Parameter Amount Units Ref EAvailable as Heat 1.15E+29 J B7 ∆HTotal = Σ∆HMH + R + SW + F + LV 1.30E+29 J EAH/∆HT 88.2% J/J Result Table 11 - Proposed Energy Balance for Mantle APPENDIX B – THERMAL CALCULATIONS OF MARS Sheet 1 Explanatory Notes — Accelerated Decay Here we calculate the energy available on the planet Mars from accelerated nuclear decay equivalent to that which would emerge over the conventionally dated age of the Earth. We consider the major radionuclides to be Uranium-235, Uranium-238, Thorium-232 and Potassium-40 with principal decay modes known to be Alpha for the heavy isotopes and Beta for potassium. In the absence of data to the contrary, the relative abundances of these isotopes have been assumed to be the same as those on Earth, with data on Thorium being available from a model for bulk Mars (2), taken from measurements of surface Thorium concentrations and the inference that this applies through the whole Martian crust, which is also assumed to contain the same current total mass of radionuclides as that in the now-depleted mantle. This results in a total decay energy just under 1/3 that calculated for Earth, which which is 9 times more massive than Mars. This would result in Mars being more intensely heated that Earth during the period of accelerated decay, even though Earth’s mass can support higher internal temperatures. If the inferred concentrations are correct, then Mars needs to have radiated much of its heat into space, just as was found for the Moon (12). The excess is more severe for Mars than the Moon but a longer cooling time could be allowed (Sheet 3). References for input data are highlighted in yellow, with cited sources in the above table. If data is taken from another cell in the same sheet, the cell reference is shown, highlighted in cyan. If it is from another sheet, the sheet number appears before the cell reference. Key result fields are highlighted to the right in magenta. No. Source 1 https://en.wikipedia.org/wiki/Mars 2 Taylor G J & Boynton W V, Global Concentrations of Thorium, Potassium and Chlorine: Implications for Martian Bulk Composition, Proc. 40th Lunar and Planetary Science Conference, 1411.pdf (2009) 3 Zuber M T, The Crust and Mantle of Mars, Nature, Vol 412, 220-227 (12 July 2001) 4 https://en.wikipedia.org/wiki/Uranium-235#Natural_decay_chain 5 https://arxiv.org/abs/hep-ph/0409152v1 6 Meslin P Y, Hamara D K, Boynton W V, Sabroux J C & Gasnault O, Analysis of Uranium and Thorium Lines in Mars Odyssey Gamma Spectra and Refined Mapping of Atmospheric Radon, Proc. 43rd Lunar and Planetary Science Conference, 2852.pdf (2012) 7 https://en.wikipedia.org/wiki/Electron 8 https://en.wikipedia.org/wiki/Avogadro_constant 9 https://en.wikipedia.org/wiki/Abundances_of_the_elements_(data_page) 10 https://en.wikipedia.org/wiki/Potassium-40 11 https://en.wikipedia.org/wiki/Age_of_the_Earth 12 Stenberg D B & Silvester R S, Stenberg-Silvester Model Calculations - Moon 2019-03-06, Excel file available from rssconsultancy@aol.com or dnstnbrg@hotmail.com (6 March 2019) References STERNBERG Craters and cracks 2023 ICC 47
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