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Comment by aashaykumar92 | Hacker News Reader

This article is fascinating but as someone who doesn't know much about this discipline, I'm hoping for someone to clarify my confusion:

In the article, it states that our core has temperatures comprable to that of the sun. However, the sun is 93 million miles away while our core seems to only be approximately 4000 miles deep. Shouldn't the Earth be hotter than or are there just so many layers that the heat decreases at such a fast rate as it approaches the surface?

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It's about thermal flux (or heat flux) [0] - the rate of heat flow (SI unit: joules per second aka watts) per surface area (SI unit: square meters).

If the Earth's inner core could be duplicated and moved to space so that its apparent size in the sky would equal the Sun's, it would indeed appear to shine just as brightly as our favorite star. However, it would cool and dim very quickly (relatively speaking), all its stored heat being able to freely radiate into the cold space, the ultimate heatsink.

This is because unlike the Sun, the Earth's core has no active energy source to speak of. A part of the heat is generated by the ongoing decay of long-lived radioactive isotopes, but most of it was created billions of years ago as a byproduct of Earth's formation.

So how do Earth's mantle and crust prevent the heat from escaping quickly? Remember the three mechanisms of heat transfer: radiation, conduction, and convection. The core cannot radiate because there's rock in the way. Rock is also a poor conductor of heat. Even though there are convective currents in the mantle, which is malleable and does flow over geological timescales (but is not liquid!) the convection is far too slow to efficiently transfer heat from the core to the surface.

If the core were to suddenly gain a more effective mechanism of generating more heat, it would cause the core temperature to rise. This would, in turn, raise the temperature of the mantle and the crust, until the thermal flux through the surface matched the extra energy created in the core. Similarly, in the core-in-space thought experiment above, the core would cool until the radiated heat was equal to that generated by the radioactive decay.

The attentive reader might have noted that the above implies a relationship between the surface temperature of a body and its radiative heat flux. This is indeed the case: given an idealized black body [1], the Stefan-Boltzmann law [2] states that the total irradiance (radiative heat flux through the whole surface of the body) is proportional to the fourth power of the temperature (in kelvins) and depends on no other variables. Planets, stars, and duplicated planetary cores are not idealized black bodies but can be approximated as such.

That our planet's core is so slow to cool has a few consequences. The convective currents of the liquid outer core generate the planetary magnetic field that protects us from the solar wind and other charged particles. The convection in the mantle, on the other hand, is responsible for volcanism and plate tectonics. Mars, our sister planet in many respects but only one tenth the mass of Earth, lost its youthful warmth much faster. If it ever did have plate tectonics or a global magnetic field, they shut down billions of years ago when the core and mantle cooled.

TLDR: The Sun continuously creates huge amounts of energy that has to go somewhere, the Earth's core a) doesn't and b) is well insulated.

[0] http://en.wikipedia.org/wiki/Heat_flux

[1] http://en.wikipedia.org/wiki/Black_body_radiation

[2] http://en.wikipedia.org/wiki/Stefan%E2%80%93Boltzmann_law

"Hotter" in terms of temperature, not heat flux. Temperature is just a statistical thing that measures the relative motion of matter. You might read about experiments where matter in a near-vacuum reaches insane temperatures, even hundreds of millions of degrees. In these experiments there is almost no matter involved and it's whizzing past other matter at nearly the speed of light, hence at high temperatures. But there's very little energy involved. The temperature is more of a statistical stunt than anything, really. At some point they stop measuring it in degrees and start measuring it in KeV.

Anyway, you can have very high temperatures without a lot of heat, just the same as you can have extremely high power without a lot of energy. If I drop my phone on a rock, the instantaneous power of the impact might be extremely high, maybe even megawatts, but only for a microsecond. The total energy involved will not be remarkable.

TL;DR: temperature != heat.

A lot of the radiation that the sun's core emits gets through its surface without interacting with it much.

You can infer that from http://en.wikipedia.org/wiki/Sun:

    Temperature:
    - Center (modeled): 1.57×10^7 K[1]
    - Photosphere (effective): 5,778 K[1]
    - Corona: ~5×10^6 K

=> The sun's surface is about its coolest part. Its core is about 3000 times as hot. That's where the solar heat comes from.

A lot of the radiation that the sun's core emits gets through its surface without interacting with it much.

This is false. The sun is very opaque; photons from the core could take millions of years to reach the surface.

https://en.wikipedia.org/wiki/Radiation_zone

https://en.wikipedia.org/wiki/Solar_core#Energy_transfer

This is the article you're looking for:

https://en.wikipedia.org/wiki/Corona#Coronal_heating_problem

> photons from the core could take millions of years to reach the surface.

And it would be most unlikely they'd be the same photons that started on the journey. Likely they'd be absorbed and different photons re-emitted many times.

The sun heats the earth surface through radiative heating, while the core is well insulated by the mantle and crust. Although they may have similar temperatures, the power output of the sun is certainly larger.

To provide some further context to ovis' (correct) statements, none of our 'heat', or other energy from the sun comes in the form of conduction. It comes in the form of radiation (light, et al) which the sun has in huge, massive, ginormous quantities. In pop culture, we often talk about the heat of the sun as if it's a direct indicator for the amount of power therein, and the amount of power output. But while it's quite hot, its also quite busy showering us with other forms of energy.

I'm afraid there are many things wrong with your model of how heat works. However a simple factor is that the surface of the sun is ~10000 times larger than the surface of the earth.

They're comparing the heat of Earth's core to the surface of the sun, not the core of the sun.

> In the article, it states that our core has temperatures comprable to that of the sun. However, the sun is 93 million miles away while our core seems to only be approximately 4000 miles deep.

I was thinking you were about to ask why in the universe are we not able to measure the temperature of earth core that's only 4000 miles away from us and yet we claim to know the temperature of something that 93 million miles away... :)

The temperatures you're comparing are between the core of the earth and the radiation temperature of the surface of the sun. It's way hotter in the sun's core (20 million Kelvin IRRC)

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