Ceres Geology |
Ceres Geology |
Jan 22 2014, 06:14 PM
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#1
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Rover Driver Group: Members Posts: 1015 Joined: 4-March 04 Member No.: 47 |
Paper out tomorrow: http://www.bbc.co.uk/news/science-environment-25849871
Very exciting that we will visit this world soon! |
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Mar 13 2015, 09:42 AM
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#2
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Member Group: Members Posts: 107 Joined: 1-August 14 Member No.: 7227 |
Recent paper:
"THE POTENTIAL FOR VOLCANISM ON CERES DUE TO CRUSTAL THICKENING AND PRESSURIZATION OF A SUBSURFACE OCEAN." http://www.hou.usra.edu/meetings/lpsc2015/pdf/2831.pdf QUOTE interior evolution models for Ceres [e.g. 2-5] suggest that differentiation is likely, forming a layered structure with a rocky interior (possibly with a separated iron core), overlain by water and ice layers. Furthermore, these models suggest that there is sufficient heat available that a liquid water layer could survive under an icy exterior to the present day. I can't yet understand where this heat come from. Does "[e.g. 2-5]" mean "references from [2] to [5]"?. QUOTE Because ice takes up a larger volume than the equivalent mass of water, the freezing of liquid water onto the base of an icy shell will cause the shell to expand slightly and lead to tensile stress in the shell. This also has the effect of increasing the pressure in the ocean, possibly to the point of driving liquid to the surface. So the model suggests NOT that there's enough heating to create a water geyser (as I supposed), but there's a "squeezing" of the ocean by the ice crust. QUOTE For Ceres (r= 475 km), which is intermediate in size between those bodies, we assume as our initial condition that the rocky core is ~300 km in radius with an overlying ocean and an icy shell 25 km thick. This corresponds to the state of Ceres 500 Myr after its formation in the models of [5]. In the models of [5], the shell thickens over the subsequent 4 Gyr at an approximately linear rate of ~20 km/Gyr. QUOTE cracks can propagate to at least 200 km depth, which is about the maximum possible thickness of an ice shell for Ceres. QUOTE for every 1 km of thickening of the shell, approximately 25 m of liquid could erupt over the entire surface but beware of QUOTE The requirement that the ice layer behave like an intact, elastic shell could pose a problem, especially in the case where the tensile strength of ice is exceeded well before the ocean pressure is sufficient to drive material to the surface.
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Mar 13 2015, 02:07 PM
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#3
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Senior Member Group: Members Posts: 2346 Joined: 7-December 12 Member No.: 6780 |
I can't yet understand where this heat come from. Here my try: Assumptions: Ceres' radius: r = 475 km = 4.75e5 m Ceres' shape: approximately spherical Ceres' mass: m = 9.43e20 kg Ceres' mean surface temperature: T1 = 168 K Temperature below ice layer (using the melting point of water): T2 = 273 K Thickness of ice layer: L = 25 km = 25e3 m Approximated thermal conductivity of ice: k = 2.0 W/(m K) Simplified assumption for K-40 decay: 1.311 MeV per atom are released on decay to Ca-40 = 1.311e6 * 1.602e-19 J = 2.10e-13 J Half-life of K-40: t_1_2 = 1.248e9 years = 3.938e16 s Mass of 1 mole K-40: 0.03996 kg Ratio of K-40 to K total: 120 ppm = 1.2e-4 Calculations: Surface area of Ceres: A = 4 pi rē = 4 pi * 475 km = 2.84e6 kmē = 2.84e12 mē Thermal conductance of the ice layer: G = k A / L = 2.0 W/(m K) * 2.84e12 mē / 25e3 m = 227e6 W/K. Transfered power: P = G * (T2 - T1) = 227e6 W/K * (273 K - 168 K) = 227e6 W/K * 105 K = 23.8e9 W = 23.8 GW Decaying ratio of K-40 per second: (1 - (1/2)^(1s/t_1_2))/s = (1 - (1/2)^(1s/3.938e16 s))/s = (1 - (1/2)^2.5391e-17)/s = 1.76e-17 / s Mean power per K-40 atom per second = (1.76e-17 / s) * 2.10e-13 J = 3.696e-30 J/s = 3.696e-30 W Number of K-40 atoms to provide transferred power: 23.8e9 W / 3.696e-30 W = 6.44e39 = 1.07e16 * 6.022e23 = 1.07e16 mole. Mass of K-40 to provide transferred power: 1.07e16 * 0.03996 kg = 4.276e14 kg. Mass ratio of K-40 needed to provide transferred power: 4.276e14 kg / 9.43e20 kg = 4.53e-7. Mass ratio of K needed to provide transferred power 4.53e-7 / 1.2e-4 = 3.78e-3 = 0.378% As a comparison: Potassium makes up about 2.6% of the weight of Earth's crust. Links to data, notions, and formulas: http://en.wikipedia.org/wiki/Thermal_conductivity http://en.wikipedia.org/wiki/Thermal_conduction http://en.wikipedia.org/wiki/Ceres_%28dwarf_planet%29 http://en.wikipedia.org/wiki/List_of_thermal_conductivities http://en.wikipedia.org/wiki/Potassium http://en.wikipedia.org/wiki/Isotopes_of_potassium http://en.wikipedia.org/wiki/File:Potassiu...ecay-scheme.svg http://en.wikipedia.org/wiki/Potassium-40 http://en.wikipedia.org/wiki/Electronvolt http://en.wikipedia.org/wiki/Mole_(unit) http://en.wikipedia.org/wiki/Sphere#Surface_area http://en.wikipedia.org/wiki/Half-life#For...ponential_decay |
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