共查询到20条相似文献，搜索用时 316 毫秒
1.
H. Claes 《Celestial Mechanics and Dynamical Astronomy》1980,21(2):193-198
The problem of A.T.E.A.S. is treated, for the zonal perturbations, in its Hamiltonian form. The method consists in eliminating angular variables from the Hamiltonian function. Nearly identity canonical transformations are used, first to remove short periodic terms, second to remove long periodic terms. The general solution, up toJ
2
3
, is represented by the generators of the transformations and by the mean motions of averaged variables, known up toJ
2
4
. Open expressions in the eccentricity are avoided as far as possible. It permits to obtain a closed second order theory with closed third order mean motions.Proceedings of the Sixth Conference on Mathematical Methods in Celestial Mechanics held at Oberwolfach (West Germany) from 14 to 19 August, 1978. 相似文献
2.
I. Stellmacher 《Celestial Mechanics and Dynamical Astronomy》1982,28(4):351-365
Résumé On développe une méthode de construction d'orbites périoldiques dans un système d'axes tournants, pour un satellite gravitant autour d'un sphéroide. Les orbites sont quasi circulaires,i est l'inclinaison sur le plan équatorial de la planète. Pour les petites inclinaisons, la solution est donnée jusqu'aux termes enJ
2
2
etJ
4.Ce modèle peut être appliqué aux satellites de Saturne. Des valeurs observées des longitudes des noeuds ascendants de Mimas et Téthys, on donne une estimation des valeurs deJ
2 etJ
4 du potentiel de Saturne. La valeur deJ
2 est très sensible aux valeurs adoptées pour le rayon équatorial de la planète.
Construction of periodic orbits of satellites in a moving system of axes, I
We give an algorithm for the construction of periodic orbits in a rotating frame for the cases of satellites moving around an oblate planet.The orbits are near to the circular case; the asymptotic developments of the periodic solutions are completely calculated for the termsJ 2 andJ 4 of the potential. The solutions for small inclinations are given up toJ 2 2 .The families of solutions depend on three parameters: the semi-major axis, the inclination of the generating orbit and the initial position on this orbit.These solutions can be applied to the motion of the Saturnian satellites. From the observed longitudes of the ascending nodes of Mimas and Tethys, we estimate the valuesJ 2 andJ 4 of the Saturnian potential, the value ofJ 2 very strongly depends on the adopted value of the planet's equatorial diameter.相似文献
3.
This paper presents a Hamiltonian approach to modelling spacecraft motion relative to a circular reference orbit based on
a derivation of canonical coordinates for the relative state-space dynamics. The Hamiltonian formulation facilitates the modelling
of high-order terms and orbital perturbations within the context of the Clohessy–Wiltshire solution. First, the Hamiltonian
is partitioned into a linear term and a high-order term. The Hamilton–Jacobi equations are solved for the linear part by separation,
and new constants for the relative motions are obtained, called epicyclic elements. The influence of higher order terms and
perturbations, such as Earth’s oblateness, are incorporated into the analysis by a variation of parameters procedure. As an
example, closed-form solutions for J2-invariant orbits are obtained. 相似文献
4.
I. Zinchenko A. Lapinov K. Mattila M. Toriseva 《Astrophysics and Space Science》1995,224(1-2):585-586
We searched for the CSJ = 2 – 1 emission towards 29 southern H2O and H2O/OH masers and 1 OH maser with the SEST radio telescope. We detected and mapped 24 CS emitting regions probably associated with 27 H2O masers. The C34SJ = 2 – 1 and COJ = 1 – 0 lines were also observed at the grid positions closest to the CS peaks. Four cores were mapped in the CSJ = 5 – 4 and C34SJ = 2 – 1 lines. 相似文献
5.
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
6.
We derive the classical Delaunay variables by finding a suitable symmetry action of the three torus T3 on the phase space of the Kepler problem, computing its associated momentum map and using the geometry associated with this structure. A central feature in this derivation is the identification of the mean anomaly as the angle variable for a symplectic S
1 action on the union of the non-degenerate elliptic Kepler orbits. This approach is geometrically more natural than traditional ones such as directly solving Hamilton–Jacobi equations, or employing the Lagrange bracket. As an application of the new derivation, we give a singularity free treatment of the averaged J
2-dynamics (the effect of the bulge of the Earth) in the Cartesian coordinates by making use of the fact that the averaged J
2-Hamiltonian is a collective Hamiltonian of the T3 momentum map. We also use this geometric structure to identify the drifts in satellite orbits due to the J
2 effect as geometric phases. 相似文献
7.
Shannon L. Coffey André Deprit Etienne Deprit 《Celestial Mechanics and Dynamical Astronomy》1994,59(1):37-72
We say that a planet is Earth-like if the coefficient of the second order zonal harmonic dominates all other coefficients in the gravity field. This paper concerns the zonal problem for satellites around an Earth-like planet, all other perturbations excluded. The potential contains all zonal coefficientsJ
2 throughJ
9. The model problem is averaged over the mean anomaly by a Lie transformation to the second order; we produce the resulting Hamiltonian as a Fourier series in the argument of perigee whose coefficients are algebraic functions of the eccentricity — not truncated power series. We then proceed to a global exploration of the equilibria in the averaged problem. These singularities which aerospace engineers know by the name of frozen orbits are located by solving the equilibria equations in two ways, (1) analytically in the neighborhood of either the zero eccentricity or the critical inclination, and (2) numerically by a Newton-Raphson iteration applied to an approximate position read from the color map of the phase flow. The analytical solutions we supply in full to assist space engineers in designing survey missions. We pay special attention to the manner in which additional zonal coefficients affect the evolution of bifurcations we had traced earlier in the main problem (J
2 only). In particular, we examine the manner in which the odd zonalJ
3 breaks the discrete symmetry inherent to the even zonal problem. In the even case, we find that Vinti's problem (J
4+J
2
2
=0) presents a degeneracy in the form of non-isolated equilibria; we surmise that the degeneracy is a reflection of the fact that Vinti's problem is separable. By numerical continuation we have discovered three families of frozen orbits in the full zonal problem under consideration; (1) a family of stable equilibria starting from the equatorial plane and tending to the critical inclination; (2) an unstable family arising from the bifurcation at the critical inclination; (3) a stable family also arising from that bifurcation and terminating with a polar orbit. Except in the neighborhood of the critical inclination, orbits in the stable families have very small eccentricities, and are thus well suited for survey missions. 相似文献
8.
We study the problem of critical inclination orbits for artificial lunar satellites, when in the lunar potential we include,
besides the Keplerian term, the J
2 and C
22 terms and lunar rotation. We show that, at the fixed points of the 1-D averaged Hamiltonian, the inclination and the argument
of pericenter do not remain both constant at the same time, as is the case when only the J
2 term is taken into account. Instead, there exist quasi-critical solutions, for which the argument of pericenter librates around a constant value. These solutions are represented by smooth
curves in phase space, which determine the dependence of the quasi-critical inclination on the initial nodal phase. The amplitude
of libration of both argument of pericenter and inclination would be quite large for a non-rotating Moon, but is reduced to
<0°.1 for both quantities, when a uniform rotation of the Moon is taken into account. The values of J
2, C
22 and the rotation rate strongly affect the quasi-critical inclination and the libration amplitude of the argument of pericenter.
Examples for other celestial bodies are given, showing the dependence of the results on J
2, C
22 and rotation rate. 相似文献
9.
A new pumping mechanism – methanol masers without population inversion is presented in this paper. It can be used to explain
the formation of a series of J
0 → J
-1
E methanol masers, while the 21 → 30
A
+ methanol masers are regarded as a driving coherent micrwave field. In the new mechanism, the intensities of J
0 - J
-1
E methanol masers are increased with the decreasing transition frequencies (or with rotational number J, approximately). These results agree with Slysh et al. (1995) and Slysh et al. (1999) J ≤ 5 observations for G3345.01+1.79 and W48, in which both J
0 → J
-1
E and 21 → 30
A
+ methanol masers are detected coincidentally. Other astronomical conditions, such as magnetic field, 21 → 30
A
+ coherent radition, incoherent pumping rate by thermal radition and so on are also discussed. The new mechanism can operate
as a complement to other ordinary maser pumping mechanisms for some class II methonal maser sources.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
10.
S. Ferraz-Mello 《Celestial Mechanics and Dynamical Astronomy》1999,73(1-4):243-248
The word "average" and its variations became popular in the sixties and implicitly carried the idea that "averaging" methods
lead to "average" Hamiltonians. However, given the Hamiltonian H = H0(J) + ∈R(θ, J), (∈ < < 1), the problem of transforming it into a new Hamiltonian H* (J*) (dependent only on the new actions J*), through a canonical transformation given by zero-average trigonometrical series has no general solution at orders higher
than the first.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
11.
Andrei Irimia 《Journal of Astrophysics and Astronomy》2007,28(2-3):157-166
Electric and magnetic multipole transitions among low-lying states of doubly ionized vanadium were computed using the multi-configuration
Hartree-Fock (MCHF) method with Breit-Pauli (BP) corrections to a non-relativistic Hamiltonian. Energy levels were determined
up to and including 3d
2(1
G)4s b 2
G
7/2 and computed energies were found to be in good agreement with experiment and other theories. In addition to Einstein A
ki
coefficients for some E2 and M1 transitions, lifetime data and selected weighted oscillator strengths are also reported. 相似文献
12.
Q. Zeng 《Astrophysics and Space Science》1996,243(2):363-369
Methanol 72–81
A
+ is mapped for the first time in Orion KL. Analysing the observed data and solving the statistical equilibrium and radiative transfer equations, it is concluded that line series ofJ
2–(J+1)1
A
+ (J=7,8,9) is in quasi-thermal emission rather than the masers in Orion KL. The maser spots of methanolJ
2–J
1
E (J=6,7) and 80–71
A
+ are distributed in the northeast part of the contour plot of 72–81
A
+. The physical conditions of the regions of maser seriesJ
0–(J–1)1
A
+ (J=7,8,9) are discussed. Also from the calculation results another maser seriesJ
1–(J–1)2
A
– (J=10,11,12) that might coexist with maser seriesJ
2–J
1
E, is found. The sizes of the 2-dimension Gaussian fit plots of methanol 72–81
A
+ and HCOOCH3 10(0,10)–9(0,9)A are almost the same, and the main parts overlap each other. 相似文献
13.
By applying the theory of slowly rotating stars to the Sun, the solar quadrupole and octopole moments J
2 and J
4 were computed using a solar model obtained from CESAM stellar evolution code (Morel, 1997) combined with a recent model of solar differential rotation deduced from helioseismology (Corbard et al., 2002). This model takes into account a near-surface radial gradient of rotation which was inferred and quantified from MDI f-mode observations by Corbard and Thompson (2002). The effect of this observational near-surface gradient on the theoretical values of the surface parameters J
2, J
4 is investigated. The results show that the octopole moment J
4 is much more sensitive than the quadrupole moment J
2 to the subsurface radial gradient of rotation. 相似文献
14.
R. A. Broucke 《Celestial Mechanics and Dynamical Astronomy》1994,58(2):99-123
We describe a collection of results obtained by numerical integration of orbits in the main problem of artificial satellite theory (theJ
2 problem). The periodic orbits have been classified according to their stability and the Poincaré surfaces of section computed for different values ofJ
2 andH (whereH is thez-component of angular momentum). The problem was scaled down to a fixed value (–1/2) of the energy constant. It is found that the pseudo-circular periodic solution plays a fundamental role. They are the equivalent of the Poincaré first-kind solutions in the three-body problem. The integration of the variational equations shows that these pseudo-circular solutions are stable, except in a very narrow band near the critical inclincation. This results in a sequence of bifurcations near the critical inclination, refining therefore some known results on the critical inclination, for instance by Izsak (1963), Jupp (1975, 1980) and Cushman (1983). We also verify that the double pitchfork bifurcation around the critical inclination exists for large values ofJ
2, as large as |J
2|=0.2. Other secondary (higher-order) bifurcations are also described. The equations of motion were integrated in rotating meridian coordinates. 相似文献
15.
Mohamed Radwan 《Astrophysics and Space Science》2003,283(2):137-154
The canonical equations of motion of an artificial lunar satellite are formulated including the effects of the asphericity
of the Moon comprising the harmonics J
2, J
22, J
3, J
31, J
4 andJ
5, the oblateness of the Earth up to the second zonal harmonic, as well as the disturbing function due to the attractions of
the Earth and of the Sun (terms are retained up to order 10-6 for the higher orbits and 10-8 for the lower orbits).
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
16.
W. Landgraf 《Solar physics》1992,142(2):403-406
From astrometric observations of minor planet (1566) Icarus from 1949 to 1987 were made solutions for improved orbital elements of Icarus and the quadrupole moment of the Sun. The formal result was J2 = -0.6±5.8 &d 10–6. From this we can conclude that J
2 is very probably less than 2 · 10–-5. 相似文献
17.
In this paper we first emphasize why it is important to know the successive zonal harmonics of the Sun's figure with high
accuracy: mainly fundamental astrometry, helioseismology, planetary motions and relativistic effects. Then we briefly comment
why the Sun appears oblate, going back to primitive definitions in order to underline some discrepancies in theories and to
emphasize again the relevant hypotheses. We propose a new theoretical approach entirely based on an expansion in terms of
Legendre's functions, including the differential rotation of the Sun at the surface. This permits linking the two first spherical
harmonic coefficients (J
2 and J
4) with the geometric parameters that can be measured on the Sun (equatorial and polar radii). We emphasize the difficulties
in inferring gravitational oblateness from visual measurements of the geometric oblateness, and more generally a dynamical
flattening. Results are given for different observed rotational laws. It is shown that the surface oblateness is surely upper
bounded by 11 milliarcsecond. As a consequence of the observed surface and sub-surface differential rotation laws, we deduce
a measure of the two first gravitational harmonics, the quadrupole and the octopole moment of the Sun: J
2=−(6.13±2.52)×10−7 if all observed data are taken into account, and respectively, J
2=−(6.84±3.75)×10−7 if only sunspot data are considered, and J
2=−(3.49±1.86)×10−7 in the case of helioseismic data alone. The value deduced from all available data for the octopole is: J
4=(2.8±2.1)×10−12. These values are compared to some others found in the literature.
Supplementary material to this paper is available in electronic form at http://dx.doi.org/10.1023/A:1005238718479 相似文献
18.
Bernard De Saedeleer 《Celestial Mechanics and Dynamical Astronomy》2005,91(3-4):239-268
This paper is a contribution to the Theory of the Artificial Satellite, within the frame of the Lie Transform as canonical
perturbation technique (elimination of the short period terms). We consider the perturbation by any zonal harmonic J
n
(n ≥ 2) of the primary on the satellite, what we call here the complete zonal problem of the artificial satellite. This is quite useful for primaries with symmetry of revolution. We give an analytical formula to compute directly the first
order averaged Hamiltonian. The computation is carried out in closed form for all terms, avoiding therefore tedious expansions
in the eccentricity or in any anomaly; this feature makes the averaging process, not only valid for all kind of elliptic trajectories
but at the same time it yields the averaged Hamiltonian in a very short and compact way. The formula allows us to now skip
the averaging process, which means an asymptotic gain of a factor 3n/2 regarding the computational cost of the n
th
zonal. Our analytical formulae have been widely checked, by comparison on one hand with published works (Brouwer, 1959) (which
contained results for particular zonal harmonics, let’s say typically from J
2 to J
8), and on the other hand with the results of 3 symbolic manipulation software, among which the MM (standing for ‘Moon’s series
Manipulator’), which has already been used and described in (De Saedeleer B., 2004). Additionally, the first order generator
associated with this transformation is given into the same closed form, and has also been validated. 相似文献
19.
Stanisław Kasperczuk 《Celestial Mechanics and Dynamical Astronomy》1995,63(3-4):245-253
The reduced Henon-Heiles system is investigated as a Hamiltonian dynamical system obtained by applying the normalization of the HamiltonianH=1/2(p
1
2
+p
2
2
+q
1
2
+q
2
2
)+1/3q
1
3
–q
1
q
2
2
to fourth-degree terms. The related equations of motion are bi-Hamiltonian and possess the Lie-Poisson structure. Each Lie-Poisson structure possesses an associated Casimir function. When reduced to level sets of these functions, the equations of motion take various symplectic forms. The various reductions give different coordinate representations of the solutions. These coordinate representations are used to seek the simplest representation of the solutions. 相似文献
20.
A first-order, semi-analytical method for the long-term motion of resonant satellites is introduced. The method provides long-term solutions, valid for nearly all eccentricities and inclinations, and for all commensurability ratios. The method allows the inclusion of all zonal and tesseral harmonics of a nonspherical planet.We present here an application of the method to a synchronous satellite includingonly theJ
2 andJ
22 harmonics. Global, long-term solutions for this problem are given for arbitrary values of eccentricity, argument of perigee and inclination. 相似文献