Transcript Document

ROYAL OBSERVATORY
OF BELGIUM
ROYAL OBSERVATORY
OF BELGIUM
Belgium-Geodesy experiment using
Direct-To-Earth Radio-link:
Application to Mars and Phobos
Rosenblatt P., Le Maistre S., M. Mitrovic, and Dehant V.
3MS3 – Session 9: New projects and instruments
October 11th 2012 – Moscow, Russia
Overview
 Why a Geodesy experiment in the Martian system?
Scientific rationale:
Mars’ deep interior (size, inner core?)
 core evolution
Phobos’ interior (internal mass distribution)
 origin of the Martian moons
Goals:
Precise measurements of the rotational state
(Mars’ nutation, Phobos’ librations)
Using dedicated payload:
X-band coherent transponder (LaRa, Lander
Radioscience, developed by Belgium)
crust
In the absence of seismic
data, geodesy brings precious
information on deep interior
mantle of terrestrial planets
outer core
(radius 3480 km)
Measurements of
tides
and rotation variations
inner core
(radius 1221 km)
Probing
Earth’s interior
Current knowledge of the Martian core from geodesy
250 km
Core radius estimates given possible mantle temperature end-members, mantle
rheology, and crust density and thickness range (Rivoldini et al., 2010).
ROB/CNES
solution
JPL solution
Tidal Love number
k2 tidal Love number determined from
orbiters (Yoder et al., 2003; Konopliv
et al., 2006; Marty et al., 2009)
 Liquid core inside Mars (k2 > 0.08), but large discrepancies (+/- 250 km).
 Better core radius estimate is required to better constrain other core parameters (sulfur
content, solid inner core…), which drive its thermal evolution.
 More data are needed. Space geodesy can play an important role by measuring
nutations of the rotation axis of Mars ( Lander(s) on Mars).
Nutations of the planet Mars
liquid core
solid core
Measured nutation
rigid nutation
=
Constraint on
deep interior
 Mars’ nutation have not been measured so far, but they can be precisely
computed considering Mars’ interior is rigid.
 If the core is liquid, nutation amplitudes can be amplified w.r.t. “rigid nutations”.
Precise measurements of nutations  Information on the deep interior structure
Amplitudes
Free core nutation and transfer function
rigid Mars’ nutations
IMPORTANT FOR:
250 days
transfer function
250 days
Amplitudes
non-rigid Mars’ nutations
• retrograde terannual nutation
• retrograde semiannual nutation
• retrograde 1/4
year nutation
• prograde semiannual nutation
250 days
ROB
Free core nutation and transfer function
• Rigid nutation amplification
→ core dimension & moment of inertia
observations
Anon rigid

FFCN
 1 
    FCN
Known from theory

 Arigid

Transfer
function
Core moment of inertia
 Constraint on core
size and shape
   FCN
 Resonance
Large amplification
Rigid nutation
FFCN 
Cf
C Cf

 FCN  
(1 

ef
)
C
(e f   )
C Cf
Amplification of rigid Mars’ nutation due to a liquid core
 Primary effect on retrograde ter-annual and prograde semi-annual nutations
> 20%
...
1.5% to 3%
Resonance
prograde semi-annual
nutation
retrograde ter-annual
Amplification at >20% of rigid nutation nutation
amplitude of 10 mas  >2 mas for
the liquid core signature.
But it can be much more if FCN period ~Ter-annual period
Amplification at ~3% of rigid nutation
amplitude of 500 mas  ~15 mas for
the liquid core signature.
1 mas = 1.6 cm at Mars’ equator
Ter-annual nutation (period of 229 days)
amplification depends on liquid core
size (i.e. FCN period).
 Improvement of core size
determination.
ROB
Amplification of rigid Mars’ nutation due to a liquid core
 Effect of an inner core on nutation amplification.
> 20%
...
1.5% to 3%
Resonance
prograde semi-annual
nutation
retrograde ter-annual
nutation
The existence of an inner core
is expected to remove FCN
semi-annual prograde amplification
 detection of inner core if it does
exist
Geodesy experiment to monitor
Mars’ spin axis nutation
X-band radiolink
LaRa
electronic box
maser




Coherent
transponder
Coherent transponder (LaRa) initially designed and constructed by Belgium: TRL-5
Mass: 850 grams. Power peak consumption (20 W).
Direct-To-Earth (DTE) radio-link between Mars and tracking stations on Earth
X-band 2-way Doppler shift measurements: Precision 0.1 mm/s
 Monitoring of the rotational motion of Mars
Direct-to-Earth radio-link (with one Lander)
Numerical simulations (1) !
 Predictions of precision and accuracy on the retrieval of nutation amplitude
Le Maistre et al., 2012
(Planet. Space Sci.)
1/3 annual retrograde
nutation amplitude
Milli-acr seconds (mas)
Milli-acr seconds (mas)
Semi-annual prograde
nutation amplitude
Mission duration (days)
FCN=230 days
FCN=240 days
Mission duration (days)
 Nutation amplitude can be retrieved with enough precision to detect liquid core
especially when the FCN period is close to the ter-annual period (229 days).
Direct-to-Earth radio-link (with one Lander)
Numerical simulations (2) !
Le Maistre et al., 2012
(Planet. Space Sci.)
 Determining transfer function parameters with one Lander at Mars’ surface
 Challenging task ! (because of non-linearity).
 Use of more Landers  Network
Opportunity of pre-network experiment
INSIGHT + ExoMars
 NASA-INSIGHT scout mission due to land on Mars in 2016.
Radioscience experiment with US instrument.
 If Radioscience transponder (possibly LaRa) onboard ExoMars (2018)
we may perform Single Beam Interferometry (SBI) experiment.
 Lander relative position known at the sub-cm precision level.
 Improvement of the determination of the Mars’ spin axis nutations.
‘Puzzling’ Phobos (and Deimos)
Capture scenario:
All model of origin
are flawed
In Situ formation
PROS:
Shape, ViS/NIR spectra
 Carbonaceous asteroid.
PROS:
Current moon orbits
Highly porous.
CONS:
Ambiguous surface
composition from
remote sensing data.
Current orbit requires
high tidal dissipation
rate inside Phobos.
Additional argument:
A silicate composition.
See recent review:
Rosenblatt P., A&A Rev.,
vol. 19, 2011.
CONS:
No modelling yet
Phobos
MEX/HRSC image
Interior relevant to the origin:
composition, mass distribution,
dissipative properties …
(Rosenblatt and Charnoz,
Accepted in Icarus, 2012)
Which ‘Bulk interior’ for Phobos ?
Blocks
of rocks
Rock+ice
No monolithic Phobos !
Murchie et al. (1991)
Highly porous rocky
body (Rubble Pile)
Compositional and/or
structural heterogeneities
inside Phobos.
From Fanale and Salvail (1989)
Stickney-induced fractures
Principal moments of
inertia to constrain it.
From Andert et al. (2010)
From Rambaux et al., accepted in A&A, 2012
See also, PD1 Poster Session
Internal mass distribution through geodetic parameters
 Internal mass distribution related to principal moments of inertia
(A<B<C).
 Principal moments of inertia also related to quadrupole gravity
coefficients C20 and C22 and the libration amplitudes θ
 Modeling internal mass distribution
 Constraining those models by measurements:
Geodetic experiment
Where M is the mass of Phobos,
r0 is the mean radius of Phobos
and e is the ellipticity of its orbit
around Mars.
Mars Express: Libration/gravity measurement
(Willner et al., 2010)
Shape model
 Monitoring of control points network (Willner et al., 2010)
θ = 1.2° +/- 0.15 ° (12.5%) (Homogeneous value from the shape = 1.1°)
 Updated shape model (Nadezhdina et al., EPSC, 2012): θ = 1.09° +/- 0.1 ° (9%)
(Homogeneous = 0.93°)
 Homogeneous/Heterogeneous …
 Gravity field C20 heterogeneity but error bar ~50% (Andert et al., EPSC, 2011)
Modeling heterogeneity inside Phobos
Probability density functions of the quadrupole gravity coefficients C20 and C22
Expected C20
value
Red line
homogeneous
Porosity:
Water ice:
10%
23%
30%
7%
40%
0%
Heterogeneous
models: rock+ice+porosity
which fit the observed
libration within its
error bar.
Expected C22
value
Red line
homogeneous
 Geodetic parameters of heterogeneous interior departs
by a few percent (<10%) from the homogeneous interior
 Precise measurement is required (geodetic experiment)
From Rivoldini et al., 2011
Radio-science instrumentation
X-band radiolink
LaRa
electronic box
maser
Coherent
transponder
 Coherent transponder (LaRa) initially designed by Belgium for Martian Lander experiment
 Direct-To-Earth (DTE) radio-link between Phobos Lander/Orbiter on Phobos and tracking
stations on Earth (DSN, ESTRACK and VLBI)
 X-band 2-way Doppler shift measurements: Precision 0.1 mm/s
 Monitoring of the rotational and orbital motion of Phobos
Phobos libration from future Phobos Lander:
Numerical simulations (1) !
Relative moments
of inertia
𝐶−𝐵
𝛼=
𝐴
𝐶−𝐴
𝛽=
𝐵
𝛾=
Uncertainty on C versus
uncertainty on C20 (or C22 )
𝐵−𝐴
𝐶
 Phobos’ rotational model: rich spectrum of libration (Rambaux et al., 2012)
 Short periods contain information on the interior: Relative moments of inertia.
 Numerical simulations of geodesy experiment with a Lander on Phobos show:
 Short-periodic libration with a precision < 1% after a few weeks of operation
 Knowledge of quadrupole gravity coefficients is also required
Additional constraint from Tides
Amplitude of periodic tidal displacement
Expected constraint on the interior
Predictions of formal
error and accuracy
Le Maistre et al., 2012
 Phobos’ surface displacement due to Tides raised by Mars inside Phobos
(up to 5 cm), depending on its interior structure (« rubble-pile » vs monolith)
 Precise monitoring of Lander (transponder) position  interior
CONCLUSION & PERSPECTIVES
 A geodesy (radio-science) with one (or more) Lander will provide
constraints on the Martian core, (i.e. light elements content,
inner core, …), therewith on its evolution.
 Same experiment on Phobos (one Lander) will provide constraints
on its bulk interior structure (i.e. water-ice/porosity content),
therewith on its origin.
 Radioscience instrument: X-band coherent transponder LaRa (TRL 5)
easy to implement on Landing platform of future missions to Mars,
Phobos, the Moon, Ganymede, …
(ExoMars, INSPIRE, PHOOTPRINT, GETEMME, Phobos-Soil-2, JUICE …)
 Radio-science instrument part of the ‘core package’ to probe in-situ
the bulk interior structure of solar system bodies.
Lander network experiment
Landers (network) orbiter radio-link
Numerical simulations !
Core momentum factor: FFCN
FFCN
Core moment factor

 Arigid

Core moment factor
Anon rigid

F 
 1  FCN
    FCN
 FCN
Free core nutation period:  FCN
Nutation parameters are recovered (case where a liquid core is considered).
Same results for Polar Motion and Lentgh-Of-Day variations.
The effect of desaturation on the orbiter motion have been taken into account and the tracking is
assumed to be as continuous as possible (from Rosenblatt et al., Planet. Space Sci., 2004).
Acknowledgements
This work was financially supported by the
Belgian PRODEX program managed by the
European Space Agency in collaboration with the
Belgian Federal Science Policy Office.