1. Astronomy 340 Fall 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 ), 4.3 (qualitatively – compare and contrast atmospheres of terrestrial planets), 4.8
Chapter 5.3, 5.4,5.5 (through )

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:

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 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

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