Despite its similarities to Earth, our understanding of Venus remains limited, particularly regarding its long retrograde rotation period. This has been measured using both Earth-based and in-orbit methods. However, the values obtained exhibit significant variations that cannot be explained by models of various physical mechanisms that could affect the rotation period of Venus. In this study, we present a new determination of the rotation period of Venus based on the precise orbit determination method applied to the radio-tracking data of the Venus Express (VEX) spacecraft. This method consists of a least-squares adjustment of the difference between Doppler data collected by ground-based stations and simulated Doppler data from a force model governing the spacecraft’s motion. We find a rotation period of 243.02064 ± 0.0010 days, which is consistent with results from studies using tracking data from previous orbiters, and with Earth-based radar techniques for the same period covered by the VEX tracking dataset. An attempt was also made to adjust other parameters, including the precession rate, the gravitational field, and the Love number k _2 . Nevertheless, no reliable results for these parameters could be obtained due to the lack of tracking data in the low altitude part of the highly eccentric orbit of VEX. The upcoming Venus missions, such as VERITAS (NASA) and EnVision (ESA) are expected to provide accurate Doppler tracking measurements that will improve our understanding of the planet.

GUEST is a space mission concept whose central objective is the detection of gravitational waves (GWs) in the microhertz band – a physics-rich frequency window that no other present or planned detector can reach at a significant level. The concept is simple: two dense, passive spheres, covered with cube-corner retroreflectors, deployed in highly eccentric Earth orbits (e ≳ 0.7, period P ≳ 33 h), tracked continuously by the global network of satellite laser-ranging stations over a minimum observation time of 10 years, with an expected total duration of 30 years. The orbits themselves act as resonant detectors of the oscillating gravitational perturbations, with the microhertz sensitivity emerging from the selected orbital parameters. From the same data stream, GUEST delivers a programme of fundamental and applied science that cuts across particle physics, gravitational-wave astronomy, cosmology, astrophysics, and geodesy: the first coherent search for GWs from supermassive black-hole binaries in the μHz band, the exploration of primordial GW backgrounds in the unexplored energy-scale gap between pulsar-timing arrays and LISA, a dedicated probe of ultra-light dark matter in a parameter region untouched by any other experiment, a new way to search for ultra-light bosons, order-of-magnitude-improved tests of new gravitational interactions at astronomical ranges, and a step change in the absolute determination of GM_⊕ that underpins the Global Geodetic Observing System and future navigation and Earth-observation missions. This white paper presents the motivation, scientific reach, and mission concept of GUEST.

Abstract:The ESA’s Exomars2016 (TGO) spacecraft has no radio-science PI-ship. However, tracking data are regularly performed for the purpose of orbit navigation determination. As the TGO orbit is near-circular, 400 km altitude and 74 degrees inclination, it theoretically offers the opportunity to improve the determination of the seasonal variations of the second-degree zonal harmonics of Mars gravity field. These variations are indeed poorly resolved using tracking data of near-polar orbiters. Here, we attempt to improve these second-degree harmonics variations using the tracking data of TGO collected from ESOC. Theoretical basis:The orbital perturbations of Martian spacecraft due to the seasonal variations of low degree zonal harmonics are expected to be small. An amplitude of up to 70 cm is expected on polar orbiters like Mars Odyssey for the odd zonal harmonics and only 5 cm for the even zonal harmonics. Today, the best orbit accuracy is about 1 meter, which makes possible to retrieve the odd harmonics but not the even harmonics (e.g. Marty et al., 2009; Konopliv et al., 2006; 2016; Genova et al., 2016). For a TGO like orbit, the orbit perturbations from the seasonal low degree zonal harmonics are about 25 cm for both even and odd harmonics. Therefore, even harmonics could be detected with TGO tracking data if its orbit can be determined with an accuracy of 1 meter or better.Therefore, we performed Precise Orbit Determination from tracking data and a as precise as possible model of the orbital motion of TGO using the GINS software (Marty et al., 2009). Precise Orbit Determination (POD) processAny spacecraft is tracked from the Earth using the radio-link established between the spacecraft and tracking stations on Earth (Holmes et al., 2008). These stations record the variations of the carrier frequency of this radio-link (i.e Doppler effect). However, these Doppler tracking data are not a direct measurement of the variations of the gravity of the planet, but measurements of the spacecraft orbital velocity perturbations projected on to the Earth-spacecraft line-of-sight (LOS) direction. These perturbations are induced by the gravity field (including its time variations) of the planet as well as non-gravitational forces like the atmospheric drag, the solar radiation pressure and the albedo and Infrared radiation from the planet. In addition, Wheel-Off loading maneuvers are regularly performed and generate orbit perturbations. A model of all the forces driven the orbit is performed in order to generate Doppler data to get the residual with the observed Doppler data collected at tracking stations. A least-squares fit of the force model to these Doppler residuals is then performed in order to estimate parameters of the force model including seasonal variations of the zonal harmonics, a scale factor of the non-gravitational forces and a delta-velocity at each WoL event. As the non-gravitational forces act on the faces of the spacecraft, it is represented as flat plates (for the bus, the solar arrays and the High Gain Antenna – HGA) with known optical properties as provided by ESOC. The epoch and a delta-velocity a priori estimate at each WoL are also provided. The POD process is repeated over successive data-arcs of a few days’ duration. Results of POD process on TGO tracking dataTGO is tracked from the Earth 4 hours a day on average using the ESTRACK network (Holmes et al., 2008) using a coherent two-way link in X band. The WoL events are frequent, between 4 and 6 per day. Therefore, most of them are off the tracking passes and the a priori delta-velocity could not be tuned during the least-squares process. This is a limitation on the accuracy of the orbit as shown for Mars Express which shows similar poor tracking coverage (Rosenblatt et al., 2008). The orbit accuracy is estimated using the recovery method over pairs of successive data-arcs (e.g. Konopliv et al., 2006; Rosenblatt et al., 2008; Marty et al., 2009). We obtained 4 meters in the along and cross-track direction on average and about 40 cm in the radial direction (Figure2). This accuracy is worse than the accuracy on Martian polar spacecraft which is about 1-2 meters. The main source of error on TGO orbit comes probably from the frequent WoL events that are far away tracking passes. In addition to ESTRACK passes, DSN passes are daily performed adding 2 more hours of tracking each day. However, it could not compensate the lack of tracking around WoL events so that the orbit accuracy could not be improved. The current accuracy prevented us to retrieve the 25cm signal expected from the seasonal variations of both odd and even zonal harmonics. PerspectivesThe seasonal gravity variations solution could not be improved using TGO tracking data in spite of the theoretically promising opportunity. However, by-products of the POD provide a scale factor of the drag force, which can be interpreted as a scale factor of the atmosphere density model used in the force model. As the orbit altitude of TGO is 400 km, it thus provides an estimation of the density in the exosphere of Mars. Therefore, it can provide a monitoring of this density to study its interaction with the space environment around Mars. The Mars Odyssey (ODY) tracking data have also been used to perform such studies since this spacecraft also orbit Mars at 400 km altitude (e.g. Bruinsma et al., 2014). We plan to compare both ODY and TGO density estimation in order to assess whether the TGO estimates can also be used for exospheric studies. ReferencesBruinsma S. et al. (2014), J. Geophys. Res. : Planets, 119, P, 210-218; Genova A. et al. (2016), Icarus 272, 228-245; Konopliv A.S. et al. (2006), Icarus 182, 23–50; Konopliv A.S. et al. (2016), Icarus 274, 253-260; Marty J.C., et al. (2009), Planet. and Space Sci., 57(3), pp. 350-363 ; Rosenblatt P., et al. (2008), Planet. and Space Sci., 56, pp. 1043-1053.

The Radio-Science experiment of EnVision comprises two sub-experiments (the Gravity experiment and the Radio-occultation experiment) that both relies on the Telemetry, Tracking and Command (TT&C) system of the spacecraft but that have different scientific goals and different operation modes.The Gravity experiment The internal structure of Venus is still uncertain (size and state of the core, mantle viscosity, average lithospheric and crustal thicknesses, as well as their lateral variations). These are key parameters to constrain the mantle composition, thermal evolution and deep interior of the planet. Without the availability of seismic data and Venus having no internal magnetic field to constrain the core state, the gravity field and the moment of inertia can be used to determine the radial structure of the planet. Thanks to its 6 cycles mission and to a 3 to 7 hours of tracking per day, the EnVision gravity field solution will improve the Magellan solution [1] by providing a better global degree strength (l=95 or 204 km at 3-σ) as well as areas of higher resolution and accuracy (

EnVision radio science investigation will deepen our understanding of Venus’ gravity, interior structure and atmospheric properties. To address these scientific questions, a two-way link communication (configuration X/X/Ka-band) is established with the ESA ESTRACK ground stations enabling precise orbit determination (POD) during the science phase. An accurate modeling of the spacecraft’s dynamics, including the atmospheric drag acceleration, is key for retrieving EnVision’s trajectory and constraining Venus’ gravity field, tides and orientation parameters. Dedicated radio occultation campaigns are designed to characterize electron density profiles in the ionosphere and atmospheric density, pressure and temperature in the mesosphere and upper troposphere of Venus. Furthermore, an accurate POD of the spacecraft also provides complementary information on the atmospheric density at the altitudes crossed by the probe, extending the science return of the EnVision mission. The atmospheric drag perturbation strongly affects spacecraft trajectories that are characterized by a pericenter altitude above Venus’ surface of less than 220 km. By accounting for different Venus’ atmospheric models, e.g., the Venus Climate Database (VCD) and the Venus Global Reference Atmospheric Model (Venus-GRAM), we investigate the impact of potential errors and uncertainties in the predicted atmospheric properties on the orbit evolution of the spacecraft. We note significant inconsistencies between Venus’ atmospheric models at the spacecraft altitudes including atmospheric density differences of more than 200%. These discrepancies may be representative of the current knowledge of Venus’ upper atmosphere and thermosphere. Thus, we carried out a perturbative analysis of the dynamical forces by introducing a mismodeling in the atmospheric density profiles. We assumed the VCD for the simulation of the radio tracking measurements and we included as a priori model in the estimation process the Venus-GRAM. By developing a batch sequential filter that adjusts a set of atmospheric density scale factors, we compensated for the mismodeling and improved the quality of the dynamical model and of the orbit determination. The proposed approach enables an estimation of the atmospheric density at the spacecraft altitudes with an accuracy of 25% and accuracies in the orbit reconstruction of 1-2 m, 30-40 m and 20-30 m in the radial, transverse and normal directions.

The main characteristic of Venus that distinguishes it from the other planets is its rotation period, which is very long at 243 Earth days. Although several solutions of this period have been determined using different methods (either from Venus’s orbit or from Earth), this parameter remains poorly constrained. In particular, there is a difference of 7 minutes between the lowest and highest estimates of the rotation period. Currently, only a 3 minute variation in the Length Of the Day (LOD) can be explained by modeling various effects such as the tidal torque exerted on Venus by the Sun and the coupling between the atmosphere and the planet. In our study, we propose a new estimate of the rotation period of Venus using Doppler tracking data from the Venus Express spacecraft. The Venus Express (VEX) mission was launched by the European Space Agency (ESA) in November 2005 and orbited Venus for almost 8 years. The main objective of the mission was to study the planet's atmosphere. To determine a new solution for the rotation period of Venus, we use the Precise Orbit Determination (POD) method, which involves a least-squares adjustment of the difference between the Doppler data collected on Earth and the Doppler data obtained by the numerical integration of forces that can affect the spacecraft's motion. We found a rotation period for Venus of 243.0200 ± 0.0007 days, within the range of values reported in the literature and obtained using different methods and databases. However, the expected periodic variations in the rotation period or the precession rate could not be detected due to the lack of sensitivity of Doppler measurements in the signature of these parameters on the VEX’s trajectory. ESA's EnVision mission, scheduled for launch around 2031, aims to study Venus from its deep core to the top of its atmosphere. We have carried out simulations to predict EnVision's performance. The predicted uncertainty in the rotation period is 0.6 seconds, compared to the uncertainty of 1 minute obtained with VEX. For the precession rate, the predicted uncertainty is 0.2%, compared to 7% obtained with ground-based radar data. The near-polar and low eccentricity of the spacecraft's orbit will provide greater sensitivity to the planet's rotational state.

Mars Express has opened a new chapter in the exploration of Phobos, thanks to its elliptical orbit that allows for regular flybys, sometimes as close as 50 km. Initially designed for studying Mars’ surface and atmosphere, its instruments have provided a wealth of data, including precise geophysical bulk parameters, insights into Phobos’ interior, high-resolution images, remote sensing data of its surface, and observations of interactions between Phobos and the space environment. This resurgence of interest in the Martian moons revolves around the fundamental question of how they formed. Despite the abundance of data gathered by Mars Express, Phobos’ surface composition remains uncertain with many unresolved questions. This ambiguity prevents a definitive confirmation or refutation of the asteroid capture scenario, which likens Phobos to a D-type asteroid. This scenario contradicts the current orbits of the moons and poses other dynamical challenges. However, an alternative hypothesis suggests that Phobos and Deimos formed through the accretion of a rocky debris disk in Mars’ orbit. Their refined shapes, low mass, and bulk density support this idea. The non-detection of MARSIS echoes implies a porous interior, aligning with the low bulk density, indicative of high porosity. The next phase of Phobos exploration will be led by JAXA’s Mars Moon eXplorer (MMX) mission, set to quasi-orbit Phobos, land on its surface, and return a sample to Earth in 2029.

Radio occultation measurements at Venus have provided invaluable insights into the planet's atmospheric properties. One particularly intriguing phenomenon observed during these measurements is radio scintillations, characterized by rapid fluctuations in signal intensity. Radio scintillations are caused by small-scale irregularities in the refractive index associated with small-scale variations of the atmospheric density. A possible source of these density variations is vertical propagating internal gravity waves, which originate in the convective layer between about 50 and 55 km altitude.The frequency dependent radio scintillations were observed at altitude regions of enhanced atmospheric stability, where the propagation of gravity waves is supported. This suggests that gravity waves provide a plausible explanation for the occurrence of radio scintillations. Consequently, the analysis of radio scintillations offers valuable insights into the intensity and global distribution of gravity waves, as well as the strength of the convective winds.We present the results of a scintillation analysis based on Venus Express X-band radio occultation data and compare them with previous measurements and model calculations. Additionally, we discuss the expected outcomes of the EnVision radio scintillation analysis and highlight the advantages of utilizing both X-band and Ka-band radio signals.

The Radio Science Experiment (RSE) onboard EnVision comprises a Radio-Occulation and a Gravity experiment. The scientific objectives of the Gravity experiment onboard EnVision are a thorough determination of Venus’ gravitational anomalies at high spatial resolution, tidal potential Love number k2 and its phase lag, and pole orientation. Accurate measurements of the pole precession, which constrains the moment of inertia of the planet, and gravitational tides preserve key information on the size and state of the core, and the mean viscosity of the mantle. The gravity investigation will use the Doppler shift of the carrier of the telemetry radio-link (X-up and X/Ka-down) between the spacecraft and tracking stations on Earth (ESTRACK network). The Doppler tracking will be performed daily during at least 3.5 hours in the nominal mission that cover 6 entire Venus cycles (4 Earth’s years).The Doppler measurements will be used to precisely determine the spacecraft trajectory from which the gravity field, Love number and moment of inertia solutions are derived. We present numerical simulations that show the radio tracking data analysis for the precise orbit determination (POD) of the spacecraft including the gravity field inversion. Our results show a significant enhancement in spatial resolution (up to 140 km) in areas mainly located in the northern hemisphere. A joint analysis of this high-resolved gravity map and topography will improve the determination of the spatial variation of the crust and lithosphere properties, in turn providing a better understanding of the thermal evolution of the planet. A significant improvement is also obtained for the Love number k2 whose expected accuracy is 0.003. Our analysis shows tidal phase lag and moment of inertia accuracies of 0.3° and 1.5%, respectively. The combination of these geophysical measurements is well-suited to enable tighter constraints on the state and size of the core and the mantle viscosity.Further numerical simulations are carried out to detect the time-variable gravity signature expected from the atmosphere (thermal tides), especially through the estimation of the load Love number. This additional parameter also depends on the internal structure of the planet, leading to complementary information on the core state. We have also taken into account more realistic perturbations of the forces that drive the spacecraft motion, like the drag undergone by the spacecraft at low-altitude part of the orbit, and realistic perturbations of the a priori knowledge of the gravity field itself. These simulations are performed using the GINS software developed by the space French agency CNES.

The precise orbit determination for ESA's EnVision mission is critical for high-resolution surface mapping and geo-physical studies of Venus. This work presents an innovative approach to orbit determination by combining radio tracking data with altimetric crossover measurements for trajectory estimation, while accounting for atmospheric drag perturbations. Venus's dense atmosphere introduces significant drag forces, especially at low altitudes, which must be carefully modeled to ensure precise orbit prediction. Synthetic datasets are produced by estimating atmospheric density from the Venus Climate Database, providing a detailed representation of atmospheric conditions. During the orbit determination phase, corrections to the spacecraft state vector are applied using the Venus-GRAM atmospheric model to account for density time variations. A thorough combination of radio and altimetric data significantly improves the orbit determination accuracy, which is a fundamental requirement for EnVision. An accurate reconstruction of the spacecraft state will enable a precise georeferencing of the measurements that are key to enhancing our understanding of Venus's geophysical properties and atmospheric dynamics.

EnVision has been selected in the M5 call of ESA’s Cosmic Vision program as the next European led mission to Venus. It is dedicated to unravel some of the numerous open questions about Venus' past, current state and future and will help to understand why Venus and Earth evolved so differently. The Radio Science Experiment (RSE) on EnVision will perform extensive studies of the gravitational field but also Radio Occultations to sense the Venus atmosphere and ionosphere at a high vertical resolution of only a few hundred metres. These radio occultations provide electron density profiles in the ionosphere and atmospheric density, temperature and pressure profiles in the upper troposphere and mesosphere (~40 – 90 km). Additionally, they allow to study the H2SO4 absorption in the Venus cloud layer. The first radio occultation experiment at Venus was conducted during the Mariner 5 flyby in 1967, followed by Mariner 10, several Venera missions, Magellan, and the Pioneer Venus Orbiter, and Akatsuki. The most extensive radio occultation study of the Venus atmosphere so far was carried out by the VeRa experiment on Venus Express. EnVision will use two coherent frequencies (X- and Ka-band) to separate dispersive and nondispersive effects. This allows to distinguish between ionospheric wave structures and other noise induced effects in the ionosphere. The use of Ka-band, which has never been used to sense the Venus atmosphere before, allows to study the H2SO4 absorption in the Venus cloud layer due to its high sensitivity to sulfuric acid absorption. Ka-band is also sensitive to liquid H2SO4 which provides the opportunity (in combination with X-band) to distinguish between gaseous and liquid H2SO4 absorption features on Venus for the very first time. The short orbital period of EnVision in combination with its very small orbital inclination allows to cover all latitudes, longitudes, local times and solar zenith angles on Venus. Especially short-term variations caused by atmospheric waves can be identified to study traveling or stationary small scale atmospheric structures.

If Venus were a newly discovered exoplanet, it would be one of the most Earth-like yet identified. Its similarity in size, bulk density and cloud top temperatures give no clue to the hellish temperatures at its surface. Venus hosts an array of geological features as complex as Earth, but without its organisation, and sustains a chemically reactive atmosphere, but without life. Proposed in response to ESA’s M5 call, with enabling support from NASA, EnVision is currently in Phase A study for the next medium-class mission opportunity proceeding towards a final mission selection in summer 2021 for a launch in 2032. Here we discuss the science questions motivating the mission in more detail. Building on discoveries from Magellan, Venus Express and Akatsuki, EnVision will focus on three overarching questions: * Is Venus geodynamically active? * How did Venus arrive at its current state? * How does the Venus climate work and how do the interior, surface and atmosphere interact? 1 – Is Venus geodynamically active? Venus should be geologically active today and its globally young surface implies extensive volcanic resurfacing, but whether this happened in episodic global events or in a continuous process of small-scale resurfacing is uncertain. Constraining the rate of volcanic and tectonic activity can reveal whether Venus occupies one of these end members, or lies somewhere on the spectrum between.

Introduction: The primary goals of the radio-science experiment (RSE) of EnVision are to improve our knowledge of the internal structure of Venus and to contribute to the understanding of the atmospheric sulfur cycle, associated to volcanic emissions. The internal structure of Venus is still uncertain (size and state of the core, average lithospheric and crustal thicknesses, as well as their lateral variations). These are the key parameters to constrain the mantle composition and thermal evolution of the planet. Without the availability of seismic data, the gravity field is the only tool allowing to determine the radial structure of a planet, as well as the regional variations of crustal and lithospheric properties.The sulfuric acid in the atmosphere is part of the sulfur cycle and may be linked to the volcanism activity. The monitoring of its abundance is important to constrain the outgassing from the interior.RSE is then divided into two sub-experiments : the gravity experiment and the atmospheric experiment. RSE will be performed by using the transponder system onboard the spacecraft, with the addition of an Ultra-Stable Oscillator (USO) for the atmospheric experiment.Gravity experiment :The Doppler shift of the carrier frequency of the Earth-to-orbiter radio-link is used to track the spacecraft orbital motion. The asymmetrical planetary gravity field perturbs the motion of the spacecraft in orbit. This perturbed motion is reconstructed from the Doppler tracking data in order to estimate the planetary gravity field. The spatial resolution and the accuracy of this gravity solution depends on the orbital altitude, the total Doppler noise, the coverage, the a priori knowledge of the gravity field itself, the modelling of the non-gravitational forces due to the atmospheric drag, the radiation pressure (solar radiation, cloud top-layer albedo and infra-red emission) as well as residual accelerations generated by attitude maneuvers [1, 2, 3].The elliptical orbits of the Magellan spacecraft have indeed provided a gravity field solution with a spatial resolution of about 300 km on average but include large surface areas with worse (500 km) spatial resolution in the northern and southern hemisphere at mid-latitudes [2, 4]. The EnVision gravity field solution will improve the Magellan solution by providing a spatial resolution of 200 km on average. The planned orbit for the EnVision scientific nominal phase is a polar slightly elliptical orbit (220-525 km altitude), allowing to reach this averaged resolution. The accuracy of the gravity field solution is also expected to be improved because of the lower Doppler frequency noise, compared to Magellan, and of a better coverage due to the length of the mission of 6 cycles (i.e. 4 Earth’s years, with 3.5 effective hours of tracking per day on average performed during the telemetry downlink passes).It is expected that the k2 tidal potential Love number precision will be better than 3% (compared with the 22% for the Magellan solution [5]), which will result in an improved constraint of the state and the size of the core [6]. Radio-occultation experiment:Earth occultations shall be performed to derive the atmospheric structure (temperature, pressure, number density), the H2SO4 absorption and the electron density profile of the ionosphere of Venus [6]. Occultations shall be performed at the beginning and at the end of the telemetry downlink passes, up to 4 ingress and 4 egress observations per day using a one-way X-Ka downlink, thanks to the use of an USO (ADEV better than 5e-13). Because of the short orbital period of EnVision and its near polar orbit, all latitudes, longitudes, local times and solar zenith angles shall be covered. This will allow to observe short-term variations of the temperature and pressure profiles caused by atmospheric waves.The observation of the H2SO4 content is fundamental to understand the cloud formation and convection processes. In particular the sounding by Ka-band (34 GHz) for the first time will allow to derive the H2SO4 content in the altitude range between 35 and 55 km, at the 1 ppm level, because of the high sensitivity of Ka-band to sulfuric acid absorption. The dual-frequency downlinks (simultaneous X- and Ka-bands) will distinguish between gaseous and liquid H2SO4 absorption features at around 50 km altitude (detection at 1 mg/m3 level for the liquid part). H2SO4 temporal variations from hours to years during the mission time shall be investigated with very good latitudinal coverage.References : [1] Marty et al., Planet. Space Sci. 57(3), pp. 350-363 (2009);[2] Konopliv, A.S. et al., Icarus 139(1), pp. 3-18 (1999);[3] Genova et al., Icarus, 272, pp. 228-245 (2016);[4] Anderson, F.C. & Smrekar, S.E., J. Geophys. Res. 111(E8), 10.1029/2004JE002395;[5] Konopliv, A.S. & Yoder, C.F., Geophys. Res. Lett. 23(14), pp. 1857-1860 (1996);[6] Dumoulin C. et al., J. Geophys. Res. 122(6), pp. 1338-1352 (2017).

AbstractVenus remains a relatively unknown planet. The aim of this study is to determine the Venus' rotational state using the Precise Orbit Determination (POD) method with radio tracking data from Venus Express (VEX) spacecraft. We found a spin period of 243.0206 +/- 1.0028 x 10-4 days. This value is consistent with those found in the literature using different methods.IntroductionAlthough Venus is often considered as the Earth's twin sister, our knowledge of its internal structure, including the size and state of its core are limited [1]. Its rotational state, although measured by several techniques (from the orbit or from ground-based radar), is not very well constrained and shows temporal variations that remain unexplained [2]. The Venus Express (VEX) spacecraft was launched by the European Space Agency (ESA) in November 2005 and orbited the planet for nearly 8 years, from mid-2006 to 2014. This mission was dedicated to the study of the atmosphere of the planet, however, the radio-tracking data performed for navigation purposes can also be used to determine the rotational state of the planet.MethodThis study investigates the Doppler tracking data acquired by ESTRACK Network and collected by VEX Radio Science Experiment (VeRa). The data were analyzed by using the Precise Orbit Determination (POD) method. It consists of performing an iterative least-squares adjustment between Doppler data generated form a numerical integration of a force model driving spacecraft's motion and observed tracking data on successive data arcs of 7 days. For this purpose, we use the GINS (Géodésie par Intégrations Numériques Simultanées) software, developed by French space agency (CNES).As outputs, two kinds of parameters are fitted: the local and global parameters. Local ones correspond to parameters calculated for each arc whereas the global parameters are derived from all data-arcs. The rotational state of the planet is part of global parameters such as coefficients of its gravity field and the Love number k2. ResultsWe found a spin period of 243.0206 +/- 1.0028 x 10-4 days. This result is consistent with previous solutions obtained using different tracking data (PVO, Magellan) or methods, such as radar or thermal images form the ground or spacecraft. Figure 1. represents some estimates of Venus' rotation period with respect to their measurement time baseline since 1980. References and methods used for these studies are listed in Table 1.Figure 1 . Estimates of Venus' rotation period, along with their measurement time baseline and corresponding error bars (1 sigma). The outcome of our study is highlighted in red. Table 1. References for estimates of Venus' rotation period rotation presented in Figure 1.Spin period varies- from 243.018 days to 243.023 days, corresponding to a difference of approximately 7 minutes. Furthermore, we observe that the determined values differ depending on the method employed. Our study is in good agreement with the value from Konopliv et al. (1999), who employed the same method as us, as well as the result reported by Campbell et al. (2019) which used Earth-Based radar images. However, our spin period differ from that reported by Margot et al. (2021) end those using other methods such as spaceborne radar [5] or thermal imaging [6].ConclusionIn this study, an estimate of Venus' rotation period is provided. This result is consistent with the values published in the literature. It shows that navigation tracking data of planetary orbiters, such as VEX, can also be used for science investigation. Further work is ongoing to constrain other geophysical parameters that may help us to better understand Venus.AcknowledgementsThe authors want to thank Bernd Häusler and the VEX Radio Science Experiment (VeRa) team, the Centre de Calcul Intensif des Pays de la Loire (CCIPL) and the ESOC Flight Dynamics.References[1] Dumoulin, C. et al.: Tidal constraints on the interior of Venus, J. Geophys. Res. Planets 122, 1338–1352, 2017[2] Cottereau, L. et al.: The various contributions in Venus rotation rate and LOD, Astron. Astrophys. 531, A45, 2011.[3] Konopliv A. S. et al.: Venus Gravity: 180th Degree and Order Model. Icarus 139, 3–18, 1999[4] Margot, J. L. et al.: Spin state and moment of inertia of Venus, Nat Astron 5:676–683, 2021[6] Mueller, N. T. et al.:Rotation period of Venus estimated from Venus Express VIRTIS images and Magellan altimetry, Icarus 217, 474-483, 2012.[7] Campbell, B. A. et al.: The mean rotation rate of Venus from 29 years of Earth-based radar observations, Icarus 332, 19-23, 2019.

Abstract:The gravity field of planets is determined using the Doppler radio-tracking data of orbiting spacecraft. However, this method is intrinsically limited by the orbit of the spacecraft, the noise on the Doppler data, the temporal and spatial coverage of the tracking dataset, as well as the inaccuracies of the non-gravitational perturbations of the spacecraft motion and of the rotation and orientation of the planet.The monitoring of tie-points identified on planetary surface images is helpful to improve the determination of the pole precession and rotation rate of the planet performed with Doppler data alone, and in turn the determination its gravity field.This study investigates the joint inversion of tie-points identified on SAR images data and Doppler tracking data scheduled for the science phase of the EnVision mission to Venus due to be launched in 2031.1- EnVision gravity experimentThe gravity experiment onboard Envision will use the telecommunication system onboard the spacecraft to establish a coherent Doppler link (X-band uplink and dual X/Ka band downlink) between this spacecraft and on ground deep space tracking stations. This link will be established at each telemetry slot providing at least 3,5 hours of effective tracking per day throughout the science phase of the mission, i.e. 6 Venusian days (4 Earth-years). The orbit of the spacecraft is foreseen to be near-polar (inclination of 88°) and slightly elliptical (altitude between 220 km to 525 km).Numerical simulations of this Doppler tracking dataset have been performed to assess the expected precision of the determination of the gravity field (accuracy and spatial resolution) as well as of some geophysical parameters related to the internal structure of the planet, i.e. k2 tidal potential Love number, tidal phase lag and moment of inertia (MoI) of the planet (Rosenblatt et al., 2021).These simulations show that the spatial resolution is better than 200 km over almost all the surface of the planet (Rosenblatt et al., 2024). The k2 tidal Love number is determined with a precision of about 1%, the pole precession with a precision yielding to an uncertainty of 2% on the MoI value, and the tidal phase lag with a precision of about 60% (see Table 1).The uncertainty on k2, tidal phase lag, and MoI values will allow to further constrain models of the internal structure of the planet, in particular the viscosity profile of the mantle (single or multi layers models) (Dumoulin et al., 2017; Musseau et al., 2024).The uncertainty on the rotation rate or length-of-day (LOD) of the planet is 0.03 minutes which is 0.4% of the 7 minutes range of values obtained at different periods and using different methods (see Lévesque et al., 2024).Table 1: Expected uncertainty (3 times the formal error) on geophysical parameters determined with the Doppler tracking data alone.Parameter 3-sigma uncertainty Tidal Love number k2 (real part) 3.6x10-3 (1.2%) Moment of inertia (MoI) 6.4x10-3 (1.9%) Tidal phase lag (in degree) 0.3° (62.2%) Load Love number k’2 0.18 (54%) Length Of Day (LOD) 2x10-5 days (0.03 minute) 2- Simulations of tie-points In order to improve the error on the planet orientation parameters related to the interior structure (i.e. pole precession), we have simulated the monitoring of tie-points that could be built with the radar images that will be taken by the VenSAR instrument throughout the mission science phase.The radar images will be collected over Regions of Interest (RoI) corresponding to about 20% of the planetary surface, offering the opportunity to monitor, over the 6 Venusian days duration of the mission, the position variations, in a celestial reference frame, of several tie-points associated with surface craters, coronae and so on. The spatial resolution of the radar images is foreseen to be 10 meters and 3 meters for some high-resolution images at dedicated local areas. As the geographical coordinates of these tie-points are known in a frame tied to the planet, it is possible to monitor the orientation parameters as well as to determine its rotation rate.We have performed numerical simulations of the retrieval of the orientation parameters using the spatial and temporal coverage of the future VenSAR images. We have identified 104 tie-points and estimated the orientation parameters.Then, we have merged both Doppler and tie-points simulated data to improve the resolution of these parameters and in turn of the gravity field and k2 Love numbers in order to further constrain models of interior. The uncertainty on the geophysical parameters (table 1) is expected to be improved since the tie-points provide additional information on the relative position between the spacecraft and the surface of the planet (Cascioli et al., 2023).References:Cascioli G. et al. (2023), The Planetary Science Journal, 4:65 (14pp); Dumoulin C. et al. (2017), JGR-Planets, 122 (6), 1338-1352; Lévesque M. et al. (2024), this meeting, Musseau Y. et al. (2024), https://doi.org/10.5194/egusphere-egu24-3129; Rosenblatt P. et al. (2021), Remote Sensing, vol. 13, 1624; Rosenblatt et al., (2024), https://doi.org/10.5194/egusphere-egu24-10232.

The ESA mission EnVision will address its main scientific questions through a detailed mapping of the surface and interior properties of Venus. A precise reconstruction of the spacecraft trajectory is a key requirement for the EnVision scientific investigations, including radio science. To precisely constrain the orbit evolution, refined models of the dynamical forces are included in the Precise Orbit Determination (POD) process. We developed a methodology based on a batch -sequential filter that enables a joint estimation of Venus gravity and atmospheric density. Our approach yields an accurate compensation of atmospheric mismodeling, simulated through semi -empirical predictions of the atmospheric density provided by general circulation models (GCM), e.g., Venus Climate Database (VCD). Numerical simulations of the EnVision radio science investigation were carried out by using a perturbative analysis of the dynamical forces, which accounts for atmospheric density errors >= 200%. By adjusting a set of atmospheric scale factors, our proposed strategy enables an estimation of the atmospheric density at the spacecraft altitudes with an accuracy of 25%. The improved dynamical model yields accuracies in the orbit reconstruction of 1-2 m, 30-40 m and 20-30 m in the radial, transverse and normal directions.

<p>The Mars Global Surveyor (MGS), Mars Odyssey (MO), and Mars reconnaissance Orbiter (MRO) Doppler tracking data from 1999 to end of 2021 have been reprocessed, offering the longest time series ever obtained for the gravity field of a planet.</p> <p> </p> <p>The process, called Precise Orbit Determination (POD), uses the Doppler radio-tracking data acquired at the Deep Space Network (DSN) ground stations, and an accurate dynamical model for each spacecraft. This model employs identical up-to-date standards and state-of-the-art of the force models, both surface forces and gravitational forces. A macromodel of each spacecraft (surface area and optical properties of the faces of the probe) is taken into account. It is oriented in space at any time given telemered quaternions. This attitude information of the bus of the spacecraft is completed by the attitude of the articulated solar array and of the steerable high gain antenna with respect to the spacecraft body. In addition, the  self-shadowing effect is introduced for each surface force, atmospheric drag and radiation pressure form the Sun and the planet (albedo and infra-red emission). The angular momentum desaturation maneuvers are taken into account by solving for empirical accelerations at the epoch of each maneuver.</p> <p> </p> <p>This force model allows to compute theoretical Doppler tracking data, then the difference of these predicted data with the tracking data collected at ground stations is computed. Least square fit of this difference is processed over successive data-arcs with a duration of 4 days for each spacecraft. This least squares filter allows to adjust a scale factor of the drag and solar pressure force for each data-arc as well as residual accelerations at each angular momentum desaturation event. The least squares fit results in normal matrices for each data-arc and for each spacecraft. It contains partial derivatives for each coefficient of the force model (scale factors, residual accelerations) as well as for the time series the first zonal gravity field coefficients and for the degree 2 tidal Love number, k2. All the normal matrices are stacked together in order to retrieve a time series of the gravity field from 1999 to 2021 (about 10 Martian year), which has never been obtained before. The k2 Love number solution is also re-estimated.  We analyze the error on the obtained solution depending on the number of satellite we used (1 to 3) and the data timespan used.</p> <p> </p> <p>The retrieved time-varying gravity coefficients and the Love number k2 are then use to tightly constrain the seasonal variations in the mass of the polar caps and the solid tides of Mars, respectively</p>

Introduction The thermal tides are the main cause of the atmospheric pressure variations on Venus, and are expected to generate temporal variations of the low-degree coefficients of the gravity field of the planet (Bills et al., 2020). However, these gravity variations have not yet been detected since the current Venus gravity solution is not accurate enough (Konopliv et al., 1996). In this study, we model the gravity signature of the thermal tides due to surface pressure variations and analyze whether it can be retrieved with the future tracking data of the EnVision spacecraft. Modeling the thermal tides The thermal tides are computed from the output of the Venus Climate Database (Lebonnois et al., 2021). The atmospheric pressure variations are derived as variations around the mean value over the tidal period of 117 Earth days (Figure 1). The associated gravity potential is computed using the following relationships (McCarthy and Petit, 2004): where Clm(t)and Slm(t)are the time-varying part of the Stokes coefficients of the gravitational potential (land mbeing the degree and the order of the spherical harmonics expansion), R, Mand g, are the radius, the mass and the gravitational acceleration of the planet, respectively, and is the load Love number of degree l. The spherical harmonics expansion of the load variations are derived from the surface pressure variations provided by the VCD (Figure 1). This load Love number depends on the rheological properties of the internal layers of the planet (core, mantle, crust). These rheological properties mainly take into account the compressibility and the viscosity of these different layers (Dumoulin et al., 2017; Tobie et al., 2019). The EnVision gravity experiment. The EnVision spacecraft orbit is an elliptical orbit with an altitude range between 220 km and 515 km and an inclination of 88 degrees allowing for high-resolution mapping of the Venus gravity field (Rosenblatt et al., 2021). The EnVision gravity experiment relies on the two-way radio link established on daily passages of at least 3.5 hours long to guarantee the data download required by the EnVision payload. A very stable reference X-band frequency (at 7.1 GHz) is generated at the ground station and sent to the spacecraft, which then sends back to the station a coherent downlink frequency (X-band at 8.4 GHz) thanks to the radio-transponder of the spacecraft telecommunication system. An additional Ka-band downlink coherent frequency (32 GHz) is also sent back to Earth to support the telemetry volume requirements. This two-way X/X-Ka radio link provides a precise Doppler tracking of the EnVision spacecraft over the six Venusian days of the mission science phase. Figure 1: Simulation of the time-varying part of the gravity field due to the surface pressure variations. Left: Map of the pressure variations extracted from the Venus Climate Database – VCD (Lebonnois et al., 2021). It is centered on longitude 180° while the sub-solar point at longitude zero degree. The main signal is dominated by the second-degree harmonics (Bills et al., 2020). Right:time-variations of the second-degree harmonics of the gravitational potential due to the pressure variations over one tidal cycle (117 Earth-days). Simulations of the retrieval of time-varying gravitational potential from the future EnVision tracking data On the basis of the modeling of the thermal tides, we perform simulations of the EnVision gravity experiment following the procedure described in details in Rosenblatt et al. (2021). We thus use the GINS (Géodésie par Intégrations Numériques Simultanées) software developed by CNES (Marty et al., 2009). We simulate the EnVision tracking data with and without the contribution of the time-varying gravitational potential generated by the thermal tides. Then, we perform least squares fit of the difference between both simulated tracking dataset in order to assess the capacity to retrieve the temporal variations of the gravity field due to the thermal tides. The Doppler noise budget and other source of errors in the Precise Orbit Determination process are also taken into account as in Rosenblatt et al. (2021). The goal of this study is in particular to assess our ability to correct the effect of the thermal tides on the estimation of the k2 tidal potential Love number (real and imaginary part). References: Bills B.G. et al. (2020), Icarus, 340, article id. 113568 ; Dumoulin C., et al. (2017), Planets, 122 (6), 1338-1352; Konopliv A.S. & Sjogren W.L. (1996). JPL Publication 96-2 1996; Jet Propulsion Laboratory: Pasadena, CA, USA ; Lebonnois S. et al. (2021). The Venus Climate Database. EPSC2021-234, Europlanet Science Congress 2021, virtual meeting, 13-24 September, 2021; Marty J.C. et al. (2009), Planet. Space Sci. 2009,57, 350–363; McCarthy D.D. & Petit G. (Eds.) IERS Conventions (2003); IERS Technical Note 32; BKG: Frankfurt/Main, Germany, 2004; Rosenblatt P. et al. (2021),Remote Sensing, vol. 13, 1624; Tobie G. et al. (2019), Astronomy & Astrophysics, 630, id.A70, 11 pp.

The Mars Express (MEX) mission has been successfully operated around Mars since 2004. Among many results, MEX has provided some of the most accurate astrometric data of the two Mars moons, Phobos and Deimos. We present new ephemerides of the Mars moons benefitting from all previously published astrometric data to the most recent MEX SRC data. Observations from 1877 until 2018 and including spacecraft measurements from Mariner 9 to MEX were included. Assuming a homogeneous interior, we fitted the forced libration amplitude of Phobos simultaneously with the Martian tidal k 2 ∕ Q ratio and the initial state of the moons. Our solution of the physical libration 1.09 ± 0.01 degrees deviates notably from the homogeneous solution. Considering the very low error bar, however, this may essentially suggest the necessity to consider higher order harmonics with an improved rotation model in the future. While most data could be successfully fitted, we found a disagreement between the Mars Reconnaissance Orbiter and the Mars Express astrometric data at the kilometer level, probably associated with a biased phase correction. The current solution precision is expected at the level of a few hundred meters for Phobos and several hundred meters for Deimos for the coming years. The real accuracy of our new ephemerides will have to be confirmed by comparison with independent observational means.