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 coreliquid 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

plitu

des

Am

plitu

des

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 AFA

1

Core moment of inertia Constraint on core size and shape

observationsKnown from theory

)(

)1(

ff

FCN

ff

fFCN

eCC

C

eCCC

F

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

seco

nds (

mas

)

Mission duration (days)

Semi-annual prograde nutation amplitude

Mill

i-acr

seco

nds (

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.

Lander network experiment

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 AFA

1

FCNF

FCN

Core momentum factor:

Free core nutation period:

FCNF

FCN

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.