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1.
The “paraboloid” model of Mercury’s magnetospheric magnetic field is used to determine the best-fit magnetospheric current system and internal dipole parameters from magnetic field measurements taken during the first and second MESSENGER flybys of Mercury on 14 January and 6 October 2008. Together with magnetic field measurements taken during the Mariner 10 flybys on 29 March 1974 and 16 March 1975, there exist three low-latitude traversals separated in longitude and one high-latitude encounter. From our model formulation and fitting procedure a Mercury dipole moment of 196 nT ·  (where RM is Mercury’s radius) was determined. The dipole is offset from Mercury’s center by 405 km in the northward direction. The dipole inclination to Mercury’s rotation axis is relatively small, ∼4°, with an eastern longitude of 193° for the dipole northern pole. Our model is based on the a priori assumption that the dipole position and the moment orientation and strength do not change in time. The root mean square (rms) deviation between the Mariner 10 and MESSENGER magnetic field measurements and the predictions of our model for all four flybys is 10.7 nT. For each magnetic field component the rms residual is ∼6 nT or about 1.5% of the maximum measured magnetic field, ∼400 nT. This level of agreement is possible only because the magnetospheric current system parameters have been determined separately for each flyby. The magnetospheric stand-off distance, the distance from the planet’s center to the inner edge of the tail current sheet, the tail lobe magnetic flux, and the displacement of the tail current sheet relative to the Mercury solar-magnetospheric equatorial plane have been determined independently for each flyby. The magnetic flux in the tail lobes varied from 3.8 to 5.9 MWb; the subsolar magnetopause stand-off distance from 1.28 to 1.43 RM; and the distance to the inner edge of the current sheet from 1.23 to 1.32 RM. The differences in the current systems between the first and second MESSENGER flybys are attributed to the effects of strong magnetic reconnection driven by southward interplanetary magnetic field during the latter flyby.  相似文献   

2.
We present results from coronagraphic imaging of Mercury’s sodium tail over a 7° field of view. Several sets of observations made at the McDonald Observatory since May 2007 show a tail of neutral sodium atoms stretching more than 1000 Mercury radii (Rm) in length, or a full degree of sky. However, no tail was observed extending beyond 120 Rm during the January 2008 MESSENGER fly-by period, or during a similar orbital phase of Mercury in July 2008. Large changes in Mercury’s heliocentric radial velocity cause Doppler shifts about the Fraunhofer absorption features; the resultant change in solar flux and radiation pressure is the primary cause of the observed variation in tail brightness. Smaller fluctuations in brightness may exist due to changing source rates at the surface, but we have no explicit evidence for such changes in this data set. The effects of radiation pressure on Mercury’s escaping atmosphere are investigated using seven observations spanning different orbital phases. Total escape rates of atmospheric sodium are estimated to be between 5 and 13 × 1023 atoms/s and show a correlation to radiation pressure. Candidate sources of Mercury’s sodium exosphere include desorption by UV sunlight, thermal desorption, solar wind channeled along Mercury’s magnetic field lines, and micro-meteor impacts. Wide-angle observations of the full extent of Mercury’s sodium tail offer opportunities to enhance our understanding of the time histories of these source rates.  相似文献   

3.
On 14 January and 6 October 2008 the MESSENGER spacecraft passed within 200 km of the surface of Mercury. These flybys by MESSENGER provided the first observations of Mercury from a spacecraft since the Mariner 10 flybys in 1974 and 1975. Data from the Mercury Laser Altimeter (MLA) provided new information on the equatorial shape of Mercury, and Doppler tracking of the spacecraft through the flybys provided new data on the planet’s gravity field. The MLA passes were on opposite hemispheres of the planet and span collectively ∼40% of the equatorial circumference. The mean elevation of topography observed during flyby 1, in the longitude range 0-90°E, is greater than that seen during flyby 2 in the longitude range 180-270°E, indicating an offset between centers of mass and figure having a magnitude and phase in general agreement with topography determined by Earth-based radar. Both MLA profiles are characterized by slopes of ∼0.015° downward to the east, which is consistent with a long-wavelength equatorial shape defined by a best-fitting ellipse. The Doppler tracking data show sensitivity to the gravitational structure of Mercury. The equatorial ellipticity of the gravitational field, C2,2, is well determined and correlates with the equatorial shape. The S2,2 coefficient is ∼0, as would be expected if Mercury’s coordinate system, defined by its rotational state, is aligned along its principal axes of inertia. The recovered value of the polar flattening of the gravitational potential, J2, is considerably lower in magnitude than the value obtained from Mariner 10 tracking, a result that is problematic for internal structure models. This parameter is not as well constrained as the equatorial ellipticity because the flyby trajectories were nearly in the planet’s equatorial plane. The residuals from the Doppler tracking data suggest the possibility of mascons on Mercury, but flyby observations are of insufficient resolution for confident recovery. For a range of assumptions on degree of compensation and crustal and mantle densities, the allowable crustal thickness is consistent with the upper limit of about 100 km estimated from the inferred depth of faulting beneath a prominent lobate scarp, an assumed ductile flow law for crustal material, and the condition that temperature at the base of the crust does not exceed the solidus temperature. The MESSENGER value of C2,2 has allowed an improved estimate of the ratio of the polar moment of inertia of the mantle and crust to the full polar moment (Cm/C), a refinement that strengthens the conclusion that Mercury has at present a fluid outer core.  相似文献   

4.
We present a Monte Carlo model of the distribution of neutral sodium in Mercury’s exosphere and tail using data from the Mercury Atmospheric and Surface Composition Spectrometer (MASCS) on the MErcury Surface, Space ENvironment, GEochemistry, and Ranging (MESSENGER) spacecraft during the first two flybys of the planet in January and September 2008. We show that the dominant source mechanism for ejecting sodium from the surface is photon-stimulated desorption (PSD) and that the desorption rate is limited by the diffusion rate of sodium from the interior of grains in the regolith to the topmost few monolayers where PSD is effective. In the absence of ion precipitation, we find that the sodium source rate is limited to ∼106-107 cm−2 s−1, depending on the sticking efficiency of exospheric sodium that returns to the surface. The diffusion rate must be at least a factor of 5 higher in regions of ion precipitation to explain the MASCS observations during the second MESSENGER flyby. We estimate that impact vaporization of micrometeoroids may provide up to 15% of the total sodium source rate in the regions observed. Although sputtering by precipitating ions was found not to be a significant source of sodium during the MESSENGER flybys, ion precipitation is responsible for increasing the source rate at high latitudes through ion-enhanced diffusion.  相似文献   

5.
The second and third flybys of Mercury by the MESSENGER spacecraft occurred, respectively, on 6 October 2008 and on 29 September 2009. In order to provide contextual information about the solar wind properties and the interplanetary magnetic field (IMF) near the planet at those times, we have used an empirical modeling technique combined with a numerical physics-based solar wind model. The Wang–Sheeley–Arge (WSA) method uses solar photospheric magnetic field observations (from Earth-based instruments) in order to estimate the inner heliospheric radial flow speed and radial magnetic field out to 21.5 solar radii from the Sun. This information is then used as input to the global numerical magnetohydrodynamic model, ENLIL, which calculates solar wind velocity, density, temperature, and magnetic field strength and polarity throughout the inner heliosphere. WSA-ENLIL calculations are presented for the several-week period encompassing the second and third flybys. This information, in conjunction with available MESSENGER data, aid in understanding the Mercury flyby observations and provide a basis for global magnetospheric modeling. We find that during both flybys, the solar wind conditions were very quiescent and would have provided only modest dynamic driving forces for Mercury's magnetospheric system.  相似文献   

6.
During the 2867 Šteins flyby of the ROSETTA spacecraft on September 5, 2008 magnetic field measurements have been made with both the RPC orbiter magnetometer and the ROMAP lander magnetometer. These combined magnetic field measurements allow a detailed examination of any magnetic signatures caused either directly by the asteroid or indirectly by Šteins’ different modes of interaction with the solar wind. Comparing measurements with simulation results show that Šteins does not posses a significant remanent magnetization. The magnetization is estimated at less than 10−3 A m2/kg. This is significantly different from results at 9969 Braille and 951 Gaspra.  相似文献   

7.
In this study, magnetic field measurements obtained by the Venus Express spacecraft are used to determine the bow shock position at solar minimum. The best fit of bow shock location from solar zenith angle 20-120° gives a terminator bow shock location of 2.14 RV (1 RV=6052 km) which is 1600 km closer to Venus than the 2.40 RV determined during solar maximum conditions, a clear indication of the solar cycle variation of the Venus bow shock location. The best fit to the subsolar bow shock is 1.32 RV, with the bow shock completely detached. Finally, a global bow shock model at solar minimum is constructed based on our best-fit empirical bow shock in the sunlit hemisphere and an asymptotic limit of the distant bow shock which is a Mach cone under typical Mach number of 5.5 at solar minimum. We also describe our approach to making the measurements and processing the data in a challenging magnetic cleanliness environment. An initial evaluation of the accuracy of measurements shows that the data are of a quality comparable to magnetic field measurements made onboard magnetically clean spacecraft.  相似文献   

8.
Analysis of global hybrid simulations of Mercury’s magnetosphere-solar wind interaction is presented for northward and southward interplanetary magnetic field (IMF) orientations in the context of MESSENGER’s first two encounters with Mercury. The global kinetic simulations reveal the basic structure of this interaction, including a bow shock, ion foreshock, magnetosheath, cusp regions, magnetopause, and a closed ion ring belt formed around the planet within the magnetosphere. The two different IMF orientations induce different locations of ion foreshock and different magnetospheric properties: the dayside magnetosphere is smaller and cusps are at lower latitudes for southward IMF compared to northward IMF whereas for southward IMF the nightside magnetosphere is larger and exhibits a thin current sheet with signatures of magnetic reconnection and plasmoid formation. For the two IMF orientations the ion foreshock and quasi-parallel magnetosheath manifest ion-beam-driven large-amplitude oscillations, whereas the quasi-perpendicular magnetosheath shows ion-temperature-anisotropy-driven wave activity. The ions in Mercury’s belt remain quasi-trapped for a limited time before they are either absorbed by Mercury’s surface or escape from the magnetosphere. The simulation results are compared with MESSENGER’s observations.  相似文献   

9.
The composition and chemistry of Mercury’s regolith has been calculated from MESSENGER MASCS 0.3-1.3 μm spectra from the first flyby, using an implementation of Hapke’s radiative transfer-based photometric model for light scattering in semi-transparent porous media, and a linear spectral mixing algorithm. We combine this investigation with linear spectral fitting results from mid-infrared spectra and compare derived oxide abundances with mercurian formation models and lunar samples. Hapke modeling results indicate a regolith that is optically dominated by finely comminuted particles with average area weighted grain size near 20 μm. Mercury shows lunar-style space weathering, with maturation-produced microphase iron present at ∼0.065 wt.% abundance, with only small variations between mature and immature sites, the amount of which is unable to explain Mercury’s low brightness relative to the Moon. The average modal mineralogies for the flyby 1 spectra derived from Hapke modeling are 35-70% Na-rich plagioclase or orthoclase, up to 30% Mg-rich clinopyroxene, <5% Mg-rich orthopyroxene, minute olivine, ∼20-45% low-Fe, low-Ti agglutinitic glass, and <10% of one or more lunar-like opaque minerals. Mercurian average oxide abundances derived from Hapke models and mid-infrared linear fitting include 40-50 wt.% SiO2, 10-35 wt.% Al2O3, 1-8 wt.% FeO, and <25 wt.% TiO2; the inferred rock type is basalt. Lunar-like opaques or glasses with high Fe and/or Ti abundances cannot on their own, or in combination, explain Mercury’s low brightness. The linear mixing results indicate the presence of clinopyroxenes that contain up to 21 wt.% MnO and the presence of a Mn-rich hedenbergite. Mn in M1 crystalline lattice sites of hedenbergite suppresses the strong 1 and 2 μm crystal field absorption bands and may thus act as a strong darkening agent on Mercury. Also, one or more of thermally darkened silicates, Fe-poor opaques and matured glasses, or Mercury-unique Ostwald-ripened microphase iron nickel may lower the albedo. A major part of the total microphase iron present in Mercury’s regolith is likely derived from FeO that is not intrinsic to the crust but has been subsequently delivered by exogenic sources.  相似文献   

10.
Deep Space 1 at comet 19P/Borrelly: Magnetic field and plasma observations   总被引：1，自引：0，他引：1  
On September 22, 2001 the Deep Space 1 spacecraft performed a flyby at comet 19P/Borrelly at a solar distance of 1.36 AU leading the Earth by 74° in longitude. The spacecraft-comet distance at closest approach was 2171 km. The bow shock had a magnetic compression ratio of 2.5 at a distance of 147 100 km from the nucleus. Deep Space 1 first entered the sheath region essentially from the north polar region. Fluctuations from the cometary ion pickup were present throughout the sheath region and even well upstream of the shock, as expected. The magnetic field pileup region had a peak field strength of 83 nT and was shown to be consistent with a pressure equal to the solar wind ram pressure. The peak field location was offset from the time of closest approach. It is uncertain whether this is a spatial or temporal variation. Draping of magnetic fields around the nucleus was sought, but evidence for this was not apparent in the data. A possible explanation is that the interplanetary solar wind was composed of turbulent short-scale fields, and thus the fields were not symmetric about the point of closest approach. During the flyby phase there were in general few intervals of ACE data where there were large scale Parker spiral fields. With the addition of plasma data, the shock properties are investigated. The characteristics of magnetic draping, pileup and fluctuations are explored. These comet 19P/Borrelly results are contrasted with other cometary flyby results.  相似文献   

11.
MESSENGER Neutron Spectrometer (NS) observations of cosmic-ray-generated thermal neutrons provide the first direct measurements of Mercury’s surface elemental composition. Specifically, we show that Mercury’s surface is enriched in neutron-absorbing elements and has a measured macroscopic neutron-absorption cross section of 45-81 × 10−4 cm2/g, a range similar to the neutron absorption of lunar basalts from Mare Crisium. The expected neutron-absorbing elements are Fe and Ti, with possible trace amounts of Gd and Sm. Fe and Ti, in particular, are important for understanding Mercury’s formation and how its surface may have changed over time through magmatic processes. With neutron Doppler filtering - a neutron energy separation technique based on spacecraft velocity - we demonstrate that Mercury’s surface composition cannot be matched by prior models, which have characteristically low abundances of Fe, Ti, Gd, and Sm. While neutron spectroscopy alone cannot separate the relative contributions of individual neutron-absorbing elements, these results provide strong new constraints on the nature of Mercury’s surface materials. For example, if all the measured neutron absorption were due to the presence of an Fe-Ti oxide and that oxide were ilmenite, then Mercury’s surface would have an ilmenite content of 7-18 wt.%. This result is in general agreement with the inference from color imaging and visible-near-infrared spectroscopy that Mercury’s overall low reflectance is consistent with a surface composition that is enriched in Fe-Ti oxides. The incorporation of substantial Fe and Ti in oxides would imply that the oxygen fugacity of basalts on Mercury is at the upper range of oxygen fugacities inferred for basalts on the Moon.  相似文献   

12.
To examine electron transport, energization, and precipitation in Mercury's magnetosphere, a hybrid simulation study has been carried out that follows electron trajectories within the global magnetospheric electric and magnetic field configuration of Mercury. We report analysis for two solar-wind parameter conditions corresponding to the first two MESSENGER Mercury flybys on January 14, 2008, and October 6, 2008, which occurred for similar solar wind speed and density but contrasting interplanetary magnetic field (IMF) directions. During the first flyby the IMF had a northward component, while during the second flyby the IMF was southward. Electron trajectories are traced in the fields of global hybrid simulations for the two flybys. Some solar wind electrons follow complex trajectories at or near where dayside reconnection occurs and enter the magnetosphere at these locations. The entry locations depend on the IMF orientation (north or south). As the electrons move through the entry regions they can be energized as they execute non-adiabatic (demagnetized) motion. Some electrons become magnetically trapped and drift around the planet with energies on the order of 1–10 keV. The highest energy of electrons anywhere in the magnetosphere is about 25 keV, consistent with the absence of high-energy (>35 keV) electrons observed during either MESSENGER flyby. Once within the magnetosphere, a fraction of the electrons precipitates at the planetary surface with fluxes on the order of 109 cm−2 s−1 and with energies of hundreds of eV. This finding has important implications for the viability of electron-stimulated desorption (ESD) as a mechanism for contributing to the formation of the exosphere and heavy ion cloud around Mercury. From laboratory estimates of ESD ion yields, a calculated ion production rate due to ESD at Mercury is found to be on par with ion sputtering yields.  相似文献   

13.
Observations made by the ASPERA-3 experiment onboard the Mars Express spacecraft found within the martian magnetosphere beams of planetary ions. In the energy (E/q)-time spectrograms these beams are often displayed as dispersive-like, ascending or descending (whether the spacecraft moves away or approach the planet) structures. A linear dependence between energy gained by the beam ions and the altitude from the planet suggests their acceleration in the electric field. The values of the electric field evaluated from ion energization occur close to the typical values of the interplanetary motional electric field. This suggests an effective penetration of the solar wind electric field deep into the martian magnetosphere or generation of large fields within the magnetosphere. Two different classes of events are found. At the nominal solar wind conditions, a ‘penetration’ occurs near the terminator. At the extreme solar wind conditions, the boundary of the induced magnetosphere moves to a more dense upper atmosphere that leads to a strong scavenging of planetary ions from the dayside regions.  相似文献   

14.
The MARSIS (Mars Advanced Radar for Subsurface and Ionosphere Sounding) instrument on the Mars Express spacecraft provides both local and remote measurements of electron densities and measurements of magnetic fields in the martian ionosphere. The density measurements show a persistent level of large fluctuations, sometimes as much as a factor of three or more at high altitudes. Large magnetic field fluctuations are also observed in the same region. The power spectrums of both the density and magnetic field fluctuations have slopes on a log-log plot that are consistent with the Kolmogorov spectrum for isotropic fluid turbulence. The fractional density fluctuation, Δne/ne, of the turbulence increases with altitude, and reaches saturation, Δne/ne ∼ 1, at an altitude of about 400 km, near the nominal boundary between the ionosphere and the magnetosheath. The fluctuations are usually so large that a well-defined ionopause-like boundary between the ionosphere and the solar wind is seldom observed. Of mechanisms that could be generating this turbulence, we believe that the most likely are (1) solar wind pressure perturbations, (2) an instability in the magnetosheath plasma, such as the mirror-mode instability, or (3) the Kelvin-Helmholtz instability driven by velocity shear between the rapidly flowing magnetosheath and the ionosphere.  相似文献   

15.
The search for rocky exoplanets plays an important role in our quest for extra-terrestrial life. Here, we discuss the extreme physical properties possible for the first characterised rocky super-Earth, CoRoT-7b (Rpl = 1.58 ± 0.10 REarth, Mpl = 6.9 ± 1.2 MEarth). It is extremely close to its star (a = 0.0171 AU = 4.48 Rst), with its spin and orbital rotation likely synchronised. The comparison of its location in the (Mpl, Rpl) plane with the predictions of planetary models for different compositions points to an Earth-like composition, even if the error bars of the measured quantities and the partial degeneracy of the models prevent a definitive conclusion. The proximity to its star provides an additional constraint on the model. It implies a high extreme-UV flux and particle wind, and the corresponding efficient erosion of the planetary atmosphere especially for volatile species including water. Consequently, we make the working hypothesis that the planet is rocky with no volatiles in its atmosphere, and derive the physical properties that result. As a consequence, the atmosphere is made of rocky vapours with a very low pressure (P ? 1.5 Pa), no cloud can be sustained, and no thermalisation of the planet is expected. The dayside is very hot (2474 ± 71 K at the sub-stellar point) while the nightside is very cold (50-75 K). The sub-stellar point is as hot as the tungsten filament of an incandescent bulb, resulting in the melting and distillation of silicate rocks and the formation of a lava ocean. These possible features of CoRoT-7b could be common to many small and hot planets, including the recently discovered Kepler-10b. They define a new class of objects that we propose to name “Lava-ocean planets”.  相似文献   

16.
We use a global magnetohydrodynamic (MHD) model to simulate Mercury's space environment for several solar wind and interplanetary magnetic field (IMF) conditions in anticipation of the magnetic field measurements by the MESSENGER spacecraft. The main goal of our study is to assess what characteristics of the internally generated field of Mercury can be inferred from the MESSENGER observations, and to what extent they will be able to constrain various models of Mercury's magnetic field generation. Based on the results of our simulations, we argue that it should be possible to infer not only the dipole component, but also the quadrupole and possibly even higher harmonics of the Mercury's planetary magnetic field. We furthermore expect that some of the crucial measurements for specifying the Hermean internal field will be acquired during the initial fly-bys of the planet, before MESSENGER goes into orbit around Mercury.  相似文献   

17.
A Monte-Carlo model of exospheres (Wurz and Lammer, 2003) was extended by treating the ion-induced sputtering process, photon-stimulated desorption, and micro-meteorite impact vaporisation quantitatively in a self-consistent way starting with the actual release of particles from the mineral surface of Mercury. Based on available literature data we established a global model for the surface mineralogy of Mercury and from that derived the average elemental composition of the surface. This model serves as a tool to estimate densities of species in the exosphere depending on the release mechanism and the associated physical parameters quantitatively describing the particle release from the surface.Our calculation shows that the total contribution to the exospheric density at the Hermean surface by solar wind sputtering is about 4×107 m-3, which is much less than the experimental upper limit of the exospheric density of 1012 m-3. The total calculated exospheric density from micro-meteorite impact vaporisation is about 1.6×108 m-3, also much less than the observed value. We conclude that solar wind sputtering and micro-meteorite impact vaporisation contribute only a small fraction of Mercury’s exosphere, at least close to the surface. Because of the considerably larger scale height of atoms released via sputtering into the exosphere, sputtered atoms start to dominate the exosphere at altitudes exceeding around 1000 km, with the exception of some light and abundant species released thermally, e.g. H2 and He. Because of Mercury’s strong gravitational field not all particles released by sputtering and micro-meteorite impact escape. Over extended time scales this will lead to an alteration of the surface composition.  相似文献   

18.
A significant opaque component in Mercury’s crust is inferred based on albedo and spectral observations. Previous workers have favored iron-titanium bearing oxide minerals as the spectrally neutral opaque. A consequence of this hypothesis is that Mercury’s surface would have a high FeO content. An array of remote sensing techniques have not provided definitive constraints on the FeO content of Mercury’s surface. However, spectral observations have not detected a diagnostic 1 μm absorption band and have thus limited the FeO in coexisting silicates to <2 wt.% FeO. In this paper, we assess equilibrium among oxide and silicate minerals to constrain the distribution of iron between opaque oxides and silicates under a variety of environmental conditions. Equilibrium modeling is favored here because the geologic process that produced Mercury’s low-albedo intermediate terrain must have occurred globally, which favors a common widespread igneous process. Based on our modeling, we find that iron-rich ilmenite cannot occur with silicates that do not display a 1 μm absorption feature unless plagioclase abundances are high. However, such high plagioclase abundances are precluded by Mercury’s low albedo. Incorporating equilibrium crystallization modeling with spectral and albedo constraints we find the iron abundance of Mercury’s intermediate terrain is ?10 wt.% FeO. This intermediate iron composition matches constraints provided by visible albedo and total neutron absorption observed by MESSENGER. In fact, the total neutron absorption of mixtures of oxide, plagioclase, olivine and pyroxene for the oxide abundances estimated for Mercury, favor Mg-rich members of the ilmenite-geikielite solid-solution series. This work offers compositional constraints for Fe, Ti, and Mg that will be testable by various MESSENGER instrument data sets after it begins its orbital mission.  相似文献   

19.
Astronomical observations and cosmochemical calculations suggest that the planet Mercury may be composed of materials which condensed at relatively high temperatures in the primitive solar nebula and may have a basaltic crust similar to parts of the moon. These findings, plus the long standing inference that Mercury is much richer in metallic iron than the other terrestrial planets, provide important constraints which we apply to models of the thermal evolution and density structure of the planet. The thermal history calculations include explicitly the differing thermal properties of iron and silicates and account for core segregation, melting and differentiation of heat sources, and simulated convection during melting. If the U and Th abundances of Mercury are taken from the cosmochemical model of Lewis, then the planet would have fully differentiated a metal core from the silicate mantle for all likely initial temperature distributions and heat transfer properties. Density distributions for the planet are calculated from the mean density and estimates of the present-day temperature. For the fully differentiated model, the moment of inertia C/MR2 is 0.325 (J2=0.302×10?6). For models with lower heat source abundances, the planet may not yet have differentiated. The density profiles for such models give C/MR2=0.394 (J2=0.487×10?6). These results should be useful for preliminary interpretation of the Mariner 10 measurements of Mercury's gravitational field.  相似文献   

20.
The shaking of Mercury’s orbit by the planets forces librations in longitude in addition to those at harmonics of the orbital period that have been used to detect Mercury’s molten core. We extend the analytical formulation of Peale et al. (Peale, S.J., Margot, J.L., Yseboodt, M. [2009]. Icarus 199, 1-8) in order to provide a convenient means of determining the amplitudes and phases of the forced librations without resorting to numerical calculations. We derive an explicit relation between the amplitude of each forced libration and the moment of inertia parameter (B-A)/Cm. Far from resonance with the free libration period, the libration amplitudes are directly proportional to (B-A)/Cm. Librations with periods close to the free libration period of ∼12 years may have measurable (∼arcsec) amplitudes. If the free libration period is sufficiently close to Jupiter’s orbital period of 11.86 years, the amplitude of the forced libration at Jupiter’s period could exceed the 35 arcsec amplitude of the 88-day forced libration. We also show that the planetary perturbations of the mean anomaly and the longitude of pericenter of Mercury’s orbit completely determine the libration amplitudes.While these signatures do not affect spin rate at a detectable level (as currently measured by Earth-based radar), they have a much larger impact on rotational phase (affecting imaging, altimetry, and gravity sensors). Therefore, it may be important to consider planetary perturbations when interpreting future spacecraft observations of the librations.  相似文献   

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