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With MaQuIs we propose a mission to investigate the gravitational field of Mars. Observing the gravitational field over time yields information about the planets tectonic lithoshphere, mass distribution, and composition. Consequently, this mission allows to study static and dynamic processes on and under the surface of Mars, including phenomena such as melting cycles and tectonic activity.MaQuIs will deploy quantum mechanical means to measure Mars gravitational field with the highest precision yet. In addition, the nature of the proposed instrumentation achieves high sensitivities without needing more complex satellite constellations. As such, MaQuIs follows successful missions for the Earth and Moon, extending the technology to Mars.In this presentation we will outline the expected scientific merit and explain the underlying technology and planned configuration of the mission.

The Planetary Radio Interferometry and Doppler Experiment (PRIDE) technique utilize signal recording and processing technology developed originally for Very Long Baseline Interferometry (VLBI) to determine spacecraft lateral position in ICRF, as an extension of conventional radio-tracking techniques [1]. The essence of the PRIDE technique is in observing the spacecraft radio signal with a network of Earth-based radio telescopes. The PRIDE technique, developed at the Joint Institute for VLBI ERIC (JIVE), has been used for numerous experiments with several ESA planetary science missions. PRIDE has been selected by ESA as one of the eleven science experiments of the Jupiter Icy Moons Explorer (JUICE), the L-class mission scheduled for launch in 2023. Figure 1: PRIDE Experiment for the JUICE Mission The main observables of PRIDE are ultra-precise estimates of spacecraft lateral position based on the phase referenced VLBI tracking and radial Doppler measurements [3,7,8]. The methodology of PRIDE has been proven and validated with the ESA's Venus Express & Mars Express [1,2,4,7,8,9]. PRIDE will contribute to the determination of the JUICE spacecraft state vector and the improvement of the Galilean satellite ephemerides [4,5,10]. It is worth noticing the synergistic nature of PRIDE measurements to other key experiments of the JUICE mission, in particular addressing the major science goals of the mission. Figure 2: PRIDE Experiment Planning chart during the cruise phase of the JUICE Mission. Blue dots indicate celestial positions of radio sources with well-defined coordinates suitable for phase-referencing VLBI [reference on the Petrov's online catalogue]. Red dots show those potential reference sources located within 1 degree to the celestial track of the JUICE spacecraft. The paper will describe the analysis and implementation of system engineering methodologies of the PRIDE inputs into the operational design of the JUICE mission. A particular emphasis will be given on cross instrumental analysis and consolidation of top synergies of PRIDE with other JUICE experiments using the ESA science planning tools. The paper will demonstrate advanced methods of efficient experiment planning and block scheduling. The identification of celestial areas of interest in near-field VLBI (PRIDE) observations of interplanetary spacecraft on all phases of their missions, especially during the cruise phase will also be covered in this paper. References 1) D. A. Duev. et al.: Spacecraft VLBI and Doppler tracking: algorithms and implementation, Astronomy & Astrophysics, 541, A43, 2012 2) G. Molera Calves. et al.: Observations and analysis of phase scintillation of spacecraft signal on the interplanetary plasma". In: A&A 564, A4, 2014 3) D. A. Duev. et al.: Planetary Radio Interferometry and Doppler Experiment (PRIDE) technique: A test case of the Mars Express Phobos fly-by, Astronomy & Astrophysics, Vol. 593, 2016 4) Dirkx D. et al.: Dynamical modeling of the Galilean moons for the JUICE mission, Planetary and Space Science 134 (2016) 82–95 5) Dirkx D. et al.: On the contribution of PRIDE JUICE to Jovian system ephemerides, Planetary and Space Science, 14–27, 2017 6) G. Molera Calves. et al.: Analysis of an Interplanetary Coronal Mass Ejection by a Spacecraft Radio Signal: A Case Study, Space Weather, 15 7) T. M. Bocanegra-Bahamón. et al.: Planetary Radio Interferometry and Doppler Experiment (PRIDE) technique: A test case of the Mars Express Phobos Flyby II. Doppler tracking: Formulation of observed and computed values, and noise budget, Astronomy & Astrophysics, 609, A59, 2018 8) T. M. Bocanegra-Bahamón. et al.: Venus Express radio occultation observed by PRIDE, Astronomy & Astrophysics, 624, A59, 2019 9) G. Molera Calvés. Et a.: High spectral resolution multi-tone Spacecraft Doppler tracking software: Algorithms and implementations, Publications of the Astronomical Society of Australia (PASA), 2021 10) Fayolle et al., Decoupled and coupled moons’ ephemerides estimation strategies - Application to the JUICE mission, submitted to Planetary & Space Science, 2022

There are more than 200 moons in the Solar System, however no exomoon detection has been confirmed so far. Extrasolar gas giants are expected to host exomoons, which could scale in mass with their parent planet up to Earth radii. Two of the gas giant planet-moon systems are in long-lived mean motion resonances (MMRs) and it is expected that the latter would prevail in extrasolar systems as well. Since tidal dissipation depends on the orbital and physical properties of the system, there is a chance that Tidally Heated Exomoons (THEMs; Peters and Turner 2015) are detectable with MIRI/JWST in infrared (IR) wavelengths. ε Eridani b is one of the few known exoplanets with mass greater than 1 MJ and angular separation larger than 0.5 arcseconds on the sky. The proximity to Earth makes ε Eridani b a suitable candidate for the search of THEMs in the IR. Taking the Jovian satellites as an archetype for an exomoon system around ε Eridani b, this would mean that an MMR between two or more exomoons could make them detectable for larger timescales. We explore the parameter space of exomoon orbital and physical properties, conclude which values would make an exomoon around ε Eridani b detectable with MIRI/JWST and investigate the interior structures of the putative exomoon that are consistent with these properties. Our model assumes a layered, radially symmetric moon, consisting of a silicate mantle and a liquid core. We present our results for the Andrade rheology model, different heat transfer mechanisms (mantle convection, heat piping), and constrain feasible interior structures and orbital parameters for several values of (observed) surface heat fluxes.

Introduction The Tudat software was created at the Astrodynamics & Space Missions Section (AS) at TU Delft, as a generic C++ tool for astrodynamics research and education. Since 2020, a Python interface named Tudatpy, has been developed. The core of the software is numerical state propagation and estimation functionality. It has been used for research publications over a wide range of topics, and is embedded in the TU Delft Spaceflight M.Sc. curriculum. The software is released as a conda package. Tudat is hosted on GitHub (https://github.com/tudat-team/), under open-source BSD 3-clause license, with its functionality covered by >200 unit tests. Example applications for planetary missions We start by showing three illustrative examples of past and ongoing work with Tudatpy: Small body orbit design and optimization using fully numerical modeling The dynamical environment around small bodies is highly non-linear. In addition, the uncertainty of the gravity field complicates the search for stable spacecraft orbits. In this context, Tudat has been used for several projects, such as the design of a quasi-stable orbit (QSO) around Phobos (Fig. 1), the optimization of an orbit (for maximum coverage/minimum distance) around an asteroid, and the design of robustly stable spacecraft orbits under uncertainties in the asteroid gravity field. Fig. 1 QSO orbits around Phobos designed using Tudatpy and Pygmo [1] Galilean satellite ephemerides determination from JUICE tracking data The JUICE mission will provide data on the dynamics of the Galilean moons to unprecedented accuracy. Using a simulated set of radio tracking data, Tudat has been used to simulate uncertainty of the ephemerides of the Galilean satellites during and after the JUICE mission (see Fig. 2). This analysis will be extended to provide a flexible tool to analyze the potential for a global inversion of Earth- and space-based radio and optical data for satellite ephemerides. Fig. 2 Galilean satellite ephemeris uncertainty obtained from covariance analysis in a coupled estimation, using simulated JUICE radio tracking data [2] Interplanetary trajectory design using multiple gravity assists (MGA), deep space maneuvers (DSM), and shape-based low-thrust Tudat includes a framework for interplanetary trajectory design (see Fig. 3 for example), where the typical MGA-DSM functionality is enhanced with shape-based (spherical shaping and hodographic shaping) legs. Although the interplanetary trajectory is evaluated/optimized using a (semi-)analytical inner loop, the numerical propagatio of Tudat allows for a direct verification of the final trajectory under perturbations and for the use of differential correction to generate a high-fidelity transfer orbit. Fig. 3 Earth-Mercury transfer using EEVM sequence, one DSM per leg, in patched conic approximation(taken from one of the examples on the Tudatpy website) Functionality Tudat functionality falls into the following broad categories: Numerical propagation of dynamics, with modular setup and options for solar system bodies, accelerations, propagation schemes, etc. In addition to translation state, it can combine different types of dynamics for any number of bodies, including coupled orbital-rotational motion. No fundamental distinction is made between natural and artificial bodies, and the propagation is capable of both single- and multi-arc (or a combination). Tudat has a broad set of outputs (‘dependent variables’) that it can generate during numerical propagation that are useful for visualization/post-processing. State and parameter estimation: Tudat contains a large amount of functionality for performing (simulated) state and parameter estimation/covariance analysis from observational data. The framework is set up in a modular fashion, allowing for a combined analysis of a diverse set of types of observations and parameters. It has been used in a large number of simulation studies, with work ongoing to extend the functionality to processing DSN tracking data. It has been applied to the orbit determination of LRO, as well as to preliminary Doppler/VLBI data analysis of Mars and Venus Express. Mission design and optimization: Modules containing mission design tools, such as Lambert targeters and multiple gravity-assist transfers, are included in Tudat. Additionally, Tudat provides an interface to the Pagmo2 optimization software. Documentation and development In 2020, development of a Python interface, named TudatPy, was initiated. This has now become the default interface for Tudat and associated documentation, including: An installation and top-level user guide, supported by a growing set of example applications (https://docs.tudat.space/) Documentation for the Application Programmer Interface (API) of TudatPy (https://py.api.tudat.space/) Both parts of the documentation now cover the core aspects of the functionality, and are being continuously expanded. At the time of writing, some C++ functions have yet to be exposed to Python, while other functions are missing their API documentation. If you are interested in using or developing Tudat(py), you are most welcome to do so! Any questions about its functionality or suggestions for future implementation are always welcome, and can be addressed to the first author of this abstract. Tudat discussions primarily take place over Slack, open to any potential interested parties. [1] Plumaris et al. (2022). "Cold Atom Interferometry for enhancing the Radio Sciencegravity experiment: a Phobos case study" Remote Sensing, (submitted) [2] Fayolle et al. (2022). "Decoupled and coupled moons’ ephemerides estimation strategiesApplication to the JUICE mission" Planetary and Space Science, (revision submitted)

Tidal response of the Moon provides crucial insight into the structure and rheology of the lunar interior (Williams et al. 2013). The body deformation subject to forces raised by external objects, most evidently Earth and the Sun, induces a variability of the gravitational field, which is characterized by the Love number, k. This effect may, in turn, manifest itself over time in the perturbed motion of orbiting spacecraft (Konopliv et al. 2013; Lemoine et al. 2013).For an elastic body the response to the periodic excitation is instantaneous and relaxation times resulting in phase lags of the response are thus neglected. In reality, the lunar interior exhibits a degree of viscosity and dissipates energy through friction, in which case k not only varies with frequency but also comprises an imaginary part that represents a phase lag in tidal response (Williams et al. 2013).Here, we investigate the signatures of the frequency-dependent Love number in the motion of a lunar orbiter. We formulate the problem following Williams & Boggs (2015), and focus on the variability of five Stokes' coefficients of the second degree effected by k2. The time-varying components are expanded at given characteristic frequencies associated with (linear combinations of) the Delaunay arguments. We make use of the Technical University Delft Astrodynamics Toolbox (Dirkx et al., 2019; https://tudat-space.readthedocs.io/) to investigate the orbit evolution of lunar orbiters, e.g., the Lunar Reconnaissance Orbiter (Mazarico et al. 2018), subject to the time-varying lunar gravitation. Meanwhile, we leverage the analytic theory of Kaula (1966) to illuminate the impact of such specific yet minute perturbations, especially non-short-period variations of the spacecraft orbit (Kaula 1964; Lambeck et al. 1974; Felsentreger et al. 1976).A particular interest here is in the potential estimability of the frequency-dependent phase lag. Following Dirkx et al. (2016), we conduct a preliminary study of the sensitivity of spacecraft orbit adjustment to the said tidal effects. That is, we investigate if, under which conditions, and to what degree, the signals in question will be absorbed by the adjustment of initial states or other parameters, a consequence that will effectively prohibit the detection of the tidal effects. The outcome is expected to shed light on the minimum criteria of their estimation and thus instructive to real-world data analysis in the future. ReferenceDirkx, D., et al. (2016), PSS, 134, 84-95Dirkx, D., et al. (2019), Astrophysics and Space Science, 364:37Kaula W.M. (1964), Reviews of Geophysics, 2, 661-685Kaula W.M. (1966), Theory of Satellite Geodesy, Dover Publications, Inc.Konopliv, A.S., et al. (2013), GRL, 41, 1452-1458 Lambeck, K., et al. (1974), Reviews of Geophysics and Space Physics, 12, 412-434Felsentreger, T.L. et al. (1976), JGR, 81, 2557-2563Lemoine, F.G., et al. (2013), JGRP, 118, 1676-1698Mazarico, E., et al. (2018), PSS, 162, 2-19Williams J.G., et al. (2013), JGRP, 119, 1546-1578Williams J.G., and Boggs, D.H. (2015), JGRP, 120, 689-724

ContextWhen generating ephemerides of natural satellites, available tracking data from different space missions, and/or Earth-based photo-/astrometric observations, are not systematically combined in the estimation. Exploiting the complementarity between different data types and data sets is however a key possibility for improving current solutions [1]. In the near future, this will be particularly crucial for Jupiter’s Galilean moons: the synergy between past and upcoming missions (e.g. Galileo, Juno, JUICE, Europa Clipper) and Earth-based observations is critical to better determine their strongly coupled dynamics [2,3].To facilitate such moons’ ephemerides analyses, we are developing a multi-mission, multi-observation estimation tool. This simulation tool is part of the Tudat(py) open-source software (Python/C++ interfaces, C++ back-end), developed by TU Delft’s Astrodynamics & Space Missions department [4].Estimation tool capabilities Our estimation tool can simulate multiple missions and various observation types. Regarding space missions, any number of spacecraft can be included in the estimation, around any natural body. The simulator typically takes SPICE kernels as inputs for the spacecraft’s trajectories [5]. Any change in mission design can therefore be easily investigated by updating the kernel of interest.The traditional radiometric observables are available (range, Doppler, VLBI), along with direct photo-/astrometry, either Earth- or spacecraft-based. In addition to the spacecraft's and natural bodies' states, various dynamical parameters are estimable, including gravity field coefficients, tidal dissipation parameters, as well as spacecraft- and mission-specific properties (empirical accelerations, observation biases, etc.).The entire estimation software is freely available to the community [4]. As such, it is directly usable and modifiable, also greatly facilitating verification work. An open-source simulator will be provided for the Galilean moons specifically.Ongoing and future applicationsRegarding Galilean moons’ ephemerides, our software has already been used to compare different state estimation strategies, using JUICE tracking data only, as well as to study a novel approach to include mutual approximations in the estimation [6].The upgraded multi-mission, multi-observation tool now allows to quantify the contribution of diverse data types and/or data sets. Furthermore, it provides the means to analyse the solution’s sensitivity to spacecraft’s trajectories, dynamical modelling choices, as well as to the observations’ quality and schedule. This is essential to determine which combination of data sets or which observations planning strategy would benefit the solution most.We will first apply this multi-mission functionality to investigate the unique opportunity for concurrent in-system observations offered by JUICE and Europa Clipper. We will particularly focus on (PRIDE) VLBI data [2], including the possibility for VLBI measurements between the two spacecraft, which would provide valuable information about their relative angular position.We will also extend our tool’s current capabilities, implementing additional observable types to simulate more diverse Earth-based observations (radar, stellar occultations, mutual events, mutual approximations). This will allow us to assess their contribution to the solution, and thus to define priorities, for both observations planning and data merging.[1] Lainey et al., 2020[2] Dirkx et al., 2017[3] Magnanini et al., in preparation[4] https://github.com/tudat-team/tudat-bundle[5] Acton et al., 1996[6] Fayolle et al., 2021

ESA’s JUICE and NASA’s Europa Clipper (EC) are the next two missions to the Jupiter system, focusing on three of the Galilean moons: Europa, Ganymede, and Callisto.JUICE will spend four years in the Jovian system and after tens of flybys of Europa, Ganymede, and Callisto will enter into orbit around Ganymede where it will nominally remain for nine months, until its end of mission. EC will also spend about four years in orbit around Jupiter, performing more than 50 flybys of Europa, the main mission target, but it will also fly by Ganymede and Callisto several times. Combining the data of the two missions will enable a better global estimation of the moons’ gravity fields and ephemerides.During the Jupiter tours of both missions and JUICE’s Ganymede orbital phase, radiometric tracking data will be acquired at Earth ground stations, enabling precise spacecraft orbit determination, and joint estimation of the main dynamical parameters of the Jupiter system. The two missions rely on different radio links: JUICE is endowed with a triple two-way radio link configuration in two frequency bands (X/X, X/Ka and Ka/Ka) which will allow for a full calibration of dispersive noise sources. EC is capable of X/X and X/Ka links, with X/X being the nominal configuration during Europa flybys. Range, range-rate, as well as VLBI (lateral positioning) tracking data, from both missions, will allow to retrieve the static gravity field and tidal parameters of the moons, together with their orbital position. This will also provide crucial information about Jupiter’s gravity tidal parameters, in particular the imaginary part of its Love numbers at the frequency of the Galilean moons. A better characterization of tidal interactions between Jupiter and the Galilean moons can unveil crucial information about the stability and the evolution of the Laplace resonance, governing the dynamics of the three innermost Galilean moons.In this study, we analyze the attainable uncertainties for the parameters characterizing the ephemerides reconstruction of the Galilean moons using range, range-rate, and VLBI simulated observables. VLBI data mainly provide the spacecraft angular position with respect to reference radio sources (quasars) tied to an inertial frame (“plane of sky”), while range and range and range-rate (being computed along the line of sight) especially constrain the spacecraft state within their orbital plane. Including VLBI data is thus expected to be particularly effective in improving the uncertainty of the moon ephemerides in the out-of-plane direction. We will quantify the synergy between the different radiometric observable types, assess their respective contribution to the moons' ephemerides, the imaginary part of Jupiter’s Love number and analyze the sensitivity of the estimation solution to various parameters (observation planning, expected data quality, etc.)

Abstract When generating ephemerides from planetary missions' tracking data, the natural bodies' dynamics are typically estimated separately from the spacecraft's state. A different approach, in which the spacecraft orbit determination and natural bodies' state determination are performed concurrently, allows to fully account for the coupling of the spacecraft's and natural bodies' dynamics. Using JUICE data, we will compare the concurrent spacecraft's and natural satellite's state estimation with the per-flyby estimation of the natural satellite's state followed by a simulated ephemeris determination. The strong coupling between the three inner Galilean moons' dynamics due to Laplace resonances, combined with an unbalanced data set for these moons, makes the JUICE mission a very special test case which is particularly well-adapted to compare the two estimation strategies. 1. Introduction In ephemerides generation, the spacecraft's and natural bodies' dynamics are typically not solved concurrently. When determining the natural bodies' ephemerides from a series of flybys, the state of the central body and the state of the spacecraft with respect to this natural body are first solved for each flyby. The natural bodies' dynamics are then reconstructed in a subsequent step, combining all per-flyby single data points and using them as inputs in a second estimation (e.g. Lainey et al., 2020). However, obtaining a dynamically consistent solution reconciling the natural bodies' states estimated at the different flybys is not always achievable (e.g. Titan's ephemeris from Cassini's flybys, Durante et al., 2019). When using both range and Doppler measurements collected during an orbital phase, the spacecraft orbit determination and ephemeris generation are also conducted in two separate, consecutive steps. The spacecraft's state with respect to the central body is usually first determined using Doppler data. Range measurements can then be translated from spacecraft-centred to body-centred and used to solve for the natural body's dynamics. This is generally a practical approach, as the frequencies of interest are so distinct (Dirkx et al, 2019). However, such estimation approaches do not fully account for the coupling between the spacecraft's and natural bodies' dynamics, thus hindering the achievement of a consistent solution. An alternative strategy therefore consists in concurrently estimating both the spacecraft's and natural bodies' states, the former being solved for in a multi-arc manner while the latter is determined in a single arc. Such a coupled method reduces the risk of a signal in the spacecraft's dynamics being wrongly captured in the natural body's estimated state. The detailed mathematical description of this coupled state estimation, while already used in many other studies (e.g. Dirkx et al, 2019 ; Lari et al., 2019), is not provided in literature and is thus explicitly laid out in Section 2. 2. Coupled estimation To estimate both the spacecraft's and natural bodies' states, the state transition matrix is required. We note the full state at time t (for clarity, dimensions are added as superscripts when needed). It combines the states of n natural bodies yS(t) and the arc-wise spacecraft's state yM,i(t), with t∈[ti,ti+1] (ti being the starting time of arc i). The initial states vector to be estimated is defined as and contains the natural bodies' initial single-arc states and N spacecraft states yM,i(ti), defined at the start of each arc i (N multi-arcs in total). The state transition matrix Φ is then given by where ΦSS and ΦMM,i designate the single-arc and multi-arc state transition matrices, respectively. The matrix ΦMS,i describes the influence of the natural bodies' initial states on the spacecraft's dynamics. On the contrary, the natural bodies' trajectory is assumed to be independent of the spacecraft's. Both Φ and the sensitivity matrix S, necessary to also solve for dynamical parameters q, are propagated and used to perform the estimation. JUICE mission test case The improvement in the ephemerides solution achieved by a concurrent estimation rather than decoupled techniques remains to be quantified. The Galilean moons' ephemerides generation from the JUICE data represents a perfect test case for a comparative analysis. The Laplace resonances between the three innermost Galilean moons indeed induce a very strong coupling between their dynamics. It thus strengthens the need for a consistent concurrent estimation approach when reconstructing their ephemerides. This effect is further enhanced by the unique orbital design of the JUICE mission, which consists in a series of flybys, unevenly distributed between Europa, Ganymede and Callisto, before a long orbital phase around Ganymede. This results in an unbalanced data set, making the highly coupled dynamics of the Galilean moons even more challenging to solve for. We will perform the concurrent state estimation for these satellites, focusing primarily on the flyby phase. We will also check whether a dynamically consistent solution can be achieved when conducting the ephemerides generation separately from the spacecraft orbit determination. If achievable, this solution will be compared with the coupled strategy's one. We will also assess the impact of a fully coupled approach on the estimation of dynamical parameters, investigating tidal dissipation rates in particular, as tidal dissipation processes are key to understanding the long-term evolution of the Jovian system. Future plans The coupled estimation framework presented here will eventually be applied to develop and disseminate an open-source Python estimation simulator for the JUICE mission, with flexible data planning and acquisition scenarios (using Tudat(Py) software: Python interface, C++ back-end). Another future step is to investigate the possible synergy between JUICE and other Jovian system missions: Europa Clipper and possibly IVO. The data sets of these three missions are indeed expected to complement each other, as they separately focus on the three Galilean moons in resonance. The possibility for the Europa Clipper and JUICE spacecraft to be in the Jovian system simultaneously also represents a unique opportunity to perform concurrent in-system measurements. The contribution of such observations to the estimation solution will be quantified. This multi-mission analysis will be achieved by expanding the current coupled estimation framework and developing a global inversion tool to concurrently perform the orbit determination of multiple spacecraft while generating ephemerides for several natural bodies. This extended estimation software, applicable to any tracking scenarios, will also be disseminated open-source with a Python interface.

Thousands of exoplanets have been discovered; however, the detection of exomoons remains elusive. Tidally heated exomoons have been proposed as candidate targets for observation; vigorous tidal dissipation can raise the moon’s surface temperature, making direct imaging possible, and cause widespread volcanism that can have a signature in transits. We assess whether the required amounts of tidal dissipation can be attained and how long it can be sustained. In a first step, we look at the thermal state of a super-Io for different orbital configurations. We show that close-in exomoons with moderate ( e ∼ e Io ) to high ( e ∼ 0.1 ) orbital eccentricities can feature surface heat fluxes 1–3 orders of magnitude higher than that of Io if heat transfer is dominated by heat piping or the moon has a magma ocean. In a second step, we investigate the longevity of a super-Io. The free eccentricity of an isolated close-in exomoon is quickly dampened due to tides; high orbital eccentricities can be maintained if the moon is in a mean-motion resonance with another moon and the planet is highly dissipative. However, this scenario leads to fast orbital migration. For a Mars-sized exomoon, we find that tides alone can raise the surface temperatures to more than 400 K for 10 million yr, and surface heat fluxes higher than that of Io can be maintained for billions of years. Such tidally active bodies are expected to feature more vigorous volcanic activity than Io. The material outgassed via volcanism might be detected in transits.

This work evaluates the added benefit of using laser altimeter measurements for orbit reconstruction. As a spacecraft orbits a celestial body, its altimetry swaths progressively cross previous swaths. These locations, known as crossover points, yield valuable information about the orbited body and the spacecraft trajectory. The mathematical expressions for the inclusion of crossover measurements into orbit determination algorithms are presented and evaluated. It is shown that a first-order approximation of these expressions is insufficient and a more detailed expression is developed. To evaluate the impact of altimetry crossover measurements on orbit determination, the planetary mission Jupiter Icy moons Explorer (JUICE) by the European Space Agency (ESA) is used as a case study by means of a covariance analysis. In this initial analysis, the assumption is made that all altimetry measurements are obtained with nadir pointing which limits the direct applicability of our method until pointing is accounted for.

Context. The apparent close encounters of two satellites in the plane of the sky, called mutual approximations, have been suggested as a different type of astrometric observation to refine the moons’ ephemerides. The main observables are then the central instants of the close encounters, which have the advantage of being free of any scaling and orientation errors. However, no analytical formulation is available yet for the observation partials of these central instants, leaving numerical approaches or alternative observables (i.e. derivatives of the apparent distance instead of central instants) as options. Aims. Filling that gap, this paper develops an analytical method to include central instants as direct observables in the ephemerides estimation and assesses the quality of the resulting solution. Methods. To this end, the apparent relative position between the two satellites is approximated by a second-order polynomial near the close encounter. This eventually leads to an expression for mutual approximations’ central instants as a function of the apparent relative position, velocity, and acceleration between the two satellites. Results. The resulting analytical expressions for the central instant partials were validated numerically. In addition, we ran a covariance analysis to compare the estimated solutions obtained with the two types of observables (central instants versus alternative observables), using the Galilean moons of Jupiter as a test case. Our analysis shows that alternative observables are almost equivalent to central instants in most cases. Accurate individual weighting of each alternative observable, accounting for the mutual approximation’s characteristics (which are automatically included in the central instants’ definition), is however crucial to obtain consistent solutions between the two observable types. Using central instants still yields a small improvement of 10–20% of the formal errors in the radial and normal directions (RSW frame), compared to the alternative observables’ solution. This improvement increases when mutual approximations with low impact parameters and large impact velocities are included in the estimation. Conclusions. Choosing between the two observables thus requires careful assessment, taking into account the characteristics of the available observations. Using central instants over alternative observables ensures that the state estimation fully benefits from the information encoded in mutual approximations, which might be necessary depending on the application of the ephemeris solution.

Introduction Planetary Radio Interferometry and Doppler Experiment (PRIDE) will exploit the signal recording and processing technology developed originally for Very Long Baseline interferometric (VLBI). The essence of PRIDE is in observing the spacecraft radio signal with a network of Earth-based radio telescopes. The PRIDE technique developed at the Joint Institute for VLBI ERIC (JIVE) together with its partners was used for several experiments with several ESA planetary science missions. It has been chosen by ESA as one of the eleven experiments of the Jupiter Icy Moons Explorer (JUICE), the first Large-class mission in the ESA’s Cosmic Vision 2015–2025 program. The mission is scheduled for launch in 2022. Figure 1: A typical PRIDE Experiment 1. PRIDE for JUICE Mission PRIDE is a multidisciplinary component of the JUICE science suite. The main measured deliverables of PRIDE are lateral coordinates L(φ, θ) of spacecraft and the radial velocity of spacecraft. The former (main) measurable of PRIDE requires the phase-referencing VLBI observations (see Duev et al. [1]). The latter employs the Doppler extraction technique described in [7,8]. Its prime deliverable will be used primarily for improvement of the Jovian system ephemerides in support to a variety of applications, ranging from gravimetry to geodynamics to fundamental physics. A typical PRIDE experiment is shown in Figure 1. PRIDE observations are carried out by the ground segment when the spacecraft emits a radio signal for communication or radio science purposes. The methodology of PRIDE has been demonstrated with the ESA's Venus Express & Mars Express by Duev et al. 2012 [1], Molera Calvés et al. 2014 [2], Duev et al. 2016 [4], Molera Calvés et al. 2017 [8], Bocanegra et al. 2018 [7], Bocanegra et al. 2019 [8]. In addition to nominal science objectivities, the team is considering ad hoc observations around the Venus and Mars flybys during the cruise phase. A covariance analysis for a broad scope of the PRIDE measurable and Jovian system parameters have been performed to optimize the observation planning and the overall science impact of the JUICE mission (Dirkx. D et al. 2016 [4] & Dirkx. D et al. 2017 [5]). 2. Ongoing PRIDE observing projects In 2020, we have begun a campaign to gather PRIDE tracking data of the InSight lander, with up to three tracking epochs scheduled for each of the three 2020 EVN sessions. The primary goal of these experiments is to serve as a preparatory activity for more intensive operations for ExoMars-LaRa [9]. The primary manner in which PRIDE will be able to contribute to the science objectives of LaRa is through the use of the Doppler data obtained by all receiving stations. As shown by the analysis of Bocanegra et al. 2018 [7], PRIDE Doppler data at X-band is similar, and in some cases, higher quality compared to regular closed-loop tracking data. One advantage of PRIDE lies in its diversity of receiving stations, making the data quality much less dependent on the meteorological or operational conditions at a single telescope. Figure 2: Frequency detections of Mars Insight (NASA) as seen from the University of Tasmania network of radio telescopes. The spacecraft signal was detected at the sky frequency of 8407.25 MHz and Doppler shift of 50 kHz along 70 minutes of tracking Besides, we propose to merge the three-way Doppler data generated at each receiving station, to fully exploit the data encoded in all downlinks. This would allow an improved calibration of receiving station noise levels, as the noise incurred locally at the receiving ground station (including Earth tropospheric and ionospheric noise on the downlink) is independent for each station. We will use the InSight tracking data to test different practical approached to achieving this conceptual aim, and apply these ‘lessons learned’ to ExoMars-LaRa data analysis. In particular, we will apply the InSight tracking data to investigate different manners in which to weigh the data, considering the fact that the three-way Doppler noise generated at all receiving stations is highly correlated, and to investigate how inter-station biases and drifts can best be calibrated for. The results of the ongoing PRIDE observations of NASA's InSight probe will be reported elsewhere (Dirkx. D, Le Maistre. S, Dehant. V et al., in preparation). References D. A. Duev. et al.: Spacecraft VLBI and Doppler tracking: algorithms and implementation, Astronomy & Astrophysics, 541, A43, 2012 G. Molera Calves. et al.: Observations and analysis of phase scintillation of spacecraft signal on the interplanetary plasma". In: A&A 564, A4, 2014 D. A. Duev. et al.: Planetary Radio Interferometry and Doppler Experiment (PRIDE) technique: A test case of the Mars Express Phobos fly-by, Astronomy & Astrophysics, Vol. 593, 2016 Dirkx D. et al.: Dynamical modeling of the Galilean moons for the JUICE mission, Planetary and Space Science 134 (2016) 82–95 Dirkx D. et al.: On the contribution of PRIDE JUICE to Jovian system ephemerides, Planetary and Space Science, 14–27, 2017 G. Molera Calves. et al.: Analysis of an Interplanetary Coronal Mass Ejection by a Spacecraft Radio Signal: A Case Study, Space Weather, 15 T. M. Bocanegra-Bahamón. et al.: Planetary Radio Interferometry and Doppler Experiment (PRIDE) technique: A test case of the Mars Express Phobos Flyby II. Doppler tracking: Formulation of observed and computed values, and noise budget, Astronomy & Astrophysics, 609, A59, 2018 T.M. Bocanegra-Bahamón. et al.: Venus Express radio occultation observed by PRIDE, Astronomy & Astrophysics, 624, A59, 2019 Dehant V. et al.: The radioscience LaRa instrument onboard ExoMars 2020 to investigate the rotation and interior of Mars, Planetary and Space Science 180, 104776, 2020

Full list of authors: Blanc, Michel; Prieto-Ballesteros, Olga; André, Nicolas; Gomez-Elvira, Javier; Jones, Geraint; Sterken, Veerle; Desprats, William; Gurvits, Leonid I.; Khurana, Krishan; Balmino, Georges; Blöcker, Aljona; Broquet, Renaud; Bunce, Emma; Cavel, Cyril; Choblet, Gaël; Colins, Geoffrey; Coradini, Marcello; Cooper, John; Dirkx, Dominic; Fontaine, Dominique; Garnier, Philippe; Gaudin, David; Hartogh, Paul; Hussmann, Hauke; Genova, Antonio; Iess, Luciano; Jäggi, Adrian; Kempf, Sascha; Krupp, Norbert; Lara, Luisa; Lasue, Jérémie; Lainey, Valéry; Leblanc, François; Lebreton, Jean-Pierre; Longobardo, Andrea; Lorenz, Ralph; Martins, Philippe; Martins, Zita; Marty, Jean-Charles; Masters, Adam; Mimoun, David; Palumba, Ernesto; Parro, Victor; Regnier, Pascal; Saur, Joachim; Schutte, Adriaan; Sittler, Edward C.; Spohn, Tilman; Srama, Ralf; Stephan, Katrin; Szegő, Károly; Tosi, Federico; Vance, Steve; Wagner, Roland; Van Hoolst, Tim; Volwerk, Martin; Wahlund, Jan-Erik; Westall, Frances; Wurz, Peter, Europa is the closest and probably the most promising target to search for extant life in the Solar System, based on complementary evidence that it may fulfil the key criteria for habitability: the Galileo discovery of a sub-surface ocean; the many indications that the ice shell is active and may be partly permeable to transfer of chemical species, biomolecules and elementary forms of life; the identification of candidate thermal and chemical energy sources necessary to drive a metabolic activity near the ocean floor. In this article we are proposing that ESA collaborates with NASA to design and fly jointly an ambitious and exciting planetary mission, which we call the Joint Europa Mission (JEM), to reach two objectives: perform a full characterization of Europa's habitability with the capabilities of a Europa orbiter, and search for bio-signatures in the environment of Europa (surface, subsurface and exosphere) by the combination of an orbiter and a lander. JEM can build on the advanced understanding of this system which the missions preceding JEM will provide: Juno, JUICE and Europa Clipper, and on the Europa lander concept currently designed by NASA (Maize, report to OPAG, 2019). We propose the following overarching goals for our Joint Europa Mission (JEM): Understand Europa as a complex system responding to Jupiter system forcing, characterize the habitability of its potential biosphere, and search for life at its surface and in its sub-surface and exosphere. We address these goals by a combination of five Priority Scientific Objectives, each with focused measurement objectives providing detailed constraints on the science payloads and on the platforms used by the mission. The JEM observation strategy will combine three types of scientific measurement sequences: measurements on a high-latitude, low-altitude Europan orbit; in-situ measurements to be performed at the surface, using a soft lander; and measurements during the final descent to Europa's surface. The implementation of these three observation sequences will rest on the combination of two science platforms: a soft lander to perform all scientific measurements at the surface and sub-surface at a selected landing site, and an orbiter to perform the orbital survey and descent sequences. We describe a science payload for the lander and orbiter that will meet our science objectives. We propose an innovative distribution of roles for NASA and ESA; while NASA would provide an SLS launcher, the lander stack and most of the mission operations, ESA would provide the carrier-orbiter-relay platform and a stand-alone astrobiology module for the characterization of life at Europa's surface: the Astrobiology Wet Laboratory (AWL). Following this approach, JEM will be a major exciting joint venture to the outer Solar System of NASA and ESA, working together toward one of the most exciting scientific endeavours of the 21st century: to search for life beyond our own planet. © 2020, The authors received support from the sponsors of their home institutions during the development of their projects, particularly at the two institutes leading this effort: at IRAP, Toulouse, MB and NA acknowledge the support of CNRS, University Toulouse III - Paul Sabatier and CNES. At CAB, Madrid, OPB and JGE acknowledge the support of INTA and Spanish MINECO project ESP2014-55811-C2-1-P and ESP2017-89053-C2-1-P and the AEI project MDM-2017-0737 Unidad de Excelencia "Maria de Maeztu". We would also like to extend special thanks to the PASO of CNES for its precious assistance and expertise in the design of the mission scenario.

We report on our efforts to test the Einstein Equivalence Principle by measuring the gravitational redshift with the VLBI spacecraft RadioAstron, in an eccentric orbit around Earth with geocentric distances as small as $\sim$ 7,000 km and up to 350,000 km. The spacecraft and its ground stations are each equipped with stable hydrogen maser frequency standards, and measurements of the redshifted downlink carrier frequencies were obtained at both 8.4 and 15 GHz between 2012 and 2017. Over the course of the $\sim$ 9 d orbit, the gravitational redshift between the spacecraft and the ground stations varies between $6.8 \times 10^{-10}$ and $0.6 \times 10^{-10}$. Since the clock offset between the masers is difficult to estimate independently of the gravitational redshift, only the variation of the gravitational redshift is considered for this analysis. We obtain a preliminary estimate of the fractional deviation of the gravitational redshift from prediction of $\epsilon = -0.016 \pm 0.003_{\rm stat} \pm 0.030_{\rm syst}$ with the systematic uncertainty likely being dominated by unmodelled effects including the error in accounting for the non-relativistic Doppler shift. This result is consistent with zero within the uncertainties. For the first time, the gravitational redshift has been probed over such large distances in the vicinity of Earth. About three orders of magnitude more accurate estimates may be possible with RadioAstron using existing data from dedicated interleaved observations combining uplink and downlink modes of operation., Comment: 16 pages, 6 figures, accepted for publication in Advances in Space Research. arXiv admin note: text overlap with arXiv:1710.10074

Next-generation planetary tracking methods, such as interplanetary laser ranging (ILR) and same-beam interferometry (SBI) promise an orders-of-magnitude increase in the accuracy of measurements of solar system dynamics. This requires a reconsideration of modelling strategies for the translational and rotational dynamics of natural bodies, to ensure that model errors are well below the measurement uncertainties. The influence of the gravitational interaction of the full mass distributions of celestial bodies, the so-called figure-figure effects, will need to be included for selected future missions. The mathematical formulation of this problem to arbitrary degree is often provided in an elegant and compact manner that is not trivially relatable to the formulation used in space geodesy and ephemeris generation. This complicates the robust implementation of such a model in operational software packages. We formulate the problem in a manner that is directly compatible with the implementation used in typical dynamical modelling codes: in terms of spherical harmonic coefficients and Legendre polynomials. An analytical formulation for the associated variational equations for both translational and rotational motion is derived. We apply our methodology to both Phobos and the KW4 binary asteroid system, to analyze the influence of figure-figure effects during estimation from next-generation tracking data. For the case of Phobos, omitting these effects during estimation results in relative errors of $0.42\%$ and $0.065\%$ for the $\bar{C}_{20}$ and $\bar{C}_{22}$ spherical harmonic gravity field coefficients, respectively. These values are below current uncertainties, but orders of magnitude larger than those obtained from past simulations for accurate tracking of a future Phobos lander., 29 pages, 4 figures (accepted for publication by Astrophysics and Space Science)

This paper presents a software-defined testbed to perform hardware-in-The-loop test of miniaturized coherent transponders. Such a setup has been designed to minimize the access threshold for future users, heavily relying on available open source applications and commercial hardware, targeting future coherent transponders for interplanetary CubeSats. The paper presents the overall architecture of the testbed, a tradeoff to select the most suited development framework and the detailed design of the different blocks. Upcoming interplanetary CubeSat missions that would require a coherent transponder are also presented to highlight the need sof such a system. Software qualification, given the use of third-party software with multiple developers, was also addressed to guarantee performances can be consistent and reliable.

At present, tracking data for planetary missions largely consists of radio observables: range-rate range and angular position. Future planetary missions may use Interplanetary Laser Ranging (ILR) as a tracking observable. Two-way ILR will provide range data that are about 2 orders of magnitude more accurate than radio-based range data. ILR does not produce Doppler data, however. In this article, we compare the relative strength of radio Doppler and laser range data for the retrieval of parameters of interest in planetary missions, to clarify and quantify the science case of ILR, with a focus on geodetic observables. We first provide an overview of the near-term attainable quality of ILR, in terms of both the realization of the observable and the models used to process the measurements. Subsequently, we analyze the sensitivity of radio-Doppler and laser-range measurements in representative mission scenarios. We use both an analytical approximation and numerical analyses of the relative sensitivity of ILR and radio Doppler observables for more general cases. We show that mm-precise range normal points are feasible for ILR, but mm-level accuracy and stability is unlikely to be attained, due to a combination of instrumental and model errors. ILR has the potential for superior performance in observing signatures in the data with a characteristic period of greater than 0.33-1.65 hours This indicates that Doppler tracking will typically remain the method of choice for gravity field determination and spacecraft orbit determination in planetary missions. Laser ranging data, however, are shown to have a significant advantage for the retrieval of rotational and tidal characteristics from landers. Similarly, laser ranging data will be superior for the construction of planetary ephemerides and the improvement of solar system tests of gravitation., Accepted for publication in Journal of Geodesy

We present an approach to testing the gravitational redshift effect using the RadioAstron satellite. The experiment is based on a modification of the Gravity Probe A scheme of nonrelativistic Doppler compensation and benefits from the highly eccentric orbit and ultra-stable atomic hydrogen maser frequency standard of the RadioAstron satellite. Using the presented techniques we expect to reach an accuracy of the gravitational redshift test of order $10^{-5}$, a magnitude better than that of Gravity Probe A. Data processing is ongoing, our preliminary results agree with the validity of the Einstein Equivalence Principle., Comment: Submitted to Physics Letters A

Laser ranging is an emerging technology for tracking interplanetary missions, offering both range accuracy and precision at the level of several millimeters. The ground segment uses existing Satellite Laser Ranging (SLR) technology, whereas the space segment requires an active system for either one- or two-way ranging. We numerically investigate the performance of one- and two-way active planetary laser ranging systems to quantify the difference in science return from missions employing this technology. In doing so, we assess the added value of the more complicated two-way system compared to its one-way counterpart. We simulate range measurement errors for both types of systems, using clock error time histories generated from Allan variance profiles. We use two test cases: a lunar polar orbiter and a Phobos lander. In the Phobos lander simulations, we include the estimation of Phobos librations and (C) over bar (2,2) gravity field coefficient. For the lunar orbiter, we include an empirical force-error model in our truth model. We include the estimation of clock parameters over a variety of arc lengths for one-way range data analysis and use a variety of state arc durations for the lunar orbiter simulations. For the lunar orbiter, performance of the one- and two-way system is similar for sufficiently short clock arcs. This indicates that dynamical-model error, not clock noise, is the dominant source of estimation uncertainty. However, correlations between the clock and state parameters cause an exchange between clock and state signal for the one-way system, making these results less robust. The results for the Phobos lander show superior estimation accuracy of the two-way system. However, knowledge of Phobos' interior mass distribution from both the one- or two-way system would currently be limited to the same level by inaccuracies in our knowledge of Phobos' volume. Both the lunar orbiter and Phobos lander simulations show that the use of two-way planetary laser ranging should be accompanied by improvements in associated measurements and models to allow this data type to be exploited to its full potential. (C) 2015 Elsevier Ltd. All rights reserved.

In this paper we investigate the influence of atmospheric turbulence on the performance of the uplink of a planetary transceiver laser ranging system using a single photon detector. We numerically combine the influence of turbulence in the mean intensity profile variations, scintillation, beam-wander induced pointing errors and stochastic time-of-flight variations, using the Hufnagel–Valley turbulence profile to model the ground turbulence behavior. We map the intensity variations due to turbulence to variations in the probability distribution of the arrival time of the 1st photon in a laser pulse, which influences the range measurement error probability distribution. The turbulence models are applied to assess the influence on single-pass range accuracy and precision statistics, as well as the parameter estimation quality of a Phobos Laser Ranging (PLR) mission. The difference in range measurement error between weak and strong turbulence is 3–4 mm in a PLR concept. This indicates that turbulence is a potentially important contributor to the error budget of interplanetary laser ranging missions, which aim at mm-level accuracy and precision. The single-shot precision is weakly influenced by turbulence, but strong turbulence is found to cause a strong decrease in detected pulse fraction, reducing normal point precision. We show that a trade-off between range accuracy and precision must be made when selecting laser system parameters, considerations for which are influenced by atmospheric turbulence effects. By consistently operating at the single-photon signal strength level, accuracy variations can be largely removed, at the expense of normal point precision, due to the reduced detection probability. We perform parameter estimation of Phobos initial state and observation biases using simulated measurements with and without turbulence, using a daily periodic turbulence strength model. We show that the parameter estimation quality is degraded significantly below that of the turbulence-free case only in the presence of strong turbulence. This shows the existence of a limit of ground turbulence strength below which its influence on parameter estimation becomes negligible.

Time measured by an ideal clock crucially depends on the gravitational potential and velocity of the clock according to general relativity. Technological advances in manufacturing high-precision atomic clocks have rapidly improved their accuracy and stability over the last decade that approached the level of 10$^{-18}$. Based on a fully relativistic description of the background gravitational physics, we discuss the impact of those highly-precise clocks on the realization of reference frames and time scales used in geodesy. We discuss the current definitions of basic geodetic concepts and come to the conclusion that the advances in clocks and other metrological technologies will soon require the re-definition of time scales or, at least, clarification to ensure their continuity and consistent use in practice. The relative frequency shift between two clocks is directly related to the difference in the values of the gravity potential at the points of clock's localization. According to general relativity the relative accuracy of clocks in 10$^{-18}$ is equivalent to measuring the gravitational red shift effect between two clocks with the height difference amounting to 1 cm. We show how clock measurements can provide geopotential numbers for the realization of gravity-field-related height systems and can resolve discrepancies in classically-determined height systems as well as between national height systems. Another application of clocks is the direct use of observed potential differences for the improved recovery of regional gravity field solutions. Finally, clock measurements for space-borne gravimetry are analyzed along with closely-related deficiencies of this method like an extra-ordinary knowledge of the spacecraft velocity, etc. For all these applications besides the near-future prospects, we also discuss the challenges that are related to using those novel clock data in geodesy., Will be published in Space Science Reviews as special issue on High Performance Clocks which is organized by ISSI

The JUICE mission will perform detailed measurements of the properties of the Galilean moons, with a nominal in-system science-mission duration of about 3.5 years. Using both the radio tracking data, and (Earth- and JUICE-based) optical astrometry, the dynamics of the Galilean moons will be measured to unprecedented accuracy. This will provide crucial input to the determination of the ephemerides and physical properties of the system, most notably the dissipation in Io and Jupiter. The data from Planetary Radio Interferometry and Doppler Experiment (PRIDE) will provide the lateral position of the spacecraft in the ICRF. In this article, we analyze the relative quantitative influence of the JUICE-PRIDE observables to the determination of the ephemerides of the Jovian system and the associated physical parameters. We perform a covariance analysis for a broad range of mission and system characteristics. We analyze the influence of VLBI data quality, observation planning, as well as the influence of JUICE orbit determination quality. This provides key input for the further development of the PRIDE observational planning and ground segment development. Our analysis indicates that the VLBI data are especially important for constraining the dynamics of Ganymede and Callisto perpendicular to their orbital planes. Also, the use of the VLBI data makes the uncertainty in the ephemerides less dependent on the error in the orbit determination of the JUICE spacecraft itself. Furthermore, we find that optical astrometry data of especially Io using the JANUS instrument will be crucial for stabilizing the solution of the normal equations. Knowledge of the dissipation in the Jupiter system cannot be improved using satellite dynamics obtained from JUICE data alone, the uncertainty in Io's dissipation obtained from our simulations is similar to the present level of uncertainty., Comment: 18 pages, 4 figures, accepted for publication in PSS

Laser ranging is emerging as a technology for use over (inter)planetary distances, having the advantage of high (mm-cm) precision and accuracy and low mass and power consumption. We have performed numerical simulations to assess the science return in terms of geodetic observables of a hypothetical Phobos lander performing active two-way laser ranging with Earth-based stations. We focus our analysis on the estimation of Phobos and Mars gravitational, tidal and rotational parameters. We explicitly include systematic error sources in addition to uncorrelated random observation errors. This is achieved through the use of consider covariance parameters, specifically the ground station position and observation biases. Uncertainties for the consider parameters are set at 5 mm and at 1 mm for the Gaussian uncorrelated observation noise (for an observation integration time of 60 s). We perform the analysis for a mission duration up to 5 years. It is shown that a Phobos Laser Ranging (PLR) can contribute to a better understanding of the Martian system, opening the possibility for improved determination of a variety of physical parameters of Mars and Phobos. The simulations show that the mission concept is especially suited for estimating Mars tidal deformation parameters, estimating degree 2 Love numbers with absolute uncertainties at the 10−2 to 10−4 level after 1 and 4 years, respectively and providing separate estimates for the Martian quality factors at Sun and Phobos-forced frequencies. The estimation of Phobos libration amplitudes and gravity field coefficients provides an estimate of Phobos׳ relative equatorial and polar moments of inertia with an absolute uncertainty of 10−4 and 10−7, respectively, after 1 year. The observation of Phobos tidal deformation will be able to differentiate between a rubble pile and monolithic interior within 2 years. For all parameters, systematic errors have a much stronger influence (per unit uncertainty) than the uncorrelated Gaussian observation noise. This indicates the need for the inclusion of systematic errors in simulation studies and special attention to the mitigation of these errors in mission and system design.

During the conceptual design of a re-entry vehicle, the vehicle shape and geometry can be varied and its impact on performance can be evaluated. In this study, the shape optimization of two classes of vehicles has been studied: a capsule and a winged vehicle. Their aerodynamic characteristics were analyzed using local-inclination methods, automatically selected per vehicle segment. Entry trajectories down to Mach 3 were calculated assuming trimmed conditions. For the winged vehicle, which has both a body flap and elevons, a guidance algorithm to track a reference heat-rate was used. Multi-objective particle swarm optimization was used to optimize the shape using objectives related to mass, volume and range. The optimizations show a large variation in vehicle performance over the explored parameter space. Areas of very strong non-linearity are observed in the direct neighborhood of the two-dimensional Pareto fronts. This indicates the need for robust exploration of the influence of vehicle shapes on system performance during engineering trade-offs, which are performed during conceptual design. A number of important aspects of the influence of vehicle behavior on the Pareto fronts are observed and discussed. There is a nearly complete convergence to narrow-wing solutions for the winged vehicle. Also, it is found that imposing pitch-stability for the winged vehicle at all angles of attack results in vehicle shapes which require upward control surface deflections during the majority of the entry.

Using the methods and models described in the previous chapters, we present the results of the shape optimization of the capsule vehicle in this chapter. We start by discussing the results of a Monte Carlo analysis of the search space, from which we draw preliminary conclusions on the influence of the various contraint functions. Subsequently, we show the optimization results for the following objective functions: optimal heat load, volumetric efficiency and ground track length. Both the double-objective results (for each combination) and the full triple-objective results are shown. By comparing these results, it is clear that full three-dimensional Pareto front could not have been reproduced or deduced from the three two-dimensional fronts, indicating the need for considering multiple competing objectives.

Using the methods and models described in the previous chapters, we present the results of the shape optimization of the winged vehicle in this chapter. We start by discussing the results of a Monte Carlo analysis of the search space, from which we draw preliminary conclusions on the influence of the various constraint functions, and their correlation with the shape parameters. Subsequently, we show the optimization results for the following objective functions: vehicle mass, fuselage volume and ground track length. Both the double-objective results (for each combination) and the full triple-objective results are shown. We perform two additional alternative optimizations, one for which the pitch stability constrain is imposed for all angles of attach (instead of \(\alpha > 20^{\circ }\)) and one where the range objective is replaced with a maximum time at reference heat flux objectives. The results of these optimizations provide insight into the influence of a change in vehicle and mission requirements, respectively.

Radio tracking and astrometric data obtained by the JUICE mission, using the PRIDE, 3GM and JANUS instruments, will allow the dynamics of the Galilean moons to be measured to unprecedented accuracy. As a result, the dynamical models used for creating ephemerides from these data will most likely require the inclusion of various heretofore neglected physical effects. To determine which effects will need to be included, we perform a sensitivity analysis of the influence on the dynamics of the system for a wide array of gravitational, tidal and rotational characteristics of the system. We estimate the dynamics of the Galilean moons with a given perturbation turned off, using ideal three-dimensional measurements of the satellites' positions generated with these perturbations turned on. In doing so, we assess the capabilities of the nominal dynamical model to absorb the influence of this perturbations. We analyze the dynamical behaviour over a period of five years, and limit our analysis to effects that may be observable from JUICE radio tracking and optical astrometry data. Our simulations comprise a short-period (5 years) sensitivity analysis of the dynamics of the moons, and not a simulation of the tracking data inversion for JUICE. Our analysis indicates that the nominal dynamical model of the Galilean satellites can very efficiently absorb the influence of the current uncertainties in most of the physical parameters of the Jovian system, to a level where these uncertainties will not be influential for JUICE-derived ephemerides. An important exception is the influence of tidal dissipation: the k 2 / Q of Io will be clearly observable by JUICE tracking data, which will be strongly correlated with the weaker effect of Jupiter's k 2 / Q . The dissipation inside Europa may also be weakly constrained by JUICE tracking data. Without improvements in the Jovian gravity field from the Juno mission, the estimation of Jupiter zonal gravity field coefficients at degrees 2, 3 and 5 should be included in the ephemerides generation. The influence of the deviation from perfect tidal locking of the moons' rotation is at the limit of observability. Furthermore, we have verified that the present uncertainty in the a priori ephemeris of Jupiter will not influence the (Jupiter-centered) dynamics of the Galilean moons at an observable level.

Context. Radio occultation is a technique used to study planetary atmospheres by means of the refraction and absorption of a spacecraft carrier signal through the atmosphere of the celestial body of interest, as detected from a ground station on Earth. This technique is usually employed by the deep space tracking and communication facilities (e.g., NASA’s Deep Space Network (DSN), ESA’s Estrack). Aims. We want to characterize the capabilities of the Planetary Radio Interferometry and Doppler Experiment (PRIDE) technique for radio occultation experiments, using radio telescopes equipped with Very Long Baseline Interferometry (VLBI) instrumentation. Methods. We conducted a test with ESA’s Venus Express (VEX), to evaluate the performance of the PRIDE technique for this particular application. We explain in detail the data processing pipeline of radio occultation experiments with PRIDE, based on the collection of so-called open-loop Doppler data with VLBI stations, and perform an error propagation analysis of the technique. Results. With the VEX test case and the corresponding error analysis, we have demonstrated that the PRIDE setup and processing pipeline is suited for radio occultation experiments of planetary bodies. The noise budget of the open-loop Doppler data collected with PRIDE indicated that the uncertainties in the derived density and temperature profiles remain within the range of uncertainties reported in previous Venus’ studies. Open-loop Doppler data can probe deeper layers of thick atmospheres, such as that of Venus, when compared to closed-loop Doppler data. Furthermore, PRIDE through the VLBI networks around the world, provides a wide coverage and range of large antenna dishes, that can be used for this type of experiments.

This article reviews a spectral forward gravity field modelling method that was initially designed for topographic/isostatic mass reduction of gravity data. The method transforms 3D spherical density models into gravitational potential fields using a spherical harmonic representation. The binomial series approximation in the approach, which is crucial for its computational efficiency, is examined and an error analysis is performed. It is shown that, this method cannot be used for density layers in crustal and upper mantle regions, because it results in large errors in the modelled potential field. Here, a correction is proposed to mitigate this erroneous behaviour. The improved method is benchmarked with a tesseroid gravity field modelling method and is shown to be accurate within ±4 mGal for a layer representing the Moho density interface, which is below other errors in gravity field studies. After the proposed adjustment the method can be used for the global gravity modelling of the complete Earth's density structure.

We used one-way laser ranging data from International Laser Ranging Service (ILRS) ground stations to NASA's Lunar Reconnaissance Orbiter (LRO) for a demonstration of orbit determination. In the one-way setup, the state of LRO and the parameters of the spacecraft and all involved ground station clocks must be estimated simultaneously. This setup introduces many correlated parameters that are resolved by using a priori constraints. Moreover the observation data coverage and errors accumulating from the dynamical and the clock modeling limit the maximum arc length. The objective of this paper is to investigate the effect of the arc length, the dynamical and modeling accuracy and the observation data coverage on the accuracy of the results. We analyzed multiple arcs using lengths of 2 and 7 days during a one-week period in Science Mission phase 02 (SM02, November 2010) and compared the trajectories, the post-fit measurement residuals and the estimated clock parameters. We further incorporated simultaneous passes from multiple stations within the observation data to investigate the expected improvement in positioning. The estimated trajectories were compared to the nominal LRO trajectory and the clock parameters (offset, rate and aging) to the results found in the literature. Arcs estimated with one-way ranging data had differences of 5–30 m compared to the nominal LRO trajectory. While the estimated LRO clock rates agreed closely with the a priori constraints, the aging parameters absorbed clock modeling errors with increasing clock arc length. Because of high correlations between the different ground station clocks and due to limited clock modeling accuracy, their differences only agreed at the order of magnitude with the literature. We found that the incorporation of simultaneous passes requires improved modeling in particular to enable the expected improvement in positioning. We found that gaps in the observation data coverage over 12 h (≈6 successive LRO orbits) prevented the successful estimation of arcs with lengths shorter or longer than 2 or 7 days with our given modeling.

Many physical parameters that can be estimated from space mission tracking data influence both the translational dynamics and proper time rates of observers. These different proper time rates cause a variability of the time transfer observable beyond that caused by their translational (and rotational) dynamics. With the near-future implementation of (interplanetary) transponder laser ranging, these effects will become increasingly important, requiring a re-evaluation of the common data analysis practice of using a priori time ephemerides, which is the goal of this paper. We develop a framework for the simultaneous estimation of the initial translational state and the initial proper time of an observer, with the goal of facilitating robust tracking data analysis from next-generation space missions carrying highly accurate clocks and tracking equipment. Using our approach, the influence of physical parameters on both translational and time dynamics are considered at the same level in the analysis, and mutual correlations between the signatures of the two are automatically identified. We perform a covariance analysis using our proposed method with simulated laser data from Earth-based stations to both a Mars and Mercury lander. Using four years of tracking data for the Mars lander simulations, we find a difference between our results using the simultaneous space-time dynamics estimation and the classical analysis technique (with an ta priori time ephemeris) of around 0.1 % in formal errors and correlation coefficients. For a Mercury lander this rises to around 1% for a 1-month mission and 10 % for a 4-year mission. By means of Monte Carlo simulation, we find that using an a priori time ephemeris of representative accuracy will result in estimation errors that are orders of magnitude above the formal error when processing highly accurate laser time transfer data., 10 pages, 5 figures, Accepted for publication by A&A

The planet Uranus, one of the two ice giants in the Solar System, has only been visited once by the Voyager 2 spacecraft in 1986. Ice giants represent a fundamental class of planets, and many known exoplanets fall within this category. Therefore, a dedicated mission to an ice giant is crucial to improve the understanding of the formation, evolution and current characteristics of such planets in order to extend the knowledge of both the Solar System and exoplanetary systems. In the study at hand, the rationale, selection, and conceptual design for a mission to investigate the Uranian system, as an archetype for ice giants, is presented. A structured analysis of science questions relating to the Uranian system is performed, categorized by the themes atmosphere, interior, moons and rings, and magnetosphere. In each theme, science questions are defined, with their relative importance in the theme quantified. Additionally, top-level weights for each theme are defined, with atmosphere and interior weighted the strongest, as they are more related to both exoplanetary systems and the Uranian system, than the other two themes (which are more specific for the planet itself). Several top level mission architecture aspects have been defined, from which the most promising concepts were generated using heuristic methods. A trade-off analysis of these concepts is presented, separately, for engineering aspects, such as cost, complexity, and risk, and for science aspects. The science score for each mission is generated from the capability of each mission concept to answer the science questions. The trade-off results in terms of relative science and engineering weight are presented, and competitive mission concepts are analyzed based on the preferred mission type. A mission design point for a typical flagship science mission is selected from the trade space. It consists of a Uranus orbiter with a dry mass of 2073 kg including 402 kg of payload and a Uranus entry probe, which is to perform measurements down 100 bar atmospheric pressure. The orbiter science phase will consist of a Uranus orbit phase of approximately 2 years in a highly elliptical orbit, during which 36 Uranus orbits are performed. Subsequently, a moon phase is performed, during which the periapsis will be raised in five steps, facilitating 9 flybys of each of Uranus’ major moons. A preliminary vehicle design is presented, seeking the best compromise between the design drivers, which basically derive from the large distance between Uranus and the Earth (e.g., high thermal load during Venus flyby, low thermal load during Uranus science phase, low data-rate during Uranus science phase, the need of radioisotope power source, etc). This paper is the result of a study carried out during the Alpbach Summer School 2012 “Exploration of the icy planets and their systems” and a one-week follow-up meeting in Graz, Austria. The results of this study show that a flagship ESA L-class mission – consisting of an orbiter with a single atmospheric entry probe and flybys of the main satellites – would be able to address the set of science questions which are identified in the study at hand as the most essential for the understanding of Uranus and its system. The spacecraft, as currently designed, could be launched with an Ariane 5, in 2026, arriving at Uranus in 2044, and operating until 2050. The development of a radioactive power source is the main requirement for feasibility for this mission.

著者人数: 114名, Accepted: 2014-08-07, 資料番号: SA1005021000

The conceptual design of entry vehicles is commonly done in a number of sequential steps. One usually begins with a generic shape to get a first estimate of the aerodynamic properties and uses a mass-point model for the initial trajectory design. Gradually, more detail is added and the outer shape is changed to accommodate specific mission and/or trajectory requirements. This shape will largely define the aerothermodynamic characteristics of the vehicle. Since aerothermodynamic challenges, such as vehicle heating, remain one of the most difficult problems in atmospheric re-entry, an exploration of the possible shapes for a vehicle early in the design is advisable. It is advantageous to use a continuous model for the analysis, so that one is not limited to the analysis and comparison of a limited number of shapes, but is instead free to analyze any shape in the design space. With only 5 geometric parameters it is possible to already model the geometry of Apollo-like shapes, as demonstrated later in Section IV. The internal layout of the subsystems is usually addressed only at a later stage and the designers have to make sure that the mass properties (total mass, location of the center of mass and inertia tensor) meet the requirements. Deviations from these requirements can jeopardize the entire mission, because the loads on the vehicle may change, or the stability and control properties cannot be handled by the Guidance, Navigation, and Control (GNC) system any more. Further, uncertainties related to the entry conditions, environment, the characteristics of the thermal protection system, and the design characteristics and allocation of the equipments on board, pose the multidisciplinary problem to be particularly cumbersome. In this paper we propose a multidisciplinary, robust optimization approach for the design of unmanned entry capsules in support of the activities of the International Space Station. This problem is handled by minimizing the total mass of the capsules, while maximizing the internal available volume for carrying payload. As a third objective, we propose the maximization of the re-usability of the capsules, which can be seen as an attempt to push towards cheaper and more efficient solutions. The shape, aerothermodynamic, and dynamic mathematical models are adapted from the work of Dirkx and Mooij. It was demonstrated that the proposed simplified aerodynamic model can predict the aerodynamic forces and moments for ballistic shapes sufficiently well for use at a conceptual design stage. The multidisciplinary design framework is now enriched with a Thermal-Protection System (TPS) model, encompassing re-usable and ablative materials, as well as active cooling mechanisms. This allows for a complete conceptual design of an entry capsule. Uncertainties of the design variables and environmental factors are integrated into the optimization process to handle probabilistic constraints. A probabilistic constraint is a constraint in the design or objective space that shall be satisfied with a pre-defined confidence level. The optimizer thus drives the search of optimal capsules towards those solutions that have the best expected performance under uncertain conditions, and that also meet the constraints with a given confidence level, pre-selected by the designer/decision-maker. A sampling-based approach is used to estimate the expected performance of the capsules and to determine the compliance with the probabilistic constraints. For each design point to be evaluated by the optimizer, a set of additional design points is generated around it, according to the joint Probability Density Function (PDF) of the uncertain variables and uncertain environmental factors, and evaluated. To limit the computational effort of the robust optimization, we adopt a double-repository archive maintenance scheme to save all the design-variable combinations computed during the process such that previous design points can be reused at future steps. The double-repository scheme allows to preserve the joint PDF of the input uncertain variables, therefore it is generally applicable with any type of multivariate distribution as input. This paper is structured as follows. In Section II we provide a brief overview of related work. We then introduce the robust optimization approach and the double-repository archive maintenance scheme in Section III. A short overview of the mathematical models used for the analysis can be found in Section IV. In Section V results are discussed and in Section VI we provide conclusions and recommendations. Two appendix sections, namely Sections VII and VIII provide the thermophysical properties of the materials used for the TPS concepts and the results of the validation of the thermal models respectively.

During the conceptual design phase of a re-entry vehicle, the vehicle shape can be varied and its impact on performance evaluated. To this end, the continuous modeling of the aerodynamic characteristics as a function of the shape is useful in exploring the full design space. Local inclination methods for aerodynamic analysis have proven sufficiently accurate for use at such a design stage, but manual selection of methods over the vehicle is inefficient for the exploration of a large number of design possibilities. This paper describes the model of an aerodynamic analysis code, written for use in conceptual vehicle shape optimization, which includes an automatic method selection algorithm. Panel shielding is also included in the analysis code to allow for the analysis of more complex geometries. The models used for the shape and aerodynamics are described and results for the Space Shuttle and Apollo are compared to wind tunnel data. They show an accuracy of better than 15% for most cases, which is sufficient for the use in conceptual design. Panel shielding is shown to be important in the prediction of control derivatives at low angle of attack, as well as the prediction of lateral stability derivatives. Finally, a simple guidance algorithm is used to assess the impact of the errors in the aerodynamic coefficients on the vehicle heat load and ground track length. Both show discrepancies of less than 10%.

Planetary Radio Interferometry and Doppler Experiment (PRIDE) will exploit the signal recording and processing technology developed originally for Very Lonag Baseline interferometric (VLBI). The essence of PRIDE is in observing the spacecraft radio signal with a network of Earth-based radio telescopes. The PRIDE technique developed at the Joint Institute for VLBI ERIC (JIVE) together with its partners was used for several experiments with several ESA planetary science missions. It has been chosen by ESA as one of the eleven experiments of the Jupiter Icy Moons Explorer (JUICE), the first Large-class mission in the ESA’s Cosmic Vision 2015–2025 program. The mission is scheduled for launch in 2022.