Patrick Bonnel

Nicolas Coulombel

Emmanuel Prados

Peter Sturm

Elise Arnaud

Cédric Boittin

Louafi Bouzouina

Jorge Cabrera Delgado

Thomas Capelle

Jean Delons

Laurent Gilquin

Vincent Hilaire

Matthieu De Lapparent

Dany Nguyen-Luong

Jean-Pierre Nicolas

Mathieu Saujot

Anthony Tschirhard

Arthur Vidard

A survey on the calibration and validation of integrated land use and transportation models

Context and motivation

A fundamental goal of Land Use -Transport Interaction (LUTI) models is to capture the strong interplay between land use and transportation in metropolitan areas. Inherently, sector-specific models, transport and urban alike, cannot take this interaction into account and thus miss one side of the story. LUTI models aim to fill this gap, and ultimately to provide better decision helping tools for urban and regional long term planning. LUTI models first appeared in the 1960s. The complexity of LUTI models, combined with computational limitations at the time (see [START_REF] Lee | Requiem for large scale models[END_REF] for a discussion on these points), caused a pause in their development. However, interest in LUTI models has risen again in the 1990s and their number and complexity have been growing steadily ever since. This goes hand in hand with increasing expectations from end users as well as with new theoretical developments and a drastic increase in computational capacities, the latter enabling for instance the development of micro-simulation models.

Following the glossary set by David Simmonds Consultancy et al. [START_REF] Simmonds | Review of land-use/transport interaction models[END_REF], currently the two main families of LUTI models are spatial economics models (e.g. MEPLAN, TRANUS, PECAS, RUBMRIO, . . . ) and activity based models (e.g. UrbanSim, IRPUD, DELTA, . . . ). The former are essentially based on an equilibrium approach1 , which comes together with a relatively aggregate representation of space and of the economic agents and activities. The latter focus on the system dynamics and on the processes of change. They aim at more realism in how things are represented and are usually much more disaggregated. Micro-simulation is also widespread in this branch.

While spatial economics models may be mathematically more complex to handle, due to the requirement of reaching an equilibrium for a complex set of parameters and equations, activity-based models usually have more parameters and larger data requirements for their instantiation. Besides these differences, all LUTI models share several needs, among which -like for most models in general -a need for calibration (parameter estimation) methods in order to instantiate them and for validation approaches in order to justify their operational capacity. Both of these, parameter estimation and model validation, are complex issues; in this document we focus on numerical/computational aspects. The survey reported here is motivated by our conviction that the high complexity of current LUTI models requires the best possible numerical tools for calibration and validation. Developing and applying these tools is the primary objective set by the CITiES project funded by the French ANR (Agence Nationale de la Recherche). A starting point of this endeavor is a survey of existing state of the art reported in the LUTI literature. This document describes the scope of this ongoing study and some intermediate conclusions.

Methodology

Terminology. Model calibration is sometimes considered as the whole process of setting up the model structure: choice of theoretical model(s), of the spatial and economic disaggregation levels, choice of the functional form of the equations and of explanatory variables, and finally estimation of the model parameters. Although we are aware that in practice, this joint and usually iterative procedure is probably always necessary, in the scope of this study the term calibration specifically refers to the estimation of model parameters. Inputs to calibration primarily consist of data (observations made in the study area) but may also comprise prior knowledge on the parameters to estimate (such as typical values or expected ranges) or on expected model outputs.

Model validation is a vast question with less consensus on definition. Some consider a model to be validated if, once it is calibrated, the model outputs correctly match observed values. This is not usually a good practice, since the observed values are almost always used in the calibration. A model should be validated against its intended usage, which in the case of LUTI models typically involves simulations for a future horizon. The predictive capacity of the model may be assessed by confronting simulation results against actual observations that were not used for calibration; this is a standard approach in disciplines where experimentation is possible. Generally speaking, available data are split between a "training" set used for model calibration and a "test" set used purely for validation. Historical validation is the most frequent form of this approach: the model is calibrated for a given year (or time interval), and then tested against another year (or time interval). However, doing so may prove difficult for a LUTI model, considering that the sole data collection for the calibration step is already a very lengthy process. Furthermore, it is widely acknowledged that an appropriate usage of LUTI models may not be in interpreting model outcomes as accurate predictions, but rather as general trends. A more "behavioral" validation may thus be in order, including assessment by experts or sensitivity analysis. Finally, let us note that strictly speaking, one may never validate a model but only invalidate it, for instance by performing an uncertainty analysis (which aims to determine how the uncertainty on data used for calibration propagates to parameter values); if a model is found to be invalid, the reason may be that the model itself is inappropriate or that it is too disaggregated, or rather that the data are insufficient, etc.

Calibration. As explained above, calibration refers here to the estimation of model parameters and more specifically, to their estimation using numerical methods. This requires defining several elements: an overall estimation strategy (e.g. the sequence in which parameters are estimated), a mathematical formulation of the estimation problem, and actual estimation methods. Our survey analyzes the LUTI literature based on taxonomies for these components.

Concerning the overall estimation strategy, we adopt the taxonomy proposed by Abraham [START_REF] Abraham | Parameter Estimation in Urban Models: Theory and Application to a Land Use Transport Interaction Model of the Sacramento, California Region[END_REF], which distinguishes: piecewise (estimation carried out module by module), limited view (black box calibration of the entire model), simultaneous (estimation of all model parameters, but unlike black box, consid-eration of outputs of individual modules), sequential (piecewise followed by simultaneous), Bayesian sequential (like sequential, using confidence intervals on parameters in addition). As for the mathematical formulation of the estimation problem, we study if and how existing LUTI calibration approaches are based on an explicit formulation in terms of a numerical optimization problem, i.e. on the basis of one or multiple cost functions. We also examine if constraints or prior knowledge on parameters or model outputs are used in the formulation (e.g. via constrained optimization problems).

Finally, the actual estimation methods used are surveyed, ranging from ad hoc search methods over gradient descent, to more complex optimization methods.

Validation. Like for calibration, we scrutinize the LUTI literature in order to determine what kind of validation is carried out and how. As seen previously, the main forms of validation are: validation using only data used for calibration, validation against additional data (including "historical" validation), validation by experts, uncertainty analysis and sensitivity analysis.

Intermediate conclusions

While our systematic review of the LUTI literature is still underway, we can draw some intermediate conclusions based on our readings so far. The first obvious fact is that there is not one standard approach to calibration and validation. The model type (spatial-economic or activity based), available data, and the features of the software used, among other things, strongly determine the methods that are used. Other than that, there is no consensus on which objective function to use for calibration for instance, or what indicators to use when doing historical validation. This being said, some general facts already emerge. First, piecewise calibration is still the dominant strategy. It is probably the simplest one to implement, but also rather suboptimal: modules are calibrated individually, without taking into account the interplay between them that makes up the entire model. A few exceptions exist though, such as the sequential-type calibration approach for MEPLAN proposed in [START_REF] Abraham | Parameter Estimation in Urban Models: Theory and Application to a Land Use Transport Interaction Model of the Sacramento, California Region[END_REF]. Calibration methods vary depending on the model type, but the use of prior knowledge and of constraints on the parameter values is extremely rare. Regarding validation, historical validation is more and more frequent, and largely prevails compared to other potential forms of validation against additional data. Sensitivity analysis is not frequent, and when carried out, it is often under the form of test scenarios [START_REF] Nicolai | Coupling an urban simulation model with a travel modela first sensitivity test[END_REF]. Last, uncertainty analysis starts to rise, but works on this topic remain seldom and this field is far from being mature.

Several spatial-economic models are not exactly equilibrium models as they consider some dynamics in the land-use system. Typically, when there is an exogenous change in the system (new transport line, increase in population, etc.) they do not shift from one long-term equilibrium to another instantly: some friction factors ensure a smoother transition between the two steady states.

Acknowledgment: This work is supported by the CITiES project funded by the Agence Nationale de la Recherche (grant ANR-12-MONU-0020).


Nathalie Long
email: nlong@univ-lr.fr

Arnaud Bellec

Erwan Bocher

Gwendall Petit

Influence of the methodology (pixel-based vs object-based) to extract urban vegetation from VHR images in different urban zones

Keywords: Remote sensing, spatial analysis, image processing and analysis, vegetation

In a context of sustainable development, the cities have become the main problem for spatial planning directives. Rapid urbanization has a real impact on several natural processes like the meteorological cycles. So to reduce the side-effects of urban development, consistent and accurate data are required to define urban land cover and, especially, the vegetation surface. Indeed, the vegetation presents a particular interest because of its influence on components of the urban environment like temperature or air quality. Images with a very high spatial resolution allow to obtain more details. If object-based approach (OBA) seems to give better results than pixel-based approach (PBA) to classify urban land covers, at a zone scale, this statement can be qualified according to the type of zone. On seven zones of Nantes, France, results of OBA and PBA are compared from 10 m spatial resolution image and impact of spatial resolution of images is also analyzed. Furthermore, this study explores a straightforward spatial analysis method to assess the impact of OBA and PBA. On zones where the land cover is more homogeneous, PBA and 10m image give vegetation surfaces close to surfaces obtained from OBA and 2,5m image. Zones where land covers are mixed, OBA and 2,5m image are essential to detect vegetation accurately.

Introduction

Urban area is a complex system because of multiplicity of the objects and materials consisting urban fabric. If the spatial resolution of images increases, urban objects are more easily identified, spectral mix is reduced but the level of details increases too and complicates automatic detection of urban land covers. [START_REF] Myint | Per-pixel vs. object-based classification of urban cover extraction using high spatial resolution imagery[END_REF]. With a spectral approach, the spatial resolution allows to analyze the spectral properties of urban objects and to avoid per-pixel spectral heterogeneity. Because of the spatial heterogeneity of the urban fabric [START_REF] Long | Sensitivity of spatial indicators for urban terrain characterization[END_REF], the object-based approach could be a solution to classify urban land covers.

In this study, we analyze seven zones of the city characterized by several built density, buildings gradually making way for the vegetation. We focus only on vegetation surface to analyze influence of methodologies. First, the difference between the vegetation surfaces detected from an object-based approach (OBA) and those from a pixel-based approach (PBA) is evaluated for each zone. Second, influence of the image spatial resolution to detect vegetation surface is also evaluated. Our objective is to show that the kind of zone, its land cover less or more homogeneous and its urban structure must to be take into account to choose methodology and spatial resolution of image. Furthermore, this study explores a straightforward spatial analysis method to assess the impact of OBA and PBA (Gustafon, 1998;[START_REF] Herold | Remote sensing and landscape metrics to describe structures and changes in urban land use[END_REF]. Performed with GIS, we propose a Map Similarity Index to compare vegetation maps.

Study area

Nantes is the sixth city of France and is located in the northwest of France, near the estuary of the Loire river. Nantes belongs to the Urban Community of Nantes, grouping 24 communities on 523 km². Within this urban community, seven zones ranging from low building density to high building density were selected (the zone number is noted between bracket) : rural zone (5), predominantly rural (7), predominantly urban (6), multifamily building (3), high density single family building (4), pericenter district (2) and city center district (1).

Methodology

The methodology is divided into two steps: land cover classification (1) and calculation of Map Similarity Index (2). Each zone covers 1 km². Surfaces of vegetation are divided into herbaceous vegetation (HV) and trees vegetation (TV). Vegetated surfaces are computed in percentage as well as a relative change from the formulae ((x -x reference ) /x reference ) *100.

Land cover classification

Land covers are defined from SPOT images (june 2004): a multispectral image (green, red and near infrared channels, Lambert 93) with a 10 meters of spatial resolution and a second one with a 2.5 m of spatial resolution (VHR image) are used. All land covers are identified from images but the result comparison is produced only on the vegetation surfaces. Two methods are tested according to the spatial resolution of images: (1) a pixel-based classification (PBA) using the supervised method Maximum Likelihood and (2) an object-based classification (OBA) with segmentation into three levels and a hierarchical classification [START_REF] Baatz | Multiresolution Segmentation: an optimization approach for high quality multi-scale image segmentation[END_REF]. Thresholds are fixed from 4 features: GLCM (Grey Level Co-Occurence Matrices) homogeneity, NDVI (Normalized Difference Vegetation Index), BSI (Brilliance Soil Index) and shape. Then, a confusion matrix based on images is employed to perform each classified image and to evaluate overall accuracy [START_REF] Congalton | A review of assessing the accuray of classifications of remotely sensed data[END_REF].

The Map Similarity index (MSI)

The MSI equals the percent area for each patch of a "map A" that overlaps each patch of the "map B". The MSI is computed for each study zones and offers a way to identify joint coincidence in both geographic spaces (geometry) and data classes, thanks to OrbisGIS [START_REF] Bocher | OrbisGIS : Geographical Information System designed by and for research, in Innovative Software Development in GIS[END_REF]. Its spatial language [START_REF] Bocher | GDMS: an abstraction layer to enhance Spatial Data Infrastructures usability[END_REF]) is used to perform geometry processing (union, overlapping) and to aggregate the results (statistics). Indeed, this similarity index is used to indicate the main changes of the classes occurring between the two maps. Are the vegetation maps different? If so, where and in what manner?

Results

The overall accuracy varies between 89 and 91% according the images and the approaches. The methodology's influence on the images' spatial resolution is more important for the detection of herbaceous surfaces than for that of trees (Fig. 1). The relative change between the OBA and PBA is higher (> 90%) on zones with a high building city (zones 1, 2 and 4) and decreases under 40% on zones 7 and 5, predominantly rural. Trees vegetation results are more heterogeneous and do not appear linked to the building density. But the influence of the approach is less important because of a relative change always inferior to 40%. In city centre, multifamily building zone and predominantly urban zone, the surface difference is low (<10%) and in high density single family building zone and rural zone, the detected surfaces of vegetation vary between 30 and 40%. The trees vegetation surfaces are underestimated with the OBA. The same profile is obtained for herbaceous vegetation between a 2.5m image and a 10m image. The relative change is the highest on zones with a high building density (zones 1, 2 and 4) and decreases with the building density. For the trees vegetation, the spatial resolution of images seems less important to detect theses surfaces and the relative change stays inferior to 50%. The MSI method confirmed these results (Fig. 2). The MSI is built: (1) between PBA_10m and OBA_10m, (2) between OBA_10m and OBA_2.5m.

The figure 2 collects the results about the vegetation classes and presents them using a dataviz approach. The first bubble row shows that the vegetation surface area is most covered using the PBA_10m than the OBA_10m except for the zone 5. However, the differences are quite small because of the maximum is only about 10 points. Focused on the second row, the OBA_2.5m highlights a growth of the vegetation area. The maximum difference between PBA_10m and OBA_2.5m is up to 32 points. The last two rows illustrate the overlapping areas calculated by the MSI method. Firstly, we note that there are not major changes from PBA to OBA. Except for the zones 1, 2 and 3 where the orange circle (that represents the part of the superposed area) does not fill all the vegetation areas (colored in green and purple).

We notice a certain level of consistency between vegetation classes (light and dark orange). The herbaceous vegetation is always underestimated, apart from the zone 5 where the ratio is reversed.

Conclusion

Because of the multiplicity of urban objects and materials consisting urban fabric, the choice of methodology to analyze images and of the pixel size are fundamental to obtain an accurate land cover classification. The accuracy of the classification depends on the land cover variability, urban morphology and so, spectral heterogeneity. An OBA and VHR images must be used to analyze images in districts where the building density and the building height is high. On the contrary, the vegetation detection should be more accurate in rural zone with the same method but the detection of the trees vegetation is less accurate from OBA than from PBA. The MSI method confirms these results and highlights the differences between the maps of vegetation.

Figure 1 :

 1 Figure 1 : pericenter zone : aerial images (a), OBA results from 10m image (b), PBA results from 10m image (c) and OBA results from 2.5m image (d); and predominantly urban zone : aerial images (e), OBA results from 10m image (f), PBA results from 10m image (g) and OBA results from 2.5m image (h) (dark green : trees vegetation, light green : herbaceous vegetation, black : buildings (from BDTOPO database IGN), white : no information)

Figure 2 .

 2 Figure 2. Map Similarity Index dataviz for vegetation

Acknowledgements

This study was conducted in the scope of the BDMOS project, funded by the GEOPAL Program and the European Regional Development Fund.


A K Verma

A Fienga

J Laskar

H Manche

M Gastineau

Use of MESSENGER radioscience data to improve planetary ephemeris and to test general relativity

Keywords:

The current knowledge of Mercury's orbit has mainly been gained by direct radar ranging obtained from the 60s to 1998 and by five Mercury flybys made with Mariner 10 in the 70s, and with MESSENGER made in 2008 and 2009. On March 18, 2011, MESSENGER became the first spacecraft to orbit Mercury. The radioscience observations acquired during the orbital phase of MESSENGER drastically improved our knowledge of the orbit of Mercury. An accurate MESSENGER orbit is obtained by fitting one-and-half years of tracking data using GINS orbit determination software. The systematic error in the Earth-Mercury geometric positions, also called range bias, obtained from GINS are then used to fit the INPOP dynamical modeling of the planet motions. An improved ephemeris of the planets is then obtained, INPOP13a, and used to perform general relativity tests of the parametrized post-Newtonian (PPN) formalism. Our estimations of PPN parameters (γ and β) are more stringent than previous results.

Introduction

Mercury is the smallest and least explored terrestrial planet of the solar system. Mariner 10 was the first spacecraft to make three close encounters (two in 1974 and one in 1975) to this mysterious planet, and it provided most of our current knowledge of the planet until early 2008 (Smith et al. 2010). In addition to Mariner 10 flyby observations, ground-based radar measurements were the only observations to be used to study Mercury's gravity field and its physical structure (spherical body with slight flattening at the poles and a mildly elongated equator) [START_REF] Anderson | [END_REF](Anderson et al. , 1996)). In 2004, the National Aeronautics and Space Administration (NASA) launched a dedicated mission, MErcury Surface, Space ENvironment, GEochemistry, and Ranging (MESSENGER), to learn more about this planet. MESSENGER made three close encounters (two in 2008 and one in 2009) to Mercury and became the first spacecraft to observe Mercury from its orbit.

Untill now, MESSENGER has completed more than two years on orbit at Mercury. During the orbital period, radio tracking of MESSENGER routinely measured the Doppler and range observables at Deep Space Network (DSN) stations. These observables are important for estimating the spacecraft state vectors (position and velocity) and improving the knowledge of Mercury's gravity field and its geophysical properties (Srinivasan et al. 2007). Using the first six months of radioscience data during the orbital period, Smith et al. (2012) computed the gravity field and gave better constraints on the internal structure (density distribution) of Mercury. This updated gravity field becomes crucial for the present computation of MESSENGER orbit and for performing precise relativistic tests.

The primary objectives of this work are to determine the precise orbit of the MESSENGER spacecraft around Mercury using radioscience data and then to improve the planetary ephemeris INPOP [START_REF] Fienga | [END_REF](Fienga et al. , 2009[START_REF] Fienga | IAU Symp[END_REF]. The updated spacecraft and planetary ephemerides are then used to perform sensitive relativistic tests of the parametrized post-Newtonian (PPN) formalism [START_REF] Will | Theory and Experiment in Gravitational Physics[END_REF](Will , 2001[START_REF] Will | [END_REF].

Nowadays, spacecraft range measurements are the most accurate measurements used for constructing planetary ephemerides. These measurements cover approximately 56% of all INPOP data [START_REF] Fienga | IAU Symp[END_REF]) and impose strong constraints on the planet orbits and on the other solar system parameters, including asteroid masses. However, until now, only five flybys (two from Mariner 10 and three from MESSENGER) range measurements have been available for imposing strong constraints to Mercury's orbit [START_REF] Fienga | IAU Symp[END_REF]. Therefore, range measurements obtained by MESSENGER spacecraft during its mapping period are important for improving our knowledge of Mercury's orbit.

Moreover, high-precision radioscience observations also offered an opportunity to perform sensitive relativistic tests by estimating possible violation of the two relativistic parameters (γ and β) of the Parametrized Post Newtonian (PPN) formalism of general relativity (GR) [START_REF] Will | Theory and Experiment in Gravitational Physics[END_REF]. The previous estimations of these parameters using different techniques and a different data set, can be found in (Bertotti et al. 2003;[START_REF] Müller | [END_REF]Pitjeva 2009;Williams et al. 2009;[START_REF] Manche | Journées 2010 Systèmes de Référence Spatio-temporels[END_REF][START_REF] Konopliv | [END_REF][START_REF] Fienga | IAU Symp[END_REF]. However, because of Mercury's relatively high eccentricity and its close proximity to the Sun, its orbital motion provides one of the best solar system tests of GR (Anderson et al. 1997). In addition, [START_REF] Fienga | IAU Symp[END_REF][START_REF] Fienga | IAU Symp[END_REF] Article published by EDP Sciences A115, page 1 of 13 also demonstrated, Mercury observations are far more sensitive to PPN modification of GR than other data used in the planetary ephemerides. We, therefore, also performed the test of GR with the latest MESSENGER observations to obtain one of the most precise value for PPN parameters.

In this paper, we introduce the updated planetary ephemeris INPOP13a and summarize the technique used for estimating the PPN parameters. The outline of the paper is as follows Sect. 2 discusses the radioscience data analysis of the MESSENGER spacecraft. The dynamic modeling of MESSENGER and the results obtained during orbit computation are also discussed in the same section. In Sect. 3, we discuss the construction of INPOP13a using the results obtained in Sect. 2. In Sect. 4, we discuss the gravitational tests using updated MESSENGER and Mercury ephemerides. Section 5 follows with conclusions and perspectives.

MESSENGER data analysis

Under NASA's Discovery program, the MESSENGER spacecraft is the first probe to orbit the planet Mercury. It was launched in August 3, 2004, from Pad B of Space Launch Complex 17 at Cape Canaveral Air Force Station, Florida, aboard a threestage Boeing Delta II rocket. On March 18, 2011, MESSENGER successfully entered Mercury's orbit after completing three flybys of Mercury following two flybys of Venus and one of Earth (Solomon et al. 2007).

The MESSENGER spacecraft was initially inserted into a ∼12 h, near-polar orbit around Mercury, with an initial periapsis altitude of 200 km, initial periapsis latitude of 60°N, and apoapsis at ∼15 200 km altitude in the southern hemisphere. After a successful first-year flight in this orbit, the mission was extended to one or more years which began on March 18 2012. During first extended mission, two orbit-correction maneuvers were executed, four days apart, in April 2012 to reduce MESSENGER's orbital period from ∼12 to ∼8 h [START_REF] Flanigan | 23rd Space Flight Mechanics Meeting[END_REF].

The MESSENGER spacecraft was tracked by NASA's DSN stations at X-band frequency, 7.2 GHz for a uplink from the ground stations and 8.4 GHz for a downlink from the spacecraft. Communications were accomplished via the 34 m and 70 m antennas of DSN stations in Goldstone, CA; Madrid, Spain; and Canberra, Australia. MESSENGER's X-band tracking consists in measuring the round-trip time delay (two-way range) and the two-and three-way ramped Doppler shift of the carrier frequency of the radio link between the spacecraft and the DSN stations on Earth. The precision of the Doppler measurement for the radio frequency subsystem is within ±0.1 mm/s over 10 s to several minutes of integration time (Srinivasan et al. 2007).

Data analysis and dynamic modeling

We have analyzed one-and-half years of tracking data collected by the DSN during the MESSENGER orbital period. These data belong to one year of the prime mission and six months of the first extended mission (see Table 1). The complete data set that was used for the analysis is available on the Geoscience node1 of the NASA's Planetary Data System (PDS). For precise orbit determination, all available observations were analyzed with the help of the Géodésie par Intégrations Numériques Simultanées (GINS) software, which was developed by the Centre National d'Études Spatiales (CNES) in collaboration with Royal Observatory of Belgium (ROB). GINS numerically integrates the equations of motion and the associated variational equations. It simultaneously retrieves the physical parameters of the force model using an iterative least-squares technique.

Dynamic modeling and orbit determination processes

The precise orbit determination is based on a full dynamical approach. The dynamic modeling includes gravitational (gravitational attraction of Mercury, third-body gravity perturbations from the Sun and other planets, and relativistic corrections) and nongravitational (solar radiation pressure; Mercury radiation pressure) forces that are acting on the spacecraft. These forces have been taken into account in the force budget of MESSENGER. The latest spherical harmonic model (Smith et al. 2012) of Mercury's gravity field, HgM0022 developed up to degree and order 20, and the associated Mercury's orientation model [START_REF] Margot | [END_REF]) have been considered for precise computation.

The measurement (Doppler and range) models and the light time corrections that are modeled in GINS correspond to the formulation given by [START_REF] Moyer | Formulation for Observed and Computed Values of Deep Space Network Data Types for Navigation[END_REF]. During computations, DSN station coordinates were corrected from the Earth's polar motion, from solid-Earth tides, and from the ocean loading. In addition to these corrections, radiometric data have also been corrected from tropospheric propagation through the meteorological data3 (pressure, temperature, and humidity) of the stations.

The complex geometry of the MESSENGER spacecraft was treated as a combination of flat plates arranged in the shape of a box, with attached solar arrays, the so-called Box-Wing macro-model. The approximated characteristics of this macromodel, which includes cross-sectional area and specular and diffuse reflectivity coefficients of the components, were taken from (Vaughan et al. 2002). In addition to the macro-model characteristics, orientations of the spacecraft were also taken into account. The attitude of the spacecraft and of its articulated panels in inertial space were defined in terms of quaternions. The approximate value of these quaternions was extracted from the C-kernel4 system of the SPICE Navigation and Ancillary Information Facility (NAIF) software. The macro-model and its orientation allowed calculation of the nongravitational accelerations that are acting on the MESSENGER spacecraft due to the radiation pressure from Sun and Mercury (albedo and thermal infrared emission).

For orbit computation and parameters estimation, a multiarc approach was used to get independent estimates of the MESSENGER accelerations. In this method, we integrated the equations of motion using the time-step of 50 s then, and orbital fits were obtained from short data arcs fitted over the observations span of one day using an iterative process. The short data arcs of one day were chosen to account for the model imperfections. To initialize the iteration, the initial position and velocity vectors of MESSENGER were taken from the SPICE NAIF spk-kernels5 .

Solve-for parameters

An iterative least-squares fit was performed on the complete set of Doppler-and range-tracking data arcs that correspond to the orbital phase of the mission using an INPOP10e [START_REF] Fienga | [END_REF]) planetary ephemeris6 . We have processed data from May 17 2011 to September 18 2012 excluding the periods of the maneuvers. A summary of these tracking data is given in Table 1. MESSENGER fires small thrusters to perform momentum dump maneuver (MDM) for reducing the spacecraft angular momentum to a safe level. Normal operations (during orbital periods) includes only one commanded momentum dump every two weeks. In addition, orbit correction maneuvers (OCM) were also performed (typically once every Mercury year, 88 Earth days) to maintain the minimum altitude below 500 kilometers. Such large intervals between the MESSENGER maneuvers facilitate the orbit determination. The data arcs that correspond to the maneuver epochs are thus not included in the analysis. The total 440 one-day data arcs were then used for the analysis.

Several parameters were estimated during orbit computation: spacecraft state vectors at the start epoch of each data arc, for a total of 440 × 6 = 2640 parameters; one scale factor per data arc for taking into account the mismodeling of the solar radiation force (total of 440 parameters); one Doppler bias per arc for each DSN station to account for the systematic errors generated by the devices at each tracking station (total of 440 1 1 × n parameters, where n is the number of stations participating in the data arc); one station bias per arc for each DSN station to account for the uncertainties on the DSN antenna center position or the instrumental delays (total of 440 1 1 × n parameters); and one range bias per arc for ranging measurements to account for the systematic geometric positions error (ephemerides bias) between the Earth and the Mercury (total of 440 parameters).

Orbit determination

Postfit residuals

The root mean square (rms) values of the post-fitted Doppler and range residuals give some indication about the quality of the orbit fit and the estimated parameters. Moreover, the quality of the used parameters associated to the physical model can also be judged from these residuals. Figure 1 illustrates the time history of the residuals estimated for each measurement type. In this figure, panel a represents the rms values of the two-and threeway Doppler residuals that were obtained for each data arc and are expressed in millihertz (mHz). As Mercury has shorter orbit than other planets, it experiences five superior conjunctions (when the Earth, the Sun and the spacecraft lie on the same line, with the spacecraft located on the opposite side of the Sun with respect to Earth) during the time interval covered by the analysis. Because of a lack of modelisation of the solar corona perturbations within the GINS software, no model of solar plasma was applied during the computations of the MESSENGER orbit. The peaks shown in Fig. 1, therefore, demonstrate the clear effect of the solar conjunctions on the typical fit to the Doppler and range data residuals.

Excluding the solar conjunction periods (about 100 data arcs), when Sun-Earth-Probe angle remained below 10 • , an average value of Doppler residuals has been found to be approximately 4.8 ± 2.2 mHz (∼0.09 ± 0.04 mm/s), which is comparable with values given by (Smith et al. 2012;[START_REF] Stanbridge | AAS/AIAA Astrodynamics Specialist Conference[END_REF]Srinivasan et al. 2007). The mean value of the estimated Doppler bias for each DSN station tracking pass was found to be very small (a few tenths of mHz), which is lower than the Doppler post-fit residuals for each data arc. It demonstrated that we have no large bias in the modeling of the Doppler shift measurements at each tracking station.

The range measurements were also used to assist in fitting the Doppler data for a precise orbit determination. Panel b of Fig. 1 represents the rms values of two-way range residuals that were obtained for each data arc. An average value of these range residuals is 1.9 ± 1.4 m, which is comparable with the values given in Srinivasan et al. (2007).

Scale factor and range bias

We fitted one scale factor per data arc for the solar radiation force to account the inaccuracy in the force model. Panel a of Fig. 2 represents the time history of these scale factors. These scale factors are overplotted with the beta angle, which is the angle between MESSENGER orbital plane and the vector from the Sun direction. The variation in the MESSENGER orbital plane (beta angle) relative to the Sun occurs as Mercury moves around the Sun. For example, at 10 • , 100 • , and 180 • of Mercury's true anomaly, the corresponding beta angles are 83 • , 0 • , and -78 • , respectively [START_REF] Ercol | Thermal and Fluids Analysis Workshop[END_REF]. At 0 • beta angle, the spacecraft travels directly between the Sun and the planet, while at 90 • , the spacecraft is in sunlight 100% of the time. As one can see from panel a of Fig. 2, the solar pressure coefficients have variations that approximately follow those of the beta angle. This implies that, whenever MESSENGER orbital plane approaches the maximum beta angle, it is fully illuminated by direct sunlight (no shadow affect). To protect the spacecraft from the direct sunlight, the automatic orientation of the solar panels therefore balances the need for power and the temperature of the surface of the panel. Thus, imperfection in the modeling of these orientations is then taken care of by the scale factor to reduce the error in the computation of solar radiation pressure (see Fig. 2). The fitted scale factor for solar radiation pressure is, therefore, typically in the range of about 2.1 ± 0.5. This value is nearly twice the a priori value and it reflects the imperfection in the force model due to the approximate representation of the macro-model.

Spacecraft transponder group delay calibration

Planetary ephemerides are a good tool for testing the gravity model and GR [START_REF] Fienga | IAU Symp[END_REF]) and performing solar corona 9.0 9.0 (-0.3738 ± 3 ) 0 studies (Verma et al. 2013). Moreover, it is also possible to calibrate the transponder group delay from the planetary ephemeris.

The spacecraft receives and transmits the signal to the Earth station through the on-board transponder, which causes the time delay in the range measurements. This delay varies from one spacecraft to another depending on the radio frequency configuration. Usually an average value for this delay is measured at different occasions on the ground before launch. However, the group delay is not perfectly stable and can fluctuate by a few ns, depending upon variations in a number of parameters such as temperature and signal strength.

For MESSENGER, we estimated this group delay with the planetary ephemeris. This procedure becomes an alternate method of testing the procedure and quality of the orbit fit by comparing estimated group delay with the delay tested on the ground. Since the transponder delay does not affect the Doppler measurements we were therefore, able to compute the precise orbit of the spacecraft without considering the transponder delay in the range measurements. With this configuration, we then reanalyzed the entire radio tracking data (see Table 1). To check the precision on the knowledge of the spacecraft orbit, we compared the radial, along-track, and cross-track components of the orbit for each data arc with the solution obtained in Sect. 2.2.1. An average rms value of radial, along-track, and cross-track difference is 0.015 m, 0.16 m, and 0.19 m, respectively. Less than a meter level of differences in the orbit implies that the transponder delay has negligible impact on the orbit, since the spacecraft orbit is mostly constrained by the Doppler tracking data. However, there is a dramatic change in the estimation of range bias, which now includes ephemeris bias plus the bias due to the transponder delay. Using these range biases to fit the planetary ephemeris, we found a clear off-set in the Earth-Mercury geocentric distances of about 410 ± 20 m (two-way) during the orbital period of the MESSENGER. This estimation of transponder delay is compatible with the one found during ground testing, which ranged from 1,356.89 ns (∼407 m) to 1,383.74 ns (∼415 m) (Srinivasan et al. 2007). Thus these results also suggested that there is not a large error in the spacecraft and the planetary orbit fit procedure.

Improvement of planetary ephemeris, INPOP

Since 2003, INPOP planetary ephemerides have been built on a regular basis and provided to users thought the IMCCE website 7 . The INPOP10e ephemeris was the latest release [START_REF] Fienga | [END_REF]) that was delivered as the official Gaia mission planetary ephemerides used for the navigation of the satellite as well as for the analysis of the data. Specific developments and analysis were done for the Gaia release such as the TCB time-scale version or an accurate estimation of the INPOP link to ICRF. With the delivery of the MESSENGER radio science data, a new opportunity was offered to improve drastically our knowledge of 7 www.imcce.fr/inpop the orbit of Mercury and to perform tests of gravity at a close distance from the Sun.

The use of the 1.5 year range measurements deduced from the previous analysis (see Sect. 2) is then a crucial chance to obtain better knowledge over the ∼0.3 year Mercury orbit. The accuracy of a few meter for the MESSENGER range data will give big constraints over short period perturbations on Mercury's orbit. The five flyby positions obtained with Mariner and the MESSENGER flybys will still be significant for the measurements of long period (10 or more years) perturbations (see Fig. 8). Only the addition of the Bepi-Colombo range data will be able to disentangle such long period effects.

INPOP13a

The constants and dynamical modeling used for constructing the new ephemerides, INPOP13a, are similar to INPOP10e. A complete adjustment of the planet initial conditions (including Pluto and the Moon), the mass of the Sun, the oblateness of the Sun, the ratio between the mass of the Earth and the Moon, and 62 asteroid masses is operated. Values of the obtained parameters are given in Tables 2 and3. Even if Mercury is not directly affected by the main belt asteroids, the use of the range measurements between MESSENGER and the Earth does have an impact on the Earth's orbit and then could bring some information on asteroid masses perturbing the Earth orbit. On Table 3, we only gave the masses that are significantly different from those obtained with INPOP10e and inducing detectable signatures below five meters. These masses are also compared with the [START_REF] Konopliv | [END_REF] on the same table. The masses of the biggest objects differ from the two ephemerides inside their two-sigma error bars, and one can notice the new determination of the mass of (51) Nemausa inducing slightly bigger perturbations on Mercury (7 m) and Venus (8 m) geocentric distances than on Mars (5 m).

Table 4 gives the postfit residuals obtained with INPOP13a and compared with those obtained with INPOP10e. One can see a noticeable improvement in Mercury's orbit over all the periods of the fit including direct radar observations. The result is of course more striking for MESSENGER range measurements that were deduced from Sect. 2, and not used for the fit of INPOP10e. In this particular case, the improvement reaches a factor of almost 16 on the estimation of the distance between Mercury and the Earth (see Fig. 3). The extrapolated residuals given in Table 4 are not really significant since INPOP10e was fitted over a very similar interval of time ending at about 2010.4 when INPOP13a was fitted up to 2011.4.

Figure 4 plots the differences between INPOP13a, INPOP10e and DE423 for Mercury geocentric right ascension, declination, and distance, and the Earth-Moon barycenter longitudes, latitudes, and distances in the BCRS. These differences give estimations of the internal accuracy of INPOP13a. By comparison, the same differences between INPOP10a and DE421 are also plotted. They present the improvements 2013) by a different method of computing the orbit of the Sun relative to the solar system barycenter, as well as a different distribution of planetary and asteroid masses.

In conclusion, INPOP13a shows an important improvement in the Mercury orbit especially during the MESSENGER orbital and flyby phases of the mission. The improvement over the EMB orbit in the BCRS is less important but still a systematic trend noticeable in the EMB barycentric distance differences between INPOP10a and DE421 seems to be removed in the new comparisons.

Reconstruction of MESSENGER orbit with INPOP13a

As given in Table 4, geometric distances between Earth and Mercury are ∼16 times better in INPOP13a than the INPOP10e. To analyze the impact of the improvement of the planetary ephemeris on the spacecraft orbit, we reanalyzed the entire one and half years of radioscience data (see Table 1) using INPOP13a ephemeris. The dynamical modeling and orbit determination process for this analysis are the same as discussed in Sect. 2.1. To compare the results of this analysis with the one obtained from INPOP10e (see Sect. 2.2.1), the differences in the Doppler and range postfit residuals along with the changes that occurred in the periapsis and apoapsis altitudes of MESSENGER are plotted in Fig. 5.

An average value of these differences and its 1σ mean dispersion for Doppler, and range postfit residuals was estimated as 0.008 ± 0.04 mHz and 0.05 ± 0.3 m, respectively. These values are far below the estimated accuracy of 4.8 ± 2.2 mHz and 1.9 ± 1.4 m (see Sect. 2.2.1) for Doppler and range postfit residuals, respectively. In addition to these residuals, we also compared the orbit of MESSENGER computed with INPOP13a and INPOP10e ephemerides. The differences in the periapsis δp and apoapsis δa altitudes of MESSENGER due to the change in planetary ephemeris are plotted in panels c and d of Fig. 5. An average and 1σ dispersion of δp and δa was found as 0.05 ± 1.2 m and 0.03±1.2 m, respectively. These values are also far below the required accuracy of 10 m (Srinivasan et al. 2007) for the MESSENGER orbit. This analysis is therefore consistent with the fact that change in the planetary ephemeris during the construction of the spacecraft orbit does not alter the radioscience analysis significantly.

Test of general relativity

General presentation

INPOP13a was built in the framework of GR in using the PPN formalism. A detailed description of the modeling used for the INPOP ephemerides is given in [START_REF] Fienga | IAU Symp[END_REF]. Specific relativistic timescales have been set up and integrated in INPOP (TCB, TDB) and mainly two parameters characterized the relativistic formalism in modern planetary ephemerides: the parameter β that measures the nonlinearity of gravity and γ, measuring the deflexion of light. In GR, both are supposed to be equal to 1 and were fixed to 1 for the INPOP13a construction.

The GINS software used for the analysis of the radio science data and the reconstruction of the MESSENGER orbit is also coded in the PPN framework, including both β and γ PPN parameters.

Up to now, general relativity theory (GRT) has successfully described all available observations, and no clear observational evidence against GR has been identified. However, the discovery of Dark Energy which challenges GRT as a complete Among all possibilities for testing GRT, the tests of the motion and light propagation in the solar system were historically the first ones, and they are still very important since they give highest accuracy since the dynamics of the solar system is well understood and supported by a long history of observational data. Concerning the Einstein field equations, the most important framework used for the tests in the solar system is the PPN formalism (such as [START_REF] Will | Theory and Experiment in Gravitational Physics[END_REF]. The PPN formalism is a phenomenological scheme with ten dimensionless parameters covering certain class of metric theories of gravity, among them the β and γ parameters parts of the INPOP and A115, page 8 of 13 Table 5. Intervals of violation for PPN parameters β and γ deduced from Fig. 7 Ref.

(β -1) GINS modelings. The tracking data of space missions give a good possibility to test GRT since the data is very sensitive to the GRT-effects in both dynamics of the spacecraft and signal propagation. However, some factors, such as navigation unknowns (AMDs, solar panel calibrations), planet unknowns (potential, rotation, etc.), effect of the solar plasma, or the correlation with planetary ephemerides limit this sort of gravity test. Dynamics of the solar system are, however, less affected by poorly modeled accelerations and technical unknowns. Up to now, the best constraints for β come from the planetary data in INPOP [START_REF] Fienga | IAU Symp[END_REF]. Constraints on other PPN parameters can be found in [START_REF] Will | [END_REF]. A number of theoretical models predict deviations of PPN parameters that are smaller than current constraints. Typical examples here are certain types of tensor-scalar theories where cosmological evolution exhibits an attractor mechanism towards GRT (Damour & Nordtvedt 1993) or string-inspired scalar-tensor theories where the scalar field can decouple from matter (Damour & Polyakov 1994).

× (γ -1) INPOP13a Limit [%] (β -1) × (γ -1) × 10 5 × 10 5 All data 25 (β -1) = (0.2 ± 2.5) INPOP10a (β -1) = (-6.2 ± 8.1) (γ -1) = (-0.3 ± 2.5) (γ -1) = (4.5 ± 7.5) 10 (β -1) = (-0.15 ± 0.70) (γ -1) = (0.0 ± 1.1) K11 (β -1) = (4 ± 24) 5 (β -1) = (0.02 ± 0.12) (γ -1) = (18 ± 26) (γ -1) = (0.0 ± 0.18) M08-LLR-SEP * (β -1) = (15 ± 18) Least squares (β -1) * * = (1.34 ± 0.043) W09-LLR-SEP * (β -1) = (12 ± 11) (γ -1) * * = (4.53 ± 0.540) B03-CASS (γ -1) = (2.1 ± 2.3) No flyby 25 (β -1) = (-0.5 ± 4.5) L11-VLB (γ -1) = (-8 ± 12 ) (γ -1) = (12.5 ± 17.5) 10 (β -1) = (0.0 ± 2.0) P13 (β -1) = (-2 ± 3) (γ -1) = (0.5 ± 3.5) (γ -1) = (4 ± 6) 5 (β -1) = (-0.25 ± 1.25) (γ -1) = (-0.1 ± 2.
Another phenomenological test concerns the constancy of the Newtonian gravitational constant G in time. A variable G is produced say by alternative theories of gravity such tensorscalar theory (see e.g. Damour et al. 1990 andUzan 2003) or some models of dark energy [START_REF] Steinhardt | [END_REF][START_REF] Alimi | AIP Conf. Ser[END_REF]. The ratio is now constrained at the level of 10 -13 with LLR analysis (Williams et al. 2004).

Estimation of PPN parameters, γ and β

In this section, we propose to use the improvement of Mercury's orbit as an efficient tool for testing the consistency between planetary ephemerides built with MESSENGER radio science data and non-unity PPN parameters.

Method

A first estimation of PPN β and γ is possible by least square methods during the adjustment of the INPOP planetary ephemerides, and the results are given in Table 5. Figure 6 gives the correlations between the first 71 over the 343 parameters estimated in the adjustments. As one can see in Fig. 6 no correlation greater than 0.3 affects the determination of the PPN parameters β and γ, as well as the fit of the Sun oblateness, when the gravitational mass of the Sun is highly related to the Mercury and to the Earth orbits.

However to go further in the analysis of the uncertainties and the construction of acceptable intervals of violation of GR throught the PPN β and γ, we also considered the same method as the one that was used and described in [START_REF] Fienga | IAU Symp[END_REF] for determining acceptable intervals of violation of GR when the PPN formalism. Small variations in these two parameters near unity are imposed when constructing alternative planetary ephemerides that are fit over the whole data sets presented in Table 4 and with the same parameters and hypothesis as INPOP13a. A minimum of three iterations in the adjustment process is required for building new ephemerides, and comparisons between these ephemerides and INPOP13a are done to scale up what variations to GR are acceptable at the level of uncertainty of the present planetary ephemerides.

The improvement of Mercury's orbit in INPOP13a justifies these new estimations. Indeed, Mercury played a historical role in testing gravity and GR in 1912(Einstein 1912) and it is still the planet the most influenced by the gravitational potential of the Sun. Its orbit can then lead to the most efficient constraints on β, hence on γ in the PPN formalism. Before the recent input of MESSENGER flyby and orbital radio science data in the INPOP construction, Mars was the most constraining planet for the PPN parameters [START_REF] Fienga | IAU Symp[END_REF]. The reason was the long range of high accurate observations on Mars. The implementation of the first MESSENGER flyby data reduces the interval of violation of β to 50%. The first estimation of the γ interval of violation was made possible thanks to the gain in uncertainty on the Mercury orbit. With INPOP13a, even better improvement is achieved.

Results

The results obtained by direct least squares fit are presented in Table 5. As expected, the estimated uncertainties are very Fig. 6. Correlation between the first 71 (over 343) parameters estimated during the fit of the planetary ephemerides. The red frame frames the correlations related to the initial conditions of planet orbits and the blue rectangle frames the correlations related to the Sun J 2 (JS ), the PPN parameters β (BE) and γ (GA) and the gravitational mass of the Sun (GS). The magenta rectangle frames the correlations related to the gravitational masses of the first most perturbing asteroids including the gravitational mass of the asteroid ring (GR). m 1 , ...m 6 expresses the initial conditions of the Mercury orbit in equinoctial coordinates: semi-major axis, mean motion, k, h, q, and p respectively. The other planet initial conditions are indicated by the first letter of the planet (V for Venus, M for Mars etc...) and by the figures of the corresponding initial conditions as given for Mercury.

optimistic and a more detailed analysis is done based on the method proposed by [START_REF] Fienga | IAU Symp[END_REF].

Results obtained in terms of percentages of the variations in postfit residuals between a planetary ephemeris fitted and built up with PPN parameters different from one and INPOP13a are given in Fig. 7. Panel a in Fig. 7 gives the map of the variations in percent of the full dataset postfit residuals. Panel b in Fig. 7 gives the same map but without taking the variations of the Mercury flyby data into account. For panel b, the Mercury flyby data are indeed used in the ephemerides fit but not in the analysis of the postfit residuals for testing GR. The map of panels a and b is then dramatically different: where the limits for β and γ are stringent the map including the Mariner data, the constraints are greatly enlarged for these two parameters. These phenomena were expected since the variations in PPN parameters induce long-term perturbations in the geocentric distances of Mercury as one can see in Fig. 8. Panels c and d are similar to a and b, but they are obtained with ephemeris INPOP10a. In this ephemeris, MESSENGER flyby data were included in its fits but not in the orbital data. By comparing panels a and c, one can see that the use of the MESSENGER orbital data significantly reduce the intervals of violation for both PPN parameters by a factor 10. The same manner, in the most pessimistic case and without considering the Mercury flybys in analysing of the variations in the postfit residual, one can see in panels b and d that the improvement of Mercury's orbit is again crucial for reducting the violation intervals of PPN parameters.

Table 5 collects the acceptable violation intervals obtained from INPOP10a and INPOP13a. Values extracted from INPOP10a were obtained at 5% of postfit residual variations [START_REF] Fienga | IAU Symp[END_REF]. With INPOP13a, we extracted values from i) panel a of Fig. 7 obtained at 5%, but also at 10% and 25%; and ii) from panel b of Fig. 7 obtained at 5%, which is consistent with the 25% of intervals extracted from panel a.

All given intervals are compatible with GR with an uncertainty at least ten times smaller than our previous results with INPOP10a. In Table 5, comparisons to least squares estimations of other planetary ephemerides or Moon ephemerides like Pitjeva & Pitjev (2013), [START_REF] Konopliv | [END_REF][START_REF] Müller | [END_REF]), and Williams et al. (2009), as well as estimations deduced from VLBI observations Lambert & Le Poncin-Lafitte (2011), are also given. The most stringent published constraint for the PPN parameter γ has been obtained so far during a dedicated phase of the Cassini mission by Bertotti et al. (2003). This value is compatible with our 25% estimation when our 5% and 10% estimations give more restrictive intervals of GR violations.

Confirmations of the results presented in Table 5 will be obtained by the use of the radioscience data obtained during the future Bepi-Colombo mission. In addition, the recovery of the Mariner flyby data would also be a great help for such confirmations. Unfortunately, the Mariner data seem to have been lost, and access to these data seems to be unrealistic. Indeed as one can see in Fig. 8, perturbations induced by a slight change in the PPN parameters ((β -1) = 1.5 × 10 -5 and (γ -1) = -2.2 × 10 -5 ) inducing an effect of about six meters on the Mariner range data (12%) will induce a signature of about the same level at the Bepi-Colombo epoch. With the improved Bepi-Colombo radio science tracking, the expected accuracy in the range measurement is planned to be about 50 centimeters. With such accuracy, detecting the perturbations induced by the same modification of the PPN parameters should be done at 1200%! Two orders of magnitude are expected as a gain in the uncertainty for the β and γ estimations.

Impact on MESSENGER orbit

As stated previously, the GINS software was modeled in the framework of the PPN formalism which includes β and γ parameters. To analyze the combined impact of PPN parameters over the MESSENGER orbit and the planetary ephemerides construction, we analyzed the entire one and half years of radioscience data again using the PPN parameters that are different from unity. The same procedure as described in Sect. 2.1 has been used for reconstructing the MESSENGER orbit. Two sets of MESSENGER orbits were then built, one with β and γ equal to unity and the other with β and γ different from unity (in this case, β -1 = γ -1 = 1 × 10 -4 ). Hereafter, the solution obtained from β and γ equal to unity is referred to as SOL Ref (for the reference solution), and the solution corresponds to β and γ different from unity referred to as SOL βγ 1 .

To maintain consistency in constructing the MESSENGER orbit, we used corresponding planetary ephemerides that were built with the same configurations of PPN parameters as used for SOL Ref and SOL βγ 1 . In Fig. 9, we plotted the differences between solve-for parameters obtained for SOL Ref and SOL βγ 1 . The error bars shown in the same figure represent the 1σ uncertainties in the estimation of solve-for parameters corresponding to SOL Ref . From this figure, one can notice the differences in the parameters are always below the 1σ uncertainties. The estimated solve-for parameters for SOL βγ 1 are analogous to SOL Ref , and there is no significant change in the MESSENGER orbit due to the change in PPN parameters. In contrast, as shown in Fig. 7, this configuration of PPN parameters (β -1 = γ -1 = 1 × 10 -4 ) in the construction of planetary ephemerides led to ∼65% of change in the postfit residuals, which shows that, the planetary ephemerides are more sensitive to GR effects. This can be explained from the fitting intervals of the data set. Usually planetary ephemerides are fitted over long intervals of times (see Table 4) to exhibit long-term effects, while a spacecraft orbit is usually constructed over much shorter intervals (usually one day to a few days) of data arcs to account for the model's imperfections. The short fitting interval of the spacecraft orbit would absorb such effects.

Moreover, it is worth noticing that, unlike state vectors and scale factor F S (see panels a-g of Fig. 9), the range bias differences between SOL Ref and SOL βγ 1 solutions (see panel h) shows systematic behavior. This trend in the range bias can be explained from the contribution of the relativistic deflection of light by the Sun (a function of PPN parameter γ, Shapiro 1964) in the light time computations. Explicitly this effect was not absorbed during the computation of range bias and it becomes important to examine this effect when constructing planetary ephemerides.

We, therefore, reconstruct the planetary ephemerides using the range bias obtained from SOL βγ 1 and the PPN parameters β -1 = γ -1 = 1 × 10 -4 . The newly estimated postfit range bias is then compared with the range bias (prefit) corresponding to SOL βγ 1 . This investigation shows that, the postfit residuals are modified by ∼6% for MESSENGER and ∼1% for Mariner 10 with respect to prefit residuals. This modification in the residuals is negligible compared to a ∼65% of change with respect to reference residuals obtained from INPOP13a. As a result, the supplementary contributions in the range bias due to the relativistic deflection between DSN station and MESSENGER did not bring any significant change in the planetary ephemerides construction.

Conclusions

We analyzed one and half years of radioscience data of the MESSENGER spacecraft using orbit determination software GINS. An accurate orbit of MESSENGER was then constructed with the typical range of Doppler, and two-way range residuals of about 4.8 ± 2.2 mHz (∼0.09 ± 0.04 mm/s), and 1.9 ± 1.4 m. Such accuracies are comparable to those in Smith et al. (2012); [START_REF] Stanbridge | AAS/AIAA Astrodynamics Specialist Conference[END_REF]; Srinivasan et al. (2007). Range measurements obtained by the MESSENGER spacecraft during its mapping period were then used to construct improved planetary ephemerides called INPOP13a. This ephemeris showed an accuracy of about -0.4 ± 8.4 m in the Mercury-Earth geometric distances, which is two orders of improvement compared to DE423 and INPOP10e, and one order compared to the latest DE430.

Such high precision Mercury ephemeris allowed us to perform one of the best GR tests of PPN-formalism. To determine the acceptable intervals of the violation of GR through the PPN parameters (β, γ), small variations of these two parameters near unity were imposed in the construction of alternative planetary ephemerides fitted over the whole data sets. The percentage difference between these ephemerides to INPOP13a are then used to defined the interval of PPN parameters β and γ.

As expected, our estimations of PPN parameters are more stringent than previous results. We considered the 5%, 10% and 25% of changes in the postfit residuals. That the PPN intervals correspond to these changes is compatible with GR with an uncertainty at least ten times smaller than our previous results with INPOP10a. Moreover, one of the best estimation of parameter γ has so far been estimated from the Cassini observations by Bertotti et al. (2003), which is compatible with our 25% estimation.

To further the accuracy of the PPN parameters improve, and to confirm the results given in Table 5, one needs to analysis the radioscience data of the future Bepi-Colombo mission.

Fig. 1 .

 1 Fig. 1. Quality of the MESSENGER orbit in terms of rms values of the post-fit residuals for each one-day data arc: (a) two-and three-way Doppler given in millihertz (multiply by 0.0178 to obtain residuals in mm/s), and (b) two-way range given in meters.

Fig. 2 .

 2 Fig. 2. History of the fitted scale factor and estimated range bias: a) scale factor (for solar radiation acceleration) fitted over each one-day data arc to account inaccuracy in the force model, and b) one-way range bias, represent the systematic error in the Earth-Mercury positions, estimated for each one-day arc using INPOP10e (•), DE423 ( ), and DE430 ( ) planetary ephemerides.

  Panel b of Fig. 2 illustrates the one-way range bias estimated for the ranging measurements for each data arc. These biases represent the systematic uncertainties in the Earth-Mercury geometric positions. The black (•), brown ( ) and blue ( ) bullets in this figure correspond to INPOP10e (Fienga et al. 2013), DE423 (Folkner 2010), and DE430 (Williams et al. 2013), respectively. An average value of these range bias for INPOP10e, DE423 and DE430 is 21 ± 187 m, 15 ± 105 m, and -0.5 ± 42 m, respectively. This range bias is then used in the planetary ephemerides to fit the dynamical modeling of the planet motions (see Sect. 3). Thus, MESSENGER ranging measurements were used to reconstruct the orbit of Mercury around the Sun. The improved planetary ephemeris, INPOP13a (see Sect. 3.1) was then used to reanalyze the MESSENGER radiometric data to study the impact of planetary ephemeris over the computation of MESSENGER orbit and associated parameters (see Sect. 3.2).

Fig. 3 .

 3 Fig. 3. MESSENGER one-way range residuals obtained with INPOP13a, INPOP10a, DE423, and DE430.

Fig. 4 .

 4 Fig. 4. In Mercury panel, differences in geocentric Mercury right ascension (RA), declination (DE) and distances between INPOP13a, INPOP10e and DE423. In EMB panel, differences in BCRF longitudes, latitudes and distances of the EMB between INPOP13a, INPOP10e and DE423. Differences between INPOP10a and DE421 are also given.

Fig. 5 .

 5 Fig. 5. Comparison between INPOP13a and INPOP10e estimations of MESSENGER orbit: a) differences in the postfit Doppler residuals; b) differences in the postfit range residuals; c) differences in the periapsis altitude δp; d) differences in the apoapsis altitude δa.

  panel a) labelled INPOP13a and Fig. 7 panel b) labelled INPOP13aWF.

  6)Notes. Values from INPOP10a are extracted from[START_REF] Fienga | IAU Symp[END_REF][START_REF] Fienga | IAU Symp[END_REF] with a threshold for the variations of the postfit residuals of 5% given in Col. 4. K11 stands for[START_REF] Konopliv | [END_REF], M08 for Müller et al. (2008), W09 for Williams et al. (2009), B03 for Bertotti et al. (2003), P13 for Pitjeva & Pitjev (2013) and L11 for Lambert & Le Poncin-Lafitte (2011). The least squares section gives the fitted values of β and γ at 1σ as obtained by a global fit of INPOP presented in Sect. 4.2.1. ( * ) values obtained for (γ -1) B03-CASS ; ( * * ) least square results given at 1σ.

Fig. 7 .

 7 Fig. 7. Variations in postfit residuals obtained for different values of PPN β (x-axis) and γ (y-axis). Panels a) and c) are obtained by considering the variations in the whole data sets when for panels b) and d), variations in the Mercury flyby data (from Mariner and MESSENGER missions) are excluded from the analysis. The dashed line indicates the limit in γ given byBertotti et al. (2003).

Fig. 8 .

 8 Fig. 8. Differences in geocentric Mercury distances between INPOP13a and a planetary ephemerides built with PPN β and γ different from 1. The indicated area shows intervals of time corresponding to Mariner observations, MESSENGER and the future Bepi-Colombo.

Fig. 9 .

 9 Fig. 9. Differences between solve-for parameters obtained from the solutions SOL Ref and SOL βγ 1 (see text): panels a)-f) represent the changes in the initial state vectors, panel g) represents the changes in the scale factors estimated for solar radiation pressure, panel h) represents the changes in the estimated range bias. The error bars represent the 1σ uncertainties in the estimation of solve-for parameters obtained with the reference solution SOL Ref .

Table 1 .

 1 Summary of the Doppler and range tracking data used for orbit determination.

	Mission	Begin date	End date	Number of	Number of	Number of
	phase	dd-mm-yyyy dd-mm-yyyy 2-way Doppler 3-way Doppler	range
	Prime	17-05-2011	18-03-2012	2108980	184138	11540
	Extended	26-03-2012	18-09-2012	1142974	23211	5709

Table 2 .

 2 Values of parameters obtained in the fit of INPOP13a and INPOP10e to observations including comparisons to DE423 and DE430.

		INPOP13a	INPOP10e	DE423	DE430
		±1σ	±1σ	±1σ	±1σ
	(EMRAT-81.3000) × 10 -4	(5.770 ± 0.020) (5.700 ± 0.020) (5.694 ± 0.015) (5.691 ± 0.024)
	J 2 × 10 -7	(2.40 ± 0.20)	(1.80 ± 0.25)	1.80	(2.1 ± 0.7)
	GM -132 712 440 000 [km 3 s -2 ]	(48.063 ± 0.4)	(50.16 ± 1.3)	40.944	41.94
	AU -1.49597870700 × 10 11 [m]

Table 3 .

 3 Asteroid masses obtained with INPOP13a, significantly different from values found in INPOP10e, and inducing a change in the Earthplanets distances smaller than 5 meters over the fitting interval.

	IAU designation	INPOP13a	INPOP10e	Konopliv et al. (2011)
	number	10 12 × M	10 12 × M	10 12 × M
	1	468.430 ± 1.184 467.267 ± 1.855	467.90 ± 3.25
	2	103.843 ± 0.982 102.654 ± 1.600	103.44 ± 2.55
	9	3.637 ± 0.400	4.202 ± 0.670	3.28 ± 1.08
	15	14.163 ± 0.555	15.839 ± 0.950	14.18 ±1.49
	16	11.212 ± 1.373	12.613 ± 2.208	12.41 ± 3.44
	19	5.182 ± 0.342	4.892 ± 0.513	3.20 ± 0.53
	46	3.076 ± 0.446	3.525 ± 0.743	-
	51	3.287 ± 0.485	0.009 ± 0.004	-
	65	8.789 ± 2.266	4.210 ± 0.863	-
	78	1.486 ± 0.504	2.562 ± 0.574	-
	105	2.070 ± 0.365	3.046 ± 0.635	-
	106	3.369 ± 0.408	3.870 ± 0.411	-
	134	3.451 ± 0.595	1.014 ± 0.368	-
	194	4.872 ± 0.452	5.601 ± 0.636	-
	324	5.087 ± 0.189	4.769 ± 0.435	5.34 ± 0.99

Notes. The uncertainties are given at 1 published sigma and compared with

[START_REF] Konopliv | [END_REF]

.

Table 4 .

 4 Statistics of the residuals obtained after the INPOP13a fit.Notes. For comparison, means and standard deviations of residuals obtained with INPOP10e are given. The label GINS range indicates that the corresponding data set was obtained after orbit reconstruction of the spacecraft in using the GINS software. For MGS, seeVerma et al. (2013).

	Type of data		Nbr	Time interval	INPOP13a	INPOP10e
					mean	1σ	mean	1σ
	Mercury	range [m]	462	1971.29-1997.60	-108	866	-45	872
	Mercury Messenger	GINS range [m] 314	2011.39-2012.69	2.8	12.0	15.4	191.8
	Out from SC *	GINS range [m] 267	2011.39-2012.66	-0.4	8.4	6.2	205.2
	Mercury Mariner	range [m]	2	1974.24-1976.21	-124	56	-52.5	113
	Mercury flybys Mess	ra [mas]	3	2008.03-2009.74	0.85	1.35	0.73	1.48
	Mercury flybys Mess	de [mas]	3	2008.03-2009.74	2.4	2.4	2.4	2.5
	Mercury flybys Mess	range [m]	3	2008.03-2009.74	-1.9	7.7	-5.05	5.8
	Venus	VLBI [mas]	46	1990.70-2010.86	1.6	2.6	1.6	2.6
	Venus	range [m]	489	1965.96-1990.07	502	2236	500	2235
	Venus Vex	range [m]	24970 2006.32-2011.45	1.3	11.9	1.1	11.9
	Mars	VLBI [mas]	96	1989.13-2007.97	-0.02	0.41	-0.00	0.41
	Mars Mex	range [m]	21 482 2005.17-2011.45	-2.1	20.6	-1.3	21.5
	Mars MGS	GINS range [m] 13 091 1999.31-2006.83	-0.6	3.3	-0.3	3.9
	Mars Ody	range [m]	5664	2006.95-2010.00	1.6	2.3	0.3	4.1
	Mars Path	range [m]	90	1997.51-1997.73	6.1	14.1	-6.3	13.7
	Mars Vkg	range [m]	1257	1976.55-1982.87	-0.4	36.1	-1.4	39.7
	Jupiter	VLBI [mas]	24	1996.54-1997.94	-0.5	11.0	-0.3	11.0
	Jupiter Optical	ra [mas]	6532	1914.54-2008.49	-40	297	-39	297
	Jupiter Optical	de [mas]	6394	1914.54-2008.49	-48	301	-48	301
	Jupiter flybys	ra [mas]	5	1974.92-2001.00	2.6	2.9	2.4	3.2
	Jupiter flybys	de [mas]	5	1974.92-2001.00	-11.0	11.5	-10.8	11.5
	Jupiter flybys	range [m]	5	1974.92-2001.00 -1065	1862	-907	1646
	Saturne Optical	ra [mas]	7971	1913.87-2008.34	-6	293	-6	293
	Saturne Optical	de [mas]	7945	1913.87-2008.34	-12	266	-2	266
	Saturne VLBI Cass	ra [mas]	10	2004.69-2009.31	0.19	0.63	0.21	0.64
	Saturne VLBI Cass	de [mas]	10	2004.69-2009.31	0.27	0.34	0.28	0.33
	Saturne Cassini	ra [mas]	31	2004.50-2007.00	0.8	3.4	0.8	3.9
	Saturne Cassini	de [mas]	31	2004.50-2007.00	6.5	7.2	6.5	7.2
	Saturne Cassini	range [m]	31	2004.50-2007.00 -0.010 18.44 -0.013 18.84
	Uranus Optical	ra [mas]	13 016 1914.52-2011.74	7	205	7	205
	Uranus Optical	de [mas]	13 008 1914.52-2011.74	-6	234	-6	234
	Uranus flybys	ra [mas]	1	1986.07-1986.07	-21		-21
	Uranus flybys	de [mas]	1	1986.07-1986.07	-28		-28
	Uranus flybys	range [m]	1	1986.07-1986.07	20.7		19.7
	Neptune Optical	ra [mas]	5395	1913.99-2007.88	2	258	0.0	258
	Neptune Optical	de [mas]	5375	1913.99-2007.88	-1	299	-0.0	299
	Neptune flybys	ra [mas]	1	1989.65-1989.65	-12		-12
	Neptune flybys	de [mas]	1	1989.65-1989.65	-5		-5
	Neptune flybys	range [m]	1	1989.65-1989.65	66.8		69.6
	Pluto Optical	ra [mas]	2438	1914.06-2008.49	-186	664	34	654
	Pluto Optical	de [mas]	2461	1914.06-2008.49	11	536	7	539
	Pluto Occ	ra [mas]	13	2005.44-2009.64	6	49	3	47
	Pluto Occ	de [mas]	13	2005.44-2009.64	-7	18	-6	18
	Pluto HST	ra [mas]	5	1998.19-1998.20	-42	43	33	43
	Pluto HST	de [mas]	5	1998.19-1998.20	31	48	28	48
	Venus Vex * *	range [m]	2827	2011.45-2013.00	51	124	52	125
	Mars Mex * *	range [m]	4628	2011.45-2013.00	-3.0	11.5	4.2	27.5

( * )

Solar corona period. ( * * ) Extrapolation period.

http://pds-geosciences.wustl.edu/messenger/

http://pds-geosciences.wustl.edu/missions/ messenger/rs.htm

http://pds-geosciences.wustl.edu/messenger/mess-v_ h-rss-1-edr-rawdata-v1/messrs_0xxx/ancillary/wea/

ftp://naif.jpl.nasa.gov/pub/naif/pds/data/mess-e_v_ h-spice-6-v1.0/messsp_1000/data/ck/

ftp://naif.jpl.nasa.gov/pub/naif/pds/data/mess-e_v_ h-spice-6-v1.0/messsp_1000/data/spk/

http://www.imcce.fr/inpop/

Acknowledgements. We are very thankful to the CNES and Région Franche-Comté, who gave us financial support. Part of this work useds GINS software, so we would like to acknowledge the CNES for providing access to this software. A. K. Verma is thankful to P. Rosenbatt and S. Le Maistre for fruitful discussions. We are also thankful to G.Esposito-Farese for his constructive remarks and comments.