certainly of exotic properties. Importantly, I can safely say the equivalent of 5g of TNT wouldn't bring a garden wood shed down never mind causing devastation over a 90 mile radius.



#9
Jun414, 02:58 PM

P: 94

Just to bring a laypersons thought to the OP. There is no doubt that matterwave and Drak are all over the correct happenings with this, and their conclusions are accurate, but one thing to keep in mind webboffin, the people that speculate these 'what ifs' aren't scientifically minded and pose the question/fact in a way which violates multiple laws in the process. I too remember a factoid based on your OP, and I think it was meant to imply that a grain of sand or (insert small sized object here) at the temperate of the core of the sun (that doesn't follow any of the laws which should govern it) would burn anything within (set distance) by its thermal radiation alone.
Damo 


#10
Jun414, 11:25 PM

Emeritus
Sci Advisor
P: 7,636

If P = 250 billion bars, and V = 1 mm^3 (looked up on the internet, please correct if they're too far off), PV = 25 megajoules, so it's probably more than the thermal energy (but I"m not sure what the constant factor is). However, assuming the constant is 1 or less, I don't think you'd have to stay 90 miles away to be safe, even so. 


#11
Jun514, 01:01 AM

Sci Advisor
P: 2,853

But maybe I did my calculation wrong... Oh, you know what, you're right, I messed up and multiplied by Avagadro's number instead of dividing by 1 amu. I guess I got confused. Using the right formula: $$E=\frac{3}{2}\frac{100 g/cm^3}{1 amu}k(15,000,000K)(1 mm^3)\approx 19,000,000J$$ Off by a factor of 1000! Thanks for catching my mistake! This is equivalent to 4.5kg of TNT, which although much more than the previous estimate of 5 grams, is still not Earth shattering. 


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