Mars orientation and rotation angles

The rotation and orientation of Mars is commonly described using two different sets of angles, namely the Euler angles wrt the Mars orbit plane and the right ascension, declination, and prime meridian location angles wrt the Earth equator at J2000 (as adopted by the IAU). We propose a formulation for both these sets of angles, which consists of the sum of a second degree polynomial and of periodic and Poisson series. Such a formulation is shown here to enable accurate (and physically sound) transformation from one set of angles to the other. The transformation formulas are provided and discussed in this paper. In particular, we point that the quadratic and Poisson terms are key ingredients to reach a transformation precision of 0.1 mas, even 30 years away from the reference epoch of the rotation model (e.g. J2000). Such a precision is required to accurately determine the smaller and smaller geophysical signals observed in the high-accuracy data acquired from the surface of Mars. In addition, we present good practices to build an accurate Martian rotation model over a long time span (30 years around J2000) or over a shorter one (e.g. lifetime of a space mission). We recommend to consider the J2000 mean orbit of Mars as the reference plane for Euler angles. An accurate rotation model should make use of up-to-date models for the rigid and liquid nutations, relativistic corrections in rotation, and polar motion induced by the external torque. Our transformation model and recommendations can be used to define the future IAU solution for the rotation and orientation of Mars using right ascension, declination, and prime meridian location. In particular, thanks to its quadratic terms, our transformation model does not introduce arbitrary and non-physical terms of very long period and large amplitudes, thus providing unbiased values of the rates and epoch values of the angles.Comment: 42 page

The Hera Radio Science Experiment at Didymos

Hera represents the European Space Agency's inaugural planetary defence space mission, and plays a pivotal role in the Asteroid Impact and Deflection Assessment international collaboration with NASA DART mission that performed the first asteroid deflection experiment using the kinetic impactor techniques. With the primary objective of conducting a detailed post-impact survey of the Didymos binary asteroid following the DART impact on its small moon called Dimorphos, Hera aims to comprehensively assess and characterize the feasibility of the kinetic impactor technique in asteroid deflection while conducting in-depth investigation of the asteroid binary, including its physical and compositional properties as well as the effect of the impact on the surface and/or shape of Dimorphos. In this work we describe the Hera radio science experiment, which will allow us to precisely estimate key parameters, including the mass, which is required to determine the momentum enhancement resulting from the DART impact, mass distribution, rotational states, relative orbits, and dynamics of the asteroids Didymos and Dimorphos. Through a multi-arc covariance analysis we present the achievable accuracy for these parameters, which consider the full expected asteroid phase and are based on ground radiometric, Hera optical images, and Hera to CubeSats InterSatellite Link radiometric measurements. The expected formal uncertainties for Didymos and Dimorphos GM are better than 0.01% and 0.1%, respectively, while their J2 formal uncertainties are better than 0.1% and 10%, respectively. Regarding their rotational state, the absolute spin pole orientations of the bodies can be recovered to better than 1 degree, and Dimorphos spin rate to better than 10^-3%. Dimorphos reconstructed relative orbit can be estimated at the sub-m level [...

Atmospheric Science with InSight

International audienceIn November 2018, for the first time a dedicated geophysical station, the InSight lander, will be deployed on the surface of Mars. Along with the two main geophysical packages, the Seismic Experiment for Interior Structure (SEIS) and the Heat-Flow and Physical Properties Package (HP3), the InSight lander holds a highly sensitive pressure sensor (PS) and the Temperature and Winds for InSight (TWINS) instrument, both of which (along with the InSight FluxGate (IFG) Magnetometer) form the Auxiliary Sensor Payload Suite (APSS). Associated with the RADiometer (RAD) instrument which will measure the surface brightness temperature, and the Instrument Deployment Camera (IDC) which will be used to quantify atmospheric opacity, this will make InSight capable to act as a meteorological station at the surface of Mars. While probing the internal structure of Mars is the primary scientific goal of the mission, atmospheric science remains a key science objective for InSight. InSight has the potential to provide a more continuous and higher-frequency record of pressure, air temperature and winds at the surface of Mars than previous in situ missions. In the paper, key results from multiscale meteorological modeling, from Global Climate Models to Large-Eddy Simulations, are described as a reference for future studies based on the InSight measurements during operations. We summarize the capabilities of InSight for atmospheric observations, from profiling during Entry, Descent and Landing to surface measurements (pressure, temperature, winds, angular momentum), and the plans for how InSight’s sensors will be used during operations, as well as possible synergies with orbital observations. In a dedicated section, we describe the seismic impact of atmospheric phenomena (from the point of view of both “noise” to be decorrelated from the seismic signal and “signal” to provide information on atmospheric processes). We discuss in this framework Planetary Boundary Layer turbulence, with a focus on convective vortices and dust devils, gravity waves (with idealized modeling), and large-scale circulations. Our paper also presents possible new, exploratory, studies with the InSight instrumentation: surface layer scaling and exploration of the Monin-Obukhov model, aeolian surface changes and saltation / lifing studies, and monitoring of secular pressure changes. The InSight mission will be instrumental in broadening the knowledge of the Martian atmosphere, with a unique set of measurements from the surface of Mars

Moonraker — Enceladus Multiple Flyby Mission

Enceladus, an icy moon of Saturn, possesses an internal water ocean and jets expelling ocean material into space. Cassini investigations indicated that the subsurface ocean could be a habitable environment having a complex interaction with the rocky core. Further investigation of the composition of the plume formed by the jets is necessary to fully understand the ocean, its potential habitability, and what it tells us about Enceladus's origin. Moonraker has been proposed as an ESA M-class mission designed to orbit Saturn and perform multiple flybys of Enceladus, focusing on traversals of the plume. The proposed Moonraker mission consists of an ESA-provided platform with strong heritage from JUICE and Mars Sample Return and carrying a suite of instruments dedicated to plume and surface analysis. The nominal Moonraker mission has a duration of ∼13.5 yr. It includes a 23-flyby segment with 189 days allocated for the science phase and can be expanded with additional segments if resources allow. The mission concept consists of investigating (i) the habitability conditions of present-day Enceladus and its internal ocean, (ii) the mechanisms at play for the communication between the internal ocean and the surface of the South Polar Terrain, and (iii) the formation conditions of the moon. Moonraker, thanks to state-of-the-art instruments representing a significant improvement over Cassini's payload, would quantify the abundance of key species in the plume, isotopic ratios, and the physical parameters of the plume and the surface. Such a mission would pave the way for a possible future landed mission

Martian Lander Radio Science Data Calibration for Mars Troposphere

The tropospheric propagation effect is one of several sources of error in radio science measurements. Systematically calibrated for the Earth troposphere disturbances, the ranging and Doppler data provided by the Martian landers have not been corrected so far for Mars troposphere effects. These effects were considered negligible because the Mars atmosphere is a hundred times less dense than that of the Earth. The constantly improving lander data accuracy and the challenging science objectives of the InSight-Rotation and Interior Structure Experiment (RISE) and ExoMars-2022-LaRa radio science experiments motivated this work. We propose here a simple model to compute the Mars troposphere errors affecting a radio wave transponded from the surface of Mars. The troposphere zenithal delay is first derived from the surface pressure at the lander location. We use a mapping function to infer the slant delay (range errors) induced by the troposphere of Mars. Being proportional to range rates, the contribution of Mars troposphere to the Doppler measurements is derived from the slant delays. Using our model, an elevation threshold of 15° above the lander is identified, below which the Doppler data should be calibrated for Mars troposphere. When applied to the X-band Doppler data from Mars surface missions, the model predicts significant Mars troposphere contribution for less than 1% of RISE data, 2% of Opportunity data, and 2.5% of Pathfinder data. Among these tracking passes, some are strongly affected by the troposphere of Mars, with Doppler errors reaching sometimes more than 3 times the nominal noise level (>10 mHz at 60 s integration time)

The rotation of Mars and Phobos from Earth-based radio-tracking observations of a lander

The knowledge of the interior structure of terrestrial planets is fundamental to our understanding of the Solar System and for our comprehension of the formation and evolution of those planets. The study of the rotation variations allows to explore such otherwise difficult to obtain global properties of those planets. Deep space missions involving landers are the most suitable ones to study the rotation of their host. Firstly, numerical simulations have been realized to assess the precision that can be obtained on the determination of the rotation parameters of Mars from Direct-To-Earth (DTE) Doppler data. Among other things, these simulations provided the precision and the accuracy that can be inferred on the physical properties of the liquid core of Mars (size, moments of inertia and dynamical flattening) from future Mars nutation measurements. In the same way, the precision that can be achieved on the Phobos libration estimates has been predicted still using DTE Doppler data from a lander. Secondly, we have analyzed Viking lander 1, Pathfinder, Spirit and Opportunity real DTE Doppler data. From this dataset, we have estimated new Mars rotation parameters including a new precession rate solution appreciably smaller than the current one. The liquid core contribution to nutations has likely been observed, but the large error bars in the nutation parameter estimates prevent to constrain Mars interior models.(SC - Sciences) -- UCL, 201

Small bodies global gravity inversion via the level-set method

We propose an approach to infer large-scale heterogeneities within a small celestial body from measurements of its gravitational potential, provided for instance by spacecraft radio-tracking. The non-uniqueness of the gravity inversion is here mitigated by limiting the solutions to piecewise-constant density distributions, thus composed of multiple regions of uniform density (mass anomalies) dispersed in a background medium. The boundary of each anomaly is defined implicitly as the 0-level surface of a scalar field (called the level-set function), so that by modifying this field the shape and location of the anomaly are varied. The gravitational potential associated with a density distribution is here computed via a line-integral polyhedron method, yielding the coefficients of its spherical harmonics expansion. The density distribution is then adjusted via an iterative least-squares approach with Tikhonov regularization, estimating at every iteration corrections to the level-set function, the density contrast of each anomaly, and the background density, in order to minimize the residuals between the predicted gravity coefficients and those measured. Given the non-convexity of the problem and the lack of prior knowledge assumed (save for the shape of the body), the estimation process is repeated for several random initial distributions, and the resulting solutions are clustered based on global properties independent of the input measurements. This provides families of candidate interior models in agreement with the data, and the spread of the local density values across each family is used to assess the uncertainties associated with the estimated distributions. We present multiple synthetic tests with increasingly more realistic settings (in terms of gravity resolution and precision, and of shape, size and distribution of the internal heterogeneities), showing that our method is generally able to retrieve a ground-truth mass distribution even with noisy data. For further validation, we present an application of the method to real data, namely the Bennu gravity coefficients measured by the OSIRIS-REx team

Expected constraints on Phobos interior from the MMX gravity and rotation observations

The origin of the Martian moons is still uncertain, and knowledge about their interior could provide support to some of its leading theories. In preparation for the JAXA Martian Moons eXploration (MMX) mission, we review our current knowledge on the interior of Phobos, and provide synthetic tests showing how the gravity and rotation determination could allow the detection of specific interior-structure properties. The inversion of the geodetic observables for the retrieval of the internal mass distribution of a set of synthetic interior models is performed via non-linear least-squares, where the interior parameterization is based on the level-set method. We additionally provide simple expressions allowing to relate some of these interior models to the geodetic observables of Phobos. The results, based on realistic measurement resolution and noise scenarios, show good retrievals for most of the models at the data resolutions expected from MMX. Specifically, we find the gravity information is realistically sufficient for the detection of mass anomalies below the Stickney crater, as well as large scale heterogeneous regions within plausible rubble-pile structures. Libration helps retrieve the more degenerate models for gravity, such as those with concentric layers or with density varying linearly with depth. The incremental improvement from further adding a hypothetical mean obliquity measurement is marginal. Finally, we apply the level-set inversion and the analytical formulas to estimate possible interior characteristics of the ‘real’ Phobos from the currently-available scarce geodetic observables. The level-set solutions for the real-data inversion generally converge to a higher mass concentration towards the surface in the equatorial region. Markov chain Monte Carlo estimations of parameters relative to a simple 2-layer model or a radial density distribution similarly hint at a lighter region inside of Phobos

A view into the deep interior of Mars from nutation measured by InSight RISE

We report the results of more than 2 years of monitoring the rotation of Mars with the RISE instrument on InSight. Small periodic variations of the spin axis orientation, called nutations, can be extracted from the Doppler data with enough precision to identify the influence of the Martian fluid core. For the first time for a planetary body other than the Earth, we can measure the period of the Free Core Nutation (FCN), which is a rotational normal mode arising from the misalignment of the rotation axes of the core and mantle. In this way, we confirm the liquid state of the core and estimate its moment of inertia as well as its size. The FCN period depends on the dynamical flattening of the core and on its ability to deform. Since the shape and gravity field of Mars deviate significantly from those of a uniformly rotating fluid body, deviations from that state can also be expected for the core. Models accounting for the dynamical shape of Mars can thus be tested by comparing core shape predictions to nutation constraints. The observed FCN period can be accounted for by interior models having a very thick lithosphere loaded by degree-two mass anomalies at the bottom. The combination of nutation data and interior structure modeling allows us to deduce the radius of the core and to constrain its density, and thus, to address the nature and abundance of light elements alloyed to iron. The inferred core radius agrees with previous estimates based on geodesy and seismic data. The large fraction of light elements required to match the core density implies that its liquidus is significantly lower than the expected core temperature, making the presence of an inner core highly unlikely. Besides, the existence of an inner core would lead to an additional rotational normal mode the signature of which has not been detected in the RISE data

About the improvement in Mars Polar Motion determination from radio tracking of two landers

The polar motion of Mars is defined as the movement of the rotation axis with respect to a body-fixed frame tied to the crust of the planet. It is composed of forced motion at annual and sub-annual frequencies caused by the seasonal mass redistribution, formation of the polar ice caps and angular momentum variations of the atmosphere, and of the free mode called the Chandler wobble. Radio-tracking data from landers offers the most suitable means to measure the rotation of Mars, including its polar motion. The latter, however, has not yet been achieved using lander data alone. In this study, we assess the uncertainties associated with Mars polar motion estimation using Direct-To-Earth Doppler, range and Same-Beam Interferometry (SBI) observables between multiple landers on the surface of Mars. We evaluate the improvement enabled by combining data from multiple landers with respect to one-lander scenarios, and identify the optimal mission architectures for polar motion estimation by considering the influence of respective mission parameters on the estimation uncertainty. In particular, we consider the effects of absolute and relative locations of the landers and of mission scheduling. We re-evaluate the possibility of estimating the polar motion using data from landers in proximity to the equator, and apply our considerations to simulated data consistent in number and accuracy with that collected by past Martian missions. We notice and explain a strong longitude dependence of the formal errors when the polar motion parameters are estimated concurrently with the seasonal spin variation parameters, making it impossible to properly determine all components of polar motion with a single lander regardless of its location. However, the use of two or more landers in optimal locations with respect to each other eliminates those limitations. We evaluate the influence of latitudinal and longitudinal separation on polar motion determination in such cases. In particular, we are able to determine polar motion well even in cases where the longitudes of the two landers make determination from each single lander impossible