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1.
Kurt Lambeck 《Celestial Mechanics and Dynamical Astronomy》1974,10(2):179-182
Douglaset al. (1973) have estimated tidal parameters from the orbits of GEOS 1 and GEOS 2. Their results, interpreted in terms of Love numbers, are rather dispersive due in part to their neglect of the ocean tides. The ocean tidal corrections are estimated in this paper, but although they do not explain all of the discrepancy they do emphasise the importance of these perturbations on the motion of close Earth satellites. The remaining discrepancies could result in part from the fact that part of the long period tidal perturbations have been absorbed by the zonal harmonics in the Earth's gravity field. 相似文献
2.
Knowledge of the interior structure of Mars is of fundamental importance to the understanding of its past and present state as well as its future evolution. The most prominent interior structure properties are the state of the core, solid or liquid, its radius, and its composition in terms of light elements, the thickness of the mantle, its composition, the presence of a lower mantle, and the density of the crust. In the absence of seismic sounding only geodesy data allow reliably constraining the deep interior of Mars. Those data are the mass, moment of inertia, and tides. They are related to Mars’ composition, to its internal mass distribution, and to its deformational response to principally the tidal forcing of the Sun. Here we use the most recent estimates of the moment of inertia and tidal Love number k2 in order to infer knowledge about the interior structure of the Mars.We have built precise models of the interior structure of Mars that are parameterized by the crust density and thickness, the volume fractions of upper mantle mineral phases, the bulk mantle iron concentration, and the size and the sulfur concentration of the core. From the bulk mantle iron concentration and from the volume fractions of the upper mantle mineral phases, the depth dependent mineralogy is deduced by using experimentally determined phase diagrams. The thermoelastic properties at each depth inside the mantle are calculated by using equations of state. Since it is difficult to determine the temperature inside the mantle of Mars we here use two end-member temperature profiles that have been deduced from studies dedicated to the thermal evolution of Mars. We calculate the pressure and temperature dependent thermoelastic properties of the core constituents by using equations state and recent data about reference thermoelastic properties of liquid iron, liquid iron-sulfur, and solid iron. To determine the size of a possible inner core we use recent data on the melting temperature of iron-sulfur.Within our model assumptions the geodesy data imply that Mars has no solid inner core and that the liquid core contains a large fraction of sulfur. The absence of a solid inner is in agreement with the absence of a global magnetic field. We estimate the radius of the core to be 1794 ± 65 km and its core sulfur concentration to be 16 ± 2 wt%. We also show that it is possible for Mars to have a thin layer of perovskite at the bottom of the mantle if it has a hot mantle temperature. Moreover a chondritic Fe/Si ratio is shown to be consistent with the geodesy data, although significantly different value are also possible. Our results demonstrate that geodesy data alone, even if a mantle temperature is assumed, can almost not constrain the mineralogy of the mantle and the crust. In order to obtain stronger constraints on the mantle mineralogy bulk properties, like a fixed Fe/Si ratio, have to be assumed. 相似文献
3.
In the frame of a comparison between Earth, Venus, and Mars, a vision on future geodesy missions to Mars is discussed with particular focus on furthering our understanding of the interior, rotation, and orientation of this terrestrial planet. We explain how radioscience instruments can be used to observe the rotation and orientation and therewith to study the deep interior of Mars and its global atmosphere dynamics. Transponders in X-band and Ka-band are proposed with radio links between a lander or a rover and an orbiter around Mars and/or directly to the Earth. The radio budget links are studied in the frame of possible mission constraints and simulations are performed, which show that important information on the interior of Mars can be obtained from the radioscience data. From the observation of Mars’ orientation in space and of tidal effects on a spacecraft orbiting around Mars we show that it is possible for instance to constrain the dimension and composition of the core, the percentage of light element within the core, and to determine the presence of a pressure-induced mineral-phase transition at the bottom of the mantle. 相似文献
4.
Charles F. Yoder 《Icarus》1982,49(3):327-346
The Martian satellites Phobos and Deimos move along nearly circular coplanar, stable orbits and have created surfaces older than ～ 109 years. The accretion hypothesis suggests that their primordial orbits were also very regular. However, tides raised on Mars and Phobos can substantially alter the semimajor axis a of Phobos' orbit over time. The effect of the Martian tidal torque alone on Phobos' orbit implies that the primordial e was ～0.1 to 0.2 about 4.6 × 109 years ago if the present observed e = 0.015 is naively interpreted as a tidally damped remnant. Significant tidal friction in Phobos reduces the time scale for Phobos to achieve a crossing orbit with Deimos to less than 109 years and permits the primodial e to approach unity. The consequences of orbital intersections cannot easily be resolved by assuming either a catastrophic origin for both satellites (namely, that both are fragments of a common parent body fractured by an impact) or that they were captured sequentially by Mars. Either hypothesis is difficult to accept, given that Deimos' orbit, which is only slightly affected by tides, is now so regular. An alternative scenario is proposed in this paper in which the observed e of Phobos results from several gravitational resonance excitations within the last 109 years, assuming tidal friction in Phobos has had only a small effect on its orbit. In facr, both the primordial e and the inclination i may have been much smaller than presently observed. The constraints imposed on tidal friction in Phobos by both the apparent age of Phobos' surface (> 109yrs) and the above scenario can be satisfied only of μQ > 1012dynes/cm2. Since the Q factor is ～102, the rigidity μ > 1010dynes/cm2. Thus Phobos should have substantial internal strength. 相似文献
5.
M. Burša 《Earth, Moon, and Planets》1988,42(1):49-53
A dynamic homogeneous model of Phobos is used: its boundary is an equipotential surface specified by the second zonal and the second sectorial harmonics plus the constant part of the tidal potential due to Mars. The principal moments of inertia, the hydrostatic second zonal harmonic and the secular Love number of Phobos have been estimated. They support the hypothesis that Phobos is formed out of primordial matter by accretion in orbit. 相似文献
6.
The relation between gravity anomalies, topography and volcanism can yield important insights about the internal dynamics of planets. From the power spectra of gravity and topography on Earth, Venus and Mars we infer that gravity anomalies have likely predominantly sources below the lithosphere up to about spherical harmonic degree l=30 for Earth, 40 for Venus and 5 for Mars. To interpret the low-degree part of the gravity spectrum in terms of possible sublithospheric density anomalies we derive radial mantle viscosity profiles consistent with mineral physics. For these viscosity profiles we then compute gravity and topography kernels, which indicate how much gravity anomaly and how much topography is caused by a density anomaly at a given depth. With these kernels, we firstly compute an expected gravity-topography ratio. Good agreement with the observed ratio indicates that for Venus, in contrast to Earth and Mars, long-wavelength topography is largely dynamically supported from the sublithospheric mantle. Secondly, we combine an empirical power spectrum of density anomalies inferred from seismic tomography in Earth’s mantle with gravity kernels to model the gravity power spectrum. We find a good match between modeled and observed gravity power spectrum for all three planets, except for 2?l?4 on Venus. Density anomalies in the Venusian mantle for these low degrees thus appear to be very small. We combine gravity kernels and the gravity field to derive radially averaged density anomaly models for the Martian and Venusian mantles. Gravity kernels for l?5 are very small on Venus below ≈800 km depth. Thus our inferences on Venusian mantle density are basically restricted to the upper 800 km. On Mars, gravity anomalies for 2?l?5 may originate from density anomalies anywhere within its mantle. For Mars as for Earth, inferred density anomalies are dominated by l=2 structure, but we cannot infer whether there are features in the lowermost mantle of Mars that correspond to Earth’s Large Low Shear Velocity Provinces (LLSVPs). We find that volcanism on Mars tends to occur primarily in regions above inferred low mantle density, but our model cannot distinguish whether or not there is a Martian analog for the finding that Earth’s Large Igneous Provinces mainly originate above the margins of LLSVPs. 相似文献
7.
滞弹地球自转速率的潮汐变化 总被引：5，自引：0，他引：5
本文根据勒夫数和负荷载夫数的数值扰动原理，利用ｈａｎｄｌｅｒ摆动的理论周期作为滞弹吸收带模型参数估计的约束条件，讨论了地幔滞弹性对有效勒夫数ｋ的直接影响，以及滞弹地球对平均海潮的响应所产生的间接扰动，分析了它们对带谐潮尺度因子ｋ／Ｃ的影响，由此定义了一个具有动力学海潮、滞弹地幔和液核地球的世界时ＵＴ１潮汐变化序列，与天文新技术观测结果相比较表明，高频带谐潮变化的理论值与实测值是一致的。频散效应对低 相似文献
8.
Recent Viking results indicate the Martian satellites are composed of carbonaceous chondritic material, suggesting that Phobos and Deimos were once asteroids captured by Mars. On the other hand, the low eccentricities and inclinations of their orbits on the equator of Mars argue against that hypothesis. This paper presents detailed calculations of the tidal evolution of Phobos and Deimos, considering dissipation in both Mars and its satellites simultaneously and using a new method applicable for any value of the eccentricity. In particular, including precession of the satellites' orbits indicates that they have always remained close to their Laplacian plane, so that the orbital planes of Phobos and Deimos switched from near the Martian orbital plane to the Martian equator once the perturbations due to the planetary oblateness dominated the solar perturbations, as they do presently. The results show that Deimos has been little affected by tides, but several billion (109) years ago, Phobos was in a highly eccentric orbit lying near the common plane of the solar system. This outcome is obtained for very reasonable values of dissipation inside Mars and inside Phobos. Implications for the origin of the Martian satellites are discussed. 相似文献
9.
简要说明了天文地球动力学范畴内所研究的潮汐现象，包括由日月引潮力引起的固体潮、海洋潮、大气潮和由于地球自转轴的极移引起的极潮，以及这些潮汐对地球自转和地球自转的测量产生的效应。重点阐述中国天文学界在这一领域里的研究成果。这些研究涉及潮汐影响地球自转的机制，也就是各种潮汐效应与极移、自转速率变化和章动的关系，包括构建这类关系的理论模型，分析潮汐对它们的影响，利用中国古代丰富的天象记录计算地球自转的长期减慢，计算弹性或滞弹地球的洛夫数，依据某一地球模型计算潮汐效应或章动序列等等。研究也涉及在测量地球自转参数的不同技术中各种潮汐效应对测量结果产生的影响及其改正，并涉及与潮汐有关的观测方法的优化和数据处理过程的改进。最后介绍了中国学者所发现的脉冲星的周期和周期变率测量中的潮汐效应，尽管它们的量级甚微，但不容忽视。 相似文献
10.
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. 相似文献
11.
The effect of the dense atmosphere of Titan on the tidal variations of the external gravitational potential of degree two is quantified. The atmospheric tides perturb the external gravitational potential of Titan in two ways. First, the atmosphere itself contributes directly to the external gravitational potential with a period of 15.945 days. Second, the variable loading of the atmosphere induces mass redistribution within Titan, which also changes the external gravitational potential. It is shown that the relative atmospheric contributions to the tides are most likely less than 2% and vanish almost completely for the most plausible models with a subsurface ocean. This suggest that atmospheric tidal perturbations will contribute only negligibly to Cassini measurements of Titan's gravitational field so that the tidal Love numbers derived from these observations can be directly interpreted in terms of the satellite's interior. 相似文献
12.
The long-wavelength topography of Titan has an amplitude larger than that expected from tidal and rotational distortions at its current distance from Saturn. This topography is associated with small gravity anomalies, indicating a high degree of compensation. Both observations can be explained if Titan has a floating, isostatically-compensated ice shell with a spatially-varying thickness. The spatial variations arise because of laterally-variable tidal heating within the ice shell. Models incorporating shell thickness variations result in an improved fit to the observations and a degree-two tidal Love number h2t consistent with expectations, without requiring Titan to have moved away from Saturn. Our preferred models have a mean shell thickness of ≈100 km in agreement with the observed gravity anomalies, and a heat flux appropriate to a chondritic Titan. Shell thickness variations are eliminated by convection; we therefore conclude that Titan’s ice shell is not convecting at the present day. 相似文献
13.
Reductions of Mariner 9 TV data of Phobos and Deimos tend to corroborate the existence of a secular acceleration of Phobos commensurate with two recently reported values based on a reprocessing of Earth-based data. These values of secular acceleration have been used together with Mariner 9 data on the physical size of Phobos and Earth-based photoelectric observations which infer a carbonaceous composition for Phobos to place bounds of 50 < Q < 150 on the tidal dissipation function of Mars. The corresponding bounds on the tidal lag angle are 0.19° < Φ < 0.57°. 相似文献
14.
《天文和天体物理学研究(英文版)》2010,(8)
This review provides explanations of how geodesy, rotation and gravity can be addressed using radioscience data of an orbiter around a planet or of the lander on its surface.The planet Mars is the center of the discussion.The information one can get from orbitography and radioscience in general concerns the global static gravitational field, the time variation of the gravitational field induced by mass exchange between the atmosphere and the ice caps, the time variation of the gravitational field induced by the tides, the secular changes in the spacecraft's orbit induced by the little moons of Mars named Phobos and Deimos, the gravity induced by particular targets, the Martian ephemerides, and Mars' rotation and orientation.The paper addresses as well the determination of the geophysical parameters of Mars and, in particular, the state of Mars' core and its size, which is important for understanding the planet's evolution.Indeed, the state and dimension of the core determined from the moment of inertia and nutation depend in turn on the percentage of light elements in the core as well as on the core temperature, which is related to heat transport in the mantle.For example, the radius of the core has implications for possible mantle convection scenarios and, in particular, for the presence of a perovskite phase transition at the bottom of the mantle.This is also important for our understanding of the large volcanic province Tharsis on the surface of Mars. 相似文献
15.
G. Metris P. Exertier Y. Boudon F. Barlier 《Celestial Mechanics and Dynamical Astronomy》1993,57(1-2):175-188
The main effects of tesseral harmonics of a gravity potential expansion on the motion of a satellite, are short period variations as well as long period variations due to resonances. However, other smaller long period and secular variations can arise from interactions between tesseral terms of the same order. The analytical integration of these effects is developed, using numerical evaluation of Kaula eccentricity and inclination functions. Examples for some Earth's geodetic satellites show that secular effects can reach a few decameters per year. The secular variations can even reach several hundred of meters per year for the Mars natural satellite Phobos. 相似文献
16.
Along with the development of the observing technology, the observation and study on the exoplanets’ oblateness and apsidal precession have achieved significant progress. The oblateness of an exoplanet is determined by its interior density profile and rotation period. Between its Love number k2 and core size exists obviously a negative correlation. So oblateness and k2 can well constrain its interior structure. Starting from the Lane-Emden equation, the planet models based on different polytropic indices are built. Then the flattening factors are obtained by solving the Wavre's integro-differential equation. The result shows that the smaller the polytropic index, the faster the rotation, and the larger the oblateness. We have selected 469 exoplanets, which have simultaneously the observed or estimated values of radius, mass, and orbit period from the NASA (National Aeronautics and Space Administration) Exoplanet Archive, and calculated their flattening factors under the two assumptions: tidal locking and fixed rotation period of 10.55 hours. The result shows that the flattening factors are too small to be detected under the tidal locking assumption, and that 28% of exoplanets have the flattening factors larger than 0.1 under the fixed rotation period of 10.55 hours. The Love numbers under the different polytropic models are solved by the Zharkov's approach, and the relation between k2 and core size is discussed. 相似文献
17.
J.C. Marty G. Balmino P. Rosenblatt S. Le Maistre A. Rivoldini V. Dehant T. Van Hoolst 《Planetary and Space Science》2009,57(3):350-1027
We present results of several years of research and data processing aimed at modelling the Mars gravity field and its longest wavelength time variations. The new solution includes tracking data from Mars Global Surveyor (MGS) from 1998 to 2006 (end of mission) and from Mars Odyssey from 2002 to the spring of 2008; this is the longest analyzed data set from these two orbiter missions as compared to previous works. The new model has been obtained by a team working in Europe, independently from the works of groups at NASA Jet Propulsion Laboratory (JPL) and Goddard Space Flight Center (GSFC), also with totally independent software. Observations consist in two and three-way Doppler measurements (also one way for MGS), and range tracking data collected by the Deep Space Network and have been processed in 4 day arcs, taking into account all disturbing forces of gravitational and non-gravitational origins; for each arc the state vector, drag and solar pressure model multiplying factors, and angular momentum dump parameters are adjusted. The static field (MGGM08A) is represented in spherical harmonics up to degree and order 95 and is very close to previously published models (in terms of spectral components and also over specific features); correlations with the global Mars topography are established and apparent depths of compensation by degree are derived. Lumped zonal harmonics of degree two and three are solved for every 10 days, exhibiting variations in line with previous results (including authors’ ones); the work also shows the difficulty of finding clean signatures (annual and semi-annual) for the zonal coefficient of second degree. The k2 Love number is also derived from the ensemble of data, as well as from subsets of them; values between 0.110 and 0.130 are found, which are consistent with the existence of a Martian fluid core of significant radius. 相似文献
18.
Marianne Greff-Lefftz Laurent Métivier Hilaire Legros 《Celestial Mechanics and Dynamical Astronomy》2005,93(1-4):113-146
Tidal forces acting on the Earth cause deformations and mass redistribution inside the planet involving surface motions and
variation in the gravity field, which may be observed in geodetic experiments. Because for space geodesy it is now necessary
to achieve the mm level in tidal displacements, we take into account the hydrostatic flattening of the Earth in the computation
of the elasto-gravitational deformations. Analytical solutions are derived for the semi-diurnal tides on a slightly elliptical
homogeneous incompressible elastic model. That simple analytical Earth’s model is not a realistic representation of any real
planet, but it is useful to understand the physics of the problem and also to check numerical procedures. We rediscover and
discuss the Love’s solutions and obtain new analytical solutions for the tangential displacement. We extend these analytical
results to some geodetic responses of the Earth to tidal forces such as the perturbation of the surface gravity field, the
tilt and the deviation of the vertical with reference to the Earth’s axis. 相似文献
19.
Jürgen Oberst Valéry Lainey Christophe Le Poncin-Lafitte Veronique Dehant Pascal Rosenblatt Stephan Ulamec Jens Biele J?rn Spurmann Ralph Kahle Volker Klein Ulrich Schreiber Anja Schlicht Nicolas Rambaux Philippe Laurent Beno?t Noyelles Bernard Foulon Alexander Zakharov Leonid Gurvits Denis Uchaev Scott Murchie Cheryl Reed Slava G. Turyshev Jesus Gil Mariella Graziano Konrad Willner Kai Wickhusen Andreas Pasewaldt Marita W?hlisch Harald Hoffmann 《Experimental Astronomy》2012,34(2):243-271
GETEMME (Gravity, Einstein??s Theory, and Exploration of the Martian Moons?? Environment), a mission which is being proposed in ESA??s Cosmic Vision program, shall be launched for Mars on a Soyuz Fregat in 2020. The spacecraft will initially rendezvous with Phobos and Deimos in order to carry out a comprehensive mapping and characterization of the two satellites and to deploy passive Laser retro-reflectors on their surfaces. In the second stage of the mission, the spacecraft will be transferred into a lower 1500-km Mars orbit, to carry out routine Laser range measurements to the reflectors on Phobos and Deimos. Also, asynchronous two-way Laser ranging measurements between the spacecraft and stations of the ILRS (International Laser Ranging Service) on Earth are foreseen. An onboard accelerometer will ensure a high accuracy for the spacecraft orbit determination. The inversion of all range and accelerometer data will allow us to determine or improve dramatically on a host of dynamic parameters of the Martian satellite system. From the complex motion and rotation of Phobos and Deimos we will obtain clues on internal structures and the origins of the satellites. Also, crucial data on the time-varying gravity field of Mars related to climate variation and internal structure will be obtained. Ranging measurements will also be essential to improve on several parameters in fundamental physics, such as the Post-Newtonian parameter ?? as well as time-rate changes of the gravitational constant and the Lense-Thirring effect. Measurements by GETEMME will firmly embed Mars and its satellites into the Solar System reference frame. 相似文献
20.
We present the results of extensive numerical modeling of the Martian interior. Yoder et al. in 2003 reported a mean moment of inertia of Mars that was somewhat smaller than the previously used value and the Love number k2 obtained from observations of solar tides on Mars. These values of k2 and the mean moment of inertia impose a strong new constraint on the model of the planet. The models of the Martian interior are elastic, while k2 contains both elastic and inelastic components. We thoroughly examined the problem of partitioning the Love number k2 into elastic and inelastic components. The information necessary to construct models of the planet (observation data, choice of a chemical model, and the cosmogonic aspect of the problem) are discussed in the introduction. The model of the planet comprises four submodels—a model of the outer porous layer, a model of the consolidated crust, a model of the silicate mantle, and a core model. We estimated the possible content of hydrogen in the core of Mars. The following parameters were varied while constructing the models: the ferric number of the mantle (Fe#) and the sulfur and hydrogen content in the core. We used experimental data concerning the pressure and temperature dependence of elastic properties of minerals and the information about the behavior of Fe(γ-Fe ), FeS, FeH, and their mixtures at high P and T. The model density, pressure, temperature, and compressional and shear velocities are given as functions of the planetary radius. The trial model M13 has the following parameters: Fe#=0.20; 14 wt % of sulfur in the core; 50 mol % of hydrogen in the core; the core mass is 20.9 wt %; the core radius is 1699 km; the pressure at the mantle-core boundary is 20.4 GPa; the crust thickness is 50 km; Fe is 25.6 wt %; the Fe/Si weight ratio is 1.58, and there is no perovskite layer. The model gives a radius of the Martian core within 1600–1820 km while ≥30 mol % of hydrogen is incorporated into the core. When the inelasticity of the Martian interior is taken into account, the Love number k2 increases by several thousandths; therefore, the model radius of the planetary core increases as well. The prognostic value of the Chandler period of Mars is 199.5 days, including one day due to inelasticity. Finally, we calculated parameters of the equilibrium figure of Mars for the M13 model: J 2 0 = 1.82 × 10?3, J 4 0 = ?7.79 × 10?6, e c-m D = 1/242.3 (the dynamical flattening of the core-mantle boundary). 相似文献