Astronomy 340 Fall 2005 Class #13 18 October 2005

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.

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)

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

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

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

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

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?

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