Interior of the terrestrial planets; time variable gravity field; tides; rotation; from planetary geodesy

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Interior of the terrestrial planetstime
variable gravity field tidesrotationfrom
planetary geodesy

• V. Dehant,
• Royal Observatory of Belgium

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Measurement principle
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Ionosphere
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Interior Structure of terrestrial planets

• Interior Structure models aim at determining
• the bulk chemistry of the planet
• the masses of major chemical reservoirs
• the depths of chemical discontinuities and phase
  transition boundaries
• the variation with depth of thermo-dynamic state
  variables (r, P, T)

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Many open questions!
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Time variable gravity field

• Seasonal variations of J2 J3 J4 J5
• Atmosphere and ice caps
• (see poster Karatekin et al.)
• Tidal variations / determination of Love number
  k2
• Interior of the planets
• Presentation of Balmino et al.

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CO2 sublimation/condensation process
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SEASONAL CO2 EXCHANGE
Current seasonal variations of estimated
from the Viking Lander range data (Yoder et al.,
1997).
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LOD SEASONAL CO2 EXCHANGE

• .

• Contributions to ?LOD

Deviations from AAM annual mean

1. Zonal winds
2. Surface mass distribution

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Detection of time variable gravity MGS Tracking
data vs GCM and HEND
J3
J2

• Smith et. al (2001), (J1, J2, J3)

• Yoder et al. (2003), (J2, J3)

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MGS tracking data processing
Edge-on
J3 signature max
Face-on
J2 signature max
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Tidal features

• Site displacements (radioscience)
• Gravity variations at the surface (seismology)
• External gravitational potential variations
• influence satellite orbits (radioscience)

• Modeling of these effects to correct measurements
• Interpret effects in terms of interior structure

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Tides and interior structure

• tides can be used for the determination of core
  properties
• Core radius between 1300 km and 1700 km
• Core liquid?
• Tides depend on interior structure e.g. larger
  tidal displacement for fluid core
• Driving force precisely known

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Orders of magnitude

• Tidal potential UT ?GM?r2/d3 7 of Earth
• Relative to U-GM/r, gGM/r2
• UT/U ? 1 10-8 Earth 2.5 10-8
• ? ? UT/g ? 3 cm
• gT/g ? 2UT/U ? 2UT/U ? 2 10-8 gT ? mgal
• UT/U ? 1 10-8 ?r ? UT/g ? 3 cm

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Tidal potential

• Direct effect of Sun, Phobos, Deimos
• Indirect effect of other solar system bodies
  (ephemerides)
• Phobos/Sun 8, Deimos/Sun 0.08
• Up to degree 4
• Truncation at 10-6 m2/s2 (0.1 ngal) 203 tidal
  waves

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Love numbers

• Reaction of Mars to unit forcing
• Latitude and frequency dependence included
• h, l for tidal station displacements
• k for external potential perturbation
• Gravimetric factor ? for surface gravity
  variations
• Degree 2 Love number are very sensitive to the
  core changes of 35 for different models

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Love numbers
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Site displacements

• Variations of 1 cm
• Core signature at mm level, too small to measure
  with NetLander

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• Relative differences between models ?UT ?10-10
  (?r lt1mm)
• Recent JPL and GSFC gravity maps of Mars give
  uncertainties in estimated Clm and Slm
  coefficients of 10-10.
• Total signal same order of magnitude as ice cap
  loading

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k Love numbers for solid/liquid core and
different core sizes
liquid
solid
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Rotation

• Best studied with landers (fixed on the planet
  and seen from space)
• Orientation parameters
• Precession, nutation
• Polar motion
• Length-of-day variations, librations
• Interior of the planets
• Atmosphere and ice caps

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rotation rate/ variations of length-of-day
polar motion
precession/ nutations
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Torque between Mars and its fluid layer
Pressure torque
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Torque between Mars and its fluid layer
Gravitational torque
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Torque between Mars and its fluid layer
Friction torque
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Length-Of-Day (LOD) Variations
meter
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Definition of the Chandler Wobble(CW)
Rotation axis
Figure axis
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Definition of the Free Core Nutation (FCN)
This mode does only exist if the core is
liquid
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Definition of the Free Inner Core Nutation (FICN)
This mode does only exist if the core is
liquid
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Definition of the Inner Core Wobble (ICW)
This mode does only exist if the core is
liquid
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Definition of the rotational normal modes
Chandler wobble (CW)
Free Core Nutation (FCN)
Rotation axis of the mantle
Rotation axis of the core
Rotation axis
Figure axis
Free Inner Core Nutation (FICN)
Inner Core wobble (ICW)
rotation axis of the inner core
figure axis of the inner core
rotation axis of the outer core
rotation axis of the inner core
The three core modes do only exist if the core is
liquid
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Adjustment of the liquid core and solid inner
core densities
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Density of the outer core and inner core
Before the eutectic
After the eutectic
For 14 Sulfur
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CW and ICW periods
20 Sulfur 14 Sulfur 5 Sulfur
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Chandler Wobble for Mars

• influence from core radius implying changes in
  A/Am, k, ?
• influence from state of the core (liquid/solid)
• influence from mantle inelasticity

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Rotational normal modes of Mars, their
resonances, and their amplitudes
ICW
days
CW
0
0 400 600 800 1000
1200 1400
km
eutectic
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Amplitude of the FCN and FICN as a function of
the inner core radius (14 S)
Before the eutectic
After the eutectic
annual period
ICW
Period (days)
semi-annual period
CW
inner core radius (km)
eutectic
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Polar Motion
cm
cm
?
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Precession and nutation of Mars
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Nutation Amplitudes
Residuals between solid and liquid case
solid core
liquid core
in Dy
in De
De (in meter)
meter
Dy (in meter)
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Comparison Earth/Mars
liquid/solid?
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Nutations of the planet Mars

• Solid or liquid core?
• Existence of the FCN?
• Existence of an inner core?
• Dimension of the core?

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Definition of the FCN
This mode does only exist if the core is
liquid
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annual nutation semi-annual nutation 1/3-annual
nutation 1/4 annual nutation
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Remember the quasi-diurnal modes of Mars

• If Mars has a liquid core, there exists a normal
  mode called the Free Core Nutation this mode is
  diurnal in a frame tied to Mars and has a long
  retrograde period in the inertial frame it
  appears as a resonance in the motion of the
  rotation axis of Mars (nutations).
• If Mars has a solid inner core, there exists a
  normal mode called the Free Inner Core Nutation
  this mode is diurnal in a frame tied to Mars and
  has a long prograde period in the inertial frame
  it appears as a resonance in the motion of the
  rotation axis of Mars (nutations).

rotation axis of the outer core
rotation axis of the inner core
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prograde annual nutation
600 400 200 0 -200 -400 -600
prograde semi-annual
FICN
FCN
prograde ter-annual
Period (days)
retrograde ter-annual
inner core radius (km)
eutectic
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Nutation Amplitudes
could be infinitely high if close to FCN (if
core liquid)
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Solid core
Liquid core
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Impact of the core on the spin rate of Mercury
from SONYR model
Cm/C 1
Cm/C 0.7
Cm/C 0.5
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Conclusions

• Interesting results for Mars from orbiter
  (gravity, k2, seasonal changes in the atmosphere
  and ice caps).
• NASA MGS, Odyssey, MRO / ESA Mars Express
• Planetary interior / Mars Interior
• But fundamental new science remains to be done
  with in situ investigations/network on Mars for
  instance (GEP). Landers would provide a large
  step forward.
• ESA AURORA ExoMars mission
• Future results for Venus from orbiter (gravity,
  k2)
• Planetary interior / Venus Interior
• Very promising results to be expected from
  MESSENGER and BepiColombo
• Planetary interior / Mercurys Interior
• NASA mission 2004 ESA cornerstone mission 2013.

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