Post on 22-Dec-2015
3MS3 – Session 9: New projects and instruments October 11th 2012 – Moscow, Russia
Belgium-Geodesy experiment using Direct-To-Earth Radio-link:
Application to Mars and Phobos
Rosenblatt P., Le Maistre S., M. Mitrovic, and Dehant V.
ROYAL OBSERVATORYOF BELGIUM
ROYAL OBSERVATORYOF BELGIUM
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
mantle
outer core(radius 3480 km)
inner core(radius 1221 km)
Probing Earth’s interior
In the absence of seismicdata, geodesy brings preciousinformation on deep interior
of terrestrial planets
Measurements oftides and rotation variations
Current knowledge of the Martian core from geodesy
JPL solution ROB/CNESsolution
Tidal Love number
250
km
Core radius estimates given possible mantle temperature end-members, mantle rheology, and crust density and thickness range (Rivoldini et al., 2010).
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).
k2 tidal Love number determined from orbiters (Yoder et al., 2003; Konopliv et al., 2006; Marty et al., 2009)
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
Nutations of the planet Mars
Measured nutation-
rigid nutation=
Constraint on deep interior
solid core
liquid core
• retrograde ter-annual nutation• retrograde semi-annual nutation• retrograde 1/4 year nutation• prograde semi-annual nutation
transfer function
250 days
250 days
250 days
Am
plit
udes
Am
plit
udes
rigid Mars’ nutations
non-rigid Mars’ nutations
IMPORTANT FOR:
ROB
Free core nutation and transfer function
• Rigid nutation amplification → core dimension & moment of inertia
rigidFCN
FCNrigidnon A
FA
1
Core moment of inertia Constraint on core size and shape
observationsKnown from theory
)(
)1(
ff
FCN
ff
fFCN
eCC
C
eCC
CF
FCN
Resonance Large amplification Rigid nutation
Transferfunction
Free core nutation and transfer function
Amplification of rigid Mars’ nutation due to a liquid core
...
prograde semi-annualnutation
1.5% to 3%
> 20%
retrograde ter-annualnutation
Primary effect on retrograde ter-annual and prograde semi-annual nutations
Resonance
Amplification at ~3% of rigid nutationamplitude of 500 mas ~15 mas forthe liquid core signature.Amplification at >20% of rigid nutation
amplitude of 10 mas >2 mas forthe liquid core signature.But it can be much more if FCN period ~Ter-annual period 1 mas = 1.6 cm at Mars’ equator
ROB
Ter-annual nutation (period of 229 days)amplification depends on liquid core size (i.e. FCN period).
Improvement of core size determination.
Amplification of rigid Mars’ nutation due to a liquid core
...
prograde semi-annualnutation
1.5% to 3%
> 20%
retrograde ter-annualnutation
Effect of an inner core on nutation amplification.
Resonance
The existence of an inner core is expected to remove FCN semi-annual prograde amplification detection of inner core if it does exist
X-band radiolink
Uplink in [7.145,7.190] GHz
Downlink in [8.400,8.450] GHz Coherenttransponder
maser
Geodesy experiment to monitor Mars’ spin axis nutation
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
LaRa electronic box
Mill
i-acr
sec
onds
(mas
)
Mission duration (days)
Semi-annual prograde nutation amplitude
Mill
i-acr
sec
onds
(mas
)
Mission duration (days)
1/3 annual retrograde nutation amplitude
Direct-to-Earth radio-link (with one Lander)Numerical simulations (1) !
Predictions of precision and accuracy on the retrieval of nutation amplitude
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).
FCN=230 days
FCN=240 days
Le Maistre et al., 2012 (Planet. Space Sci.)
Direct-to-Earth radio-link (with one Lander)Numerical simulations (2) !
Determining transfer function parameters with one Lander at Mars’ surface Challenging task ! (because of non-linearity).
Use of more Landers Network
Le Maistre et al., 2012 (Planet. Space Sci.)
Opportunity of pre-network experimentINSIGHT + 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)
In Situ formation
PROS:Current moon orbitsHighly porous.
Additional argument:A silicate composition.
CONS:No modelling yet(Rosenblatt and Charnoz, Accepted in Icarus, 2012)
All model of originare flawed
MEX/HRSC image
Capture scenario:
PROS:Shape, ViS/NIR spectra Carbonaceous asteroid.
CONS: Ambiguous surface composition from remote sensing data.Current orbit requires high tidal dissipation rate inside Phobos.
Phobos
Interior relevant to the origin:composition, mass distribution, dissipative properties …
See recent review:Rosenblatt P., A&A Rev., vol. 19, 2011.
Which ‘Bulk interior’ for Phobos ?
Murchie et al. (1991)
From Fanale and Salvail (1989)
From Rambaux et al., accepted in A&A, 2012
See also, PD1 Poster Session
Rock+iceBlocksof rocks
Stickney-induced fractures
Highly porous rocky body (Rubble Pile)
From Andert et al. (2010)
No monolithic Phobos !
Compositional and/or structural heterogeneitiesinside Phobos.
Principal moments of inertia to constrain it.
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
Where M is the mass of Phobos, r0 is the mean radius of Phobos and e is the ellipticity of its orbit around Mars.
Modeling internal mass distribution
Constraining those models by measurements:
Geodetic experiment
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)
(Willner et al., 2010)
Mars Express: Libration/gravity measurement
Shape model
Modeling heterogeneity inside Phobos
Porosity: 10% 30% 40%Water ice: 23% 7% 0%
Probability density functions of the quadrupole gravity coefficients C20 and C22
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
Expected C20 value
Expected C22 value
Red linehomogeneous
Red linehomogeneous
Heterogeneousmodels: rock+ice+porosity
which fit the observed libration within its
error bar.
X-band radiolink
Uplink in [7.145,7.190] GHz
Downlink in [8.400,8.450] GHzCoherent
transpondermaser
Radio-science instrumentation
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
LaRa electronic box
Phobos libration from future Phobos Lander:Numerical simulations (1) !
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
Uncertainty on C versus uncertainty on C20 (or C22 )
𝛼=𝐶−𝐵𝐴
𝛾=𝐵− 𝐴𝐶
𝛽=𝐶−𝐴𝐵
Relative momentsof inertia
Additional constraint from Tides
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
Le Maistre et al., 2012
Predictions of formal error and accuracy
Expected constraint on the interiorAmplitude of periodic tidal displacement
CONCLUSION & PERSPECTIVES
A geodesy (radio-science) with one (or more) Lander will provideconstraints on the Martian core, (i.e. light elements content, inner core, …), therewith on its evolution.
Same experiment on Phobos (one Lander) will provide constraintson 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.
Cor
e m
omen
t fac
tor
Cor
e m
omen
t fac
tor
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).
Landers (network) orbiter radio-link Numerical simulations !rigid
FCN
FCNrigidnon A
FA
1
FCNF
FCN
Core momentum factor:
Free core nutation period:
FCNF
FCN