Signatures of the Martian rotation parameters in the Doppler and range observables

The position of a Martian lander is affected by different aspects of Mars' rotational motions: the nutations, the precession, the length-of-day variations and the polar motion. These various motions have a different signature in a Doppler observable between the Earth and a lander on Mars' surface. Knowing the correlations between these signatures and the moments when these signatures are not null during one day or on a longer timescale is important to identify strategies that maximize the geophysical return of observations with a geodesy experiment, in particular for the ones on-board the future NASA InSight or ESA-Roscosmos ExoMars2020 missions. We provide first-order formulations of the signature of the rotation parameters in the Doppler and range observables. These expressions are functions of the diurnal rotation of Mars, the lander position, the planet radius and the rotation parameter. Additionally, the nutation signature in the Doppler observable is proportional to the Earth declination with respect to Mars. For a lander on Mars close to the equator, the motions with the largest signature in the Doppler observable are due to the length-of-day variations, the precession rate and the rigid nutations. The polar motion and the liquid core signatures have a much smaller amplitude. For a lander closer to the pole, the polar motion signature is enhanced while the other signatures decrease. We also numerically evaluate the amplitudes of the rotation parameters signature in the Doppler observable for landers on other planets or moons.Comment: 30 pages 7 figures, In press PS

Titan's Obliquity as evidence for a subsurface ocean?

On the basis of gravity and radar observations with the Cassini spacecraft, the moment of inertia of Titan and the orientation of Titan's rotation axis have been estimated in recent studies. According to the observed orientation, Titan is close to the Cassini state. However, the observed obliquity is inconsistent with the estimate of the moment of inertia for an entirely solid Titan occupying the Cassini state. We propose a new Cassini state model for Titan in which we assume the presence of a liquid water ocean beneath an ice shell and consider the gravitational and pressure torques arising between the different layers of the satellite. With the new model, we find a closer agreement between the moment of inertia and the rotation state than for the solid case, strengthening the possibility that Titan has a subsurface ocean.Comment: 11 pages, 4 figure

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

Mercury's Moment of Inertia from Spin and Gravity Data

Earth-based radar observations of the spin state of Mercury at 35 epochs between 2002 and 2012 reveal that its spin axis is tilted by (2.04 plus or minus 0.08) arc min with respect to the orbit normal. The direction of the tilt suggests that Mercury is in or near a Cassini state. Observed rotation rate variations clearly exhibit an 88-day libration pattern which is due to solar gravitational torques acting on the asymmetrically shaped planet. The amplitude of the forced libration, (38.5 plus or minus 1.6) arc sec, corresponds to a longitudinal displacement of ∼450 m at the equator. Combining these measurements of the spin properties with second-degree gravitational harmonics (Smith et al., 2012) provides an estimate of the polar moment of inertia of MercuryC/MR2 = 0.346 plus or minus 0.014, where M and R are Mercury's mass and radius. The fraction of the moment that corresponds to the outer librating shell, which can be used to estimate the size of the core, is Cm/C = 0.431 plus or minus 0.025

Obliquity of the Galilean satellites: The influence of a global internal liquid layer

The obliquity of the Galilean satellites is small but not yet observed. Studies of cycloidal lineaments and strike-slip fault patterns on Europa suggest that Europa's obliquity is about 1 deg, although theoretical models of the obliquity predict the obliquity to be one order of magnitude smaller for an entirely solid Europa. Here, we investigate the influence of a global liquid layer on the obliquity of the Galilean satellites. Io most likely has a fully liquid core, while Europa, Ganymede, and Callisto are thought to have an internal global liquid water ocean beneath an external ice shell. We use a model for the obliquity based on a Cassini state model extended to the presence of an internal liquid layer and the internal gravitational and pressure torques induced by the presence of this layer. We find that the obliquity of Io only weakly depends on the different internal structure models considered, because of the weak influence of the liquid core which is therefore almost impossible to detect through observations of the obliquity. The obliquity of Europa is almost constant in time and its mean value is smaller (0.033-0.044 deg) with an ocean than without (0.055 deg). An accuracy of 0.004 deg (about 100 m on the spin pole location at the surface) would allow detecting the internal ocean. The obliquity of Ganymede and Callisto depends more on their interior structure because of the possibility of resonant amplifications for some periodic terms of the solution. Their ocean may be easily detected if, at the measuring time, the actual internal structure model lead to a very different value of the obliquity than in the solid case. A long-term monitoring of their shell obliquity would be more helpful to infer information on the shell thickness.Comment: 27 pages, 6 tables, 7 figure

Détermination des paramètres de rotation de Mars à partir de mesures de poursuite Doppler : Théorie et Simulations

L'expérience NEIGE (NEtlander Ionosphere and Geodesy Experiment) permettra d'obtenir des informations sur la structure interne de la planète Mars ainsi que sur son atmosphère grâce à l'observation de ses paramètres de rotation (précession, nutation, longueur du jour, mouvement du pôle). Pour quantifier la précision sur ces paramètres grâce à NEIGE, une formulation analytique de l'observable Doppler entre les landers et un orbiteur a été développée, basée sur une orbite Keplerienne précessante sous l'effet de l'aplatissement de la planète et sur un développement au premier ordre en série de Taylor par rapport aux petits paramètres caractérisant les variations de l'orientation de Mars. Cette formulation permet de comprendre simplement le jeu relatif des différents paramètres et permet également de modéliser leurs corrélations. Dans les conditions nominales de l'expérience, les paramètres liés au mouvement du pôle et aux variations saisonnières de l'angle de rotation sont retrouvés avec une précision meilleure que 3 milli-secondes d'arcs. L'incertitude sur le taux de précession ainsi que sur les paramètres liés à l'exitence d'un possible noyau liquide visible dans l'observable Doppler grâce à une amplification (résonance) des nutations, a également été étudiée. Nous montrons qu'à partir des mesures NEIGE, il sera possible de déduire des informations sur la structure interne de Mars, comme l'état liquide ou solide du noyau, son moment d'inertie et son aplatissement. D'autres paramètres ont été pris en compte dans notre étude, notamment les positions des landers, les éléments orbitaux du satellite et les amplitudes des variations du terme d'aplatissement. La modélisation utilisée permet de tester différentes configurations de mission comme le changement d'orbites, de position et nombre de landers ou l'influence du bruit de mesures, afin d'identifier les conditions minimisant les incertitudes sur les paramètres de rotation. Les incertitudes obtenues grâce aux simulations numériques réalisées avec un logiciel d'orbitographie développé par le CNES et celles obtenues par la méthode analytique sont cohérentes. En comparant ces résultats avec ceux des observables Range et Doppler lander-Terre (représentant les mesures réalisées pendant les missions Viking et Pathfinder), on remarque que l'observable Dopple lander-orbiteur est plus efficace pour détecter de petits mouvements en surface grâce à l'effet amplificateur du Doppler quand la distance entre l'observateur et le lander est petite.(PHYS 3)--UCL, 200

Mars rotational elements: how to explain the long period terms in the IAU standard?

In order to describe the orientation of the spin axis of Mars, the IAU (International Astronomical Union) Working Group on Cartographic Coordinates and Rotational Elements (WGCCRE) uses the right ascension and declination angles, the equatorial coordinates orienting the planet with respect to the Earth equator. This solution is useful to make cartographic products. Differently from IAU, the radioscience community commonly uses Euler angles, with obliquity and node’s longitude defined with respect to the planet mean orbit at epoch. In both sets of angles, a third angle, the rotation angle, is used to position the prime meridian. Its trend is the diurnal rotation