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1.
J.R. Roach 《Planetary and Space Science》1975,23(1):173-181
Results from the OSO-6 Rutgers Zodiacal Light Analyzer experiment show photometric perturbations above the background in the anti-Sun line of sight. Sixteen successive lunations were examined, and the accumulated perturbations show a maximum value in the direction of the L4 and L5 Earth-Moon libration points. This is interpreted as a counterglow from a cloud of particles at the libration points. The average brightness of these libration clouds is 20 S10 Vis. The average angular size of the libration clouds is approximately 6 degrees. Their position varies from one lunation to the next, within an ellipsoidal zone centered on the libration point direction, with its semi-major axis, of approximately 6 degrees, nominally in the ecliptic and its semi-minor axis, of approximately 2 degrees perpendicular to the ecliptic. The position of these clouds with respect to the Lagrangian L4 and L5 points, is towards the Moon in the northern summer and away from the Moon in the northern winter. 相似文献
2.
N. Sekiguchi 《Earth, Moon, and Planets》1970,2(2):129-135
In the present paper, the problem of whether the interplanetary matter has a tendency to accumulate around the Lagrangian libration pointsL
4 andL
5, is examined statistically. It is concluded that: (1) If the particles are initially assumed to be distributed uniformly, they keep the uniformity ever after around the libration points. (2) If the particles receive random stochastic perturbations, their distribution tends to become uniform even if initially they have non-uniform distributions. (3) If the particles mutually collide inelastically, they have a tendency to avoid the regions near the libration points. Therefore, the interplanetary matter will not tend to accumulate near the libration points. Even if the observations of the libration cloud so far reported are confirmed, the clouds are likely to be but temporary objects. 相似文献
3.
In a recent paper, published in Astrophys. Space Sci. (337:107, 2012) (hereafter paper ZZX) and entitled “On the triangular libration points in photogravitational restricted three-body problem
with variable mass”, the authors study the location and stability of the generalized Lagrange libration points L
4 and L
5. However their study is flawed in two aspects. First they fail to write correctly the equations of motion of the variable
mass problem. Second they attribute a variable mass to the third body of the restricted three-body model, a fact that is not
compatible with the assumptions used in deriving the mathematical formulation of this model. 相似文献
4.
Trojan type orbits in the system of two gravitational centers with variable separation are studied within the framework of the restricted problem of three bodies. The backward numerical integration of the equations of motion of the bodies starting in the triangular libration pointsL
4 andL
5 (reverse problem) finds the breakdown of librations as the separation decreases because of the mass gain of the smaller component and an approach of the body of negligible, mass to the latter up to the distance below its sphere of action with a relative velocity approximately equal to the escape one on this sphere. The breakdown of librations aboutL
5 occurs under the mass gain of the smaller component considerably larger than in the case ofL
4 and implications are made for the asymmetry of the number of librators aboutL
4 andL
5 in the solar system (Greeks and Trojans). Other parameters of the libration motion near 1/1 commensurability are obtained, namely, the asymmetry of the libration amplitudes about the triangular points as well as the values of periods and amplitudes within the limits of those for real Trojan asteroids. Trojans could be supposedly, formed inside the Proto-jupiter and escape during its intensive mass loss. 相似文献
5.
We study the effect of eccentricity and inclination on small amplitude librations around the equilibrium points L
4 and L
5 in the circular restricted three-body problem. We show that the effective libration centres can be displaced appreciably
from the equilateral configuration. The secular extrema of the eccentricity as a function of the argument of pericentre are
shifted by ∼25 °
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
6.
H.J. Reitsema 《Icarus》1981,48(1):23-28
Previously published positions of Dione B are combined with new observations reported in this paper to determine the motion. The data are fit to the analytic solution of Erdi (1978) to derive the parameters of the libratory motion. The satellite oscillates about the leading equilateral libration point (L4) of Dione with a period of 785.0±0.5 days. The maximum sepaparation in orbital longitude from Dione of 76.7° was reached on UT 1980 April 20.3±1 days; the minimum separation is 46.7°. 相似文献
7.
F. Mignard 《Celestial Mechanics and Dynamical Astronomy》1984,34(1-4):275-287
The restricted three-body problem is generalized with the inclusion of solar radiation pressure. For small particles (typically 1 m to 1 mm) the familiar equilibrium triangular points L4 and L5 no longer exist. However libration orbits are not completely destroyed, although an effect of resonance causes their amplitude to be very large, for a particle initially at rest at either of the triangular point. Finally the results of a study of the linearized equations of motion, supplemented by a numerical integration, rule out the possibility of an accumulation of dust at the Earth-Moon lagrangian triangular points. 相似文献
8.
The configuration space around the triangular libration points in the Earth-Moon system is partitioned according to the stability of the motion. The regions aroundL
4 andL
5 are established where particles placed with zero initial velocity will librate. The complexity of the partitioning is revealed. 相似文献
9.
Bálint Érdi 《Celestial Mechanics and Dynamical Astronomy》1978,18(2):141-161
The problem is considered within the framework of the elliptic restricted three-body problem. The asymptotic solution is derived by a three-variable expansion procedure. The variables of the expansion represent three time-scales of the asteroids: the revolution around the Sun, the libration around the triangular Lagrangian pointsL
4,L
5, and the motion of the perihelion. The solution is obtained completely in the first order and partly in the second order. The results are given in explicit form for the coordinates as functions of the true anomaly of Jupiter. As an example for the perturbations of the orbital elements the main perturbations of the eccentricity, the perihelion longitude and the longitude of the ascending node are given. Conditions for the libration of the perihelion are also discussed. 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.
《New Astronomy》2020
This paper deals with the existence and stability of libration points in linear sense in the central-body square configuration of restricted six-body problem. It is found that there exist twelve libration points, four collinear and eight non-collinear. All libration points lie on the concentric circles C1, C2 and C3 centered at origin. The libration points L1,3,5,7 lie on circle C1, L9,10,11,12 on C2 and L2,4,6,8 on C3. This is also observed that the eight libration points are on the axes and four are off the axes, i.e., L1,2,3,4 are on x-axis, L5,6,7,8 on y-axis and rest are off the axes. The libration points on circles C1 and C3 are unstable for all values of mass parameter µ while the libration points on circle C2 are stable for the critical mass parameter µc = 0.00910065. 相似文献
12.
This paper investigates the triangular libration points in the photogravitational restricted three-body problem of variable
mass, in which both the attracting bodies are radiating as well and the infinitesimal body vary its mass with time according
to Jeans’ law. Firstly, applying the space-time transformation of Meshcherskii in the special case when q=1/2, k=0, n=1, the differential equations of motion of the problem are given. Secondly, in analogy to corresponding problem with constant
mass, the positions of analogous triangular libration points are obtained, and the fact that these triangular libration points
cease to be classical ones when α≠0, but turn to classical L
4 and L
5 naturally when α=0 is pointed out. Lastly, introducing the space-time inverse transformation of Meshcherskii, the linear stability of triangular
libration points is tested when α>0. It is seen that the motion around the triangular libration points become unstable in general when the problem with constant
mass evolves into the problem with decreasing mass. 相似文献
13.
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
14.
Bálint Érdi 《Celestial Mechanics and Dynamical Astronomy》1984,34(1-4):435-441
The author's earlier solution for Trojan asteroids is developed further. It is shown that depending on the amplitude of libration around the Lagrangian point L4, there is a critical inclination which determines the sign of the variation of the ascending node. If the orbital inclination of a Trojan is smaller than the critical one, then the ascending node decreases and otherwise it increases. The variation of the eccentricity and of the longitude of the perihelion has also a dependence on the critical inclination. 相似文献
15.
Maciej Winiarski 《Earth, Moon, and Planets》1989,47(2):193-215
The paper contains results of three-colour photographic observations of positions and brightness of the cloud in the vicinity of the Earth-Moon libration point L5. The real character of the images obtained is confirmed by an agreement of their positions on different plates exposed at the same time. The colours of the cloud obtained are essentially different from those of the counterglow. The clouds appeared to be much redder than the counterglow, which may indicate that the particles constituting them are of different nature than those causing the counterglow. 相似文献
16.
GP. Horedt 《Astrophysics and Space Science》1973,22(2):321-327
We show within the framework of the restricted three body problem that
- Only in the immediate neighbourhood of the Lagrangian pointsL 4 andL 5 the distribution of a cloud of particles tends to become uniform under the influence of random stochastic perturbations. No consequences can be derived from this fact for a tendency of dispersion of clouds librating at arbitrary distances around the Lagrangian points.
- From an elementary inspection of the Jacobi integral we cannot conclude that mutual completely inelastic collisions tend to drive the particles away from the vicinity of the libration points.
17.
Alessandro Margheri Rafael Ortega Carlota Rebelo 《Celestial Mechanics and Dynamical Astronomy》2012,113(3):279-290
We present some analytical results about the existence of periodic orbits for the planar restricted three body problem with dissipation considered recently by Celletti et?al. (CMDA 109, 265, 2011) We show that, under fairly general conditions on the dissipation term, the circular orbits cannot be continued to the dissipative framework. Moreover, we give general conditions for the occurrence or not of a Hopf bifurcation around the libration points L 4 and L 5. Our results are consistent with the numerical findings of Celletti et?al. 相似文献
18.
The faint E ring of Saturn appears as a narrow ring 246,000 ± 4,000 km from the center of Saturn on photographs taken when the ring-plane inclination was 5°.4. The apparent brightness of the ring was uniform at all observed orbital longitudes and permits an estimate of the normal optical thickness. A faint satellite (1981S1) was observed near the L4 triangular libration point of Tethys and is probably the same object as 1980S13. 相似文献
19.
A. M. Tatarnikov V. I. Shenavrin P. A. Whitelock M. W. Feast B. F. Yudin 《Astronomy Letters》2001,27(8):534-539
The infrared photometric observations of V4334 Sgr in 2000 are presented. They show that a gradual, but nonmonotonic increase in the optical depth of its dust envelope, which was formed early in 1997, had continued until the mid-summer. In July 1999 and July 2000, τ(1.25 µm)≈7.7 and 11.3, respectively. From July through October 2000, the optical depth decreased appreciably. From October 1998 (the first deep minimum of visual brightness) until now, the amplitude of the bolometric-magnitude variations in V4334 Sgr is $ \sim 0^m .5$ . The relation between the bolometric and L magnitudes (m bol, L) can be fitted by a linear function, m bol = 1.25L + 4.04. In the dust-envelope model chosen, the percentage of large (a gr=0.2–0.3 µm) dust grains by particle number increased by a factor of ～4. In the summer of 2000, their fraction by mass was ～78%, and they mainly contributed to the optical depth of the dust envelope. No appreciable correlation between optical depth and bolometric flux was observed. 相似文献
20.
B. P. Kondratyev 《Solar System Research》2012,46(5):341-351
The effect of the Earth??s compression on the physical libration of the Moon is studied using a new vector method. The moment of gravitational forces exerted on the Moon by the oblate Earth is derived considering second order harmonics. The terms in the expression for this moment are arranged according to their order of magnitude. The contribution due to a spherically symmetric Earth proves to be greater by a factor of 1.34 × 106 than a typical term allowing for the oblateness. A linearized Euler system of equations to describe the Moon??s rotation with allowance for external gravitational forces is given. A full solution of the differential equation describing the Moon??s libration in longitude is derived. This solution includes both arbitrary and forced oscillation harmonics that we studied earlier (perturbations due to a spherically symmetric Earth and the Sun) and new harmonics due to the Earth??s compression. We posed and solved the problem of spinorbital motion considering the orientation of the Earth??s rotation axis with regard to the axes of inertia of the Moon when it is at a random point in its orbit. The rotation axes of the Earth and the Moon are shown to become coplanar with each other when the orbiting Moon has an ecliptic longitude of L ? = 90° or L ? = 270°. The famous Cassini??s laws describing the motion of the Moon are supplemented by the rule for coplanarity when proper rotations in the Earth-Moon system are taken into account. When we consider the effect of the Earth??s compression on the Moon??s libration in longitude, a harmonic with an amplitude of 0.03?? and period of T 8 = 9.300 Julian years appears. This amplitude exceeds the most noticeable harmonic due to the Sun by a factor of nearly 2.7. The effect of the Earth??s compression on the variation in spin angular velocity of the Moon proves to be negligible. 相似文献