Parameter Amount Units Ref Uniformitarian Decay Time (tTotal) 4.54E+09 year 13 tHalf( 235U) 7.04E+08 year 6 tHalf( 238U) 4.47E+09 year 7 tHalf( 232Th) 1.40E+10 year 7 tHalf( 40K) 1.28E+09 year 7 tTotal/tHalf( 235U) 6.45 year/year tTotal/tHalf( 238U) 1.02 year/year tTotal/tHalf( 232Th) 0.32 year/year tTotal/tHalf( 40K) 3.55 year/year 2tT/tHU235 = 2^[t Total/tHalf( 235U)] 87.47 kg/kg 2tT/tHU238 = 2^[t Total/tHalf( 238U)] 2.02 kg/kg 2tT/tHTh232 = 2^[t Total/tHalf( 232Th)] 1.25 kg/kg 2tT/tHK40 = 2^[t Total/tHalf( 40K)] 11.69 kg/kg MCurrent( 235U) 1.02E+13 kg F28 MCurrent( 238U) 1.41E+15 kg F30 MCurrent( 232Th) 5.11E+15 kg F25 MCurrent( 40K) 1.36E+15 kg F26 MInitial( 235U) = 2tT/tHU235MC( 235U) 8.93E+14 kg MInitial( 238U) = 2tT/tU238MC( 238U) 2.85E+15 kg MInitial( 232Th) = 2tT/tHTh232MC( 232Th) 6.40E+15 kg MInitial( 40K) = 2tT/tHK40MC( 40K) 1.59E+16 kg ∆M(235U) = MI( 235U) – MC( 235U) 8.83E+14 kg ∆M(238U) = MI( 238U) – MC( 238U) 1.44E+15 kg Table 4 - Accelerated Decay Energy ∆M(232Th) = MI( 232Th) – MC( 232Th) 1.29E+15 kg ∆M(40K) = MI 40K) – MC( 40K) 1.45E+16 kg ESpecific( 235U) 1.92E+13 J/kg B26 ESpecific( 238U) 2.10E+13 J/kg B27 ESpecific( 232Th) 1.78E+13 J/kg B28 ESpecific( 40K) 3.18E+12 J/kg B29 ETotal( 235U) = ES( 235U)∆M(235U) 1.70E+28 J ETotal( 238U) = ES( 238U)∆M(238U) 3.02E+28 J ETotal( 232Th) = ES( 232Th)∆M(232Th) 2.29E+28 J ETotal( 40K) = ES( 40K)∆M(40K) 4.63E+28 J EGrand Total Decay 1.16E+29 J Result Here we calculate the gravitational potential difference that would be met by the decay-heat-induced expansion of the Moon, which is currently divided into the layers with the labels Inner Core, Outer Core, Lunar Mantle and Lunar Crust. As it is assumed to be initially cool and solid, with a homogeneous mantle, the initial Moon is partitioned simply into Core Initial and Mantle Initial, with trial values for initial radii. Volumes emerging from these trials are then fed into Sheet 3 for a calculation of initial temperature. The trial values are then adjusted to yield an initial temperature of order 300 K (27°C). There are, listed and derived above, formulae used to calculate potential energy for spherically symmetric bodies. 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 a trial input, such as initial surface and core radii, that are designed to produce the initially ambient temperature before thermal expansion, details of which appear in Sheet 3. No. Source 1 https://en.wikipedia.org/wiki/Gravitational_constant 2 https://en.wikipedia.org/wiki/Inner_core 3 https://en.wikipedia.org/wiki/Outer_core 4 https://en.wikipedia.org/wiki/Mantle_(geology) 5 Anderson D L, Theory of the Earth, Boston: Blackwell Scientific Publications (1989) http://resolver.caltech.edu/ CaltechBOOK:1989.001 (see image below) 6 https://en.wikipedia.org/wiki/Earth_mass References STERNBERG Craters and cracks 2023 ICC 34
RkJQdWJsaXNoZXIy MTM4ODY=