Sheet 3 Explanatory Notes — Overall Heat Balance Here we calculate the heat available from accelerated decay, after subtracting the small amount needed to provide expansion against gravity. Unlike the parallel set of calculations for the Earth, there is more than enough energy to heat the Moon up to its currently estimated core temperature in the range 1600-1700 K. There is thus a need to account for the excess heat available via various loss channels, such as radiation, loss of water vapour and partial melting of lunar mantle material. Drake et al (18) suggested that all radionuclides could have been quantitatively extracted from the mantle into what has become the current crust. This could have selectively heated this material to nearly its boiling point (Table 4) before delivering it to the surface, from which radiative heat transfer (Table 6) can be estimated. It is not essential for the whole lunar surface to be molten, as the vigorous volcanic processes produced by accelerated decay would atomise the hot lava into fine droplets, which would have increased the effective surface area dramatically. The initial breakthrough of lava would have been through deep vertical channels near weak points in the lunar surface and would have happened at a catastrophic rate, creating mountains as high as the current crustal thickness. This could account for the greater radiometric “ages” of highland regions. The boiling point of crustal lava has been estimated from that for SiO2 and the melting point for Mg2SiO4, the chief constituent of the mantle. The ratio of boiling to melting point has been assumed to be the same for both minerals, as this is true of the high-melting metals considered in Table 4. The prospect of heating minerals to their boiling points opens the door to evaporative heat loss, here estimated in Table 10, after that due to sensible heating of the mantle (Table 7), boiling of water (Table 8) and partial melting of the mantle (Table 9). The estimate for initial heating of the eventual crustal material (Table 5) is not included in the proposed heat balance (Table 11), as its heat would eventually find a place somewhere within the sinks indentified in Tables 6 to 10. References for input data are highlighted in yellow, with cited sources in the References 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. Along with key results, a magenta highlight indicates achievement of the goal of an initially ambient temperature before thermal expansion, using trial values of initial lunar radii. No. Source 1 Doin M P & Fleitout L, Thermal evolution of the oceanic lithosphere: an alternative view, Elsevier, Earth and Planetary Science Letters, 142, 121-136 (1996) 2 https://en.wikipedia.org/wiki/Mantle_(geology) 3 https://en.wikipedia.org/wiki/Outer_core 4 Aitta A, Iron melting curve with a tricritical point, A.Aitta@damtp.cam.ac.uk 5 https://en.wikipedia.org/wiki/Iron 6 Kandpal D & Gupta B R K, Analysis of thermal expansivity of iron (Fe) metal at ultra high temperature and pressure, Indian Academy of Sciences, Pramana Journal of Physics, Vol. 68, No. 1, 129-164 (2007) 7 Desai P D, Thermodynamic Properties of Iron and Silicon, J Phys. Chem. Ref. Data, Vol. 15, No. 3 (1986) 8 https://en.wikipedia.org/wiki/Internal_structure_of_the_ Moon 9 https://en.wikipedia.org/wiki/Tungsten 10 http://ltmlab.fr/wiki-materials/index.php?title=Silicon_dioxide_-_SiO2 11 https://en.wikipedia.org/wiki/Forsterite 12 https://en.wikipedia.org/wiki/Boltzmann_constant 13 https://en.wikipedia.org/wiki/Planck_constant 14 https://en.wikipedia.org/wiki/Speed_of_light 15 https://en.wikipedia.org/wiki/Stefan-Boltzmann_constant 16 https://en.wikipedia.org/wiki/Stefan-Boltzmann_law 17 https://en.wikipedia.org/wiki/Water_(data_page)#Water/ steam_equilibrium_properties 18 Stacey F D & Davis P M, Physics of the Earth, 4th Edition, Cambridge University Press (2008) 19 Stacey F D & Davis P M, Physics of the Earth, 4th Edition, Cambridge University Press (2008) 20 Drake M J, Lowe J P, Righter K, Zuber M T & Clark P E, Uranium in the Lunar Crust: Implications for Lunar Origin and Evolution, Proc. 61st Annual Meteoritical Society Meeting, 5174.pdf (1998) References STERNBERG Craters and cracks 2023 ICC 40
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