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Astronomy 340 Fall 2005 Class #13 18 October 2005
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Announcements Midterm: Thursday in class (EMW will be out of town)
Homework #2 coming back today – last problem will be graded separately Note – all HWs will be worth the same amount even if they are graded differently.
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Appropriate Book Sections
Chapter 1 Chapter 2.1, 2.2, 2.6 Chapter 3 Chapter 4.1, 4.2 (through ), 4.3 (qualitatively – compare and contrast atmospheres of terrestrial planets), 4.8 Chapter 5.3, 5.4,5.5 (through )
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Terrestrial Planet Interiors
What we want to know What determines the internal structure/conditions of a terrestrial planet? How do we measure/determine the internal structure of a terrestrial planet? Book Sections:
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Ways of studying planetary interiors
In situ probes of interior “Earth”quakes Variation of sound speed in different media Remote probes of the interior Geological activity indicates molten interior Past geological activity/crater density indicates previously molten interior Global magnetic field dynamo gravity Moment of inertia (I=kMR2, where 0 < k < 1) L = I x ω (angular momentum) I = ∫∫∫ ρ(r) dc dr (dc = distance from axis in question) So angular mo reflects the distribution of mass within the planet requires accurate measurements of L
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Heat Sources Accretion kinetic energy of impacts melting
vcollision ~ vescape Eaccretion~ GM/R Per mass E/m = (GM/r2)dr = -GM/Rs Heating via conductivity = ρcpΔT, but some gets radiated away so ρΔTcp = [(GM/R)-σ(T4(r)-To4)] Differentiation just gravity Radioactivity very important
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Radioactivity Key elements: K, Ur, Th Lifetime is limited
238U 206Pb + 8He + 6β (4.5 Gyr, ~3 J g-1 yr-1) 235U 207Pb + 7He + 7β (0.7Gyr, ~19 J g-1 yr-1) 237Th, 40K both yield ~0.9 J g-1 yr-1 Lifetime is limited -(dP/dt) = (dD/dt)λP -ln(P) = λt + constant ln(P) – ln(P0) = λ t = (1/λ)ln((D-D0)/P + 1) For Earth radioactive heating was ~ 10 times more important right after formation than it is now
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Distribution of Elements
Starting assumption formation by accretion Net loss of volatiles Differentiation Chemical siderophiles vs lithophiles Physical denser material sinks Inner core density solid Fe Outer core density lower density, liquid, Fe plus something else (K?) Mantle partially molten, chemical inhomogeneous Mid-ocean ridge basalt (MORB) differentiation, more pristine? Ocean Island Basalt (OIB) less depleted, not primitive?
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Chemical Heterogeneity
Implies differentiation Accretion heats, Fe sinks Differentiation (20-30 Myr post formation) Density isn’t only parameter chemically, which elements stick to which other elements? Guiding question what do elemental ratios tell us about the history of the accretion/differentiation process? Relatve (not absolute) abundances are key
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