共查询到20条相似文献，搜索用时 31 毫秒
1.
Bernard De Saedeleer 《Celestial Mechanics and Dynamical Astronomy》2006,95(1-4):407-423
We present here the first numerical results of our analytical theory of an artificial satellite of the Moon. The perturbation method used is the Lie Transform for averaging the Hamiltonian of the problem, in canonical variables: short-period terms (linked to l, the mean anomaly) are eliminated first. We achieved a quite complete averaged model with the main four perturbations, which are: the synchronous rotation of the Moon (rate
), the oblateness J
2 of the Moon, the triaxiality C
22 of the Moon (
) and the major third body effect of the Earth (ELP2000). The solution is developed in powers of small factors linked to these perturbations up to second-order; the initial perturbations being sorted ( is first-order while the others are second-order). The results are obtained in a closed form, without any series developments in eccentricity nor inclination, so the solution apply for a wide range of values. Numerical integrations are performed in order to validate our analytical theory. The effect of each perturbation is presented progressively and separately as far as possible, in order to achieve a better understanding of the underlying mechanisms. We also highlight the important fact that it is necessary to adapt the initial conditions from averaged to osculating values in order to validate our averaged model dedicated to mission analysis purposes. 相似文献
2.
Donald H. Eckhardt 《Celestial Mechanics and Dynamical Astronomy》1993,57(1-2):307-324
The acceleration of the mean lunar longitude has a small effect on the periods of most terms in a Fourier expansion of the longitude. There are several planetary perturbation terms that have small amplitudes, but whose periods are close to the resonant period of the lunar libration in longitude. Some of these terms are moving toward resonance, some are moving away from resonance, and the periods of those terms that do not include the Delaunay variables in their arguments are not moving. Because of its acceleration of longitude, the Moon is receding from the Earth, so the magnitude of the restoring torque that the Earth exerts on the rotating Moon is gradually attenuating; thus resonance itself is moving, but at a much slower rate than the periods of the accelerating planetary perturbations. There are five planetary perturbation terms from the ELP-2000 Ephemeris (with amplitudes of 0.00001 or greater) that have passed through resonance in the past two million years. One of them is of special interest because it appears to be the excitation source of a supposed free libration in longitude that has been detected by the lunar laser ranging experiment. The amplitude of the term is only 0.00021 but it could be the source of the 1 amplitude free libration term if the viscoelastic properties of the Moon are similar to those of the Earth. 相似文献
3.
The technique of the general planetary theory has been proposed for constructing a theory of motion of the Moon. This method enables us to elaborate the consistent theory of motion of the principal planets and the Moon, which is of particular importance for determining planetary perturbations in lunar motion. As an initial approximation for lunar motion, an intermediate orbit generalizing the Hill's variational curve has been built. This orbit includes all solar and planetary inequalities independent of eccentricities and inclinations of the Moon, Sun and planets. In calculating this orbit, the motion of the principal planets in quasi-periodic intermediate orbits has been taken into account. This solution was produced with the aid of the Universal Poissonian Processor (UPP) elaborated in the Institute for Theoretical Astronomy (Leningrad).Proceedings of the Conference on Analytical Methods and Ephemerides: Theory and Observations of the Moon and Planets. Facultés universitaires Notre Dame de la Paix, Namur, Belgium, 28–31 July, 1980. 相似文献
4.
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
5.
The location and the stability in the linear sense of the libration points in the restricted problem have been studied when there are perturbations in the potentials between the bodies. It is seen that if the perturbing functions satisfy certain conditions, there are five libration points, two triangular and three collinear. It is further observed that the collinear points are unstable and for the triangular points, the range of stability increases or decreases depending upon whetherP> or <0 wherep depends upon the perturbing functions. The theory is verified in the following four cases:
- There are no perturbations in the potentials (classical problem).
- Only the bigger primary is an oblate spheroid whose axis of symmetry is perpendicular to the plane of relative motion (circular) of the primaries.
- Both the primaries are oblate spheroids whose axes of symmetry are perpendicular to the plane of relative motion (circular) of the primaries.
- The primaries are spherical in shape and the bigger is a source of radiation.
6.
B. P. Kondratyev 《Astrophysics and Space Science》2018,363(9):186
From the observations of the gravitational field and the figure of the Moon, it is known that its center of mass (briefly COM) does not coincide with the center of figure (COF), and the line “COF/COM” is not directed to the center of the Earth, but deviates from it to the South–East. Here we study the deviation of the lunar COM to the East from the mean direction to Earth.At first, we consider the optical libration of a satellite with synchronous rotation around the planet for an observer at a point on second (empty) orbit focus. It is found that the main axis of inertia of the satellite has asymmetric nonlinear oscillations with amplitude proportional to the square of the orbit eccentricity. Given this effect, a mechanism of tidal secular evolution of the Moon’s orbit is offered that explains up to \(20\%\) of the known displacement of the lunar COM to the East. It is concluded that from the alternative—evolution of the Moon’s orbit with a decrease or increase in eccentricity—only the scenario of evolution with a monotonous increase in orbit eccentricity agrees with the displacement of lunar COM to the East. The precise calculations available confirm that now the eccentricity of the lunar orbit is actually increasing and therefore in the past it was less than its modern value, \(e = 0.0549\).To fully explain the displacement of the Moon’s COM to the East was deduced a second mechanism, which is based on the reliable effect of tidal changes in the shape of the Moon. For this purpose the differential equation which governs the process of displacement of the Moon’s COM to the East with inevitable rounding off its form in the tidal increase process of the distance between the Earth and the Moon is derived. The second mechanism not only explains the Moon’s COM displacement to the East, but it also predicts that the elongation of the lunar figure in the early epoch was significant and could reach the value \(\varepsilon\approx0.31\). Applying the theory of tidal equilibrium figures, we can estimate how close to the Earth the Moon could have formed. 相似文献
7.
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
8.
Yu Cheng Gerard Gómez Josep J. Masdemont Jianping Yuan 《Celestial Mechanics and Dynamical Astronomy》2017,128(4):409-433
This paper is devoted to the study of the transfer problem from a libration point orbit of the Earth–Moon system to an orbit around the Moon. The transfer procedure analysed has two legs: the first one is an orbit of the unstable manifold of the libration orbit and the second one is a transfer orbit between a certain point on the manifold and the final lunar orbit. There are only two manoeuvres involved in the method and they are applied at the beginning and at the end of the second leg. Although the numerical results given in this paper correspond to transfers between halo orbits around the \(L_1\) point (of several amplitudes) and lunar polar orbits with altitudes varying between 100 and 500 km, the procedure we develop can be applied to any kind of lunar orbits, libration orbits around the \(L_1\) or \(L_2\) points of the Earth–Moon system, or to other similar cases with different values of the mass ratio. 相似文献
9.
A new solution for the planetary perturbations of the Moon is being built in the frame of ELP 2000, using Bretagnon's planetary theories, and achieved at the first order. It contains the two actions commonly distinguished: direct and indirect. The internal precision of computation is 2×10–6 arcsec. First-order planetary perturbations, in the direct case (Venus & Mars), have been compared to Standaert's solution. The major discrepancy reaches 70 cm in the longitude of Venus. Perturbations of the second order with respect to planetary masses, have been undertaken and illustrations are given. Finally, new values for the perigee and node motions are proposed.Proceedings of the Conference on Analytical Methods and Ephemerides: Theory and Observations of the Moon and Planets. Facultés universitaires Notre Dame de la Paix, Namur, Belgium, 28–31 July, 1980. 相似文献
10.
K. B. Bhatnagar Usha Gupta Rashmi Bhardwaj 《Celestial Mechanics and Dynamical Astronomy》1994,59(4):345-374
The non-linear stability of the libration pointL
4 in the restricted problem has been studied when there are perturbations in the potentials between the bodies. It is seen that the pointL
4 is stable for all mass ratios in the range of linear stability except for three mass ratios depending upon the perturbing functions. The theory is applied to the following four cases:
相似文献
| (i) | There are no perturbations in the potentials (classical problem). |
| (ii) | Only the bigger primary is an oblate spheroid whose axis of symmetry is perpendicular to the plane of relative motion (circular) of the primaries. |
| (iii) | Both the primaries are oblate spheroids whose axes of symmetry are perpendicular to the plane of relative motion (circular) of the primaries. |
| (iv) | The primaries are spherical in shape and the bigger is a source of radiation. |
11.
《Chinese Astronomy and Astrophysics》2022,46(4):346-390
The 1:1 mean motion resonance may be referred to as the lowest order mean motion resonance in restricted or planetary three-body problems. The five well-known libration points of the circular restricted three-body problem are five equilibriums of the 1:1 resonance. Coorbital motion may take different shapes of trajectory. In case of small orbital eccentricities and inclinations, tadpole-shape and horseshoe-shape orbits are well-known. Other 1:1 libration modes different from the elementary ones can exist at moderate or large eccentricities and inclinations. Coorbital objects are not rare in our solar system, for example the Trojans asteroids and the coorbital satellite systems of Saturn. Recently, dozens of coorbital bodies have been identified among the near-Earth asteroids. These coorbital asteroids are believed to transit recurrently between different 1:1 libration modes mainly due to orbital precessions, planetary perturbations, and other possible effects. The Hamiltonian system and the Hill’s three-body problem are two effective approaches to study coorbital motions. To apply the perturbation theory to the Hamiltonian system, standard procedures involve the development of the disturbing function, averaging and normalization, theory of ideal resonance model, secular perturbation theory, etc. Global dynamics of coorbital motion can be revealed by the Hamiltonian approach with a suitable expansion. The Hill’s problem is particularly suitable for the studies on the relative motion of two coorbital bodies during their close encounter. The Hill’s equation derived from the circular restricted three-body problem is well known. However, the general Hill’s problem whose equation of motion takes exactly the same form applies to the non-restricted case where the mass of each body is non-negligible, namely the planetary case. The Hill’s problem can be transformed into a “canonical shape” so that the averaging principle can be applied to construct a secular perturbation theory. Besides the two analytical theories, numerical methods may be consulted, for example the approach of periodic orbit, the surface of section, and the computation of invariant manifolds carried by equilibriums or periodic orbits. 相似文献
12.
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
13.
14.
S. Ferraz-Mello 《Celestial Mechanics and Dynamical Astronomy》2002,83(1-4):275-289
Explicit construction of the solutions of the Hamiltonian system given by H = H
0(J) – A(J) cos (ideal resonance problem), two orders of approximation beyond the well-known pendulum approximation. The given solutions are valid for libration amplitudes of order
. The procedure used is extended to allow the construction of the solutions of Hamiltonians with perturbations involving two degrees of freedom; the post-pendulum solution of an example of this kind is constructed. 相似文献
15.
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.
16.
G. P. Horedt 《Celestial Mechanics and Dynamical Astronomy》1984,33(4):367-374
The librational motion round the Lagrangian triangular points L4, L5 with mass exchange of the primaries is investigated according to Brown's theory. The results are the same as in the case of isotropic mass variation studied earlier (Horedt, 1974a): (i) The extrema of the elongations with respect to the small mass are unaffected by mass exchange. (ii) The equations for the extrema of the Trojan's distance from the Sun and for the libration period are formally the same as in the constant mass problem, but with the understanding that the masses are now time dependent quantities. A Trojan cannot leave the libration domain due to a mass variation of the primaries obeying the constraints from Equation (2.4), with a mass ratio of the primaries m/M≤0.0401. 相似文献
17.
18.
We describe global bifurcations from the libration points of non-stationary periodic solutions of the restricted three body problem. We show that the only admissible continua of non-stationary periodic solutions of the planar restricted three body problem, bifurcating from the libration points, can be the short-period families bifurcating from the Lagrange equilibria L
4, L
5. We classify admissible continua and show that there are possible exactly six admissible continua of non-stationary periodic solutions of the planar restricted three body problem. We also characterize admissible continua of non-stationary periodic solutions of the spatial restricted three body problem. Moreover, we combine our results with the Déprit and Henrard conjectures (see [8]), concerning families of periodic solutions of the planar restricted three body problem, and show that they can be formulated in a stronger way. As the main tool we use degree theory for SO(2)-equivariant gradient maps defined by the second author in [25].This revised version was published online in October 2005 with corrections to the Cover Date. 相似文献
19.
John E. Cochran 《Celestial Mechanics and Dynamical Astronomy》1972,6(2):127-150
A method of general perturbations, based on the use of Lie series to generate approximate canonical transformations, is applied to study the effects of gravity-gradient torque on the rotational motion of a triaxial, rigid satellite. The center of mass of the satellite is constrained to move in an elliptic orbit about an attracting point mass. The orbit, which has a constant inclination, is free to precess and spin. The method of general perturbations is used to obtain the Hamiltonian for the nonresonant secular and long-period rotational motion of the satellite to second order inn/0, wheren is the orbital mean motion of the center of mass and0 is a reference value of the magnitude of the satellite's rotational angular velocity. The differential equations derivable from the transformed Hamiltonian are integrable and the solution for the long-term motion may be expressed in terms of Jacobian elliptic functions and elliptic integrals. Geometrical aspects of the long-term rotational motion are discussed and a comparison of theoretical results with observations is made. 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