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1.
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
2.
3.
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
4.
Jean-Luc Margot 《Celestial Mechanics and Dynamical Astronomy》2009,105(4):329-336
Planetary orientation models describe the orientation of the spin axis and prime meridian of planets in inertial space as
a function of time. The models are required for the planning and execution of Earth-based or space-based observational work,
e.g. to compute viewing geometries and to tie observations to planetary coordinate systems. The current orientation model
for Mercury is inadequate because it uses an obsolete spin orientation, neglects oscillations in the spin rate called longitude
librations, and relies on a prime meridian that no longer reflects its intended dynamical significance. These effects result
in positional errors on the surface of ~1.5 km in latitude and up to several km in longitude, about two orders of magnitude
larger than the finest image resolution currently attainable. Here we present an updated orientation model which incorporates
modern values of the spin orientation, includes a formulation for longitude librations, and restores the dynamical significance
to the prime meridian. We also use modern values of the orbit normal, spin axis orientation, and precession rates to quantify
an important relationship between the obliquity and moment of inertia differences. 相似文献
5.
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
6.
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
7.
Analytical description of physical librations of saturnian coorbital satellites Janus and Epimetheus
Janus and Epimetheus are famously known for their distinctive horseshoe-shaped orbits resulting from a 1:1 orbital resonance. Every 4 years these two satellites swap their orbits by a few tens of kilometers as a result of their close encounter. Recently Tiscareno et al. (Tiscareno, M.S., Thomas, P.C., Burns, J.A. [2009]. Icarus 204, 254-261) have proposed a model of rotation based on images from the Cassini orbiter. These authors inferred the amplitude of rotational librational motion in longitude at the orbital period by fitting a shape model to Cassini ISS images. By a quasi-periodic approximation of the orbital motion, we describe how the orbital swap impacts the rotation of the satellites. To that purpose, we have developed a formalism based on quasi-periodic series with long- and short-period librations. In this framework, the amplitude of the libration at the orbital period is found proportional to a term accounting for the orbital swap. We checked the analytical quasi-periodic development by performing a numerical simulation and find both results in good agreement. To complete this study, the results obtained for the short-period librations are studied with the help of an adiabatic-like approach. 相似文献
8.
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
9.
The Euler equations for the forced physical librations of the Moon have already been solved by using a digital computer to perform the semi-literal mathematical manipulations. Very near resonance, the computer solution for the physical libration in longitude is complemented by the solution of the appropriate Duffing equation with a dissipation term. Because of its apparent proximity to a resonant frequency, the term whose argument is 2 - twice the mean angular distance of the Moon's perigee from the ascending node of its orbit - is especially important. Its phase, which soon should be measurable, is related to the Moon's anelasticity. The term's frequency, in units of the sidereal month, increases as the semi-major axis of the Moon's orbit about the Earth increases. Using the Moon's mechanical ellipticity of Koziel and the rate of increase of the semi-major axis of MacDonald, it is estimated that the 2 term will cross the resonant frequency in 130 million years and, if the rate of energy dissipation is sufficiently low, a transient libration will be induced. 相似文献
10.
Benoît Noyelles 《Icarus》2009,202(1):225-239
The rotation of the main natural satellites of the Solar System is widely assumed to be synchronous, because this corresponds to an equilibrium state. In the case of the Moon, 3 laws have been formulated by Cassini, assuming a spin-orbit resonance and a 1:1 nodal resonance. The recent gravitational data collected by the spacecrafts Galileo (in the jovian system) and Cassini (in the saturnian system) allows us to study the rotation of other natural satellites, and to check the universality of Cassini's laws. This paper deals with the rotation of the Galilean satellites of Jupiter J-4 Callisto. In this study we use both analytical (like Lie transforms) and numerical methods (numerical detection of chaos, numerical integration, frequency analysis) to first check the reliability of Cassini Laws for Callisto, and then to give a first theory of its rotation, Callisto's being considered as a rigid body. We first show that the Third Cassini Law (i.e. the nodal resonance), is not satisfied in every reference frame, in particular in the most natural one (i.e. the J2000 jovian equator). The difference of the nodes presents a chaotic-like behavior, that we prove to be just a geometrical illusion. Moreover, we give a mathematical condition ruling the choice of an inertial reference frame in which the Third Cassini Law is fulfilled. Secondly, we give a theory of Callisto's rotation in the International Celestial Reference Frame (ICRF). We highlight a small motion (i.e. <200 m) of its rotation axis about its body figure, a 11.86-yr periodicity in Callisto's length-of-day, and the proximity of a resonance that forces 182-yr librations in Callisto's obliquity. 相似文献
11.
Ahmed Kamel Donald Ekman Richard Tibbitts 《Celestial Mechanics and Dynamical Astronomy》1973,8(1):129-148
A closed form solution, for longitude and semimajor axis deviations in the neighborhood of a prespecified station, is obtained for nearly synchronous satellites. The model use includes the important terms in Earth's zonal and tesseral harmonics as well as the luni-solar perturbations. The initial semimajor axis for two-maneuver east-west stationkeeping is then deduced. Due to the luni-solar effects, it is found that the initial semimajor axis deviation from synchronous orbit value is highly dependent on the initial position of the satellite relative to the Moon and the Sun. Verifications of the results by means of numerical integrations are also included. 相似文献
12.
Donald H. Eckhardt 《Earth, Moon, and Planets》1973,6(1-2):127-134
The existence of third and fourth harmonics of the lunar gravity potential gives rise to sizable lunar physical librations. Using one recent set of potential estimates, the following effects are noted: the mean sub-Earth point is displaced from the earthward principal moment of inertia axis by 168″; the inclination of the lunar equator to the ecliptic is decreased by 14″.5; and a six year period libration in longitude, with amplitude 13″.1, is induced. 相似文献
13.
R. R. Allan 《Planetary and Space Science》1967,15(12):1829-1845
For a satellite in a nominally circular orbit at arbitrary inclination whose mean motion is commensurable with the Earth's rotation, the dependence of gravity on longitude leads to a resonant variation in eccentricity as well as the long-period oscillation in longitude. Provided forces capable of processing perigee are present, it is shown that the change in eccentricity for a satellite captured in librational resonance is not secular but periodic.
There are corresponding resonance effects for a satellite in a nominally equatorial but eccentric orbit. Here the commensurability condition is that the longitudes of the apses shall be nearly repetitive relative to the rotating Earth. There will be a long-period oscillation in longitude which can take the form of either a libration (trapped) or a circulation (free), and there will also be an oscillation of the orbital plane having the same period as the precession of perigee relative to inertial space. 相似文献
14.
O. C. Winter L. A. G. Boldrin E. Vieira Neto R. Vieira Martins S. M. Giuliatti Winter R. S. Gomes F. Marchis P. Descamps 《Monthly notices of the Royal Astronomical Society》2009,395(1):218-227
The triple asteroidal system (87) Sylvia is composed of a 280-km primary and two small moonlets named Romulus and Remus ( Marchis et al. 2005b ). Sylvia is located in the main asteroid belt, with semi-major axis of about 3.49 au, eccentricity of 0.08 and 11° of orbital inclination. The satellites are in nearly equatorial circular orbits around the primary, with orbital radius of about 1360 km (Romulus) and 710 km (Remus). In this work, we study the stability of the satellites Romulus and Remus. In order to identify the effects and the contribution of each perturber, we performed numerical simulations considering a set of different systems. The results from the three-body problem, Sylvia–Romulus–Remus, show no significant variation of their orbital elements. However, the inclinations of the satellites present a long-period evolution with amplitude of about 20° when the Sun is included in the system. Such amplitude is amplified to more than 50° when Jupiter is included. These evolutions are very similar for both satellites. An analysis of these results shows that Romulus and Remus are librating in a secular resonance and their longitude of the nodes are locked to each other. Further simulations show that the amplitude of oscillation of the satellites' inclination can reach higher values depending on the initial values of their longitude of pericentre. In those cases, the satellites get caught in an evection resonance with Jupiter, their eccentricities grow and they eventually collide with Sylvia. However, the orbital evolutions of the satellites became completely stable when the oblateness of Sylvia is included in the simulations. The value of Sylvia's J 2 is about 0.17, which is very high. However, even just 0.1 per cent of this value is enough to keep the satellite's orbital elements with no significant variation. 相似文献
15.
A catalog of asteroids in two-body orbital resonances with the planets of the Solar System has been created. The AstDyS database was a source of the input data, and all the numbered objects (467303 objects at the time of the analysis) were considered. The orbits were integrated in the framework of a pure gravitational problem considering all the planets of the Solar System and Pluto. From the analysis of the behavior of the resonant argument and the semimajor axis on the 100-kyr interval, the resonance membership and the libration type (pure or transient) were verified for each of the asteroids. A more accurate method to identify the resonant argument librations was developed on the basis of the analysis of mutual periodograms. We found 23251 resonant asteroids, ~36% of which (8397 objects) are in pure resonances. 相似文献
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.
Norbert Wex 《Monthly notices of the Royal Astronomical Society》1998,298(1):67-77
In binary radio pulsars with a main-sequence star companion, the spin-induced quadrupole moment of the companion gives rise to a precession of the binary orbit. As a first approximation one can model the secular evolution caused by this classical spin-orbit coupling by linear-in-time changes of the longitude of periastron and the projected semi-major axis of the pulsar orbit. This simple representation of the precession of the orbit neglects two important aspects of the orbital dynamics of a binary pulsar with an oblate companion. First, the quasiperiodic effects along the orbit, owing to the anisotropic 1/ r 3 nature of the quadrupole potential. Secondly, the long-term secular evolution of the binary orbit, which leads to an evolution of the longitude of periastron and the projected semi-major axis, which is non-linear in time. In this paper a simple timing formula for binary radio pulsars with a main-sequence star companion is presented which models the short-term secular and most of the short-term periodic effects caused by the classical spin-orbit coupling. I also give extensions of the timing formula that account for long-term secular changes in the binary pulsar motion. It is shown that the short-term periodic effects are important for the timing observations of the binary pulsar PSR B1259–63. The long-term secular effects are likely to become important in the next few years of timing observations of the binary pulsar PSR J0045–7319. They could help to restrict or even determine the moments of inertia of the companion star and thus probe its internal structure. Finally, I reinvestigate the spin-orbit precession of the binary pulsar PSR J0045–7319 since the analysis given in the literature is based on an incorrect expression for the precession of the longitude of periastron. A lower limit of 20° for the inclination of the B star with respect to the orbital plane is derived. 相似文献
18.
Ahmed Aly Kamel 《Celestial Mechanics and Dynamical Astronomy》1975,12(4):425-438
Ignoring luni-solar perturbations, analytical solution for longitude deviation of the ‘stroboscopic’ mean center of 24-h satellites ground trace in the neighborhood of a prespecified station is obtained. The initial semimajor axis for two-maneuver east-west stationkeeping is then deduced. Finally, the luni-solar long and short period effects on this initial semimajor axis are discussed. 相似文献
19.
A substantial fraction of the Edgeworth-Kuiper belt objects are presently known to move in resonance with Neptune (the principal commensurabilities are 1/2, 3/5, 2/3, and 3/4). We have found that many of the distant (with orbital semimajor axes a > 50 AU) trans-Neptunian objects (TNOs) also execute resonant motions. Our investigation is based on symplectic integrations of the equations of motion for all multiple-opposition TNOs with a > 50 AU with allowance made for the uncertainties in their initial orbits. Librations near such commensurabilities with Neptune as 4/9, 3/7, 5/12, 2/5, 3/8, 4/27, and others have been found. The largest number of distant TNOs move near the 2/5 resonance with Neptune: 12 objects librate with a probability higher than 0.75. The multiplicity of objects moving in 2/5 resonance and the longterm stability of their librations suggest that this group of resonant objects was formed at early formation stages of the Solar system. For most of the other resonant objects, the librations are temporary. We also show the importance of asymmetric resonances in the large changes in TNO perihelion distances. 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