Lander radioscience for obtaining the rotation and orientation of Mars

ARTICLE IN PRESS Planetary and Space Science 57 (2009) 1050–1067

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Lander radioscience for obtaining the rotation and orientation of Mars Veronique Dehant a,, William Folkner b, Etienne Renotte c, Daniel Orban d, Sami Asmar b, Georges Balmino e, Jean-Pierre Barriot f, Jeremy Benoist g, Richard Biancale e, Jens Biele h, Frank Budnik i, ¨ zgur Karatekin a, Se´bastien Le Maistre a, Stefaan Burger d, Olivier de Viron j, Bernd Ha¨usler k, O j l Philippe Lognonne´ , Michel Menvielle , Michel Mitrovic a, Martin Pa¨tzold m, Attilio Rivoldini a, Pascal Rosenblatt a, Gerald Schubert n, Tilman Spohn h, Paolo Tortora o, Tim Van Hoolst a, Olivier Witasse p, Marie Yseboodt a a

Royal Observatory of Belgium (ROB), 1180 Bruxelles, Belgium Jet Propulsion Laboratory (JPL), USA Centre Spatial de Lie`ge (CSL), Belgium d Orban Microwave Products (OMP), Leuven, Belgium e ´ode´sie Spatiale (GRGS)/ Centre National d’Etudes Spatiales (CNES), France Observatoire Midi-Pyre´ne´es/ Groupe de Recherche de Ge f Universite´ de Polyne´sie Franc- aise, Tahiti g CNES, France h ¨ r Luft-und Raumfahrt (DLR), Berlin, Germany Deutsches Zentrum fu i European Space Operations Centre (ESOC)/ESA, Germany j University Paris 7 and IPGP, Paris, France k ¨t der Bundeswehr Mu ¨ nchen, Germany Universita l ´ tudes des Environnements Terrestre et Plane´taire (CETP), Paris, France Centre d’E m ¨t zu Ko ¨ln, Germany Universita n University of California Los Angeles (UCLA), USA o University of Bologna, Italy p European Space research and Technology Centre (ESTEC)/ESA, The Netherlands b c

a r t i c l e in f o

a b s t r a c t

Article history: Received 14 March 2008 Received in revised form 21 July 2008 Accepted 13 August 2008 Available online 22 August 2008

The paper presents the concept, the objectives, the approach used, and the expected performances and accuracies of a radioscience experiment based on a radio link between the Earth and the surface of Mars. This experiment involves radioscience equipment installed on a lander at the surface of Mars. The experiment with the generic name lander radioscience (LaRa) consists of an X-band transponder that has been designed to obtain, over at least one Martian year, two-way Doppler measurements from the radio link between the ExoMars lander and the Earth (ExoMars is an ESA mission to Mars due to launch in 2013). These Doppler measurements will be used to obtain Mars’ orientation in space and rotation (precession and nutations, and length-of-day variations). More specifically, the relative position of the lander on the surface of Mars with respect to the Earth ground stations allows reconstructing Mars’ time varying orientation and rotation in space. Precession will be determined with an accuracy better by a factor of 4 (better than the 0.1% level) with respect to the present-day accuracy after only a few months at the Martian surface. This precession determination will, in turn, improve the determination of the moment of inertia of the whole planet (mantle plus core) and the radius of the core: for a specific interior composition or even for a range of possible compositions, the core radius is expected to be determined with a precision decreasing to a few tens of kilometers. A fairly precise measurement of variations in the orientation of Mars’ spin axis will enable, in addition to the determination of the moment of inertia of the core, an even better determination of the size of the core via the core resonance in the nutation amplitudes. When the core is liquid, the free core nutation (FCN) resonance induces a change in the nutation amplitudes, with respect to their values for a solid planet, at the percent level in the large semi-annual prograde nutation amplitude and even more (a few percent, a few tens of percent or more, depending on the FCN period) for the retrograde terannual nutation amplitude. The resonance amplification depends on the size, moment of inertia, and

Keywords: Radioscience X-band signal Mars nutation Mars length-of-day

 Corresponding author.

E-mail address: [email protected] (V. Dehant). 0032-0633/$ - see front matter & 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.pss.2008.08.009

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flattening of the core. For a large core, the amplification can be very large, ensuring the detection of the FCN, and determination of the core moment of inertia. The measurement of variations in Mars’ rotation also determines variations of the angular momentum due to seasonal mass transfer between the atmosphere and ice caps. Observations even for a short period of 180 days at the surface of Mars will decrease the uncertainty by a factor of two with respect to the present knowledge of these quantities (at the 10% level). The ultimate objectives of the proposed experiment are to obtain information on Mars’ interior and on the sublimation/condensation of CO2 in Mars’ atmosphere. Improved knowledge of the interior will help us to better understand the formation and evolution of Mars. Improved knowledge of the CO2 sublimation/condensation cycle will enable better understanding of the circulation and dynamics of Mars’ atmosphere. & 2008 Elsevier Ltd. All rights reserved.

1. Scientific background and introduction 1.1. Mars’ interior and evolution Only indirect information is currently known about the interior of Mars. Available observations relevant to the interior are those of the static Martian gravity field and topography, the tidal effect on an orbiter, and the precession of the spin axis derived from radio tracking of orbiting and landed spacecraft (e.g., Smith et al., 1998; Folkner et al., 1997; Konopliv et al., 2006; Rosenblatt et al., 2008a). These observations are complemented by geochemical constraints deduced from analysis of SNC meteorites (Shergottite, Nakhlite, and Chassigny meteorites) or chondrite data and by extrapolation of the Earth’s internal structure to the lower pressures of Mars’ interior (Sohl and Spohn, 1997; Sanloup et al., 1999; Bertka and Fei, 1998; Sohl et al., 2005; Verhoeven et al., 2005). Geochemical studies argue in favor of a relative enrichment in iron of the Martian mantle with respect to the Earth’s mantle, and a relative enrichment in sulfur content of the iron core. Recent results from geodesy experiments favor models with a large core and a hot mantle (Yoder et al., 2003; Konopliv et al., 2006). However, these results are controversial since recent evaluation (Marty et al., 2008) of the tidal Love number k2 (the ratio between the mass redistribution potential to the tidal potential) suggests smaller cores, which could be favored by thermal evolution models sustaining large plumes possibly responsible for Tharsis’ rise (Breuer et al., 1997; Spohn et al., 2001; Van Thienen et al., 2007). Theoretical models of Mars’ interior that incorporate all these possible hypotheses and match the measured quantities lead to values of the outer core radius ranging from 1400 to 1800 km, i.e., 40–50% of the mean radius of the planet (e.g., Schubert and Spohn, 1990; Schubert et al., 1990; Dupeyrat et al., 1996; Sohl and Spohn, 1997; Zharkov and Gudkova, 2000; Verhoeven et al., 2005; Sohl et al., 2005; Duron, 2007; van Thienen et al., 2006). The present state of the core (liquid or solid) is still an open question, although the measured tidal perturbations of the orbits of Mars Global Surveyor (MGS), Mars Odyssey, and Mars Express (MEX) suggest a core at least partially liquid (Yoder et al., 2003; Balmino et al., 2006; Konopliv et al., 2006; Marty et al., 2008; Rosenblatt et al., 2008b). Knowledge of the state of Mars’ core and its size is important for understanding the planet’s evolution. The thermal evolution of a terrestrial planet can be deduced from the dynamics of its mantle and core. The evolution of a planet and the possibility of dynamo magnetic field generation in its core are highly dependent on the planet’s ability to develop convection in the core and in the mantle. In particular, a core magnetodynamo is related either to a high thermal gradient in the liquid core (thermally driven dynamo) or to the growth of a solid inner core (chemically driven dynamo), or both (see e.g., Longhi et al., 1992; Dehant et al., 2007; Breuer et al., 2007). The state of the core depends on the percentage of light elements in the core and on

the core temperature, which is related to the heat transport in the mantle (Stevenson, 2001; Breuer and Spohn, 2003, 2006; Schumacher and Breuer, 2006). The present size and state of the core thus have important implications for our understanding of the evolution and present state of Mars (Breuer et al., 1997; Spohn et al., 2001; Stevenson, 2001; Van Thienen et al., 2007; Dehant et al., 2007). Mantle dynamics is also essential in shaping the geology of the surface and in sustaining plate tectonics (Spohn et al., 1998). The radius of the core has implications for possible mantle convection scenarios and in particular for the presence of a perovskite phase transition at the bottom of the mantle, which enables global plume-like features to exist and persist over time, i.e., it allows sustained localized upwelling of hot material as might have occurred below Tharsis (van Thienen et al., 2006). Strong and long-standing mantle plumes arising from the core–mantle boundary may explain the long-term volcanic activity in the Tharsis area. Nevertheless, their existence during the last billion years is uncertain under Martian conditions. Alternatively, Schumacher and Breuer (2006) have proposed that the thermal insulation by locally thickened crust, which has a lower thermal conductivity and is enriched in radioactive heat sources in comparison to the mantle, leads to significant lateral temperature variations in the upper mantle that are sufficient to generate partial melt even in the present Martian mantle. This provides an alternative explanation for Tharsis and its recent volcanism (Neukum et al., 2004).

1.2. Mars’ atmosphere and the CO2 sublimation/condensation process 1.2.1. Mars’ global atmosphere, length-of-day (LOD), and polar motion Knowledge of the Martian atmosphere derives from many measurements by orbiters and landers, e.g., pressure measurements, infrared spectroscopic observations, radio occultations, etc. The global circulation of the atmosphere is computed from general circulation models that are constrained by these data. The global circulation can also be constrained from knowledge of the seasonal mass exchange in the atmosphere. About one fourth of the atmosphere participates in the sublimation and condensation of the CO2 in the ice caps. This large seasonal phenomenon induces, in turn, an exchange of angular momentum with the solid planet and a change in the rotation of Mars. LOD variations are deviations from the uniform rotation speed of the planet. They are mostly related to the dynamics of the geophysical fluids of the system (the core and atmosphere of Mars). Seasonal condensation/sublimation of the icecaps induces a large change in the LOD at the seasonal periods (Cazenave and Balmino, 1981; Chao and Rubincam, 1990; Defraigne et al., 2000; Van den Acker et al., 2002; Sanchez et al., 2004; Karatekin et al.,

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2006a, b; see also Duron et al., 2003, for improvement of tracking strategy). This CO2 mass exchange between the ice caps and the atmosphere due to the seasonal sublimation/condensation process is also the main reason for polar motion (motion of the rotation axis in a frame tied to the planet). Due to the geometry of the icecaps, we expect polar motion to be very small. LOD variations, on the other hand, will be fairly large due to the large mass exchange.

1.2.2. Long-term obliquity constraint The present-day obliquity and rotation period of Mars and the Earth are similar, and daily and seasonal insolation variations are therefore comparable. The seasonal insolation variations on Mars are larger due to the about five times larger eccentricity of Mars compared to the Earth, which implies a 40% difference between the solar flux received at perihelion and aphelion. Moreover, the seasonal and diurnal temperature variations compared to the insolation variations are relatively larger for Mars than for the Earth due to the presence of oceans and a denser atmosphere on Earth. Although the current obliquity and rotation period of Mars and the Earth are similar, the long-term spin variations of the Earth and Mars differ substantially. Due to its closer distance to the Sun and the presence of a large moon, the rotation rate of the Earth has changed much more than that of Mars as a result of tidal dissipation (see Laskar and Joutel, 1993; Laskar and Robutel, 1993). Mars’ rotation rate can be considered as close to primordial. Earth’s obliquity has remained in the range of 22.1–24.51 over the last 18 Myr (Laskar et al., 1993a, b). Mars’ obliquity shows much larger variations: during the last 20 Myr, the obliquity of Mars varied between about 101 and 451 (Laskar and Robutel, 1993; Laskar et al., 2004). An important improvement in our present understanding can be provided by a better determination of the obliquity and precession rate. Indeed, they are very important parameters for getting a better present constraint on the paleoclimate of Mars (Laskar et al., 2004). The Earth owes its spin axis stability to the lunar torque, which decreases its precession period from 8.1 104 to 2.6  104 years (Ward, 1973). As a result, the motion of the Earth’s spin axis is much faster than the motion of the orbit normal and the spin axis follows the instantaneous orbit pole, keeping the obliquity nearly constant. For Mars, the precession period of the spin axis is close to periods of slow secular changes in its orbit, and large chaotic obliquity variations can occur as a result of this secular resonance overlap. It is thus important to better constrain the precession value. Progress in climate simulations involving solar insolation and the changing obliquity of Mars has provided a theoretical basis for the study of recent orbitally induced climate changes on Mars (for an overview, see Montmessin, 2006). A better knowledge of the present obliquity and precession rate will improve our understanding of the obliquity evolution of Mars over tens of million years (Laskar et al., 2004). It is known for Earth that obliquity changes have played a critical role in pacing glacial and interglacial eras. For Mars, such orbital changes have been far greater (the obliquity of Mars is strongly chaotic) and have generated extreme variations in insolation.

nutation observations, while atmospheric questions will be addressed using observations of LOD variation. As for Earth, information on Mars’ deep interior can be inferred geodetically. The study of Mars orientation in space (rotation, nutation) will allow isolation of the non-rigid response of Mars to nutational forcing, which is directly linked to the state (liquid or solid) of the core. In addition, the observation of precession will allow a better determination of the total moment of inertia of the planet, providing an additional constraint on the global mass distribution inside the planet. The experiment proposed is a radioscience experiment on board the ExoMars mission to Mars to be launched in 2013 (http:// www.esa.int/SPECIALS/ExoMars/index.html). It is called LaRa for Lander Radioscience. LaRa will measure the variation of Mars’ rotation speed (related to the LOD), the orientation of Mars’ rotation axis in space (precession and nutation), and the orientation of Mars around its rotation axis (polar motion), by monitoring the Doppler shift due to the motion of Mars relative to the Earth on the radio signal between the ExoMars lander and the tracking stations of ESA ESTRACK (ESA TRACKing) network and NASA Deep Space Network (DSN). The primary objective of LaRa is a precise measure of these quantities, which can be theoretically calculated for different states and sizes of the core, for different internal compositions, and for different interior temperature profiles. Precession and LOD variations have already been detected from spacecraft data. Precession is presently known at the 0.3% level (see Konopliv et al., 2006) and LOD variations are known at about the 10% level (see Konopliv et al., 2006). The expected precision of LaRa will be at least a factor of two better in the known quantities (even a factor of four for the precession value for a very conservative 180-day mission lifetime and better for a long stay at the surface of Mars). An analysis of LaRa data will provide (improved) estimates of Mars’ precession and nutation, polar motion, and LOD variations. LaRa thus aims at characterizing the present interior of Mars and, in conjunction with other Humboldt Payload instruments (see Section 8 on the synergies with the other instruments), will be able to determine the physical state of the core, the size of the core, the possible existence of an inner core, the core composition and the mantle mineralogy. These parameters are very important for understanding the evolution of Mars. Temperature and mineralogy are the basis for obtaining the profiles of density, thermodynamic parameters (bulk and shear moduli), and the thermal conductivity inside Mars. The mass, moment of inertia, impedances (characterizing the inductive response of the conductive planet), heat flow, and seismic velocities are all based on these interior properties. The paper is organized as follows. Sections 2 and 3 address the way we will reach the goals with LaRa. Section 4 addresses the observation strategy and Section 5 presents the results of the simulations we have performed in order to show that the radioscience data can be used to achieve the objectives. The instrument description and its performance are addressed in Sections 6 and 7. We address the synergy with other instruments on the platform of the ExoMars mission as well as the synergy with the orbiter payload in Sections 8 and 9, respectively.

2. How lander–Earth radioscience achieves the major goals 1.3. Objectives 2.1. Mars’ deep interior This paper shows how radioscience will answer major questions related to the internal structure of Mars, its climate, and the global circulation of its atmosphere. Questions related to the interior of Mars will be addressed using precession and

The direction of the rotation axis of Mars varies with time due to the gravitational attraction exerted by the Sun and, to a lesser extent, the natural satellites Phobos and Deimos. Because of the

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2.1.1. Core composition and size from precession As mentioned in the previous paragraph, the LaRa data will provide improved estimates of Mars’ precession and nutation, polar motion, and LOD variations by monitoring the Doppler shift due to the rotation of Mars on the radio signal between the ExoMars lander and the tracking stations from ESA ESTRACK and NASA DSN. LaRa will reduce the uncertainty in the precession rate by about one order of magnitude after one Martian year (at the order of a few milliarcsec/year) and therefore also in the moment of inertia (C) by the same factor. The value of C/mara2, the scaled moment of inertia, where ma is the mass of Mars and ra is the mean radius of Mars, will be determined with an uncertainty of about 0.0001. This quantity can be used to estimate likely values of core size and density, and further constrain the core temperature and composition if additional knowledge like mantle composition and crust density and thickness are provided. In addition, LaRa data will be used together with seismological and gravity data to determine crustal density and thickness as well as mantle mineralogy. This will be discussed further in the section on synergies (Sections 8 and 9). The moment of inertia is a function of the radial distribution of mass. For a given planetary mass, a low value of the moment of inertia corresponds to a mass concentration towards the center of the planet while a high value of the moment of inertia implies a more uniform distribution of mass with radius. If we know the mean density of the mantle and the thickness and density of the crust, it is possible to determine a range of values for the core radius if the density of the core is known, as was done in Sohl and

Spohn (1997). Rivoldini et al. (2008a, b, c) have taken a different approach and used two different models for the mantle composition: (1) the mineralogy of Dreibus and Wa¨nke (1985) built under the assumption that the refractory elements are derived from chondritic CI (Ivuna-type of chondrite) abundances and the volatile elements are derived from the SNC meteorites and (2) the mineralogy of Sanloup et al. (1999) based on a mixture of chondritic meteorites such that specific oxygen isotope fractions are those of the SNC meteorites. They also consider two temperature profiles, hot and cold, end-members of thermal evolution modeling under the stagnant lid convective regime. The temperature profiles are in agreement with an early episode of magnetic activity and are compatible with present-day crustal thickness estimates (Breuer and Spohn, 2003). Fig. 1 shows the core radius as a function of the normalized polar moment of inertia for models with 14-wt% sulfur in the core and fixed crust density. The figure shows results for the cold and hot mantle temperature profiles and for two different mineralogies: the mineralogy of Dreibus and Wa¨nke (1985) and the mineralogy of Sanloup et al. (1999). The moment of inertia of Mars allows core sizes corresponding to a range of crustal thicknesses from 40 to 120 km. The figure is drawn for the range of scaled moment of inertia values C/mara2 given by Konopliv et al. (2006). This range should be compared with the range reached after a few months of LaRa operation, which corresponds to a factor of 4 improvement in the precision of the scaled moment of inertia (light grey-shaded area). The precision that could be reached after one Martian year is even better and corresponds to an estimated uncertainty of 0.0001 on the scaled moment of inertia. This range is also indicated in Fig. 1 (grey shaded area). The central values of these shaded areas are chosen arbitrarily. For a given mantle temperature profile and composition, the resulting uncertainty in core size arises from two different contributions: the uncertainty in the moment of inertia and in the compatible crustal thickness, between 40 and 120 km. The improvement in the precision of the moment of inertia determination by a factor of 4 (a very conservative value for a 180day mission; a factor of 10 after one Martian year), which will be realized by LaRa, reduces the uncertainty accordingly. Without further independent improvement in the mantle temperature, one

Dreibus & Wänke 84 Sanloup & al. 99

1720 1700 rcmb [km]

existence of an equatorial bulge (like the Earth, Mars is flattened at the poles, mainly due to its rapid rotation), the Sun’s attraction continuously tends to tilt Mars’ equatorial plane towards the orbital plane. The rotating Mars reacts to this force as a gyroscope, and Mars’ rotation axis describes a broad cone around the perpendicular to the orbital plane. This forced long-term component is called precession and has a period of about 91,000 Martian years or 170,000 Earth years. Because the relative positions of the Sun and Mars periodically change with time and, to a minor extent, because of the existence of the gravitational forcing of the two moons of Mars, the rotation axis also exhibits short periodic variations in space called nutations (Reasenberg and King, 1979; Borderies, 1980; Roosbeek, 2000). Both motions are very interesting for studying the deep interior of Mars: precession because it is linked with the moment of inertia of the planet, nutations mainly because they are different for a planet with a liquid core than for a planet with a solid core. From the observation of nutation over a long period of time (at least two Martian years will be necessary to best constrain the core contribution to the nutation amplitudes), one can determine whether Mars has a liquid core or a solid core. Mars’ response to gravitational nutation forcing is influenced by the core physical state; a liquid core leads to a resonant enhancement of nutation due to a normal mode called the free core nutation (FCN) (Sasao et al., 1980; Dehant et al., 2000b). This mode is related to the existence of a flattened fluid core inside a solid mantle. The moment of inertia and the size and density of the core can also be determined from the FCN resonance related to the excitation of an angle between the rotation axis of the core and the rotation axis of the mantle if the core is liquid and flattened. In particular, the nutations driven by the gravitational force of the Sun with frequencies at multiples of the orbital frequency are influenced by the resonance effect due to the FCN (see, e.g., Dehant et al., 2000a, b; van Hoolst et al., 2000a, b). The existence of a liquid core enhances the nutation, i.e., the peak-to-peak amplitude of the nutation is larger with a liquid core than with a solid core.

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1680 1660 1640 1620 0.3660

0.3665

0.3670

0.3675

C/ma ra2 Fig. 1. Core radius rCMB as a function of the normalized polar moment of inertia C/ mara2 for cold and hot mantle models and for two different mineralogies. The full curve corresponds to the mineralogy of Dreibus and Wa¨nke (1985) and the dashed curve to the mineralogy of Sanloup et al. (1999). The black curves correspond to a hot mantle model and the grey curves to a cold mantle model. The range of scaled moments of inertia presented in the figure corresponds to the range of values proposed by Konopliv et al. (2006). Also indicated is the range reached after a few months of LaRa operation (light grey shaded area) and after one year (grey shaded area); it corresponds to a factor of four and ten improvement in the precision of the scaled moment of inertia as proposed by LaRa.

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would reduce the uncertainty in the core radius from 110 to 70 km. This shows the importance of synergies with other Humboldt Payload instruments which will provide complementary constraints on all basic model parameters. Using a model of Mars interior based on a few parameters (crustal thickness between 20 and 120 km, crustal density between 2900 and 3100 kg/m3, mantle temperature (hot or cold) and mineralogy (Dreibus and Wa¨nke, 1985; Sanloup et al., 1999)),

1800

hot mantle cold mantle

rcmb [km]

1700 1600

we can determine ranges for the core size and the light element fraction such that the values of the global mass and moment of inertia lie within their determined error bars (more detail in Rivoldini et al., 2008a). The results are presented in Fig. 2. The span of the horizontal segments in the figure results from different parameter values and the two mantle mineralogies for a given core radius. The figure shows the plausible range of core radius for the two mantle mineralogies, for different crust densities and thicknesses, for different core sulfur fractions Xs (X-axis), and for a hot and a cold mantle (black and grey points in Fig. 2). Only completely liquid core models are represented in the figure. The figure shows that the mineralogy and the crustal thickness are not the most important driver for the sulfur concentration Xs and that there is a quasi-linear relation between the radius of the core and the sulfur concentration for a given moment of inertia. The results are also reported in Table 1.

1500 1400 0.00

0.05

0.10

0.15

xS Fig. 2. Core radius rCMB vs. sulfur concentration Xs for a range of values of moment of inertia, cold and hot mantle models, different crustal densities and thicknesses, and different mantle mineralogies. The mineralogies considered are the mineralogy of Dreibus and Wa¨nke (1985) and the mineralogy of Sanloup et al. (1999). The black points correspond to a hot mantle model and the grey points to a cold mantle model.

2.1.2. Core composition and size from nutation For a core radius of around 1500 km, the FCN has an inertial period close to 250 days (Dehant et al., 2000a, b). It ranges from 230 to 280 days for other values of the core radius (see Table 1). These values of the FCN are very close to the ter-annual nutation (Dehant et al., 2000a, b; Van Hoolst et al., 2000a, b), which can be strongly influenced by the FCN resonance. Fig. 3 presents the ratio between the amplitude of the nutations for a planet with a liquid core and the amplitude of the nutations for a rigid planet. This is called the nutation transfer function or the non-rigid Mars amplification factor. The closest to the FCN the nutations are,

Table 1 Interior models and geophysical parameters of Mars Core radius (km)

Mantle temperature

Scaled moment of inertia C/mara2 factor

Sulfur concentration Xs

Inner core

Love number k2

FCN

1300

Hot mantle Cold mantle

0.3648 0.3648

0.001 0.015

rICB ¼ 1291 km rICB ¼ 1191 km

0.100 0.093

261.5 173.7

1350

Hot mantle Cold mantle

0.3649 0.3650

0.017 0.035

rICB ¼ 951 km rICB ¼ 1071 km

0.102 0.098

256.7 231.8

1400

Hot mantle Cold mantle

0.3660 0.3652

0.037 0.054

No rICB ¼ 901 km

0.107 0.103

270.4 257.5

1450

Hot mantle Cold mantle

0.3662 0.3656

0.058 0.072

No rICB ¼ 571 km

0.113 0.108

263.7 261.5

1500

Hot mantle Cold mantle

0.3654 0.3661

0.072 0.093

No No

0.119 0.115

260.1 254.4

1550

Hot mantle Cold mantle

0.3657 0.3655

0.092 0.110

No No

0.125 0.120

254.5 250.7

1600

Hot mantle Cold mantle

0.3661 0.3658

0.116 0.133

No No

0.133 0.127

249.0 245.4

1650

Hot mantle Cold mantle

0.3654 0.3661

0.133 0.157

No No

0.139 0.134

246.0 240.8

1670 1700

Hot mantle Hot mantle Cold mantle

0.3661 0.3658 0.3655

0.136 0.158 0.174

No No No

0.143 0.148 0.141

242.7 241.5 238.3

1710 1740 1750

Cold mantle Cold mantle Hot mantle Cold mantle

0.3656 0.3650 0.3661 0.3658

0.164 0.168 0.187 0.200

No No No No

0.143 0.148 0.157 0.150

236.6 236.6 237.7 234.5

1770

Hot mantle Cold mantle

0.3653

0.191 422%

No

0.160

237.4

1800

Hot mantle Cold mantle

0.3655

0.216 422%

No

0.166

235.8

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DW prograde semi−annual retrograde annual retrograde semi−annual retrograde ter−annual retrograde quater− annual

amplification factor

0.4

0.2

0.0

0.2

0.4 500

0 T days

500

Fig. 3. Liquid core resonance effects on the nutation transfer function (liquid core amplification factor) minus 1 for different core dimensions and the mineralogy of Dreibus and Wa¨nke) as a function of the period T in days. Grey (for large core) and black (for smaller core) denote the limit obtained from the different extreme values of the tidal k2 Love number observed from spacecraft by Konopliv et al. (2006). The vertical lines indicate the Martian nutation frequencies. The figure shows two extremes in the range of liquid core dimensions and the corresponding FCN frequency changes on the transfer function.

the more they are amplified. The amplification factor given in Fig. 3 has been computed for the particular mineralogy of Dreibus and Wa¨nke (1985) and for different core dimensions ranging from 1500 to 1770 km. In order to obtain the non-rigid Mars nutation amplitude, it is necessary to multiply the rigid-Mars nutation amplitude with the amplification factor presented in Fig. 3. The largest nutation amplitude is the prograde semi-annual nutation whose frequency is not close to the FCN frequency; nevertheless, the perturbation of the nutational motion (of the order of 10 cm at Mars’ surface) by the resonance would be large enough to be observed by LaRa in its most accurate configuration with the help of the lander–orbiter link (see Fig. 3). Observing the nutations with LaRa will therefore settle the question about the physical state of the core. It must however be mentioned that this objective will be hard to attain if only the lander–Earth link is used. (It would require that LaRa operate over at least one Martian year and more. A new strategy for obtaining information on the state and size of the core for less than one Martian year has been studied and is presented in a paper in preparation (Le Maistre et al., 2008).) Additionally, the size (and the flattening) of the core has an influence on the resonance frequency (see Fig. 3, where the core size range is [1500, 1770 km], corresponding to the Konopliv et al. (2006) value of the k2 Love number as determined from spacecraft radioscience). Under the hypothesis of a hydrostatic shape of the core, one can estimate the size of the core and the density jump at the core–mantle boundary from observation of resonant amplification of nutation amplitudes (Van Hoolst et al., 2000b). For a mission lifetime of two Earth years, the expected precision in the FCN period determined using all the nutations will be about 15 days, corresponding to an equivalent precision on the core radius of about 100 km. The expected value of the FCN period obtained from simulations for the ‘‘nominal’’ case is far from the periods of the nutations. For closer resonances, the resonance effects will be larger as shown in Fig. 3 and the results on the core size will be more precise. In particular, for the k2 Love number of Konopliv et al. (2006), the core would be large and therefore the FCN period would be low, close to the retrograde terannual nutation, which will be enhanced. The numerical results are also reported in Table 1. For Mars, nothing is known about the existence of an inner core. There is nevertheless some support for the absence of an

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inner core from the study of thermal evolution, using knowledge of the remnant magnetic field and the absence of plate tectonics. The core could be either completely liquid (no inner core) or completely solid (very unlikely from thermal evolution studies and not favored by the recent Mars orbiter k2 values). All situations in between, even an almost completely liquid outer core (very small inner core) or an almost completely solid outer core (very large inner core), would also be possible. A large inner core can have an effect on the nutations that could be measured by LaRa: due to the existence of another resonance, the FICN, Free Inner Core Nutation, there would be amplification in the prograde band of the nutation frequencies. The main effect on nutation would be that the amplification of the largest prograde semiannual nutation due to a liquid core (to the FCN) would be canceled (Van Hoolst et al., 2000a; Dehant et al., 2003; Defraigne et al., 2003). Failure to detect the amplification of the semi-annual nutation with LaRa in its more precise configuration, together with the detection of a liquid core from the retrograde band of the nutations and from the k2 Love number, could then be interpreted as evidence for a large inner core. 2.1.3. Mars’ interior from polar motion Since polar motion and LOD variations are mainly excited by seasonal changes in the atmosphere and ice caps (see next paragraph), it will therefore be possible to learn about the seasonal variations in the atmosphere and ice caps from the LaRa data. Polar motion will also help in determining the global deformation of the mantle and the core (Dehant et al., 2003, 2006). Polar motion is the motion of the rotation axis in a reference frame tied to the planet; it is sometimes explained as the motion of the planet around its rotation axis. Mars’ polar motion contains seasonal effects of the atmosphere as well as a resonance with a rotational normal mode of the planet, the Chandler Wobble (CW), which is the natural wobbling of an oblate planet that does not rotate around its principal moment of inertia. The period and damping of this mode are very interesting since they are linked to the interior structure of the planet. The CW period depends mainly on the dynamical flattening of the planet and it provides information on the planet’s elasticity (a change from a rigid model to an elastic model affects the expected period at the level of 11 days), inelastic behavior (effect of up to 7 days), and the existence of a fluid core (at the level of 1.5 days) (Zharkov and Molodensky, 1996; Van Hoolst et al., 2000b; Dehant et al., 2006). However, since this mode is low frequency (close to 205 days; Van Hoolst et al., 2000b), it will be very difficult to get precisely the CW period and amplitude with only one lander, unless the lander operates on the surface for more than one Martian year. The combination of LaRa data with other lander data or orbiter data will help to better constrain this normal mode of Mars. One does not expect improvement in the polar motion determination using tracking data from one single lander located near the equator of the planet since in this case the sensitivity of the Doppler signal to the Polar motion is very small (Yseboodt et al., 2003). Improvement in polar motion will be possible with a lander network mission having some of the landers not on the equator. 2.2. Atmospheric effect on rotation The changes in the rotation speed with respect to uniform rotation can best be viewed by measuring the motion of a point on the equator over the seasons, which has an amplitude of almost 10 m. This effect will be the easiest one to observe with LaRa. The main part of the signal is due to moment of inertia changes

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induced by the mass redistribution. LOD variations can be estimated from general circulation models (GCM) (e.g., Defraigne et al., 2000; Van den Acker et al., 2002; using the GCM from Forget et al., 1995, 1998) and have been determined from Viking lander data (Yoder and Standish, 1997; Folkner et al., 1997) and orbiter radioscience data (Konopliv et al., 2006), although this estimation is rather difficult since the orbiter tracking data precision is at the level of the effect of LOD variations onto the orbiter motion. The estimated annual and semi-annual rotation angle amplitudes are 394 and 192 milliarcsec, respectively, in the study of Van den Acker et al. (2002) and are consistent with the observational values of Konopliv et al. (2006) within their uncertainties. While the annual and semi-annual LOD amplitudes estimated from lander and orbiter data are in very good agreement, they are inconsistent with the estimated seasonal fluctuation of the surface loads (GCM, MOLA and HEND data) (Karatekin et al., 2006b). The differences between atmosphere general circulation models with different atmospheric dust contents and dust storms are about one order of magnitude (at 10% level) larger than the expected accuracy of future DLOD measurements (at the percent level, DLOD refers to changes in the length of day) (Defraigne et al., 2000; Van den Acker et al., 2002). Winds are found to induce rotation angle variations with an amplitude of 14 milliarcsec for the annual period and 76 milliarcsec for the semi-annual period (Van den Acker et al., 2002). Since winds induce angular momentum changes and not gravity changes (reflecting mass changes), the joint use of LaRa observations (at the few milliarcsec precision level) together with the gravity coefficient variations allows identification of the different contributions to DLOD and could therewith better constrain atmosphere dynamic models and the mass exchange between the atmosphere and the polar caps due to the seasonal CO2 sublimation and condensation processes. It must be noted that one should observe at least one Martian year to be able to estimate both the annual and semi-annual contributions to DLOD. Due to the high precision that will be obtained on the obliquity and precession rates, LaRa results will also be crucial for assessing the past climate of Mars and the evolution of the polar ice caps as explained in Section 1.

with nominal values (predicted values) calculated by nominal Earth and Mars rotation and orbital revolution models. The raw data directly recorded by the receiving system (level 1a) will be translated into a format that can be more easily handled (level 1b). Calibrated data (Level 2) will be processed from Level 1 using models for the Earth’s atmosphere and ionosphere and the orbits of Mars and Earth to compute a predicted received frequency. The Level 2 file contains information on the time of measurement in UTC and ephemeris time, the received carrier frequency, the predicted carrier frequency, the frequency residual, etc. The calibrated Doppler data (Level 2) will be fitted with a modified version of the software already developed to analyze the Viking and Pathfinder lander Doppler data, and that is presently used for working on the stable MER (Mars Exploration Rover) Doppler data at the Royal Observatory of Belgium (software called GINS/Dynamo) and JPL (software called the Solar System Dynamics Processing Software (SSDPS)). GINS stands for ‘Ge´ode´sie par Inte´grations Nume´riques Simultane´es’. This software has been developed at Observatoire Midi-Pyre´ne´es/CNES and has been adapted to the planet Mars by the Royal Observatory of Belgium for the preparation of the NEtlander Ionosphere and Geodesy Experiment (NEIGE) within the Netlander CNES mission and for the analysis of the MEX radio science data. The data will be processed continuously as acquired, with final estimates of the geophysical parameters and the other parameters one year after the end of the Humboldt Payload/ExoMars mission. A Belgian industrial firm, Orban Microwave Products (OMP), has been identified as being able to build the X-band transponder. OMP is presently working on a prototype that will be delivered in a few months for a Preliminary Design Review (PDR) (November 2008). The design and the link budget of the instrument have already been studied. The planned design is the following: an Xband uplink at 7.15 GHz and an X-band downlink at 8.4 GHz. The radio link provided by LaRa will be further complemented by a radio link between the lander and the orbiter for the telemetry and the telecommands (TMTC) in UHF (it was called SMarT, for

3. LaRa measurements and strategy The LaRa instrument is a coherent transponder using one uplink and one downlink in X-band and is proposed for the Humboldt Payload (on the fixed platform lander) of the ExoMars ESA mission. There is a corresponding ground segment in the experiment since the signal is observed by the DSN ground stations as well as by the ESA tracking stations of the ESTRACK (ESA TRACKing) network. One other complicated part of the experiment is the analysis of the data, which will be done using dedicated software built for the determination of the variations in lander position as a function of time. LaRa transponds a signal transmitted from the Earth ground stations back to the Earth. The Doppler effects from the motion of the Martian lander with respect to the Earth stations are measured at these ground stations on Earth. The ground-based reference for the Doppler is the same one that drives the transmitter. The observations are called ‘‘two-way’’. The LaRa data thus consist of Doppler shifts of the radio signals transmitted by the ESA and NASA Earth ground stations to the ExoMars lander and re-transmitted coherently by the transponder LaRa back to Earth. The Maser frequencies from the ground stations ensure the stability of the LaRa reference frequency. The required precision on the Doppler for LaRa is 0.1 mm/s at 60 s integration time. The data will be validated by comparing the observed Doppler values

Fig. 4. LaRa X-band link from the lander to Earth, UHF radio link (in practice incorporating TMTC (TeleMetry & TeleCommand)) from the orbiter to the lander, and X-band link from the orbiter to the Earth ground stations.

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Small Martian Transponder, in the Netlander mission). Fig. 4 represents all the radio links for the ExoMars lander. They incorporate a lander–Earth link in X-band, an orbiter–lander link in UHF, and an orbiter–Earth link in X-band. The Doppler measurements will be used to deduce the position and velocity of the lander in space as a function of time. The signal will be used to reconstruct the position and velocity of the lander with respect to the Earth. Knowing the orientation and rotation of the Earth in space at the centimeter level thanks to very long baseline interferometry (VLBI) measurements, it will be possible to reconstruct the orientation and rotation of Mars in space. The data processing is one of the most important parts of the experiment. The interpretation of the data in terms of the physics of the interior of Mars and of its atmosphere will be done using software developed at ROB in collaboration with IPGP, CETP, and Nantes University, based on the synergism between the geodetic, magnetometer, and seismic data (see e.g., Verhoeven et al., 2005). The Doppler measurements are performed from Earth using the ground station equipment (ground segment) at the ESA or NASA large deep space antenna complex without modification.

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However, the bandwidth of the transponder will not be very large and will require adapted uplink frequency changes. This means ramping or equivalent frequency shift at the NASA DSN stations and frequency shift during tracking at the ESA stations. There exists a procedure in the NASA DSN ground stations to tune or ramp the uplink to pre-compensate for the Doppler shift on the uplink and aim within a narrower receiver bandwidth. Nonconstant uplink is by now a proven standard procedure for many missions and one can be satisfied with the quality of the data for navigation. The coherency between the uplink and the downlink allows determination of the Doppler shift induced by the lander motion at the surface of Mars relative to Earth, without contamination of instrumental delay; it also ensures that the Doppler shift is not contaminated by the frequency instabilities of the generated signal. The plasma and ionospheric noise on the received radio signal will be small enough to be either ignored or corrected by appropriate models for the ionospheres of Mars and Earth, when the observations are not too close to solar conjunction (solar elongation angle 4201). We discuss this in Section 5.

Fig. 5. Precision achieved on geophysical parameters (core momentum and FCN period) and Mars orientation and rotation parameters (precession, rotation rate, and polar motion components) as a function of mission lifetime based on simulations of a lander–Earth radio link for a noise of 0.1 mm/s at a 60 s integration time.

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7 7 5 3 1 1 0.7 0.5 a

The orbiter–Earth link in addition to the lander–Earth does not help the determination of precession; here we present simulations for different initial value of precession.

7 7 5 5 5 3 1 1 8 6.6 5.2 3.8 2.4 1 1 1 8 7.7 7.3 7.0 6.7 6.3 6 5.7 8 7.9 7.8 7.7 7.6 7.5 7.5 7.5 8 8 8 8 8 8 8 8 22 13 5 5 5 3 2 2 35 31 29 27 23 19 14.5 10 7000 1000 100 70 70 60 15 5 50 44 38 32 27 21 15 10 50 49 48 47.5 47 46 45 44 30 27.4 26.2 25 23.8 22.6 21.4 20 30 29 28 27.5 27 26 25 25 0 100 200 300 400 500 600 1 yr

Lander–Earth link With orbiter–lander link Lander–Earth link With orbiter–lander link Lander–Earth link Lander–Earth link and with orbiter–lander linka With orbiter–lander link Lander–Earth link With orbiter–lander link

Rotation time (ms) Chandler polar motion (cm) Annual polar motion (cm) Precession rate precision (milliarcsec/ year) FCN period precision (days) Mission Core momentum (%) lifetime (days)

We now discuss the precision that LaRa will achieve on the Doppler measurements. It is at the level of 0.1 mm/s at a 60 s integration time if the solar elongation angle is 4201 as required in the LaRa strategy. This precision has been used for LaRa simulations (method presented in Yseboodt et al., 2003) performed in conjunction or not with the lander–orbiter radiolink. The main simplifications used in the simulations are neglect of the propagation effects (ionosphere and atmosphere), assumption that the lander position is determined by observing from Earth for a period of a couple of weeks just after landing, neglect of nongravitational forcing and wheel desaturation on the spacecraft, and neglect of imperfections in the static gravity field for the radio links with the spacecraft. Fig. 5 shows the precision on the different geophysical parameters measured by the radioscience experiment as a function of mission lifetime. The figure represents the evolution of the uncertainty (or precision) on the parameters determined from simulated data (value fitted to the simulated observations minus the starting ‘real’ value or nominal value used in the data simulation) as a function of mission lifetime. These parameters are the FCN period, the ‘core momentum’ corresponding to the FCN resonance amplification factor in the nutation amplitudes, the precession rate, the annual and Chandler components of polar motion, and the rotation time. The noise considered on the simulated data is of the order of 0.1 mm/s at 60 s. The precision on the determination of the parameters is also reported in Table 2. The precision obtained using a lander–orbiter link in addition to the Earth–lander link is also reported in this table. The precession rate and rotation time are the best determined parameters if the mission lifetime is small (if no mission extension). After one Martian year, however, the FCN period would be determined with a precision of about 10 days. The period could be even better determined if the core is large, since the FCN period will be closer to the ter-annual retrograde nutation and thus provide high amplification. The present precision on the precession rate is 17 milliarcsec/ year (Konopliv et al., 2006). LaRa will improve the precession rate estimate by an order of magnitude after one Martian year (see Fig. 5 and Table 2). The resulting improved moment of inertia accuracy from LaRa will tightly constrain the core size and eliminate many possible core compositions, as discussed in Section 2. In addition, the measurements of the nutation of Mars will determine whether the Martian core is fluid and, if the FCN resonance is close to one of the periods of the nutation, provide further constraints on the core density and size. However, if the FCN is not very close to one of the nutation periods, it will be difficult to observe if the mission lifetime is not more than one Martian year. The determination by LaRa of a free rotational oscillation of the planet similar to the Chandler Wobble in the Earth’s polar motion will yield independent constraints on the core size and density and on the elastic and inelastic behaviors of the mantle. Our simulations have shown that the Chandler Wobble can be detected if its amplitude is at the decimeter level or above. The seasonal polar motion components could be more difficult to determine from the LaRa lander–Earth link only (see simulations performed with an additional lander–orbiter link for a better determination). The present error on Mars’ rotation is a few ms (Konopliv et al., 2006) larger than the simulation results for LaRa of about 1 ms after about 500 days. Accurate LaRa measurements of seasonal LOD variations will thus provide detailed global information on the general circulation of the atmosphere and constrain the sublimation/condensation cycle of the polar caps.

Table 2 Geophysical parameters (core momentum and FCN period) and orientation and rotation parameters (precession, rotation rate, and polar motion components) of Mars as a function of the mission lifetime

4. Simulations

With orbiter–lander link

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Lander–Earth link

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The discussion presented here is based on a mission lifetime of 180 days as well as one Martian year, but the longer the lander operates on the surface of Mars, the more precise will be the determination of the geophysical parameters. The addition of a lander–orbiter link will improve the solutions for the geophysical parameters. A classical UHF radio link is foreseen, since the Humboldt Payload will be equipped with such a transponder for TeleMetry and TeleCommand (TMTC). Simulations similar to those for which the parameter uncertainties are determined in Fig. 5 and for a lander–orbiter link are presented in Fig. 6. The numerical values are also reported in Table 2. For these simulations we have considered a precision of 0.1 mm/s at a 60 s integration time as shown by the error budget at this frequency (Barriot et al., 2001) and as used for Fig. 5, a quasi-polar orbit at 550 km altitude, and an almost-equatorial lander. In that case, the parameters of the core will be well constrained. Combining the lander–Earth radio link with LaRa and the lander–orbiter and orbiter–Earth links will greatly help in the determination of the core parameters. The FCN period will be better determined (at the level of 10 days) for the nominal case. In the simulations, the orbiter is assumed to have a quasi-polar orbit. Such an orbit is ideal for the determination of the core effects on the nutations and the LOD variations, but it is not well adapted to the determination of polar motion, given that the lander is at an equatorial latitude. The CW will, however, be better determined, which might in this case be used for constraining the elastic properties of the planet. The precision on the precession rate and the rotation time will gain a factor 2 with respect to the case which uses the direct link only. As shown in Fig. 6, additional parameters must be considered in the simulations in order to account for the J2 and DJ2 effects on

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the orbiter motion. Not only are the precession rate and the LOD variations well determined, but so are the FCN parameters. It must be noted that the simulations have been performed for the nominal value of the core parameters, i.e., for a mean core radius of about 1500 km. In these simulations of the lander–orbiter link, we did not take into account the effects of the perturbing forces acting on the orbiter motion such as those induced by the orbiter angular momentum desaturation typically occurring once per day. Nevertheless, Rosenblatt et al. (2004) have shown that these effects should not significantly degrade the determination of the geophysical parameters, given that the orbiter could be tracked quasi-continuously from the Earth, especially when these perturbing events occur. The precision of this additional link might, however, well be affected by multipath effects, which would increase the noise level and degrade the solutions. An additional X-band link between the lander and the orbiter would avoid these problems, but the present designs of the existing orbiters do not support this. Without X-band for the lander–orbiter link, precisions similar to those in Fig. 6 could be obtained by observing longer. Simulations not shown here have led to the conclusion that the noise level impact on the retrieval of the parameters is similar to the mission lifetime effect: an increase of the noise level by a factor of two may roughly be compensated by an increase by a factor of two in the mission lifetime.

5. Instrument description The instrument consists of electronics for the transponder, a cable (or two) connecting this to the patch antenna(s) (fixed on

Fig. 6. Precision achieved on geophysical parameters (core momentum and FCN period), Mars orientation and rotation parameters (precession, rotation rate, and polar motion components), and first gravity field coefficients (J2) and its annual time variations (DJ2) as a function of mission lifetime based on simulations of a lander–orbiter radio link for a noise of 0.1 mm/s at a 60 s integration time.

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the lander), a cable connecting this to the command and data management subsystem (CDMS), and a cable connecting this to the power control and distribution unit (PCDU) as shown in Fig. 7.

The transponder electronic part has a dimension of 120  120  30 mm3 and the total weight is estimated at 600 g (200 g margin) including the antenna(s). 5.1. Characteristics of the transponder electronics Fig. 8 shows the plans for the transponder receiver and the transmitter. Two different designs can be considered, since the industry is presently studying the possibility of skipping the duplexer and replacing the antenna by a dual-band antenna (this adds a cable only). The transponder presented in these figures has a simple design. The schematics shown are classical and the circuits are typical for a spacecraft transponder. 5.2. Characteristics of the X-band antenna

Fig. 7. LaRa instrument design onboard the lander; the Rx/Tx is the receiver and the transmitter of LaRa; the PCDU is the Power Control and Distribution Unit; the CDMS is Command and Data Management Subsystem; and the TCU is the Thermal Control Unit.

We have studied the direction of the line-of-sight of the Earth in the lander sky to find the optimum design of the antenna. Fig. 9 shows the elevation angle of the line-of-sight of the Earth in the sky of the lander with respect to the horizon of the lander. The form of this area depends on the initial conditions of the mission but repeats every 2.13 years (the synodic period). The

Fig. 8. Diagram of the transponder transmitter and receiver with a duplexer. The acronyms are defined in the acronym table at the end of the document. The signal is received by the antenna at the X0 frequency; it is transmitted to the transponder after passing through a duplexer; it is amplified by a low noise amplifier (LNA) and goes in the coherent down-converter (using a voltage-controlled oscillator (VCO) and an automatic gain control (AGC)); it is then multiplied in order to account for the transponder ratio k (the ratio between the output frequency X and the input frequency X0); it then goes in the coherent up-converter and into a high power amplifier (HPA) and a filter; it is then sent back to Earth via the antenna. DC/DC stands for direct current/direct current converter; the PCDU is the power control and distribution unit; the CDMS is command and data management subsystem.

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influenced by the fundamental frequency coming from the oscillator (VCO) in a non-coherent mode and allow monitoring of the behavior (aging) of the VCO or serving as a check for any problem related to locking of the frequency by the LaRa transponder. If possible (but not absolutely necessary), the tracking should be performed at the time of the Martian day when the line-of-sight of the Earth antenna is at an elevation of about 30–401 (better LaRa antenna gain). The ground stations should be turned on before the lander LaRa transponder in order to account for the travel time of the signal (typically 20 min). A measurement cycle will consist of the following operations:

Earth elevation in the sky of LaRa landing area at 20 degrees of north latitude

90 80

Elevation angle (degree)

70 60 50 40 30 20 10 0 2013

2013.5

2014

2014.5

2015

2015.5

2016

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2016.5

2017

date in fraction of year Fig. 9. The area represents the elevation angles of the Earth in the sky of the lander for 4 years as a function of time during the ExoMars mission.

horizontality of the lander can also be accounted for in this computation. Generally speaking, there is sometimes a zone of blackout during the mission near the lander zenith. Moreover, observations close to the horizon must be avoided because of possible perturbations from the atmosphere of Mars. It is thus preferable to have a design of the antenna with optimal antenna gain centered on an elevation of about 30–401. The size of the antenna is quite small, o130 mm in diameter, and its mass is very small as well, about 125 g (25 g margin). As a result, the antenna diagram could be based on a torus concept in which the main lobes concentrate the energy favoring a reception in the elevation range between 301 and 401. 5.3. Power and energy budgets In the ‘‘transponder on’’-mode, the expected power that will be used by LaRa is 20 W (margin 5 W) for 45 min to 1 h communication with the Earth once per week for at least one Martian year. Thus, the energy consumption of LaRa is very low. In this strategy, the mission lifetime has been favored instead of the number of passes per week. In other words, if a choice must be made, it is preferable to have a longer series of measurements and less passes per week (one pass per week instead of two) than the other way around.

6. Instrument performance and expected results The transponder design will maintain the coherency of the signal, and the global precision on the Doppler is expected to be better than 0.1 mm/s at a 60 s integration time (compared to the Doppler precision of Viking: 1 mm/s, of Pathfinder: 0.15 mm/s, and of the MERs: 0.1 mm/s over 60 s integration time). After landing, the transponder will be operated when an Earth ground station is available and when the Earth is in the sky of the lander. The position of the lander will be determined with the first passes during commissioning. After this, it is expected that LaRa will operate once or twice per week at least during the whole mission lifetime. No operation is required at solar conjunction and for a solar elongation angle o201. The transponder should be turned on a few minutes before it receives the uplink signal from the ground station. This will permit reception of a signal

1. Emit the uplink signal from the ground station. 2. Turn on the transponder a few minutes before reception of the uplink signal; reception of this signal on Earth will provide the status of the oscillator or the transponder within LaRa. 3. Receive the ground station signal at the lander, apply the transponder ratio, and transmit the signal coherently back to Earth at the downlink frequency (LaRa operating configuration); the same ground station as the emitting station should be listening to the signal from Mars. 4. Turn off the transponder. The 70 m antennas of the DSN are preferred for a better link budget. This is particularly true when the Earth–Mars distance is large. A longer mission lifetime facilitates the achievement of our objectives. In the favored strategy for LaRa, we expect measurements once per week for at least one Martian year. Non-signal disturbances in a Doppler link are due to instrumental noises (random errors introduced by the ground station or the lander), propagation noises (random frequency/phase fluctuations caused by refractive index fluctuations along the line-ofsight), or systematic errors. Instrumental noises include phase fluctuations associated with finite signal-to-noise ratio (SNR) on the radio links, ground and lander–transponder electronics noise, unmodeled motion of the ground station, frequency standard noise (ground standards for a two-way radio link), and antenna mechanical noise (unmodeled phase variation within the ground station). Propagation noise is caused by phase scintillation as the radio wave passes through the troposphere, ionosphere, and solar plasma (for a complete discussion of the noise contribution, see Asmar et al., 2005). The most important remaining Doppler error sources include thermal noise (Sniffin et al., 2000), solar plasma (Dobrowolny and Iess, 1986; Iess and Boscagli, 2001; Iess et al., 2003; Morabito et al., 2003; Garcia et al., 2004), ionosphere, troposphere, and ground station delay uncertainty. We have carefully examined all the error contributions and their levels, Table 3 Error contributions to the Doppler shift (worst cases) Error sources

Level on the Doppler at 60 s integration time; in mm/s

Thermal noise of the transponder (from LaRa link budget given below) Solar plasma effects at 201 and 301 elongation starting from an evaluation of the solar plasma from the formula given in the DSN Handbook 810 (less for larger solar elongation angles) Ionosphere effects (including scintillations) Remaining troposphere at 301 elevation angle after dry troposphere corrections from model explaining 90% of the effect: from 0.060 to 0.006 Ground station Total root mean square

0.024 0.056 and 0.039

0.019 0.006

0.040 0.075 and 0.064

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considering as reference the results from Zuber et al. (2007). Table 3 shows the summary of our study. Observations should be performed at times far from solar conjunction (at a solar elongation angle larger than 201) in order to avoid the plasma effects on the signal. The known ionospheric effects are very small in X-band but may be corrected by using models of the ionospheres of Mars (Trotignon et al., 2000; Witasse et al., 2002; Pa¨tzold et al., 2005) and of the Earth. Ionosphere models for the Earth used for GNSS applications are, for example, the Klobuchar model (Klobuchar, 1986) or the NeQuick model. The ionospheric scintillation effects are shown in the table and may be considered as sporadic, irregular, and unpredictable events. They will be the largest contributions to the noise. Concerning the troposphere, the dry component of the tropospheric delay may be estimated from a model; this corresponds to 90% of the tropospheric effect; it depends mainly on atmospheric pressure on the Earth’s surface and therefore it is easy to account for from a model of the so-called standard atmosphere (Hugentobler et al., 2001). The remaining 10% of total tropospheric delay, the wet component, depends on the water vapor in the Earth’s atmosphere and it is difficult to model without water vapor radiometer measurements. The figures in Table 3 thus constitute very large extremes and a value of o0.1 mm/s seems more reasonable. On the basis of the demonstrated performances of telecom systems in previous and ongoing missions (Tyler et al., 2001; Zuber et al., 2007), the Doppler accuracy is even better than that. It is at the level of 0.02 mm/s for the MRO spacecraft, for example (Zuber et al., 2007). Additionally, working with the ‘‘Open Loop’’ technique (with adequate digital signal processing) instead of ‘‘Close Loop’’ may help to reduce these numbers further. The error budget of the uplink and downlink is shown in Tables 4 and 5 for a large Mars–Earth distance at 201 elongation (352 Mkm) and a 70 m antenna. Light grey indicates the intermediate elements considered in the sum for the total budget contribution. Grey indicates the final results. The error budget of the uplink and downlink is shown in Tables 6 and 7 for a mean Mars–Earth distance (150 Mkm) and a 34 or 35 m antenna

Table 4 Uplink budget (italics indicates what is considered for the intermediate sub-total; bold indicates the final result) For a transmit frequency of 7.15 GHz (from ground station) we give below the necessary data to compute the link budget

Effect

Transmitter output power Transmitter antenna gain EIRP Free space path loss (for 352 Mkm Earth–Mars distance) Received carrier power density System noise temperature (Te) Receiver noise power Receiver antenna gain (G) Receiver wave guide loss Atmospheric attenuation Receiver G/Te C/N0 Noise bandwidth C/N (carrier-to-noise ratio)

43 72.6 115.6 280.4 167.8 745 200 6 1 2 23.7 38.2 20 25.2

Table 5 Downlink budget (italics indicates what is considered for the intermediate subtotal; bold indicates the final result) For a transmit frequency of 8.45 GHz (from lander) we give below the necessary data to compute the link budget

Effect

Unit

Transmitter output power Transmitter antenna gain Transmitter cable loss EIRP Free space path loss (for 352 Mkm Earth–Mars distance) Received carrier power density System noise temperature (Te) Receiver noise power Receiver antenna gain (G) Receiver wave guide loss Atmospheric attenuation Receiver G/Te C/N0 Noise bandwidth C/N (carrier-to-noise ratio)

4.8 6 1 9.8 281.9 274.5 28 214.1 74 0.45 2 59.1 13.6 3 8.8

dBW dB dB dBW dB dBW K dBW/Hz dB dB dB dB/K dB-Hz Hz dB

Case of a 70 m antenna and a maximum Earth–Mars distance; worse case for all the other parameters.

Table 6 Uplink budget (italics indicates what is considered for the intermediate sub-total; bold indicates the final result) For a transmit frequency of 7.15 GHz (from ground station) we give below the necessary data to compute the link budget

Effect

Unit

Transmitter output power Transmitter antenna gain EIRP Free space path loss (for 150 Mkm Earth–Mars distance) Received carrier power density System noise temperature (Te) Receiver noise power Receiver antenna gain (G) Receiver wave guide loss Atmospheric attenuation Receiver G/Te C/N0 Noise bandwidth C/N (carrier-to-noise ratio)

43 67 110.0 273.0 166 745 200 6 1 2 23.7 40 20/3000 27/5.2

dBW dB dBW dB dBW K dBW/Hz dB dB dB dB/K dB-Hz Hz dB

Unit Case of a 34 m antenna and an Earth–Mars distance of 150 Mkm; worse case for all the other parameters. dBW dB dBW dB dBW K dBW/Hz dB dB dB dB/K dB-Hz Hz dB

Case of a 70 m antenna and a maximum Earth–Mars distance; worse case for all the other parameters. The units in the tables are dB, which stands for Decibel (10 log10 DP/P or 10 log10 Df/ f), and dBW, which stands for Decibel Watt (ratio of a power to one Watt expressed in Decibels). EIRP, effective isotropic radiated power. C/N0 means carrier-to-noise power density (ratio of the power level of a signal carrier to the noise power in a 1-Hz bandwidth) and is given in dB; C/N means carrier-to-noise ratio, also given in dB.

(we only quote 34 m in the text below but this is true for the 35 m antenna of ESA as well). The units in the tables are dB, which stands for Decibel (10 log10 DP/P or 10 log10 Df/f) and dBW, which stands for Decibel Watt (ratio of a power to one Watt expressed in Decibels). The overall carrier-to-noise (C/N) ratio is the measure of effectiveness of the communications system. This link budget can be considered as performing well if the C/N is greater than a few dB. This is the case for both the uplink and downlink budgets.

7. Impact of instrument’s science for planning mission operations LaRa uses NASA and ESA ground stations. The operation of LaRa is therefore dependent on the availability of the ground stations and the visibility of the lander from the ground stations. Changes in the uplink frequency must be performed at the ground stations in order to be within the bandwidth of the LaRa transponder. This must be computed a priori according to the relative position

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Table 7 Downlink budget (italics indicates what is considered for the intermediate subtotal; bold indicates the final result) For a transmit frequency of 8.45 GHz (from lander) we give below the necessary data to compute the link budget

Effect

Unit

Transmitter output power Transmitter antenna gain Receiver wave guide loss EIRP (effective isotropic radiated power) Free space path loss (for 150 Mkm Earth–Mars distance) Received carrier power density System noise temperature (Te) DSN/ESA Receiver noise power

4.8 6 1 9.8 274.5 267 29/70 214/ 210 68.2 0.25 2 53.3/ 49.5 15.2/11.2 3 10.4/6.4

dBW dB dB dBW dB dBW K dBW/Hz

Receiver antenna gain Receiver wave guide loss Atmospheric attenuation Receiver G/Te C/N0 Noise bandwidth C/N (carrier-to-noise ratio)

dB dB dB dB/K dB-Hz Hz dB

Case of a 34 m antenna and an Earth–Mars distance of 150 Mkm; worse case for all the other parameters.

between the lander and the ground station. The antennas must be chosen according to the geometry of the measurement. The criteria to consider are the following: (1) Lander tracking from Earth should be performed when the lander can be seen from Earth. (2) Tracking should be performed twice per week (possibly once per week during winter energy problem period) for at least one Martian year; a longer mission lifetime is preferred to more observations per week. (3) Tracking should be performed at the time of the Martian day when the line-of-sight of the Earth antenna is at an elevation of about 30–401 (better LaRa antenna gain and better sensitivity to the precession, nutation, LOD variations). (4) If possible, tracking should be performed roughly simultaneously with respect to the lander–orbiter TMTC transfer with UHF (this allows determination of one common set of parameters for both measurement sets, with no maneuver of the orbiter between the measurements, as explained in the next section); the orbiter should be tracked as often as possible and in particular when maneuvers are performed in order to constrain the orbit very well (see synergy part). (5) No observation at conjunction is foreseen when the elongation angle is lower than 201 in order to avoid a large plasma contamination to the signal. (6) Observation at large Earth–Mars distance should be performed with the 70 m antennas if the classical bandwidth of 5000 Hz is retained; there is no constraint on the antennas if the narrow bandwidth option is retained; observation at mean and short distances can be performed with any of the antennas (34 or 70 m antennas); nevertheless, for link budget reasons, it is always better to use the DSN 70 m antenna. As complementary data, the UHF link with the relay orbiter may be used for further scientific objectives as explained above. The same kinds of visibility conditions between the lander and the orbiter and between the orbiter and the Earth must be applied and are important for planning the mission. It is also desirable to have tracking of the orbiter for a long time (one orbit) without any maneuvers in order to obtain the parameters of the spacecraft orbit and to be able to obtain the other geophysical parameters

1063

(but this is known and already applied for the spacecraft radio science objectives). It is preferable (but not absolutely necessary) to have the UHF radio link almost simultaneously (at 1-day interval or so in order to avoid maneuvers of the orbiter in between the measurements) with the X-band LaRa link with the Earth. The operation of LaRa requires that (1) the Earth is seen in the lander sky or similarly the lander can be tracked from Earth and that (2) one of the ground stations is available for the tracking. For operation of LaRa, the available power supply should be able to maintain 20 W of power during the whole tracking period (about 45 min).

8. Relation to other Humboldt instruments and to the orbiter (science complementarities) 8.1. Synergy with the other Humboldt instruments One main objective of the LaRa experiment is to contribute to the determination of the mineralogy, temperature, and state of the deep interior of Mars, complementing information provided by seismology, tides, heat flow measurements, and magnetic induction measurements. Combination of the geodetic data (moment of inertia of the planet, tidal deformation, gravity, rotation and orientation variations) with other observations from the geophysical Humboldt package of ExoMars (seismology, heat flow, magnetic induction) allows us to solve for the temperature and mineralogy of Mars’ deep interior, as shown by Verhoeven et al. (2005) using a Bayesian approach. [In this paper, it is demonstrated that it is possible to provide the temperature and mineralogy profiles, by using a Bayesian approach, as the most probable values in agreement with future observations and with existing laboratory experiments.] The mineralogy and temperature of the deep interior will provide key information on the accretion of the planet, and, more generally, can be used to test theories of terrestrial planet accretion and thermal evolution. These objectives are high-priority items in the roadmap for solar system exploration. The contribution of radioscience to Mars’ interior structure will derive from the interior’s effect on variations in the rotation and orientation of Mars with respect to inertial space. LaRa is the only Humboldt Payload instrument to determine the moments of inertia and angular momentum transfers among the different parts of Mars (core, mantle, and atmosphere). But it is only by using LaRa jointly with other Humboldt Payload instruments that the ultimate goal of determining the mineralogy and temperature profile of Mars will be reached. Presently, as explained in the introduction of the paper, the composition, thermal state, and dynamics of Mars’ interior are poorly constrained. For example, the state, the size, and the composition (percentage of light element) of the core are important remaining questions. The global constraints from the moment of inertia and tidal Love number k2 provided by geodesy (Folkner et al., 1997; Yoder and Standish, 1997; Lemoine et al., 2001; Yoder et al., 2003; Konopliv et al., 2006; Marty et al., 2008) only provide constraints on the mineralogy constituents, the mineralogical phase transitions, and the temperature profile of the whole planet. The magnetometer, the seismometer, the heat flow and physical properties probe, and the geodesy experiment of the Humboldt Payload will provide additional important data: electrical conductivity, seismic velocity, heat flow, and moments of inertia. By means of a sophisticated approach based on a stochastic inversion of such geophysical data (within uncertainty ranges for the laboratory experiment data and for the observational data) we will be able to compute temperature and composition profiles of

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Mars’ interior. This method has been demonstrated on simulated data (Verhoeven et al., 2005) and validated for the Earth (Verhoeven et al., 2008) and Mars (Rivoldini, 2008). The geodetically measured value of the k2 Love number, further improved by the lander–orbiter–Earth radio links, can be jointly used with the SEIS (define) tidal output to constrain the interior modeling from tides.

called lumped coefficients. With a single orbiter, these lumped coefficients can be derived from radio science experiments. To disentangle the coefficients, a combination of observations from different orbiters with different orbit characteristics is very promising (see Karatekin et al., 2005). The calculations of Chao and Rubincam (1990) showed that the time variations of the gravity field could be large enough to have a measurable effect on the orbit of a spacecraft around Mars. The low-degree zonal coefficients of the Martian time-variable gravity field have been determined from the tracking data of the MGS spacecraft by Smith et al. (2001), Yoder et al. (2003) and most recently by Balmino et al. (2006); see also (Duron, 2007; and Marty et al., 2008) and from MGS and Odyssey by Konopliv et al. (2006). The perturbation of the orbit due to the time-variable gravity field is at the limit of detectability and the reported coefficients (‘‘lumped’’ gravity coefficients) contain the influence of higher-degree zonal coefficients, since they were obtained from the tracking data of a single spacecraft or two spacecraft with similar orbits. Nevertheless, the present-day time-variable gravity solution yields seasonal mass variations in reasonable agreement with numerical (GCM) and experimental (gamma ray spectroscopy) studies (Karatekin et al., 2006a), but it does not yet have the desired accuracy to discriminate among different models of the seasonal CO2 cycle. Time-variable gravity solutions can be significantly improved by considering the additional lander–orbiter radio link. Simulations (Karatekin et al., 2006b) have shown that a large decrease of the formal uncertainty of some of the low-degree gravity coefficients (by a factor 10) can be expected if this additional link is considered. The strategy foreseen is to determine both the gravity coefficients and the LOD variations. These geophysical quantities are both related to the CO2 sublimation and condensation process but, while the seasonal gravity variations are related to the mass transfer, the LOD variations also contain wind effects. The observation of both therefore provides complementary information.

8.2. Synergy with the UHF TMTC (at system level) and the relay orbiter The use of a lander–orbiter link in addition to an orbiter–Earth radio link greatly helps the determination of the orbiter trajectory and the parameters involved in the forces acting on the spacecraft, as shown by simulations performed by Karatekin et al. (2005). The joint use of an UHF link for this lander–orbiter link therefore provides additional science return. The joint use of LaRa and the UHF TMTC together with the orbiter–Earth radio link will further increase the precision on all parameter determinations, and hence will allow improvement of mission objectives. In particular, the lander–orbiter link helps the determination of a precise orbit for the spacecraft and therewith the determination of the orbitrelated geophysical parameters such as the gravity coefficients and their time variations or the tidal Love number k2, as discussed above. 8.2.1. Global atmosphere CO2 in the Martian atmosphere condenses and sublimes on seasonal time scales, resulting in large mass exchange between the atmosphere and surface. Since this mass redistribution is on a global scale, it mainly affects the long wavelength components of the gravity field. The exchange involves about one-fourth of the total mass of the atmosphere and induces relative gravity changes on the order of 109, which can be compared with the secondorder gravity field coefficient J2 ¼ 0.00195545 (Lemoine et al., 2001). This signature can be detected in the orbit parameters, and the variations in the lowest-degree zonal gravity coefficients have been determined (Smith et al., 2001; Yoder et al., 2003; Karatekin et al., 2005; see also Balmino et al., 2006). The induced changes in the orbit of a spacecraft are due to a linear combination of the odd coefficients and a linear combination of the even coefficients,

8.2.2. Tidal Love number k2 Similarly, the addition of a lander link to the orbiter–Earth link will greatly help to better determine the k2 tidal Love number and hence better constrain the interior modeling of Mars.

MGS+O D.2007

IAG3 B.2005

O D.2007

MGS D.2007

IAG4 B.2005 IAG2 B.2005

IAG1 B.2005

OT6 K.2006

OT5 K.2006

OT4 K.2006

OT3 K.2006 OT1 K.2006

MGS S.2001

solid core

0.10

0.05

MGS+O MGS95J K.2006

O K.2006

k2

0.15

MGS+GCO+PF+Vi K.2006

MGS Y.2003

0.20

Fig. 10. Values of the k2 tidal Love number from different radio science data. The ‘‘K2006’’ values are those of Konopliv et al. (2006); we have used the nomenclature introduced in that paper; for the ‘‘IAG1-4B2005’’, we have used the four values in the table of Balmino et al. (2006); for the MGS/O/MGS+OD2007, we have used the values computed with MGS, Mars Odyssey, and the combination of both presented at AGU2007 (Duron et al., 2007). The theoretical value of about 0.07 corresponds to a solid core and a value between 0.1 and 0.17 indicates a liquid core; the light grey area is for a warm mantle model and dark grey for a cold mantle model.

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The tidal Love number k2 value with associated uncertainties has been obtained by using radio links between orbiters around Mars and the Earth (see Fig. 10). The value of the tidal Love number k2 from MEX alone is not reported in the figure as it has too large error bars due to the discontinuity in the tracking of the orbiter. Combinations of data from all spacecraft that have been or are orbiting around Mars look very promising. It must be mentioned, however, that the strategy of data treatment is of great importance in this determination, as shown in the figure, where the same data treated by different authors give different k2 values. A recent redetermination of the k2 Love number from the same data as those used by Konopliv et al. (2006) indeed confirms differences in k2 at the 10% level (Marty et al., 2008). Continuous use of well-tracked orbiters will however further increase the precision of this determination in conjunction with improvements in the global gravity field and its time variations. But a major improvement will be provided by the use of a radio link between the lander and the orbiter (the UHF TMTC system can be used for that link). The expected precision on the k2 value will greatly help to determine the interior structure parameters, since it can be used jointly with the moment of inertia derived from the LaRa determination of precession. The increased precision on the determination of the moment of inertia from LaRa results in a reduced set of possible solutions for the interior structure in terms of crust thickness and density, and in terms of core composition and size. The tidal Love number k2 dependence on core size has been shown in Fig. 11. An increase in the precision of k2 will further help to constrain the size of the core. Fig. 11 shows core radius vs. the Love number k2 for the two mantle mineralogies, different crust densities and thicknesses, core sulfur weight fractions (the horizontally grouped points in Fig. 11) and a hot (black in the figure) and cold (grey in the figure) mantle. The results assume that the core is fully liquid. The shaded area shows the reduced range of k2 values of Konopliv et al. (2006), obtained by using the radio link between an orbiter and the Earth (as discussed previously, this range of values is however most probably underestimated). A further constraint on the k2 value (with associated lower uncertainties) is possible with a lander–orbiter radio link (see also the paragraph on synergies with the orbiter); it will significantly reduce the uncertainties associated with the determination of the interior structure parameters such as core radius. The knowledge of the k2 Love number, even with large error bars, helps to constrain the size of

1800

hot mantle cold mantle

rcmb [km]

the core, its composition in terms of sulfur weight fraction, and the temperature of the mantle. The information provided by the k2 Love number will greatly help to increase our knowledge of the interior of Mars in conjunction with the information provided by the moment of inertia. The core size and composition can thus be estimated with high confidence from both the tidal Love number k2 and the moment of inertia together. To further constrain the interior, e.g., mantle composition and thermal state, additional data such as seismic velocities and electrical conductivity are required.

9. Conclusions In this paper, we have demonstrated that with a simple radioscience experiment onboard a lander at the surface of Mars, LaRa, it is possible to obtain information on the deep interior of Mars and on the global seasonal variations of the atmosphere and icecaps. In particular, in about one-third of a Martian year we will be able to improve the precession constant from its value determined by spacecraft around Mars by a factor of 4. For a mission lifetime of one Martian year, it is possible to improve the precession constant and consequently the global moment of inertia of Mars by one order of magnitude. It will also be possible to determine the nutation of Mars, which provides important information on the state and size of the core. The use of the radio link between the lander and the orbiter improves the scientific results. In particular, the orbit of the orbiter can be improved, which further improves the determination of the k2 tidal Love number and the core size and composition. The joint use of LaRa with seismic data, heat flow measurements, and electrical conductivity profiles makes it possible to determine density, composition and temperature profiles for Mars. This demonstrates the high potential of future scientific return of the Humboldt geophysical science payload of ExoMars.

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. In particular, we would like to thank Werner Verschueren (BELSPO) and Hilde Schroeven-Deceuninck (ESA/PRODEX) for their constant support and enthusiasm and their great help to the LaRa project. We are thankful to the reviewers who helped improving our manuscript. References

1700 1600 1500 1400

0.10

1065

0.12

0.14 k2

0.16

0.18

Fig. 11. Core radius rCMB as a function of the k2 tidal Love number for hot (black) and cold (grey) mantles, for different crust densities and thicknesses, for different core sulfur fractions, and for the two mantle mineralogies (the horizontally aligned dots represents the values for the different possibilities). The horizontal dimension of the grey shaded area corresponds to the uncertainty (probably underestimated) on the k2 value of Konopliv et al. (2006). An increase of that precision as expected with LaRa will further constrain the core radius.

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