Non-gravitational force modeling of Comet 81P/Wild 2: II. Rotational evolution

In this paper, we have studied both the dynamical and the rotational evolution of an 81P/Wild 2-like comet under the effects of the outgassing-induced force and torque. The main aim is to study if it is possible to reproduce the non-gravitational orbital changes observed in this comet, and to establish the likely evolution of both orbital and rotational parameters. To perform this study, a simple thermophysical model has been used to estimate the torque acting on the nucleus. Once the torque is calculated, Euler equations are solved numerically considering a nucleus mass directly estimated from the changes in the orbital elements (as determined from astrometry). According to these simulations, when the water production rate and changes in orbital parameters for 1997, as well as observational rotational parameters for 2004 are imposed as constraints, the change in the orbital period of 81P/Wild 2, , will decrease so that to , which is similar to the actual tendency observed from 1988 up to 1997. This nearly constant decreasing can be explained as due to a slight drift of the spin axis orientation towards larger ecliptic longitudes. After studying the possible spin axis orientations proposed for 1997, simulations suggest that the spin obliquity and argument (I,Φ)=(56°,167°) is the most likely. As for rotational evolution, changes per orbit smaller than 10% of the actual spin velocity are probable, while the most likely value corresponds to a change between 2 and 7% of the spin velocity. Equally, net changes in the spin axis orientation of 4°-8° per orbit are highly expected.     

Theory of the rotation of the rigid earth

An analytical theory is developed for planes normal to the angular-momentum axis, to the figure axis, and to the rotational axis of the triaxial rigid Earth. One of the purposes of this paper is to determine the effect on nutation and precession of Eckertet al.'s improvement to Brown's tables of the Moon and to check Woolard's theory from a different point of view. The present theory is characterized by the use of Andoyer variables, a moving reference plane, and Hori's averaging perturbation method. A comparison with Woolard's results shows that (1) the maximum difference in nutation for the plane normal to the angular-momentum axis, calculated from the same constants as Woolard adopted, reaches 0.0017, (2) the discrepancy in Oppolzer terms is large compared with the discrepancy in nutation for the plane normal to the angular-momentum axis, and (3) the present theory does not include some of the secular terms that are incorporated in Woolard's theory and that have an effect on the establishment of a reference system. The nutation coefficients 0.0001 for the three above-mentioned planes are calculated by using the numerical values recommended at the working meeting of the International Astronomical Union held in Washington in September 1974. The effects on precession and nutation due to the higher geopotential (n3) are also investigated. Any future revision of the lunar theory will not alter the values of the coefficients of the nutational terms derived here.     

The orbit, mass, and albedo of transneptunian binary (66652) 1999 RZ253

We have observed (66652) 1999 RZ₂₅₃ with the Hubble Space Telescope at seven separate epochs and have fit an orbit to the observed relative positions of this binary. Two orbital solutions have been identified that differ primarily in the inclination of the orbit plane. The best fit corresponds to an orbital period, days, semimajor axis a=4660±170 km and orbital eccentricity e=0.460±0.013 corresponding to a system mass m=3.7±0.4×¹⁰¹⁸ kg. For a density of the albedo at 477 nm is p₄₇₇=0.12±0.01, significantly higher than has been commonly assumed for objects in the Kuiper belt. Multicolor, multiepoch photometry shows this pair to have colors typical for the Kuiper belt with a spectral gradient of 0.35 per 100 nm in the range between 475 and 775 nm. Photometric variations at the four epochs we observed were as large as 12±3% but the sampling is insufficient to confirm the existence of a lightcurve.     

RDAN97: An Analytical Development of Rigid Earth Nutation Series Using the Torque Approach

New series of rigid Earth nutations for the angular momemtum axis, the rotation axis and the figure axis, named RDAN97, are computed using the torque approach. Besides the classical J2 terms coming from the Moon and the Sun, we also consider several additional effects: terms coming from J3 and J4 in the case of the Moon, direct and indirect planetary effects, lunar inequality, J2 tilt, planetary‐tilt, effects of the precession and nutations on the nutations, secular variations of the amplitudes, effects due to the triaxiality of the Earth, new additional out‐of‐phase terms coming from second order effect and relativistic effects. Finally, we obtain rigid Earth nutation series of 1529 terms in longitude and 984 terms in obliquity with a truncation level of 0.1 μ (microarcsecond) and 8 significant digits. The value of the dynamical flattening used in this theory is HD=(C-A)/C=0.0032737674 computed from the initial value pa=50′.2877/yr for the precession rate. These new rigid Earth nutation series are then compared with the most recent models (Hartmann et al., 1998; Souchay and Kinoshita, 1996, 1997; Bretagnon et al., 1997, 1998. We also compute a benchmark series (RDNN97) from the numerical ephemerides DE403/LE403 (Standish et al., 1995) in order to test our model. The comparison between our model (RDAN97) and the benchmark series (RDNN97) shows a maximum difference, in the time domain, of 69 μas in longitude and 29 μas in obliquity. In the frequency domain, the maximum differences are 6 μas in longitude and 4 μ as in obliquity which is below the level of precision of the most recent observations (0.2 mas in time domain (temporal resolution of 1 day) and 0.02 mas in frequency domain). This revised version was published online in July 2006 with corrections to the Cover Date.     

The capture of interstellar dust: the Lorentz force case

The capture of arbitrarily shaped interstellar dust in the Solar System is investigated. Electromagnetic radiation and gravitational forces of the Sun and Lorentz force generated by interplanetary magnetic field are considered. The capture conditions appear to be very sensitive to the particle shape. Non-spherical particles as well as their spherical equivalents are captured only when they are moving initially in the vicinity of ecliptic plane. Capture of non-charged non-spherical dust typically occurs in the region , where R_Sun is solar radius and impact parameter b is defined as the smallest distance between the particle and the Sun if no forces existed. In contrast, charged particles are typically captured at b>150 R_Sun. The total amount of captured non-spherical sub-micron particles differs significantly from the corresponding amount of spherical dust grains. However, both amounts are comparable in the micron-sized range. It is shown that a certain mass of captured non-spherical particles may survive in the Solar System, while captured spherical ones hit the Sun or sublimate in its vicinity. Only a negligible amount of spherical particles can survive. Consideration of solar wind within around of yields that 20% of the captured non-spherical particles of the effective radius survive; the corresponding percentage for particles of the radius is 7%. The total mass of the surviving charged particles is about two orders of magnitude larger than the mass of the surviving non-charged particles. As a result, the sub-micron-sized particles are candidates to contribute to the density increase of the circumsolar dust cloud.     

Thermal infrared and optical observations of four near-Earth asteroids

We present thermal infrared photometry and spectrophotometry of four near-Earth asteroids (NEAs), namely (433) Eros, (66063) 1998 RO₁, (137032) 1998 UO₁, and (138258) 2000 GD₂, using the United Kingdom Infrared Telescope (UKIRT) in 2002. For two objects, i.e. (433) Eros and (137032) 1998 UO₁, quasi-simultaneous optical observations were also obtained, using the Jacobus Kapteyn Telescope (JKT). For (127032) 1998 UO₁, we obtain a rotation period P=3.0±0.1 h and an absolute visual magnitude HV=16.7±0.4. The Standard Thermal Model (STM), Fast Rotating Model (FRM) and near-Earth asteroid Thermal Model (NEATM) have been fitted to the IR fluxes to determine effective diameters Deff, geometric albedos pv, and beaming parameters η. The derived values are (433) Eros: Deff=23.3±3.5 km (at lightcurve maximum), pv=0.24±0.07, η=0.95±0.19; (66063) 1998 RO₁: , ; (137032) 1998 UO₁: Deff<1.13 km, pv>0.29; (138258) 2000 GD₂: Deff=0.27±0.04 km, , η=0.74±0.15. (66063) 1998 RO₁ is a binary asteroid from lightcurve characteristics [Pravec, P., and 56 colleagues, 2006. Icarus 181, 63-93] and we estimate the effective diameter of the primary (Dp) and secondary (Ds) components: and . The diameter and albedo of (138258) 2000 GD₂ are consistent with the trend of decreasing diameter for S- and Q-type asteroids found by Delbó et al. [Delbó, M., Harris, A.W., Binzel, R.P., Pravec, P., Davies, J.K., 2003. Icarus 166, 116-130]. A possible trend of increasing beaming parameter with diameter for small (less than about 3 km) S- and Q-type asteroids is found.     

Thermal inertia of near-Earth asteroids and implications for the magnitude of the Yarkovsky effect

Thermal inertia determines the temperature distribution over the surface of an asteroid and therefore governs the magnitude the Yarkovsky effect. The latter causes gradual drifting of the orbits of km-sized asteroids and plays an important role in the delivery of near-Earth asteroids (NEAs) from the main belt and in the dynamical spreading of asteroid families. At present, very little is known about the thermal inertia of asteroids in the km size range. Here we show that the average thermal inertia of a sample of NEAs in the km-size range is . Furthermore, we identify a trend of increasing thermal inertia with decreasing asteroid diameter, D. This indicates that the dependence of the drift rate of the orbital semimajor axis on the size of asteroids due to the Yarkovsky effect is a more complex function than the generally adopted D⁻¹ dependence, and that the size distribution of objects injected by Yarkovsky-driven orbital mobility into the NEA source regions is less skewed to smaller sizes than generally assumed. We discuss how this fact may help to explain the small difference in the slope of the size distribution of km-sized NEAs and main-belt asteroids.     

Long-term dynamical evolution of dusty ejecta from Deimos

We re-assess expected properties of the presumed dust belt of Mars formed by impact ejecta from Deimos. Previous studies have shown that dynamics of Deimos particles are dominated by two perturbing forces: radiation pressure (RP) and Mars’ oblateness (J2). At the same time, they have demonstrated that lifetimes of particles, especially of grains about ten of micrometers in size, may reach more than 10⁴ years. On such timescales, the Poynting-Robertson drag (PR) becomes important. Here we provide a study of the dynamics under the combined action of all three perturbing forces. We show that a PR decay of the semimajor axes leads to an adiabatic decrease of amplitudes and periods of oscillations in orbital inclinations predicted in the framework of the underlying RP+J2 problem. Furthermore, we show that smallest of the long-lived Deimos grains (radius≈5- may reach a chaotic regime, resulting in unpredictable and abrupt changes of their dynamics. The particles just above that size (≈10-) should be the most abundant in the Deimos torus. Our dynamical analysis, combined with a more accurate study of the particle lifetimes, provides corrections to earlier predictions about the dimensions and geometry of the Deimos torus. In addition to a population, appreciably inclined and shifted towards the Sun, the torus should contain a more contracted, less asymmetric, and less tilted component between the orbits of Phobos and Deimos.     

On the population, physical decay and orbital distribution of Jupiter family comets: Numerical simulations

We study the Jupiter family comet (JFC) population assumed to come from the Scattered Disk and transferred to the Jupiter’s zone through gravitational interactions with the Jovian planets. We shall define as JFCs those with orbital periods and Tisserand parameters in the range 2<T?3.1, while those comets coming from the same source, but that do not fulfill the previous criteria (mainly because they have periods ) will be called ‘non-JFCs’. We performed a series of numerical simulations of fictitious comets with a purely dynamical model and also with a more complete dynamical-physical model that includes besides nongravitational forces, sublimation and splitting mechanisms. With the dynamical model, we obtain a poor match between the computed distributions of orbital elements and the observed ones. However with the inclusion of physical effects in the complete model we are able to obtain good fits to observations. The best fits are attained with four splitting models with a relative weak dependence on q, and a mass loss in every splitting event that is less when the frequency is high and vice versa. The mean lifetime of JFCs with radii and is found to be of about 150-200 revolutions (∼. The total population of JFCs with radii within Jupiter’s zone is found to be of 450±50. Yet, the population of non-JFCs with radii in Jupiter-crossing orbits may be ∼4 times greater, thus leading to a whole population of JFCs + non-JFCs of ∼2250±250. Most of these comets have perihelia close to Jupiter’s orbit. On the other hand, very few non-JFCs reach the Earth’s vicinity (perihelion distances ) which gives additional support to the idea that JFCs and Halley-type comets have different dynamical origins. Our model allows us to define the zones of the orbital element space in which we would expect to find a large number of JFCs. This is the first time, to our knowledge, that a physico-dynamical model is presented that includes sublimation and different splitting laws. Our work helps to understand the role played by these erosion effects in the distribution of the orbital elements and lifetimes of JFCs.     

Titania's radius and an upper limit on its atmosphere from the September 8, 2001 stellar occultation

On September 8, 2001 around 2 h UT, the largest uranian moon, Titania, occulted Hipparcos star 106829 (alias SAO 164538, a V=7.2, K0 III star). This was the first-ever observed occultation by this satellite, a rare event as Titania subtends only 0.11 arcsec on the sky. The star's unusual brightness allowed many observers, both amateurs or professionals, to monitor this unique event, providing fifty-seven occultations chords over three continents, all reported here. Selecting the best 27 occultation chords, and assuming a circular limb, we derive Titania's radius: (1-σ error bar). This implies a density of using the value derived by Taylor [Taylor, D.B., 1998. Astron. Astrophys. 330, 362-374]. We do not detect any significant difference between equatorial and polar radii, in the limit , in agreement with Voyager limb image retrieval during the 1986 flyby. Titania's offset with respect to the DE405 + URA027 (based on GUST86 theory) ephemeris is derived: ΔαTcos(δT)=−108±13 mas and ΔδT=−62±7 mas (ICRF J2000.0 system). Most of this offset is attributable to a Uranus' barycentric offset with respect to DE405, that we estimate to be: and ΔδU=−85±25 mas at the moment of occultation. This offset is confirmed by another Titania stellar occultation observed on August 1st, 2003, which provides an offset of ΔαTcos(δT)=−127±20 mas and ΔδT=−97±13 mas for the satellite. The combined ingress and egress data do not show any significant hint for atmospheric refraction, allowing us to set surface pressure limits at the level of 10-20 nbar. More specifically, we find an upper limit of 13 nbar (1-σ level) at 70 K and 17 nbar at 80 K, for a putative isothermal CO₂ atmosphere. We also provide an upper limit of 8 nbar for a possible CH₄ atmosphere, and 22 nbar for pure N₂, again at the 1-σ level. We finally constrain the stellar size using the time-resolved star disappearance and reappearance at ingress and egress. We find an angular diameter of 0.54±0.03 mas (corresponding to projected at Titania). With a distance of 170±25 parsecs, this corresponds to a radius of 9.8±0.2 solar radii for HIP 106829, typical of a K0 III giant.     

Evolution of the north-polar cap of Mars: a modelling study

Celestial-mechanical computations show that, even stronger than for Earth, Mars is subject to Milankovi? cycles, that is, quasi-periodic variations of the orbital parameters obliquity, eccentricity and precession. Consequently, solar insolation varies on time-scales of 10⁴-10⁵ years. It has long been supposed that this entails climatic cycles like the terrestrial glacial-interglacial cycles. This hypothesis is supported by the light-dark layered deposits of the north- and south-polar caps indicating a strongly varying dust content of the ice due to varying climate conditions in the past. This study aims at simulating the dynamic and thermodynamic evolution of the north-polar cap (NPC) of Mars with the ice-sheet model SICOPOLIS. The boundary conditions of surface accumulation, ablation and temperature are derived directly from the solar-insolation history by applying the newly developed model MAIC. We consider steady-state scenarios under present climate conditions as well as transient scenarios over climatic cycles. It is found that the NPC is most likely not in steady state with the present climate. The topography of the NPC is mainly controlled by the history of the surface mass balance. Ice flow, which is of the order of , plays only a minor role. In order to build up the present cap during the last five million years of relatively low obliquities, a present accumulation rate of water equiv a⁻¹ is required. Computed basal temperatures are far below pressure melting for all simulations and all times.     

Compositional and physical results for Rosetta's new target Comet 67P/Churyumov-Gerasimenko from narrowband photometry and imaging

We present compositional and physical results of Comet 67P/Churyumov-Gerasimenko, the new target of ESA's Rosetta mission. A total of 16 nights of narrowband photometry were obtained at Lowell Observatory during the 1982/83 and 1995/96 apparitions, along with one night of imaging near perihelion in 1996. These data encompass an interval of −61 to +118 days from perihelion, corresponding to a range of heliocentric distances before perihelion from 1.48 to 1.34 AU, and an outbound range from 1.30 to 1.86 AU. Production rates were determined for OH, NH, CN, C₃, and C₂, along with A(θ)fρ, a proxy of the dust production. Water production, based on OH, has a steep () power-law rH-dependence post-perihelion and the minor species are somewhat less steep ( to −4), while the dust is quite shallow (), possibly due to a lingering population of large, slow-moving grains. All species exhibit larger production rates after perihelion, with water having a ∼2×pre/post-perihelion asymmetry, while minor species and dust have larger asymmetries. These asymmetries imply a strong seasonal effect and probable high obliquity of the rotational axis, along with one or more isolated source regions coming into sunlight near perihelion. Peak water production (which occurred about 1 month after perihelion) was and, when combined with a standard water vaporization model, implies an effective active area on the surface of the nucleus of ∼1.5-2.2 km² or an active fraction of only about 3-4%. Abundances of carbon-chain molecules yield a classification of slightly “depleted” in the A'Hearn et al. [A'Hearn, M.F., Millis, R.L., Schleicher, D.G., Osip, D.J., Birch, P.V., 1995. Icarus 118, 223-270] database. The peak dust production (as measured by A(θ)fρ, and uncorrected for phase angle) was ∼450 cm, while the color of the dust is moderately reddened, and the mean radial profile has a power-law slope of −1.3. Large night-to-night variability is also present, presumably due to the source region(s) rotating in and out of sunlight along with effects due to the use of differently sized apertures. A strong sunward radial feature was detected in images obtained near perihelion, along with a significant asymmetry between the two perpendicular directions from the Sun/tail line. These features may be the result of a mid-latitude source region sweeping out a cone with each rotation, which we are viewing from the side and where the sunward radial feature is one edge of the cone seen in projection. When combined with other constraints on the pole orientation, a possible pole solution is found having an obliquity of about 134° at an RA of about 223° and a Dec of −65°, with a source region located near +50° and in overall agreement with the photometric results. In comparison to the original Rosetta target Comet 46P/Wirtanen, Comet Churyumov-Gerasimenko has essentially the same peak water production but a peak dust production about 3 times greater than does Wirtanen based on A(θ)fρ (i.e., if one assumes that the properties of the dust grains are similar) (cf. Farnham and Schleicher [1998. Astron. Astrophys. 335, L50-L55]).     

Precession and nutation in the η Carinae binary system: evidence from the X-ray light curve

It is believed that η Carinae is actually a massive binary system, with the wind–wind interaction responsible for the strong X-ray emission. Although the overall shape of the X-ray light curve can be explained by the high eccentricity of the binary orbit, other features like the asymmetry near periastron passage and the short quasi-periodic oscillations seen at those epochs have not yet been accounted for. In this paper we explain these features assuming that the rotation axis of η Carinae is not perpendicular to the orbital plane of the binary system. As a consequence, the companion star will face η Carinae on the orbital plane at different latitudes for different orbital phases and, since both the mass-loss rate and the wind velocity are latitude dependent, they would produce the observed asymmetries in the X-ray flux. We were able to reproduce the main features of the X-ray light curve assuming that the rotation axis of η Carinae forms an angle of  29°± 4°  with the axis of the binary orbit. We also explained the short quasi-periodic oscillations by assuming nutation of the rotation axis, with an amplitude of about  5°  and a period of about 22 days. The nutation parameters, as well as the precession of the apsis, with a period of about 274 years, are consistent with what is expected from the torques induced by the companion star.     

Meteoroid streams that trace to candidate dormant comets

In an effort to identify space mission targets of interest, the association of known meteoroid streams with Near-Earth Objects (NEOs) was investigated. In addition to updating previous searches to include NEOs discovered up to January 1, 2007, a new dissimilarity criterion based on dynamical arguments was applied to evaluate the likelihood of each candidate association. The new criterion is based on the fact that the few established cases, such as 2003 EH1 and the Quadrantid stream, involve parent bodies that fragmented in the most recent nutation cycle of their secular orbital evolution. In established cases, the statistics speak strongly of an association due to the lack of NEOs in the a, e, i phase space occupied by these showers. The newly proposed associations are much more uncertain, because the odds of chance associations greatly increase as orbital inclination of the showers decreases. Forty-two plausible candidate dormant comets were identified, that deserve further scrutiny. Both comet and stream typically lack sufficient data to prove the association. Most candidate parent bodies pertain to NEOs with an aphelion distance just short of Jupiter's orbit, a perihelion distance near Earth orbit, and an eccentricity in the range 0.5-0.8. Surprisingly many have , which means that most candidate parent bodies are dormant Jupiter family comets that have not yet fully decoupled from Jupiter. Establishing these associations can provide further evidence that (mostly) dormant comets break frequently, making this the dominant mechanism for replenishing the zodiacal cloud.     

A global solution for the Mars static and seasonal gravity, Mars orientation, Phobos and Deimos masses, and Mars ephemeris

With the collection of six years of MGS tracking data and three years of Mars Odyssey tracking data, there has been a continual improvement in the JPL Mars gravity field determination. This includes the measurement of the seasonal changes in the gravity coefficients (e.g., , , , , , ) caused by the mass exchange between the polar ice caps and atmosphere. This paper describes the latest gravity field MGS95J to degree and order 95. The improvement comes from additional tracking data and the adoption of a more complete Mars orientation model with nutation, instead of the IAU 2000 model. Free wobble of the Mars' spin axis, i.e. polar motion, has been constrained to be less than 10 mas by looking at the temporal history of and . A strong annual signature is observed in , and this is a mixture of polar motion and ice mass redistribution. The Love number solution with a subset of Odyssey tracking data is consistent with the previous liquid outer core determination from MGS tracking data [Yoder et al., 2003. Science 300, 299-303], giving a combined solution of k₂=0.152±0.009 using MGS and Odyssey tracking data. The solutions for the masses of the Mars' moons show consistency between MGS, Odyssey, and Viking data sets; Phobos GM=(7.16±0.005)×¹⁰⁻⁴ km³/s² and Deimos GM=(0.98±0.07)×¹⁰⁻⁴ km³/s². Average MGS orbit errors, determined from differences in the overlaps of orbit solutions, have been reduced to 10-cm in the radial direction and 1.5 m along the spacecraft velocity and normal to the orbit plane. Hence, the ranging to the MGS and Odyssey spacecraft has resulted in position measurements of the Mars system center-of-mass relative to the Earth to an accuracy of one meter, greatly reducing the Mars ephemeris errors by several orders of magnitude, and providing mass estimates for Asteroids 1 Ceres, 2 Pallas, 3 Juno, 4 Vesta, and 324 Bamberga.     

Tilting Styx and Nix but not Uranus with a Spin-Precession-Mean-motion resonance

A Hamiltonian model is constructed for the spin axis of a planet perturbed by a nearby planet with both planets in orbit about a star. We expand the planet–planet gravitational potential perturbation to first order in orbital inclinations and eccentricities, finding terms describing spin resonances involving the spin precession rate and the two planetary mean motions. Convergent planetary migration allows the spinning planet to be captured into spin resonance. With initial obliquity near zero, the spin resonance can lift the planet’s obliquity to near 90\(^\circ \) or 180\(^\circ \) depending upon whether the spin resonance is first or zeroth order in inclination. Past capture of Uranus into such a spin resonance could give an alternative non-collisional scenario accounting for Uranus’s high obliquity. However, we find that the time spent in spin resonance must be so long that this scenario cannot be responsible for Uranus’s high obliquity. Our model can be used to study spin resonance in satellite systems. Our Hamiltonian model explains how Styx and Nix can be tilted to high obliquity via outward migration of Charon, a phenomenon previously seen in numerical simulations.     

Long-term evolution of the spin of Venus: II. numerical simulations

We present here the numerical application of the theoretical results derived in Correia et al. (2003, Icarus 163, 1-23) for the spin evolution of Venus since its formation. We explore a large variety of initial conditions to cover the possible formation and evolutionary scenarios. In particular, we pay special attention to the evolutions which cross the chaotic zone resulting from secular planetary perturbations (Laskar and Robutel, 1993, Nature 361, 608-612). We demonstrate that Venus’ axis can be temporarily trapped in a secular resonance with the node of Neptune’s orbit, which can prevent it from being tilted to 180° and will drive it toward 0°. We test several dissipation models and parameters to evaluate their contribution to the planet’s spin history. We confirm that despite the variations in the models, only three of the four final spin states of Venus are possible (Correia and Laskar, 2001, Nature 411, 767-770) and that the present observed retrograde spin state of Venus can be attained by two different processes. In the first scenario (π−), the axis is tilted toward 180° while its rotation rate slows down, while in the second one, the axis is driven toward 0° obliquity and the rotation rate decreases, stops, and increases again in the reverse direction to a final equilibrium value (0−).     

The effect of the internal structure of Mars on its seasonal loading deformations

Mars is continuously subjected to surface loading induced by seasonal mass changes in the atmosphere and ice caps due to the CO₂ sublimation and condensation process. It results in surface deformations and in time variations of gravity. Large wavelength annual and semi-annual variations of gravity (particularly zonal coefficients ΔJn) have been determined using present day geodetic satellite measurements. However loading deformations have been poorly studied for a planet like Mars. In this paper, we compute these deformations and their effect on spacecraft orbiting around Mars. Loading deformations of terrestrial planet are typically investigated assuming a spherical planet, radially symmetric. The mean radial structure of Mars is not well known. In particular the radius of the liquid or solid core remains not precisely determined. One may then wonder what is the effect of these uncertainties on loading deformations. Moreover, Mars presents a strong topography and probably large lateral variations of crustal thickness (relative to the Earth). The paper answer the questions of what is the effect of such lateral heterogeneities on surface deformations, and is the classical way to calculate loading deformation well adapted for a planet like Mars. In order to answer these questions we have investigated theoretically loading deformations of Mars-like planets. We first investigated classical load Love numbers. We show that for degrees inferior to 10, the load Love numbers mainly depend on the radius of the core and on its state, and that for degree greater than 10, they depend on the mean radius of mantle-crust interface. Using a General Circulation Model (GCM) of atmosphere and ice caps dynamics we show that loading vertical displacements have a 4-5 cm magnitude and present a North-South pattern with periodic transitions. Finally we investigated the effect of lateral variations of the crustal thickness on these loading deformations. We show that thickness heterogeneities perturb the deformations and the time variation of gravity at about 0.5%. However this perturbation on ΔJn is only about 1‰ due to main direct attraction of surface fluid layers. We conclude that lateral variations of crustal thickness are today negligible. However, observation of load Love numbers would bring information on the radial internal structure of the planet, particularly on the core radius. ΔJn study would permit to infer the load Love number , particularly for degree 2 and 3, knowing surface fluid layer dynamics. However load Love numbers are quite small (about 0.05), and despite the present good agreement between GCM and ΔJn observations, will only be estimated in the near future when a slightly better precision in observation and modeling will make it possible to infer these numbers. The investigation of load Love number , which are larger than numbers, would be particularly interesting. It would permit to study degree 1 contribution of atmosphere and ice caps dynamics, which is the most important component of surface fluid dynamics on Mars. Surface displacement measurements would be necessary on a few places near the pole regions, which may be possible in the future, with a project involving precise positioning of a lander on the surface of Mars.