R = 3390 km (3375/3397km) McBride and Gilmore 2004
Earth 6357/6378km
M = 0.642x10^24 kg ~ 0.012 Earth mass
I = 0.366±0.001 (Folkner 1997?)
g 3.7 m/s^2(Earth 9.8)
Mars ref
Earth ref
R
M
I
G
rCrust
rcore
Crust thickness
30-80 km Wieczorek and Zuber 2004 JGR
(independent of chemistry)
core radius
1520 -1840km, Yoder 2003 Science
(mantle depth 1550 -1870 km, independent of chemistry)
Temperature
Guest and Smrekar 2007 PEPI (? 300km 1800 K)
Fei and Bertka 2005 Science (25 Gpa, 1800 K)
Temperature
T Gradient Pressure range
Surface
BDT boundary
TZ-Top
TZ-bottom
CMB-Top
CMB-Top
EoS
Olivine (Mg# 3.3 – 3.6 g/cm^3, Inoue 2004, Liu 2006)
radius range
Spinel Mg=100 V0 =525 Å^3, Mg 80, V0 =531 A^3. Unit cell volume increases by 1%
Formular unit mass increases by 9%
Therefore, density increases by about 8%
In the crust, pressure is not sensitive to density profile (Daniela)
Fe-S liquids Secco et al. 2002, J. Physics 14. 11325
V0
KT
K’
alpha
Debye Temperature
Ol
PX
Gt
Mg-Pv
FP
Ca-Pv
gamma
Mineralogy
Crust
Basalt
UM
Ol
Px
Gt
B*F98
Comp %
(Mg0.8Fe0.2)2SiO4 60
Sanloup99
Com %
Mg#, 30%
LM
Fe/Si
Fe/O
Fe/S
Ol/px = 60:30 (Bertka and Fei 98) ? Effect of temperatre (200 K difference in Areotherm
between 1998 and 2005)
Ol/px = 26-60 (Sanloup et al 1999)
10% garnet
lower mantle: Mg- Pv (80?), Fp (20?), Ca-Pv (10%)
Bertka and Fei 1998; Hirose 2007
Core: Fe-S liquid
Approach
assume crust, upper mantle, lower mantle thickness, calculate core radius
assume mineral proportions in the upper mantle and lower mantle
(Use Bertka and Fei 1998 or Sanloup et al. 1999 as starting points)
Test 1: calculate Fe/O, Fe/Si, and Fe/S ratios and compare with known values
calculate density profile rho(0) using densities at 1 bar and 300 K
calculate pressure profile P(0) and adiabatic temperature profile T(0)
recalculate density profile rho(1) using densities at P(0) and T(0)
recalculate pressure profile P(1) and adiabatic temperature profile T(1)
repeat until converge
Test 2: calculate mean density and moment of inertia factor and compare with the
observed values