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1.
Information about the structure of lunar interior and evolution could be obtained from measurements of lunar free librations, gravitational field, dissipation etc.. In this paper the precision of determining free librations with Lunar Laser Ranging (LLR) data are estimated. Using the observing data from four telescopes for eighteen years the amplitudes and phases of free librations, the moments of inertia ratio of The Moon were determined. 相似文献
2.
从月球的自由天平动,引力场和耗散等可以研究月球内部的结构和演化.本文从理论上估计了用激光测月资料推算月球自由天平动的精确度,根据四个激光测月台站的18年的观测资料计算了月球自由天平动的振幅和相位、月球转动惯量等,并初步得到了月球的内部结构和组成成分. 相似文献
3.
Planetary perturbations of Mercury's orbit lead to forced librations in longitude in addition to the 88-day forced libration induced by Mercury's orbital motion. The forced librations are a combination of many periods, but 5.93 and 5.66 years dominate. These two periods result from the perturbations by Jupiter and Venus respectively, and they lead to a 125-year modulation of the libration amplitude corresponding to the beat frequency. Other periods are also identified with Jupiter and Venus perturbations as well as with those of the Earth, and these and other periods in the perturbations cause several arc second fluctuations in the libration extremes. The maxima of these extremes are about 30″ above and the minima about 7″ above the superposed ∼60″, 88-day libration during the 125-year modulation. Knowledge of the nature of the long-period forced librations is important for the interpretation of the details of Mercury's rotation state to be obtained from radar and spacecraft observations. We show that the measurement of the 88-day libration amplitude for the purposes of determining Mercury's core properties is not compromised by the additional librations, because of the latter's small amplitude and long period. If the free libration in longitude has an amplitude that is large compared with that of the forced libration, its ∼10-year period will dominate the libration spectrum with the 88-day forced libration and the long-period librations from the orbital perturbations superposed. If the free libration has an amplitude that is comparable to those of the long-period forced libration, it will be revealed by erratic amplitude, period and phase on the likely time span of a series of observations. However, a significant free libration component is not expected because of relatively rapid damping. 相似文献
4.
The recent long-term integration of JPL ephemeris DE403/LE403 yielded lunar physical librations covering 6000 years. A Fourier analysis of a 718-year subset of this span produced estimates of the component frequencies of the forced and free librations. A subsequent iterative least-squares estimation procedure provided precise values for phases and for time-varying amplitudes and frequencies. Two free libration modes were found; presence of a third is possible but close to the noise. 相似文献
5.
Benoît Noyelles 《Icarus》2010,207(2):887-902
The saturnian coorbital satellites Janus and Epimetheus present a unique dynamical configuration in the Solar System, because of high-amplitude horseshoe orbits, due to a mass ratio of order unity. As a consequence, they swap their orbits every 4 years, while their orbital periods is about 0.695 days. Recently, Tiscareno et al. (Tiscareno, M.S., Thomas, P.C., Burns, J.A. [2009]. Icarus 204, 254-261) got observational informations on the shapes and the rotational states of these satellites. In particular, they detected an offset in the expected equilibrium position of Janus, and a large libration of Epimetheus.We here propose to give a three-dimensional theory of the rotation of these satellites in using these observed data, and to compare it to the observed rotations. We consider the two satellites as triaxial rigid bodies, and we perform numerical integrations of the system in assuming the free librations as damped.The periods of the three free librations we get, associated with the three dimensions, are respectively 1.267, 2.179 and 2.098 days for Janus, and 0.747, 1.804 and 5.542 days for Epimetheus. The proximity of 0.747 days to the orbital period causes a high sensitivity of the librations of Epimetheus to the moments of inertia. Our theory explains the amplitude of the librations of Janus and the error bars of the librations of Epimetheus, but not an observed offset in the orientation of Janus. 相似文献
6.
Physical librations of the Moon are small cyclic perturbations with periods of one month and longer, and amplitudes of 100 arc seconds or less. These cause the selenographic axes fixed in the true Moon to have a different orientation than similar axes fixed in the mean Moon.Physical librations have two types of effects of present interest. If the orbital elements of a lunar satellite are referred to selenographic axes in the true Moon as it rotates and librates, then the librations cause changes in the orientation angles (node, inclination, and periapsis argument of the satellite) large enough that long-period perturbation theory cannot be used without compensation for such geometrical effects. As a second effect, the gravitational potential of the Moon is actually wobbled in inertial space, a condition not included in the potential expression used in perturbation theory.This paper gives data on the magnitude of the physical librations, the geometrical effects on the orbital elements and the equivalent changes in the coefficients in the potential. It is shown that geometrical effects can be accommodated either by using an inertial axes system or by compensating for the lunar librations and precession when the selenographic axes are used. Further, it is shown that physical effects are small and negligible for all but the most exacting endeavors. 相似文献
7.
N. Sekiguchi 《Earth, Moon, and Planets》1970,2(1):78-93
The relations between probable amplitude of the Moon's free libration and its exciting action are obtained using a theory of the stochastic process. Among the three modes of the free libration, the one in longitude is most prominent if the exciting effect is isotropic. If the excitations are caused by crater-producing meteoritic impacts, it is very probable that the free librations in longitude exist whose semi-amplitude exceeds 1. 相似文献
8.
The Lunar Laser Ranging experiment has been active since 1969 when Apollo astronauts placed the first retroreflector on the
Moon. The data accuracy of a few centimeters over recent decades, joined to a new numerically integrated ephemeris, DE421,
encourages a new analysis of the lunar physical librations of that ephemeris, and especially the detection of three modes
of free physical librations (longitude, latitude, and wobble modes). This analysis was performed by iterating a frequency
analysis and linear least-squares fit of the wide spectrum of DE421 lunar physical librations. From this analysis we identified
and estimated about 130–140 terms in the angular series of latitude librations and polar coordinates, and 89 terms in the
longitude angle. In this determination, we found the non-negligible amplitudes of the three modes of free physical libration.
The determined amplitudes reach 1.296′′ in longitude (after correction of two close forcing terms), 0.032′′ in latitude and
8.183′′ × 3.306′′ for the wobble, with the respective periods of 1056.13 days, 8822.88 days (referred to the moving node),
and 27257.27 days. The presence of such terms despite damping suggests the existence of some source of stimulation acting
in geologically recent times. 相似文献
9.
Yu. V. Barkin H. Hanada K. Matsumoto S. Sasaki M. Yu. Barkin 《Solar System Research》2014,48(6):403-419
An analytical theory of lunar physical librations based on its two-layer model consisting of a non-spherical solid mantle and ellipsoidal liquid core is developed. The Moon moves on a high-precision orbit in the gravitational field of the Earth and other celestial bodies. The defined fourth mode of a free libration is caused by the influence of the liquid core, with a long period of 205.7 yr, with amplitude S = 0″0395 and with an initial phase Π0 = ?134° (for the initial epoch 2000.0). Estimates of dynamic (meridional) oblatenesses of a liquid core of the Moon have been estimated: ?D = 4.42 × 10?4, μD = 2.83 × 10?4 (?D + μD = 7.24 × 10?4). These results have been obtained as a result of comparison of the developed analytical theory of physical librations of the Moon with the empirical theory of librations of the Moon constructed on the basis of laser observations. 相似文献
10.
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
11.
In the framework of the space missions to Mercury, an accurate model of rotation is needed. Librations around the 3:2 spin-orbit resonance as well as latitudinal librations have to be predicted with the best possible accuracy. In this paper, we use a Hamiltonian analysis and numerical integrations to study the librations of Mercury, both in longitude and latitude. Due to the proximity of the period of the free libration in longitude to the orbital period of Jupiter, the 88-day and 11.86-year contributions dominate Mercury’s libration in longitude (with the Hermean parameters chosen). The amplitude of the libration in latitude is much smaller (under 1 arcsec) and should not be detected by the space missions. Nevertheless, we point out that this amplitude could be much larger (up to several tens of arcsec) if the free period related to the libration in latitude approaches the period of the Jupiter-Saturn Great Inequality (883 years). Given the large uncertainties on the planetary parameters, this new resonant forcing on Mercury’s libration in latitude should be borne in mind. 相似文献
12.
We analyze the out-of-plane librations of a tethered satellite system that is nominally rotating in the orbit plane. To isolate
the librational dynamics, the system is modeled as two point masses connected by a rigid rod with the system mass center constrained
to an unperturbed circular orbit. For small out-of-plane librations, the in-plane motion is unaffected by the out-of-plane
librations and a solution for the in-plane motion is determined in terms of Jacobi elliptic functions. This solution is used
in the linearized equation for the out-of-plane librations, resulting in a Hill’s equation. Floquet theory is used to analyze
the Hill’s equation, and we show that the out-of-plane librations are unstable for certain ranges of in-plane spin rate. For
relatively high in-plane spin rates, the out-of-plane librations are stable, and the Hill’s equation can be approximated by
a Mathieu’s equation. Approximate solutions to the Mathieu’s equation are determined, and we analyze the dominant characteristics
of the out-of-plane librations for high in-plane spin rates. The results obtained from the analysis of the linearized equations
of motion are compared to numerical simulations of the nonlinear equations of motion, as well as numerical simulations of
a more realistic system model that accounts for tether flexibility. The instabilities discovered from the linear analysis
are present in both the nonlinear system and the more realistic system model. The approximate solutions for the out-of-plane
librations compare well to the nonlinear system for relatively high in-plane rotation rates, and also capture the significant
qualitative behavior of the flexible system. 相似文献
13.
An accurate model of the rotation of the Moon, constructed by numerical integration, has been presented in a previous paper. All direct perturbations capable of producing at least 10–4 seconds of arc on the Moon's rotational motion have been included, and the physical librations resulting from planetary effects and Earth-Moon figure-figure interactions have been presented. The present study deals with the Moon's physical librations resulting from the non-rigidities of the Moon and the Earth. The effects of the Moon's elasticity and of a lunar phase lag are analyzed. Physical librations due to lunar tides and those due to terrestrial tides are presented and described. 相似文献
14.
The dynamics of synchronous rotation and physical librations are revisited in order to establish a conceptually simple and general theoretical framework applicable to a variety of problems. Our motivation comes from disagreements between the results of numerical simulations and those of previous theoretical studies, and also because different theoretical studies disagree on basic features of the dynamics. We approach the problem by decomposing the orientation matrix of the body into perfectly synchronous rotation and deviation from the equilibrium state. The normal modes of the linearized equations are computed in the case of a circular satellite orbit, yielding both the periods and the eigenspaces of three librations. Libration in longitude decouples from the other two, vertical modes. There is a fast vertical mode with a period very close to the average rotational period. It corresponds to tilting the body around a horizontal axis while retaining nearly principal-axis rotation. In the inertial frame, this mode appears as nutation and free precession. The other vertical mode, a slow one, is the free wobble. The effects of the nodal precession of the orbit are investigated from the point of view of Cassini states. We test our theory using numerical simulations of the full equations of the dynamics and discuss the disagreements among our study and previous ones. The numerical simulations also reveal that in the case of eccentric orbits large departures from principal-axis rotation are possible due to a resonance between free precession and wobble. We also revisit the history of the Moon's rotational state and show that it switched from one Cassini state to another when it was at 46.2 Earth radii. This number disagrees with the value 34.2 derived in a previous study. 相似文献
15.
16.
Sarah J. Morrison Peter C. Thomas Matthew S. Tiscareno Joseph A. Burns Joseph Veverka 《Icarus》2009,204(1):262-270
High-resolution images from the Cassini Imaging Science Subsystem (ISS) show parallel sets of grooves on Epimetheus and Pandora. Grooves have previously been observed on other satellites and asteroids, including Phobos, Gaspra, Ida, Eros, and minor occurrences on Phoebe. Sets of parallel grooves are so far observed only on satellites known or likely to be subject to significant tidal stresses, such as forced librations. Grooves on asteroids and on satellites not subject to significant forced librations occur in more globally disorganized patterns that may reflect impacts, varying internal structures, or even thermal stresses. The patterns and individual morphologies of grooves on the tidally-affected satellites suggest fracturing in weak materials due to tidal stresses and forced librations. 相似文献
17.
Florent Deleflie Gilles Métris Pierre Exertier 《Celestial Mechanics and Dynamical Astronomy》2006,94(1):83-104
This paper studies the long period variations of the eccentricity vector of the orbit of an artificial satellite, under the
influence of the gravity field of a central body. We use modified orbital elements which are non-singular at zero eccentricity.
We expand the long periodic part of the corresponding Lagrange equations as power series of the eccentricity. The coefficients
characterizing the differential system depend on the zonal coefficients of the geopotential, and on initial semi-major axis,
inclination, and eccentricity. The differential equations for the components of the eccentricity vector are then integrated
analytically, with a definition of the period of the perigee based on the notion of “free eccentricity”, and which is also
valid for circular orbits. The analytical solution is compared to a numerical integration. This study is a generalization
of (Cook, Planet. Space Sci., 14, 1966): first, the coefficients involved in the differential equations depend on all zonal coefficients (and not only on
the very first ones); second, our method applies to nearly circular orbits as well as to not too eccentric orbits. Except
for the critical inclination, our solution is valid for all kinds of long period motions of the perigee, i.e., circulations
or librations around an equilibrium point. 相似文献
18.
Benoît Noyelles 《Celestial Mechanics and Dynamical Astronomy》2008,101(1-2):13-30
In Noyelles et al. (Astron. Astrophys. 478, 959–970 (2008)), a resonance involving the wobble of Titan is hinted at. This paper studies this scenario and its consequences. The first step is to build an accurate analytical model that would help to find the likely resonances in the rotation of every synchronous body. In this model, I take the orbital eccentricity of the body into account, as well as its variable inclination with respect to Saturn’s equator. Then an analytical study using the second fundamental model of the resonance is performed to study the resonance of interest. Finally, I study the dissipative consequences of this resonance. I find that this resonance may have increased the wobble of Titan by several degrees. For instance, if Titan’s polar momentum C is equal to 0.355MR T 2 (M and R T being, respectively, Titan’s mass and radius), the wobble might be forced to 41 degrees. Thanks to an original formula, I find that the dissipation associated with the forced wobble might not be negligible compared to the contribution of the eccentricity. I also suspect that, due to the forced wobble, Titan’s period of rotation may be somewhat underestimated by observers. Finally, I use the analytical model presented in this paper to compute the periods of the free librations of the four Galilean satellites as well as the Saturnian satellite Rhea. For Io and Europa, the results are consistent with previous studies. For the other satellites, the periods of the free librations are, respectively, 186.37 d, 23.38 y and 30.08 y for Ganymede, 2.44 y, 209.32 y and 356.54 y for Callisto, and 51.84 d, 2.60 y and 3.59 y for Rhea. 相似文献
19.
J. Henrard 《Celestial Mechanics and Dynamical Astronomy》1984,34(1-4):255-262
In the Galilean satellites motion, the Laplace argument 132+23 librates around the value . The amplitude of libration is very small so that the classical theories have not been set up to take into account large librations. On the other hand large librations have to be considered when we describe possible scenarii of capture into resonance by tidal effects. The aim of this paper is to present a new way of applying Hamiltonian perturbation methods to the problem of the Galilean satellites in such a way that the theory is valid for large librations. Preliminary results from such a theory are discussed. 相似文献
20.
The term “jumping” Trojan was introduced by Tsiganis et al. (Astron Astrophys 354:1091–1100, 2000) in their studies of long-term dynamics exhibited by the asteroid (1868) Thersites, which had been observed to jump from librations around \(L_4\) to librations around \(L_5\). Another example of a “jumping” Trojan was found by Connors et al. (Nature 475:481–483, 2011): librations of the asteroid 2010 TK7 around the Earth’s libration point \(L_4\) preceded by its librations around \(L_5\). We explore the dynamics of “jumping” Trojans under the scope of the restricted planar elliptical three-body problem. Via double numerical averaging we construct evolutionary equations, which allow analyzing transitions between different regimes of orbital motion. 相似文献