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I've seen in some sources that the Earth's inner temperature is because of nuclear decay, namely uranium and such.

I find it hard to believe since volcanoes aren't know for spewing long half-life materials. I was wondering if this is true or not.

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Results published (the link is the the arXiv preprint, but the paper also appeared in Phys. Rev. B) by the Borexino collaboration in 2010 are consistent (at the three sigma level) with most of the geothermal power of the Earth being due to radiological decay. These results extend an earlier, lower precision result by the KamLAND collaboration (the KamLAND geo-neutrino paper appeared in Nature).

Breaking news as of August 2011: KamLAND has published a new paper on Geo-neurtinos in Nature Geoscience, where they compute the radiothermal power from U-238 and Th-232 at 20 [+8.8/-8.6] TW (out of about 44 TW total). Heating due to K-40 is unmeasured.

These measurements also put strict upper limits on the power of a theorized natural nuclear reactor at the core (the data are now consistent with zero reactor power).

Both Borexino and KamLAND are large anti-neutrino detectors and are directly sensitive to the anti-neutrino emissions of radioactive beta decays such as those found in the uranium and thorium chains (but not potassium-40 due to limitation of the detector technology). From this data we can reconstruct the overall radioactive decay activity in the deep Earth, and compute the total power represented.

This is compared to estimates of the geothermal power obtained from temperature gradient measurements in deep bores.

To address the OP's concern about "volcanoes [...] spewing long half-life materials", the short answer is "they do", just not concentrations that are a concern.

You could, for instance look at the Wikipedia article on radiometric dating for survey of decay based dating. You'll note that many of the dating methods work on igneous rocks. Particularly potassium-argon dating of volcanic deposits has been used for dating hominid fossils and impressions in the Olduva Gorge (Wikipedia credits Tattersall (1995), ISBN 0-19-506101-2.).

Disclaimer: I worked on KamLAND for three years, but I am not named as an author on either of the papers cited herein.

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When calculations are done, the Earth's temperature seems hotter than current mechanisms can be explained. One theory for the high temperature is that the Earth has gravitationally captured dark matter. This is a main theory for what is at the core of the gas giants.

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For significant heating to arise from dark-matter interaction the combined density*cross-section will have to be large (note that "large" has a meaning more like "not as tiny as it might be") and we'll soon see evidence in the several "direct dark-matter" experiments now running or coming on line soon. – dmckee Dec 16 '11 at 16:34

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