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Astronomy 340 Fall 2005

This class covers the methods and factors that determine the internal structure and conditions of terrestrial planets, including in situ probes, seismic activity, variation of sound speed, remote probes, geological activity, global magnetic field, gravity, and moment of inertia.

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Astronomy 340 Fall 2005

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  1. Astronomy 340Fall 2005 Class #13 18 October 2005

  2. 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.

  3. Appropriate Book Sections • Chapter 1 • Chapter 2.1, 2.2, 2.6 • Chapter 3 • Chapter 4.1, 4.2 (through 4.2.2.1), 4.3 (qualitatively – compare and contrast atmospheres of terrestrial planets), 4.8 • Chapter 5.3, 5.4,5.5 (through 5.5.4.2)

  4. 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: 6.1-6.3

  5. 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

  6. 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

  7. Radioactivity • Key elements: K, Ur, Th • 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

  8. 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?

  9. 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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