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The Moon is the most well-known extraterrestrial planetary body thanks to observations from ground-based, space-borne instruments and lunar surface missions. Data from Lunar Laser Ranging (LLR), magnetic, gravity, surface observations and seismic Apollo ground stations help us to quantify the deformation undergone by the Moon due to body tides. These observations provide one of the most significant constraints that can be employed to unravel the deep interior. The Moon deforms in response to tidal forcing exerted by, to first order, the Earth, the Sun and, to a lesser extent, by other planetary bodies. We use the degree-2 tidal Love number as a tool for studying the inner structure of our satellite. Based on measurements of the tidal Love numbers k2 and h2 and quality factors from the GRAIL mission, LLR and Laser Altimetry on board the LRO spacecraft, we perform a random walk Monte Carlo samplings for combinations of thicknesses and viscosities for models of Moon with and without inner core. By comparing predicted and observed parameters of the lunar tidal deformations, we infer constraints on the outer core viscosity, for a Moon with a thin outer core and a thick inner core, and a Moon with a thicker outer core but a denser and thinner inner core. In addition, by deducing the temperature and assuming the chemical composition of the low-viscosity zone, we obtain stringent constraints on its radius, viscosity and density.

Introduction: Available gravity and topography data derived from MESSENGER mission provide a great opportunity to investigate the surface and the interior structures of Mercury’s impact basins. In contrast to previous studies, which focused on image data, topography, or gravity alone, we use the complementary data sets to obtain a more comprehensive picture of basins and possibly their related subsurface structures.Methods: In this study we use image, gravity and topography data obtained by the MESSENGER spacecraft, from the Mercury Dual Imaging System (MDIS), the Mercury Laser Altimeter (MLA) as well as a radio science experiment for gravity field modelling. Digital Terrain Models from stereo images (150m/px) [1] were used in combination with mosaiced image data (166m/px) [2] to support identification of the basins. Using the most recent gravity model [3], combined with a topography model [4], we calculated Bouguer anomalies [5] and determined a crustal thickness model[6].Results: We created an inventory of 319 impact basins (>150 km) classifying their morphological and gravitational characteristics, including measurements of gravity disturbance, Bouguer anomaly, crustal thickness and morphometrical measurements (Fig 1). Basins tend to undergo relaxation processes over time, which would explain the high number of modified basins.Fig 1: A classification scheme was chosen according to rim preservation state, appearance of terraces, filling of the basin floor, depth and diameter. With increasing diameter, basins were found to show more complex gravity signatures (Fig 2). In both gravity anomalies, gravity disturbance as well as Bouguer anomaly, strong centred anomalies reflect high mass and/or density concentrations inside the impact basins, that were caused by an uplift of mantle material after the crater excavation phase [8]. The negative collar of the Bouguer anomaly profile suspected to be a consequence of depression of crust-mantle boundary, i.e. thickening of the crust. Consequently, profiles of Bouguer anomaly reflect profiles of the crust-mantle boundary. With increasing diameter, the crustal thickness is showing a decrease in rim and centre proving a link between crustal thinning and impact basin formation (Fig 3). Fig. 2: [a]Gravity disturbance are mostly negative for small basins, but become positive for larger basins. [b] Bouguer anomaly showing positive centre and negative rim area (bullseye pattern). Fig. 3: Bouguer anomaly contrast and crustal thickness ratio from centre and rim area. References: [1] Preusker F. et al., (2017). Planetary and Space Science, 142, 26–37.doi: 10.1016/j.pss.2017.04.012. [2] Hawkins, S.E., III, et al., (2007). Space Sci Rev 131: 247–338, DOI 10.1007/s11214-007-9266-3. [3] Konopliv, A., Park, R., & Ermakov, A. (2020). Icarus, 335, 113386 doi: 10.1016/j.icarus.2019.07.020. [4] Neumann et al., (2016). 47th Annual Lunar and Planetary Science Conference (p. 2087). [6] Wieczorek et al., (2015). Treatise on Geophysics (pp. 153–193). Elsevier. doi: 10.1016/B978-0-444-53802-4. [7] Beuthe et al., (2020). Geophysical Research Letters, 47. doi: 10.1029/2020GL087261. [8] Melosh et al., (2013). Science, 340, 1552–1555.515 doi: 10.1126/science.1235768.

The primary objective of the Europa Clipper mission is to assess the habitability of Europa, an overarching goal that rests on improving our understanding of Europa’s interior structure, composition, and geologic activity. Here we describe the Gravity and Radio Science (G/RS) investigation. The primary measurement, the gravitational tidal Love number $k_{2}$ k 2 , will be an independent diagnostic of the presence of a global subsurface ocean, but G/RS will make a number of other key measurements related to Europa’s deep interior, silicate mantle-ocean interface, ice shell, ionosphere, and plasma environment. Although radio science is common to many missions, Europa Clipper’s orbit and spacecraft configuration during flybys present special challenges for the design of this experiment. The information obtained through G/RS will be complementary to the measurements by the other instruments onboard Europa Clipper, and their combined analysis will refine the geophysical understanding of Europa necessary to best assess its potential habitability.

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.

1) Introduction In the context of the Artemis program, the interest of lunar study has been renewed. The Lunar Laser Ranging (LLR) experiment allows since fifty years to determine the Earth-Moon distance at a few centimeters accuracy and the Moon’s librations at a one milliarcsecond accuracy ([4], [3]) Such accuracy allows a refined description of the Moon’s rotation. The tidal response of the Moon depends on its density and rheology and it affects its rotation. Therefore it provides important information on the lunar internal structure (e.g. [6], [7], [5], [1]). The variation of the harmonic degree 2 gravitational potential due to the tidal response can be quantified by the tidal Love number k2. The latter depends on the forcing frequency, which are mainly exerted by the Earth and the Sun. The dissipation is quantified by the dissipation factor Q which is related to the value of the time delay. 2) Time-delay lunar tides Furthermore, because of the dissipation due to the viscosity of the lunar interior, the tidal deformation is not instantaneous. The current version of the planetary and lunar ephemeris INPOP only account for unique k2 and time delay [4]. Time delay can be described by a complex Love number k2, which in this case, depends also on the forcing frequency [7]. The dissipation factor Q is related to the imaginary part of the Love number. Here we explore the introduction of tidal models in numerical ephemerides. We aim to include the k2 and Q frequency dependency in INPOP. The formulation in Fourier series of the distortion coefficients (also called variation of the Stokes coefficients) by Williams and Boggs (2015) ([7]) allows to describe the tidal gravitational variation in accounting for the frequency dependency of the complex k2. The distortion coefficients vary according to the forcing frequencies formulated as linear combinations of the Delaunay arguments, the latter being described as a polynomial expansion with respect to the time. 3) Representation of the orbit of the Moon However, the representation in series of the distortion coefficients needs to be consistent with the ephemerides that we use. For that, we can use a semi-analytical representation of the ephemerides. Numerical ephemerides can described the orbit and the rotation of the Moon with a good accuracy according to the observational error. In complement, the semi-analytical approach is useful to extract information and to disentangle the different physical contributions contains in the numerical approaches. The Éphéméride Lunaire Parisienne (ELP) provides the most accurate semi-analytical model of the orbital motion of the Moon, in the form of Fourier and Poisson series [2]. Figure 1 shows that the difference of the Earth-Moon distance between the solution of INPOP19a and the solution of ELP fitted to INPOP19a reach a maximum value of the order of 4 m. Then, we deduce the amplitude of the distortion coefficients from the fitted semi-analytical representation. Figure 1. Difference of the Earth-Moon distance between the solution of IN- POP19a and the solution of ELP fitted to INPOP19a. The origin of time is J2000. References [1] A. Briaud, A. Fienga, D. Melini, N. Rambaux, A. M ́emin, G. Spada, C. Sal- iby, H. Hussmann, and A. Stark. Constraints on the Moon’s Deep Interior from Tidal Deformation. In LPI Contributions, volume 2678 of LPI Contri- butions, page 1349, March 2022. [2] J. Chapront and G. Francou. The lunar theory ELP revisited. Introduction of new planetary perturbations. , 404:735–742, June 2003. [3] Ryan S. Park, William M. Folkner, James G. Williams, and Dale H. Boggs. The JPL Planetary and Lunar Ephemerides DE440 and DE441. , 161(3):105, March 2021. [4] V. Viswanathan, A. Fienga, O. Minazzoli, L. Bernus, J. Laskar, and M. Gastineau. The new lunar ephemeris INPOP17a and its application to fundamental physics. , 476(2):1877–1888, May 2018. [5] V. Viswanathan, N. Rambaux, A. Fienga, J. Laskar, and M. Gastineau. Observational Constraint on the Radius and Oblateness of the Lunar Core- Mantle Boundary. , 46(13):7295–7303, July 2019. [6] James Williams, Dale Boggs, Charles Yoder, James Ratcliff, and J. Dickey. Lunar rotational dissipation in solid body and molten core. Journal of Geo- physical Research, 106:27933–27968, 11 2001. [7] James G. Williams and Dale. H. Boggs. Tides on the Moon: Theory and determination of dissipation. Journal of Geophysical Research (Planets), 120(4):689–724, April 2015.

In cooperation with Russia, the Brazilian deep space mission ASTER plans to send a small spacecraft to investigate the triple asteroid 2001-SN263. The nearest launch opportunities for this project include June 2022 and June 2025. One main exploration campaign is being planned with focus on the largest asteroid (Alpha). Among the instruments under development, a laser altimeter (named ALR) was preliminarily designed and presented in 2010–2011. Many studies to define mission and instruments requirements were performed aiming at the characterization of important issues for the successful realization of the mission. Among them, the identification of a suitable trajectory that could be followed by the ASTER spacecraft in the encounter phase, when the main campaign will take place. This paper describes the effort undertaken with focus on the laser altimeter operation. Possible encounter trajectories were modelled and simulated to identify suitable approach parameters and conditions allowing the accomplishment of the intended investigation. The simulation also involves the instrument operation, considering approach geometry, attitude, relative motion, time/date, and the dynamics of the main asteroid. From the laser altimeter point of view, keeping in mind the desired coverage results (50% minimum surface coverage of asteroid Alpha, complying with horizontal and vertical resolution requirements), results point out crucial features for the encounter trajectory, like the need for a small inclination (10-6 degrees; with respect to the asteroid's orbit), the most favourable spacecraft positioning (between the Sun and the asteroid) and pointing condition (back to the Sun), the minimum amount of achievable surface coverage (58%, focused on central areas), and the most proper time to conduct the main campaign (January 2025). Concerning the instrument, results offer refined values for divergence angle (500 to 650 μrad, half-cone), pulse repetition frequencies (from 1/20 to 1 Hz), and consequent data generation rates. A simulation tool that can use any 3D generated trajectories as input data was created for the analyses presented here. Although created for the ALR in this mission, this simple analysis tool can be adapted to other instruments in this or other missions.

We provide a generalized discussion on the dynamics of a spacecraft around the equal-mass binary asteroid (90) Antiope, under the influence of solar radiation pressure at the perihelion and aphelion distances of the asteroid from the Sun. The polyhedral shape of the components of this asteroid is used to accurately model the gravitational field. Five unstable equilibrium points are determined and classified into two cases that allow classifying of the motion associated with the target as always unstable. The dynamical effects of the mass ratio of our binary system are investigated. We tested massless particles initially located at the periapsis distance on the equatorial plane of the primary of our binary asteroid. Bounded orbits around our system are not found for the longitudes λ ∈ {60, 90, 120, 240, 270, 300}. We also discuss the orbital dynamics in the full potential field of (90) Antiope. The tested motions are mainly dominated by the binary’s gravitational field; no significant effects of the SRP are detected. For λ = 180°, less perturbed orbits are identified between 420 and 700 km from the centre of the system, that corresponds to orbits with Δa < 30 km and Δe < 0.15. All the orbits with initial periapsis distance smaller than 350 km either collide with components of our asteroid or escape from the system.

The BepiColombo mission, which is a joint mission of the European Space Agency (ESA) and the Japan Aerospace Exploration Agency (JAXA), was launched successfully on October 20, 2018 from Kourou, French Guyana. The spacecraft is currently on its 7 yr cruise to Mercury. The main science campaign at Mercury will begin, however, no earlier than spring 2026, after two orbiters, the Mercury Planetary Orbiter (MPO) and the Mercury Magnetospheric Orbiter (MMO) have been inserted in their final orbits in late 2025. Mercury is an intriguing planetary object with respect to its dynamical state and evolution. The planet is differentiated and contains a large iron core overlain by a relatively thin silicate mantle and crust. Mercury is locked in a unique 3:2 spin-orbit coupling and its intrinsic magnetic dipole field shows that at least part of Mercury’s iron core is liquid. From libration measurements it has been concluded that Mercury’s outer core is liquid, decoupling the silicate mantle from the deep interior. Phases of global contraction and phases of volcanic activity are evidence for an eventful thermal evolution of the planet. In this paper the current knowledge on the evolution of Mercury, focusing on its dynamical, rotational and orbital state is summarized. Prospects for investigations with BepiColombo will be discussed.

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

The Ganymede laser-altimeter (GALA) is one of 10 instruments on ESA’s Jupiter Icy Moons Explorer (JUICE) mission. The scientific goals cover a wide range from geology, geophysics to geodesy of the icy moons Ganymede, Europa and Callisto. JUICE will explore Jupiter, its magnetosphere and satellites first in orbit around Jupiter before going finally into polar orbit around Ganymede. GALA is developed under responsibility of the DLR Institute of Planetary Research in collaboration with industry and institutes from Germany, Japan, Switzerland and Spain. GALA has two main objectives: (1) providing Ganymede’s topography from global to local scales (2) determination of Ganymede's tidal variations of surface elevations. GALA is a single-beam laseraltimeter: a laser pulse (1064 nm) is emitted by using a Nd:YAG laser firing at 30 Hz (nominal). After about 3 msec (500 km altitude) the reflection of the pulse from the surface of Ganymede is received by a telescope and transferred to the detector (Avalanche Photo Diode). The signal is digitized and transferred to the range finder module, which determines (a) time of flight (b) pulse shape, and (c) energy of the received pulse. Including information on the spacecraft position and attitude the height of the terrain above a reference surface is determined for each shot from time-of-flight measurements. The GALA flight model was delivered to ESA in August 2021. After several tests on instrument level the integration on the JUICE spacecraft started in September 2021 and first tests were performed successfully in October 2021. With the launch scheduled for 2023, GALA will go through several tests, among them an end-to-end test including laser-receiver measurements. Here we present the instrument's current status with respect hardware integration and regarding the verification of its performance.

The Moon deforms in response to tidal forcing exerted by the Earth, the Sun and, to a lesser extent, by other planetary bodies. Their observations from ground-based and space-borne instruments, as well as Lunar surface missions, provide one of the most significant constraints that can be employed to unravel the deep interior (Williams et al. [2014], Williams and Boggs [2015]). The tidal forcing generates periodic variations of the harmonic degree-2 shape and gravity that depend on the internal composition and structure of the Moon. These changes in shape and gravity of the Moon are described by three geodetic parameters, called Tidal Love numbers (TLNs). Because of their low degree, these TLNs are sensitive to the structure of the deep interior (e.g., Khan et al. [2004]). Apart from the geodetic constraints, the Moon and Mars (e.g. Zweifel et al. [2021]) are the only other bodies besides the Earth for which seismic data are available. Seismic studies using the Apollo Passive Seismic Experiment (PSE) constrain the seismic wave velocity distribution and therefore give a glimpse of the Moon’s interior structure (Garcia et al. [2011], Weber et al. [2011]). However, at greater depth, seismic data do not provide sufficient resolution on the velocity profile, leaving the near-centre Moon structure uncertain. Other studies based upon geophysical constraints (Khan et al. [2004], Harada et al. [2014, 2016], Matsumoto et al. [2015]) and the re-analysis of the Apollo seismic data suggested the existence of an attenuated region called low viscosity zone (LVZ) originated from a melting layer at the core-mantle boundary (Khan and Mosegaard [2001], Weber et al. [2011], Harada et al. [2014], Rambaux et al. [2014]).Based on geodetic observations and seismic studies, we perform Monte Carlo simulations for combinations of thicknesses, densities and viscosities for two classes of Moon’s models, one including an undifferentiated core and one including an inner and outer core, with both classes assuming an LVZ at the core-mantle boundary. By comparing predicted and observed tidal deformation parameters we find that the existence of an inner core cannot be ruled out. Furthermore, by deducing temperature profiles for the LVZ and the mantle following Earth assumptions, we obtain stringent constraints on the radius, viscosity, and density of the LVZ. We also infer the first estimation for the outer core viscosity, for our two possible scenarios.

Many moons of the Solar System, e.g. the Galilean satellites or Earth’s Moon, are subject to strong tidal deformations. Measurements of the tidal Love number h2 by laser altimeters from orbiting spacecraft may provide crucial constraints on their interior structures and rheology. Using precise observations by laser altimeters estimates for h2 were obtained for the Moon (Mazarico et al. 2014, Thor et al., 2021) and Mercury (Bertone et al., 2021), and are planned for Ganymede (Steinbrügge et al., 2015). Typically, height differences at crossing points of laser profiles, so called crossover points, are used for such measurements (Mazarico et al. 2014, Bertone et al., 2021). However, a new method based on simultaneous inversion of tidal deformations and global topography has recently been demonstrated (Thor et al. 2021) using data from the Lunar Orbiter Laser Altimeter (LOLA) on board the Lunar Reconnaissance Orbiter (LRO). Here we propose the refined “self-registration” method, which makes use of an accurate reference digital terrain model (DTM) constructed from the laser profiles themselves. This DTM is obtained by iteratively co-registering random subsets of laser profiles to an intermediate DTM produced by the other profiles. With our method we are not limited to profiles that are actually crossing themselves and can obtain height difference between all available profiles. Moreover, we can overcome the interpolation error at the crossover points as we use the entire profile with all its data points to measure the relative height differences. This method was recently successfully applied to measure the seasonal change of the ice/snow level in polar regions of Mars using Mars Orbiter Laser Altimeter (MOLA) data (Xiao et al., 2021). In order to validate our method and assess its performance we perform a simulation of a tidal signal in the LOLA data with an assumed value for the tidal Love number h2 of the Moon. Thereby the height measurement at the location of the LOLA footprint is derived from a DTM and an artificial tidal signal applied on it. Thereby, we consider viscoelastic effects on the tidal deformation and different tidal frequencies. With the help of these simulations we assess the accuracy of the h2 measurement and check the sensitivity to the measurement of the tidal phase lags. References:Mazarico et al. (2014). Detection of the lunar body tide by the Lunar Orbiter Laser Altimeter. GRL, 41(7), 2282-2288. doi:10.1002/2013GL059085Thor et al. (2021). Determination of the lunar body tide from global laser altimetry data. JoG, 95(1). doi:10.1007/s00190-020-01455-8Bertone et al. (2021). Deriving Mercury Geodetic parameters with Altimetric Crossovers from the Mercury Laser Altimeter (MLA). JGR-Planets, 126(4), e2020JE006683. doi:10.1029/2020JE006683Xiao et al. (2021). Prospects for Mapping Temporal Height Variations of the Seasonal CO2 Snow/Ice Caps at the Martian Poles by Co-registration of MOLA Profiles. Under review in PSS, https://arxiv.org/abs/2109.04899

The BepiColombo Laser Altimeter (BELA) is one of ten payloads on-board the Mercury Planetary Orbiter (MPO) on cruise to Mercury as part of the ESA and JAXA mission BepiColombo. BELA is a single beam laser altimeter operating at 1064 nm. The nominal pulse repetition is 10 Hz, while the pulse energy of each transmitted pulse is 50 mJ. The detector features a silicon avalanche photo diode (APD) with enhanced quantum efficiency for infrared radiation. The detected return pulse signal can be amplified using 16 predefined gain settings within the Analogue Electronics Unit (AEU). Finally, the amplified signal is digitized with a sampling frequency of 80 MHz, i.e. in samples of 12.5 ns, and is analysed by an on-board signal processing unit, the Range Finder Module (RFM). Within this pulse processing, nominal values for time of flight are determined for up to four alternative return pulse candidates. Additional parameters such as pulse width and pulse energy are obtained. Since launch in 2018 the receiver, power converter, and data processing modules of BELA were checked regularly twice a year. The instrument showed excellent performance and all tested parts are operating nominaly. However, the transmitter was not operated because the line-of-sight of the lasers is right in the direction of the BepiColombo transfer module. Hence, the instrument’s data acquisition and processing were tested with dark noise measurements. The expected power of the return pulse from Mercury’s surface will vary roughly between 1 and few hundred nW, depending on altitude and surface slope. In order to face this large variability, 16 gain settings with signal amplifications between 4 and 44 dB will be used for different phases within the orbit. The measurements during the cruise checkouts were used to characterize the noise of the receiver as a function of the commanded gain. By simulating realistic return pulse signals over one revolution about Mercury the commanded gain setting for each spacecraft altitude will be optimized with the ultimate goal of reaching the highest accuracy in the range measurement. Here we will report on the results of the first 5 BELA cruise checkouts, performed between 2019 and June 2021. BELA is a joint German–Swiss project with the participation of Spain. LML acknowledges financial support from the State Agency for Research of the Spanish MCIU through the "Center of Excellence Severo Ochoa" award to the Instituto de Astrofısica de Andalucia (SEV-2017-0709) and from project PGC2018-099425-B-I00 (MCI/AEI/FEDER, UE).

We investigate the tidal evolution of Tethys identifying several possible resonance scenarios that could be relevant for intense tidal heating and the formation of Ithaca Chasma early in the satellite’s history. By studying the phase-space we identify initial conditions for which Tethys and Dione can be trapped in a 2:1 mean motion resonance. From evolution models we show that capture of Tethys in this resonance is indeed possible. This scenario would imply a small semi-major axis of Tethys early in its history and small Q-values (high dissipation rates) of Saturn. Various resonance scenarios are obtained including later evolution out of resonance. As a result of the early 2:1 resonance tidal heating can be significantly enhanced in Tethys. Depending on the assumed dissipation factor of Saturn at the time of the resonance, the resulting global dissipation rate ranges between 20 and several hundred GW and could provide the heat pulse associated with the formation of Ithaca Chasma, a global rift system on Tethys. In addition, the orbital expansion due to tides will lead to surface stresses that could trigger the formation of Ithaca Chasma. The stress pattern is consistent with the orientation of faults of Ithaca Chasma at high latitudes but the orientation does not match for the equatorial regions. Expansion due to freezing of an early subsurface ocean as suggested in previous studies could be an additional factor required to explain the formation and orientation of the rift system at low latitudes.

Laser altimeters are commonly used in planetary research for their high geodetic accuracy. A key procedure in processing of laser altimeter data is the geolocation. In this process, the time-of-flight measurements are converted to coordinates of laser pulse footprints on the surface of the target body. Here, we present a consistent and systematic formulation of three commonly used geolocation models with increasing complexity: static model, spacecraft motion model, pointing aberration model and special relativity model. We show that for small velocities of the spacecraft relative to the target the special relativity model can be reduced to the pointing aberration model without significant loss in the geolocation accuracy. We then discuss the respective accuracies of the proposed models and apply them to time-of-flight measurements from the Mars Orbiter Laser Altimeter (MOLA) onboard the Mars Global Surveyor (MGS) spacecraft and the Mercury Laser Altimeter (MLA) onboard the MErcury Surface, Space ENvironment, GEochemistry and Ranging spacecraft (MESSENGER). While, the archived datasets had not considered the effect of pointing aberration, we demonstrate that a correction due to pointing aberration makes insignificant improvements of 4–5 m laterally and up to ± 3 cm radially for MOLA profiles, these figures enormously increase to up to about 150 m laterally and ± 25 m radially when applied to the MLA orbital profiles.

We assessed the impact of the uncertainties in the gravity field harmonic coefficients of Mercury on the orbital evolution of the Mercury Planetary Orbiter (MPO), part of the European-Japanese BepiColombo mission. We used in our simulations the most recent estimation of the gravity field model of Mercury determined from radio tracking data of the NASA spacecraft MESSENGER. Thereby we propagated the orbital evolution of MPO by means of plausible gravity fields compatible with the covariance matrix measured gravity field coefficients. We considered two scenarios: 1) the optimistic case, where the formal errors were considered plausible, i.e. scaled by 1; and 2) the conservative case where the formal errors were scaled with a factor of 3. With our simulations we could also demonstrate the importance of the correlation between the errors of the gravity field coefficients for the uncertainty in the trajectory evolution. As the altitude of the spacecraft above the surface is most important in Mercury's harsh thermal environment, we mostly focused our analysis on the evolution of the periherm altitude. The results of the MPO orbit propagation show a non-linear decrease in the periherm altitude over the simulated timeframe of 1000 days. However, the decrease rate varies significantly among the generated gravity fields. Moreover, the dispersion of the periherm altitude gets larger with increasing scale factor (optimistic to conservative scenario) and over the mission time. While the values of the orbital elements of MPO are still in an acceptable range after the first year, the periherm altitude may fall below a critical value of 200 km after 2 years in orbit about Mercury.

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.

Full lists of authors: Thomas, N.; Hussmann, H.; Spohn, T.; Lara, L. M.; Christensen, U.; Affolter, M.; Bandy, T.; Beck, T.; Chakraborty, S.; Geissbuehler, U.; Gerber, M.; Ghose, K.; Gouman, J.; HosseiniArani, S.; Kuske, K.; Peteut, A.; Piazza, D.; Rieder, M.; Servonet, A.; Althaus, C. Behnke, T.; Gwinner, K.; Hüttig, C.; Kallenbach, R.; Lichopoj, A.; Lingenauber, K.; Lötzke, H. -G.; Lüdicke, F.; Michaelis, H.; Oberst, J.; Schrödter, R.; Stark, A.; Steinbrügge, G.; del Togno, S.; Wickhusen, K.; Castro, J. M.; Herranz, M.; Rodrigo, J.; Perplies, H.; Weigel, T.; Schulze-Walewski, S.; Blum, S.; Casciello, A.; Rugi-Grond, E.; Coppoolse, W.; Rech, M.; Weidlich, K.; Leikert, T.; Henkelmann, R.; Trefzger, B.; Metz, B.--This is an Open Access article distributed under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/4.0/.Open Access funding provided by Universitat Bern., The BepiColombo Laser Altimeter (BELA) is the first European laser altimeter constructed for interplanetary flight. BELA uses a 50 mJ pulsed Nd:YAG laser operating at 10 Hz with a 20 cm aperture receiver to perform the ranging. The instrument also uses a digital approach for range detection and pulse analysis. The ranging accuracy is expected to be better than 2 metres and ∼20 cm in optimum conditions. With the given, only slightly elliptical, orbit, BELA should return a consistent data set for the most if not all of the planet. The instrument is required to function in an extreme environment with the thermal issues being particularly demanding. Novel solutions have been taken to resolve these issues. BELA is described in detail and its predicted performance outlined on the basis of pre-flight testing. © The Author(s) 2021, This work was supported by the Swiss State Secretariat for Education, Research and Innovation (SERI) under the PRODEX scheme (contract number C90191). The opinions expressed and arguments employed herein do not necessarily reflect the official views of the Swiss Government. DLR would like to thank all involved collaborators in the BELA transmitter team. Financial support was provided by the DLR Space Administration on behalf of the Federal Ministry of Economics and Technology of Germany. We acknowledge the financial support from the State Agency for Research of the Spanish MCIU through the “Center of Excellence Severo Ochoa” award SEV-2017-0709, and from the research projects ESP 2014-54062-R, ESP 2016-76076-R and PGC 2018-099425-B-I00. Open Access funding provided by Universitat Bern.

In this study we investigate the possibility of using terminator orbits that are stable over a period of three months to explore the triple near-earth asteroid (NEA) system 2001 SN263 with an orbiting spacecraft. We study in particular the case of the mission ASTER that is under study as the first Brazilian deep space mission [1]. Introduction The interest in the first identified Near Earth Asteroid (NEA) triple system 2001 SN263 increased greatly when the Brazilian space agency announced ASTER, a rendezvous mission to explore this unique target [2]. The analysis of the observational data of 2001 SN263 [3] suggested that the primary is approximately a spheroid with an equivalent diameter of about 2.6 km (2.8×2.7×2.5 km) and smaller companions, about 700 m and 430 m in diameter orbiting at distances of 16.6 and 3.8 km, respectively. For the spacecraft to move safely within the system, it is critical to identify and characterize regions of stability and instability (i.e., where collision or escape are imminent). Furthermore, observational and operational strategies to explore all three asteroids critically depend on availability of stable spacecraft orbits (i.e., orbits that do not requiring expensive correction maneuvers). In this study we search for stable orbits within the triple asteroid system. The orbits are considered stable when the spacecraft does not escape or collide with the system for 3 months. Data and methods We modelled the gravitational field of each body in two steps. First, we integrate the gravitational acceleration contributed by the mass of the object, represented by a polyhedron shape model (and assuming a homogeneous interior). In a second step, we replace this reference field with its spherical harmonics approximation. The spacecraft trajectories around the triple asteroid are calculated with a numerical integrator which solves the equation of motion, taking into account all relevant forces: with GM being the standard gravitational parameter of the primary body and being the spacecraft’s position and acceleration, respectively. The main acceleration acting on the spacecraft is caused by the system’s primary body, represented by a point mass, in the first term of the equation. Higher-order terms, which include the non-spherical gravity field of the main body, are included in the second term. The secondary and tertiary body are represented by the third term of the equation. Additionally, the large Solar System bodies, such as Sun and Jupiter are also included as perturbing forces in this third addend. The last term takes into account the solar radiation pressure acting on the spacecraft. The spacecraft is modelled based on the mass and dimensions as specified for ASTER mission [4]. Results and Conclusion The results show that stable terminator orbits within the triple asteroid system can be found, for which the orbital plane is perpendicular to the incoming solar radiation. These stable orbits are found between the semi-major axes of the secondary and tertiary body, i.e., at a distance between 4 km and 13 km from the primary’s centre. Figure 1: Example of stability regions of the Aster S/C model in the triple asteroid system. The stability depends on initial orientation of the orbital plane which is represented by the longitude of ascending node and the inclination. Initial elements: semi-major axis=8km, eccentricity=0, remaining elements=0°. The colour coding shows the difference between largest and shortest distance to the primary body over 3 months. The most stable region is located at semi-major axes between 7 and 12 km. In the best cases, the distance variation of the S/C absolute distance from primary’s centre (r.max-r.min) varies less than 1 km over a time frame of 3 months. Figure 1 shows these stability regions at an exemplary initial distance of 8 km. References [1] Macau, E. E. N., Winter, O. C., Velho, H. F. C., Sukhanov, A. A., Brum, A. G. V., Ferreira, J. L., Hetem, A., & Sandonato, G. M. (2011). The ASTER mission: exploring for the first time a triple system asteroid. InProceedings of the 62nd International Astronautical Congress. Cape Town, SA. [2] Sukhanov, A. A., Velho, H. F. C., Macau, E. E. N., & Winter, O. C. (2010). The Aster project: Flight to a near-Earth asteroid. Cosmic Research,48, 443–450. doi:10.1134/S0010952510050114. [3] Becker, T. M., Howell, E. S., Nolan, M. C., et al. (2015). Physical modeling of triple near-Earth Asteroid (153591) 2001 SN263 from radar and optical light curve observations. Icarus, 248, 499, doi: 10.1016/j.icarus.2014.10.048 [4] Goretov, V., Lipatov, A., Linkin V. (2018) Description of the spacecraft on the EJP for near-earth and planetary research. Acknowledgements F.D. and J.O have been supported by a grant from the German Science Foundation (DFG-OB 124/19-1) A.G.V. de Brum was supported by the São Paulo Research Foundation – FAPESP (grant#2018/22672-4).

Exploring the icy moons of Jupiter: The Ganymede Laser Altimeter (GALA) for ESA’s JUICE Mission Fabian Lüdicke (1), Hauke Hussmann (1), Kay Lingenauber (1), Reinald Kallenbach (1), Keigo Enya (2), Masanori Kobayashi (3), Nicolas Thomas (4), Luisa Lara (5), Kazuyuki Touhara (2) and the GALA team. (1) DLR Institute of Planetary Research, Berlin, Germany (fabian.luedicke@dlr.de), (2) ISAS/JAXA, (3) Chiba Institute of Technology, Japan, (4) Physikalisches Institut, University of Bern (UBE), (5) CSIC, Instituto de Astrofísica de Andalucía (IAA), Granada, Spain Abstract The Ganymede Laser Altimeter (GALA) is one of ten instruments selected for ESA’s Jupiter Icy Moons Explorer (JUICE) mission. We will present an overview on the scientific goals as well as on the status of the instrument development and performance analysis. Introduction ESA’s JUICE mission will explore Jupiter, its magnetosphere and satellites first in orbit around Jupiter before going finally into polar orbit around Ganymede [1]. GALA is one of ten payloads on-board the spacecraft and is developed under responsibility of the DLR Institute of Planetary Research in collaboration with industry and institutes from Germany, Japan, Switzerland and Spain. Its major objectives are to measure the surface topography and the tidal deformation of the satellite. The JUICE Mission JUICE (Jupiter Icy Moons Explorer) will be the first orbiter around a moon (other than Earth’s moon) in solar system exploration. Its launch is planned for May/June 2022 followed by an interplanetary cruise of 7.6 years. Jupiter orbit insertion will take place by the end of 2029. An orbit maneuver will bring the spacecraft into a 500-km circular orbit in which it will be staying for at least 132 days until end of nominal mission. The latter phase will be the main period for GALA taking data. In addition data will be taken at Europa, Ganymede, and Callisto at closest approaches of flybys in the Jupiter orbiting phase. GALA Science GALA has two main objectives: (1) by range measurements it shall obtain Ganymede’s topography on global, regional and local scales. This will reveal how surface features have formed and how they are connected with the shallow interior ice shell. Global shape measurements will tell us whether the satellite is in hydrostatic state with respect to rotational and tidal forces. (2) Obtaining range measurements distributed in time along the orbital cycle, tidal variations of surface elevations will be measured. The tidal amplitudes are indicative for the presence of a subsurface ocean and would (together with complementary measurements) constrain the ice-I shell thickness [2]. GALA GALA is a single-beam altimeter: a laser pulse (at 1064 nm wavelength) is emitted by using an actively Q-switched Nd:YAG laser firing at 30 Hz in nominal operation. A small fraction of the pulse is guided through fiber optics onto the detector characterizing the outgoing pulse and time of emission. After about 3 msec the Lambertian reflection of the pulse from the surface is received by a aperture telescope and transferred to the detector, an Avalanche Photo Diode. The signal is digitized at a sampling rate of 200 MHz and transferred to the range finder module, which determines (a) the time of flight between the emission and receiving of the pulse (b) the pulse shape, in particular the pulse-width, and (c) the energy of the received pulse. From the time of flight of the wave-package and the spacecraft position and attitude, the distance for each shot can be converted into height above a reference surface in post-processing of the data. (1) (2) (3) Figure 1: (1) GALA Tranceiver, (2) Electronics Unit (ELU), (3) Laser Electronics Unit (LEU) In 2019 the GALA EM (Engineering Model) was delivered to Airbus Defence and Space Toulouse and was successfully integrated into the JUICE EM and tested. The EM is used to test the functionality of GALA; it can be operated only under ambient conditions. Later it will be used as a ground reference model for checks for the Flight Model. For the GALA delivery in 2021 the different GALA flight model subsystems are currently tested and integrated at DLR, and at industries in Japan (Meisei) and Germany (Hensoldt Optronics). Flight hardware of the Power converter Module (PCM) and the Range Finder Module have been received from our partner institutes in Spain (IAA, CSIC) and Switzerland (UBE). The main units of GALA are the TRU, the LEU and the ELU, see Figure 1. The TRU consists of the laser/detector system, including an Avalanche Photo Diode. ELU includes the main CPU, Data Processing Module, Range Finder Module for the analysis of the laser pulses and the Power Converter Module which provides the power. A detailed description of GALA can be found in [3]. All parts were tested in terms of functionality and performance, here in particular the detector. Besides electrical testing a big part is the testing of the on-board software, the Application Software. Mainly it manages the commanding of the above mentioned parts, the memory management, FDIR (Fault Detection Isolation Recovery) and the interface (I/F) to the spacecraft (S/C). For I/F testing to the S/C a SIS (Spacecraft Interface Simulator) is used to check the GALA commanding and the data output. After testing at DLR the above mentioned GALA parts will be assembled to the GALA PFM at Hensoldt Optronics Oberkochen. Here additional tests will take place like thermal vacuum tests, EMC and further functional testing, especially for the laser system, but also for the complete system before it will be delivered for final integration into the JUICE spacecraft in 2021. References [1] Grasset, O. and 17 colleagues (2013), JUpiter ICy moons Explorer (JUICE): an ESA mission to orbit Ganymede and to characterise the Jupiter system, Planet. Space Sci., 78, 1-21. [2] Steinbrügge, G., A. Stark, H. Hussmann, F. Sohl, and J. Oberst (2015), Measuring tidal deformations by laser altimetry. A performance model for the Ganymede Laser Altimeter, Planet. Space Sci., 117, 184-191. [3] Hussmann, H. and 38 colleagues 2019. The Ganymede Laser Altimeter (GALA): key objectives, instrument design, and performance. CEAS Space Journal (Special Issue on Space Lidar and Space Optics) 11, 381 – 390.

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.

Made available in DSpace on 2019-10-06T17:13:16Z (GMT). No. of bitstreams: 0 Previous issue date: 2019-06-01 The main goal of our work is to study the orbital dynamics of a spacecraft near the (87) Sylvia system. Here, we consider a non-homogeneous mass distribution with a dense core inside the primary asteroid. The Mascon gravity framework using the shaped polyhedral source, from light-curve data, is chosen to calculate the gravitational field. The zero-velocity curves show four unstable equilibrium points. In the absence of any solar or other celestial body perturbations, a numerical analysis of the orbital dynamics in the potential field of Sylvia is done to delineate the region of stable and unstable motions. In our model, the motions of the two moons of Sylvia and of the spacecraft are integrated with the classical equations of motion in the body-fixed frame of reference. An orbit is considered stable if the variation of its periapsis radius does not exceed a threshold value (i.e. 6 km), and the variation of its eccentricity does not exceed 0.05, although the orientation of these orbits may change. We found that the first stable orbit is detected at a distance of 550 km from the centre of Sylvia. No collision occurs with the central body beyond 350 km. The collisions with Remus occur between 300 and 900 km, while with Romulus they occur between 900 and 1450 km. Moreover, the orbits escape from the system when the distance is smaller than 350 km. Finally, we found that the stability region around our system decreases when the initial eccentricity increases. Division of Space Mechanics and Control INPE, C.P. 515 School of Natural Sciences and Engineering São Paulo State University (UNESP) DLR Institute of Planetary Research, Rutherfordstr. 2 SYRTE Observatoire de Paris PSL Research University, 61 avenue de l'Observatoire School of Natural Sciences and Engineering São Paulo State University (UNESP)

We provide a brief description of the BepiColombo Laser Altimeter experiment for the joint ESA-JAXA mission to Mercury, BepiColombo. The text describes the main elements of the instrument and discusses several of the problems encountered during the instrument development. The actions taken to mitigate the issues are also described and the resulting performance of the instrument as determined by combining ground test data with models of Mercury and the spacecraft orbit is presented. The instrument has met the requirements set in 2005 and should provide a solid data set for the global study of the topography and internal structure of Mercury. © 2019, CEAS., We gratefully acknowledge financial support from the Swiss Space Office via ESA’s PRODEX programme, the German Aerospace Center’s Space Administration, the Ministerio de Ciencia e Innovación, and the Ministerio de Economía y Competitividad.

Due to its tidally heated interior, Io is a geologically very active satellite that bears many volcanic features. It is observed that the mean nearest neighbor distance of each volcanic feature, called a patera is larger than that of a random distribution, which implies that the spatial distribution of paterae is uniform rather than random. However, it is uncertain how the paterae are organized into a uniform distribution. We suggest the mechanism of Io's uniformly distributed paterae considering localized obliteration of old features. Instead of geological modeling, we performed stochastic simulations and statistical analyses for the obliteration of quiescent paterae. Monte Carlo calculations with Gaussian obliteration probability show that, if the width of obliteration probability is approximately 80 km and the volcanic generation rate is ∼ 5.0 × 10 − 6 km − 2 Ma − 1, uniform distribution and the observed number density of paterae are attained at the 2σ level on a timescale of approximately 6 million years. With this generation rate and width of the obliteration probability, the averaged distance of one patera to the nearest patera (mean nearest neighbor distance) is approximately 200 km, which is consistent with the observed value. The uniformity of the distribution is maintained once it is achieved. On regional scales, Io's paterae would naturally evolve from random into uniform distributions by the obliteration of old and quiescent features.

Jupiter’s satellites are subject to strong tidal forces which result in variations of the gravitational potential and deformations of the satellites’ surfaces on the diurnal tidal cycle. Such variations are described by the Love numbers $$k_2$$ and $$h_2$$ for the tide-induced potential variation due to internal mass redistribution and the radial surface displacement, respectively. The phase-lags $$ \phi _{k_2}$$ and $$ \phi _{h_2}$$ of these complex numbers contain information about the rheological and dissipative states of the satellites. Starting from interior structure models and assuming a Maxwell rheology to compute the tidal deformation, we calculate the phase-lags in application to Ganymede and Europa. For both satellites we assume a decoupling of the outer ice-shell from the deep interior by a liquid subsurface water ocean. We show that, in this case, the phase-lag difference $$\varDelta \phi = \phi _{k_2}- \phi _{h_2}$$ can provide information on the rheological and thermal state of the deep interiors if the viscosities of the deeper layers are small. In case of Ganymede, phase-lag differences can reach values of a few degrees for high-pressure ice viscosities $${

We assess the surface roughness of Europa by reevaluating Galileo stereo images. Roughness provides important information about surface textures, which are related to geologic processes operating at a variety of scales. Roughness also sets important performance requirements for various remote sensing instruments on board the upcoming icy satellite missions to the Jovian System. In this study, roughness is derived for different geologic terrains on Europa, which have been distinguished through geomorphological mapping. For each terrain type we derive the scale dependent root-mean-square roughness and corresponding Hurst exponents. We investigate the scale between 30 m and 5 km and show that Europa’s surface can mostly be described by a monofractal behavior over these baselines (i.e., surface roughness follows power laws with breakpoints located at a few hundred meters). Hurst exponents are higher below the breakpoints with typical values between 0.4 and 0.8 and lower above, typically between 0.2 and 0.6. This behavior is mostly controlled by ridges which are dominating the topography on Europa. At unity scale (1 m) roughness is extrapolated to be around 0.4–0.7 m with strong exceptions on chaos terrain where values over 1–2 m can be achieved, assuming that no further breakpoints are present below the resolution of the digital terrain models used in this study.

We report on recent refinements and the current status for the rotational state models and the reference frames of the planet Mercury. We summarize the performed measurements of Mercury rotation based on terrestrial radar observations as well as data from the Mariner 10 and the MESSENGER missions. Further, we describe the different available definitions of reference systems for Mercury and obtain the corresponding reference frame using data provided by instruments on board MESSENGER. In particular, we discuss the dynamical frame, the principal-axes frame, the ellipsoid frame, as well as the cartographic frame. We also describe the reference frame adopted by the MESSENGER science team for the release of their cartographic products, and we provide expressions for transformations from this frame to the other reference frames.

We explore the perspectives of the BepiColombo Laser Altimeter (BELA) onboard ESA / JAXA's Mercury mission BepiColombo and present an updated semi-analytical instrument performance model, in which we estimate signal-to-noise ratio, single shot probability of false detection, range errors and the accuracy of pulse width reconstruction. The model is generally applicable for other laser altimeters using matched filter algorithms for pulse detection and has been validated against the recently tested BELA flight model after integration on the BepiColombo spacecraft. Further, we perform numerical simulations of the instrument performance expected in orbit about Mercury. In particular, we study the measurement accuracy of topography, slopes and surface roughness, which will allow us to estimate local and global topographic coverage based on the current trajectory design. We also assess the potential for measuring the tidal Love number h 2 using cross-over points, which we estimate to be constrained with an absolute accuracy of 0.14 corresponding to a relative accuracy of about 18% after two years in Mercury orbit.

Laser altimetry is a powerful tool for addressing the major objectives of planetary physics and geodesy, and have been applied in planetary explorations of the Moon, Mars, Mercury, and the asteroids Eros, and Itokawa. The JUpiter Icy Moons Explorer (JUICE), led by European Space Agency (ESA), has started development to explore the emergence of habitable worlds around gas giants. The Ganymede Laser Altimeter (GALA) will be the first laser altimeter for icy bodies, and will measure the shape and topography of the large icy moons of Jupiter, (globally for Ganymede, and using flyby ground-tracks for Europa and Callisto). Such information is crucial for understanding the formation of surface features and can tremendously improve our understanding of the icy tectonics. In addition, the GALA will infer the presence or absence of a subsurface ocean by measuring the tidal and rotational responses. Furthermore, it also improves the accuracy of gravity field measurements reflecting the interior structure, collaborating with the radio science experiment. In addition to range measurements, the signal strength and the waveform of the laser pulses reflected from the moon's surface contain information about surface reflectance at the laser wavelength and small scale roughness. Therefore we can infer the degrees of chemical and physical alterations, e.g., erosion, space weathering, compaction and deposition of exogenous materials, through GALA measurements without being affected by illumination conditions. JUICE spacecraft carries ten science payloads including GALA. They work closely together in a synergistic way with GALA being one of the key instruments for understanding the evolution of the icy satellites Ganymede, Europa, and Callisto., 10 pages, 6 figures, accepted for publication in Trans. JSASS Aerospace Tech. Japan

The tidal Love number h 2 is a key geophysical measurement for the characterization of Europa's interior, especially of its outer ice shell if a subsurface ocean is present. We performed numerical simulations to assess the potential for estimating h 2 using altimetric measurements with a combination of radar sounding and stereo imaging data. The measurement principle exploits both delay and Doppler information in the radar surface return in combination with topography from a digital terrain model (DTM). The resulting radar range measurements at cross-over locations can be used in combination with radio science Doppler data for an improved trajectory solution and for estimating the h 2 Love number. Our simulation results suggest that the absolute accuracy of h 2 from the joint analysis of REASON (Radar for Europa Assessment and Sounding: Ocean to Near-surface) surface return and EIS (Europa Imaging System) DTM data will be in the range of 0.04–0.17 assuming full radio link coverage. The error is controlled by the SNR budget and DTM quality, both dependent on the surface properties of Europa. We estimate that this would unambiguously confirm (or reject) the global ocean hypothesis and, in combination with a nominal radio-science based measurement of the tidal Love number k 2 , constrain the thickness of Europa's outer ice shell to up to ±15 km.

We computed interior structure models of Mercury and analyzed their viscoelastic tidal response. The models are consistent with MErcury Surface, Space Environment, GEochemistry, and Ranging mission inferences of mean density, mean moment of inertia, moment of inertia of mantle and crust, and tidal Love number k2. Based on these constraints we predict the tidal Love number h2 to be in the range from 0.77 to 0.93. Using an Andrade rheology for the mantle the tidal phase-lag is predicted to be 4° at maximum. The corresponding tidal dissipation in Mercury's silicate mantle induces a surface heat flux smaller than 0.16 mW/m2. We show that, independent of the adopted mantle rheological model, the ratio of the tidal Love numbers h2 and k2 provides a better constraint on the maximum inner core size with respect to other geodetic parameters (e.g., libration amplitude or a single Love number), provided it responds elastically to the solar tide. For inner cores larger than 700 km, and with the expected determination of h2 from the upcoming BepiColombo mission, it may be possible to constrain the size of the inner core. The measurement of the tidal phase-lag with an accuracy better than ≈0.5° would further allow constraining the temperature at the core-mantle boundary for a given grain size and therefore improve our understanding of the physical structure of Mercury's core.

We computed a 3D control point network for Ganymede using combinations of 126 Voyager-1 and -2 and 87 Galileo images, benefiting from reconstructed trajectory data for the three spacecraft and a more complete Galileo image data base than was available for earlier studies. Using more than 3000 control point coordinates, we determine global shape parameters, including mean radius, spheroid- and ellipsoidal axes, and make tests for various equilibrium shape models, constrained by the most recent estimates for gravity field parameters. We confirm that Ganymede has a pronounced ellipsoidal shape, approximately aligned with the Jupiter-direction, in agreement with Ganymede being in tidal equilibrium. The point heights, suffering from large individual errors, do not reveal any large-scale topography below our typical error levels (97%

Invaluable information about the interior of icy satellites orbiting close to the giant planets can be gained by monitoring the response of the satellite's surfaces to external tidal forces. Due to its geodetic accuracy, laser altimetry is the method of choice to measure time-dependent radial surface displacements from orbit. We present an instrument performance model with special focus on the capabilities to determine the corresponding tidal Love number h2 and apply the model to the Ganymede Laser Altimeter (GALA) on board of the Jupiter Icy Moons Explorer (JUICE). Based on the instrument and spacecraft performance, we derive the range error and the measurement capabilities of the GALA instrument to determine the amplitude of the tide induced radial displacement of Ganymede's surface using the cross-over technique. We find that h2 of Ganymede can be determined with an accuracy of better than 2% by using data acquired during the nominal mission. Furthermore, we show that this accuracy is sufficient to confirm the presence of a putative subsurface water ocean and, additionally, to constrain the thickness of the overlaying ice shell to ± 20km.

The small (approximately 500 km in diameter) satellite Enceladus is moving near the equatorial plane and deep in the gravity field of its parent planet Saturn. Owing to tidal interaction with its parent, Enceladus has adopted a pronounced 3-axial ellipsoidal shape and is tidally locked, with rotational and orbital periods of about 1.37 days. As the equator of Saturn is inclined to the planet’s orbital plane, Enceladus, like most of the other satellites of Saturn, undergoes pronounced seasons. This paper gives a summary of the current status as well as shortcomings of our current knowledge regarding Enceladus’ geodetic and dynamic parameters.

第17回宇宙科学シンポジウム (2017年1月5日-6日. 宇宙航空研究開発機構宇宙科学研究所(JAXA)(ISAS)相模原キャンパス), 相模原市, 神奈川県, 17th Space Science Symposium (January 5-6, 2017. Institute of Space and Astronautical Science, Japan Aerospace Exploration Agency(JAXA)(ISAS)Sagamihara Campus), Sagamihara, Kanagawa Japan, 著者人数: 33名, 資料番号: SA6000060090, レポート番号: P-048

Regarding tidal dissipation in Saturn, usually parameterized by Saturn's quality factor Q, there remains a discrepancy between conventional estimates and the latest determination that has been derived from astrometric observations of Saturn's inner satellites. If dissipation in Saturn is as large as the astrometric observations suggest, conventional models predict that Mimas' initial orbit should be located inside Saturn's synchronous orbit or even inside its Roche limit. Using simple structure models and assuming Saturn's core to be viscoelastic, we look for dissipation models which are consistent with both the latest astrometric observations and with Mimas' orbital migration. Firstly, using a two-layer model of Saturn's interior structure, we constrain the ranges of rigidity and viscosity of Saturn's core which are consistent with Saturn's dissipation derived from astrometric observations at the tidal frequencies of Enceladus, Tethys, and Dione. Next, within the constrained viscosity and rigidity ranges, we calculate Mimas' semi-major axis considering the frequency dependence of viscoelastic dissipation in Saturn's core. By the two calculations, we evaluate (1) Saturnian models which can explain the astrometrically determined Saturnian dissipation, and (2) whether Mimas' initial semi-major axis is larger than the synchronous orbit. We show that if the core is assumed to be solid with a viscosity of 10^{13}-10^{14} Pa s, the lower boundary of the observed Saturnian dissipation at tidal frequencies of Enceladus, Tethys, and Dione can be explained by our model. In this viscosity range, Mimas can stay outside the synchronous orbit and the Roche limit for 4.5 billion years of evolution. In the case of a frequency dependent viscoelastic dissipative core, the lower boundary of the observed Saturnian dissipation can be consistent with the orbital expansion of Mimas., 5 pages, 4 figures, 1 table, Accepted for publication in A&A

We studied the motion of medium-sized and small spacecraft orbiting within the binary asteroid systems 175,706 (1996 FG3) and 65,803 Didymos (1996 GT). We have considered spacecraft motion within the binary systems distance regimes between 0.4 and 2.5 km for Didymos and 0.8–4 km for 1996 FG3. Orbital motion of spacecraft, beginning from 20,000 initial conditions lying in the orbital planes of the secondary, were simulated and evaluated for lifespan. The simulations include the effects of (1) the asteroid's mass, shape, and rotational parameters, (2) the secondary's mass and orbit parameters, (3) the spacecraft mass, surface area, and reflectivity (representing large box-wing-shaped medium-sized spacecraft as well as small satellites), and (4) the time of the mission, and therefore the relative position of the system to the sun. Stable orbital motion (i.e., not requiring thrusting maneuvers) was achieved using the Lagrange points L4/L5 and orbital resonances. This allows for long motion arcs, e.g. of 90 days (L4) and 35 days (resonance) in the Didymos system. The accuracy necessary to deploy a probe into L4, so it can remain there for 35 day, is evaluated by comparisons. Retrograde orbits were found assuring 90 days of low eccentric orbiting for a compact small satellite for a great variety of initial conditions. The comparison of simulations at aphelion and perihelion as well as the different spacecraft show the critical impact of solar radiation pressure on orbital stability. 65,803 Didymos (1996 GT) is shown to be more suitable for orbit phases at the close distances we studied compared to 175,706 (1996 FG3). Two possible obliquities of the Didymos system were considered to study the effects of the inclination on perturbing forces at equinox and solstice, showing that cases of low obliquity or times of equinox are beneficial for spacecraft orbiting.

For the saturnian satellite Enceladus, the possible existence of a global ocean is a major issue. For the stability of an internal ocean, tidal heating is suggested as an effective heat source. However, assuming Maxwell rheology ice, it has been shown that a global scale ocean on Enceladus cannot be maintained (Roberts, J.F., Nimmo, F. [2008]. Icarus 194, 675–689). Here, we analyze tidal heating and the stability of a global ocean from the aspect of anelastic behavior. The Maxwell model is the most typical and widely used viscoelastic model. However, in the tidal frequency domain, energy is also dissipated by the anelastic response involving time-dependent or transient creep mechanisms, which is different from the viscoelastic response caused by steady-state creep. The Maxwell model cannot adequately address anelasticity, which has a large effect in the high viscosity range. Burgers and Andrade models are suggested as suitable models for the creep behavior of ice in the frequency domain. We calculate tidal heating in the ice layer and compare it with the radiated heat assuming both convection and conduction of the ice layer. Though anelastic behavior increases the heating rate, it is insufficient to maintain a global subsurface ocean if the ice layer is convecting, even though a wide parameter range is taken into account. One possibility to maintain a global ocean is that Enceladus’ ice shell is conductive and its tidal response is similar to that of the Burgers body with comparatively small transient shear modulus and viscosity. If the surface ice with large viscosity is dissipative by anelastic response, the heat produced in the ice layer would supersede the cooling rate and a subsurface ocean could be maintained without freezing.

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.

We investigate the spin behavior of close-in rocky planets and the implications for their orbital evolution. Considering that the planet rotation evolves under simultaneous actions of the torque due to the equatorial deformation and the tidal torque, both raised by the central star, we analyze the possibility of temporary captures in spin-orbit resonances. The results of the numerical simulations of the exact equations of motions indicate that, whenever the planet rotation is trapped in a resonant motion, the orbital decay and the eccentricity damping are faster than the ones in which the rotation follows the so-called pseudo-synchronization. Analytical results obtained through the averaged equations of the spin-orbit problem show a good agreement with the numerical simulations. We apply the analysis to the cases of the recently discovered hot super-Earths Kepler-10 b, GJ 3634 b and 55 Cnc e. The simulated dynamical history of these systems indicates the possibility of capture in several spin-orbit resonances; particularly, GJ 3634 b and 55 Cnc e can currently evolve under a non-synchronous resonant motion for suitable values of the parameters. Moreover, 55 Cnc e may avoid a chaotic rotation behavior by evolving towards synchronization through successive temporary resonant trappings.

In support of the MarcoPolo-R mission, we have carried out numerical simulations of spacecraft trajectories about the binary asteroid 175706 (1996 FG3) under the influence of solar radiation pressure. We study the effects of (1) the asteroid's mass, shape, and rotational parameters, (2) the secondary's mass, shape, and orbit parameters, (3) the spacecraft's mass, surface area, and reflectivity, and (4) the time of arrival, and therefore the relative position to the sun and planets. We have considered distance regimes between 5 and 20 km, the typical range for a detailed characterization of the asteroids – primary and secondary – with imaging systems, spectrometers and by laser altimetry. With solar radiation pressure and gravity forces of the small asteroid competing, orbits are found to be unstable, in general. However, limited orbital stability can be found in the so-called Self-Stabilized Terminator Orbits (SSTO), where initial orbits are circular, orbital planes are oriented approximately perpendicular to the solar radiation pressure, and where the orbital plane of the spacecraft is shifted slightly (between 0.2 and 1 km) from the asteroid in the direction away from the sun. Under the effect of radiation pressure, the vector perpendicular to the orbit plane is observed to follow the sun direction. Shape and rotation parameters of the asteroid as well as gravitational perturbations by the secondary (not to mention sun and planets) were found not to affect the results. Such stable orbits may be suited for long radio tracking runs, which will allow for studying the gravity field. As the effect of the solar radiation pressure depends on the spacecraft mass, shape, and albedo, good knowledge of the spacecraft model and persistent monitoring of the spacecraft orientation are required.