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1.
A largely numerical study was made of families of three-dimensional, periodic, halo orbits near the collinear libration points in the restricted three-body problem. Families extend from each of the libration points to the nearest primary. They appear to exist for all values of the mass ratio , from 0 to 1. More importantly, most of the families contain a range of stable orbits. Only near L1, the libration point between the two primaries, are there no stable orbits for certain values of . In that case the stable range decreases with increasing , until it disappears at =0.0573. Near the other libration points, stable orbits exist for all mass ratios investigated between 0 and 1. In addition, the orbits increase in size with increasing .  相似文献   

2.
We study some aspects of the restricted three-body problem when the mass parameter is sufficiently small. First, we describe the global flow of the two-body rotating problem, =0, and we use it for the analysis of the collision and parabolic orbits when 0. Also we show that for any fixed value of the Jacobian constant and for any >0, there exists a 0>0 such that if the mass parameter [0,0], then the set of bounded orbits which are not contained in the closure of the set of symmetric periodic orbits has Lebesgue measure less than .Paper presented at the 1981 Oberwolfach Conference on Mathematical Methods in Celestial Mechanics.  相似文献   

3.
On periodic flybys of the moon   总被引：1，自引：1，他引：0  
This paper considers the plane circular restricted three-body problem for small . Symmetric periodic solutions of the second species (passing near the body of mass ) and their distance from the center of the body of mass are studied by constructing perturbations of arc-solutions (solutions with consecutive collisions) existing for =0. Orbits which also pass near the body of mass 1- are studied in detail. The results are applied to finding periodic orbits in the Earth-Moon system and in the Sun-Jupiter system.Russian version: Preprint No. 91 (1978) of Inst. Appl. Math.; present English translation was made by L. M. Perko and W. C. Schulz (February 1979).  相似文献   

4.
Infrared continuum observations of the Sun at wavelengths between 10 and 30 show a nonisothermal response of the upper photosphere to compression waves associated with the five-minute oscillations. Observations were made with four broad-band filters with effective transmission wavelengths between 10 and 26 and with a 10 aperture. Further observations at submillimeter wavelengths with a 2 aperture did not resolve oscillatory fluctuations of five-minute period.Comparisons with velocity field data of Howard (1976) suggest that the relaxation time of the photosphere exceeds (300/2) seconds at the height of formation of the 26 continuum (5000Å 10-2). The photosphere reponds to 3 mHz oscillatory motion with considerably less compression than expected for simple acoustic modes in an adiabatically responsive atmosphere, confirming the evanescent character of the five-minute oscillations.  相似文献   

5.
A comparison is made between the stability criteria of Hill and that of Laplace to determine the stability of outer planetary orbits encircling binary stars. The restricted, analytically determined results of Hill's method by Szebehely and co-workers and the general, numerically integrated results of Laplace's method by Graziani and Black are compared for varying values of the mass parameter =m 2/(m 1+m 2). For 00.15, the closest orbit (lower limit of radius) an outer planet in a binary system can have and still remain stable is determined by Hill's stability criterion. For >0.15, the critical radius is determined by Laplace's stability criterion. It appears that the Graziani-Black stability criterion describes the critical orbit within a few percent for all values of .  相似文献   

6.
The stability ofL 4 and the motion aboutL 4 in the restricted problem of three bodies is investigated when there is three-to-one commensurability between the long and short periods of motion, that is, when the mass ratio has the value =0.013516.... The two time scale method is used (1) to show thatL 4 is an unstable equilibrium point when =3, (2) to determine for what initial conditions periodic orbits occur when 3, (3) to determine the stability of the periodic orbits, and (4) to investigate the boundedness of the motions aboutL 4 when 3.  相似文献   

7.
We begin by describing the global flow of the spatial two body rotating problem, =0. The remainder of the work is devoted to study the ejection and collision orbits when >-0. We make use of the blow up techniques to show that for any fixed value of the Jacobian constant the set of these orbits is diffeomorphic to S2×R. Also we find some particular collision-ejection orbits.  相似文献   

8.
The analytic construction of the direct periodic orbits in the circular 3-body problem is given in explicit form to the linear terms in . It is shown to be in good agreement with the numerically found orbits for large values of .  相似文献   

9.
A numerical simulation of energetic particle motion in the interplanetary medium is carried out using HEOS-2 magnetometer data in order to computeD(), the pitch angle diffusion coefficient, where is cosine of pitch angle defined with respect to the local field. WhileD() exceeds that given by quasi-linear theory near 90° pitch angle, it is significantly less at higher values of , leading to a parallel transport coefficient in good accord with that given by experimental studies of solar proton propagation. In particular, =0.031 AU at a particle magnetic rigidity of 455 MV, while experimental results range from 0.05 to 0.07 AU (+100%, –50%) in this rigidity region. Furthermore, observed approximately -dependent solar proton pitch angle distributions are consistent with the computed findingD()/(1 – 2)2 ~ constant.The validity of various analytical corrections to quasi-linear theory as 0 are also investigated numerically.  相似文献   

10.
Three-dimensional computer plots were drawn for various zero-velocity contours of the restricted three-body problem (=0.1, 0.3, 0.5) and the restricted four-body problem (1=2=3==0.33). The infinitesimal mass was constrained to the plane of the finite masses. The three-dimensional representations yield a clear insight into the regions of motion and the stability of motion near the equilibrium points.  相似文献   

11.
In the theory of supergravity (N=1), the supersymmetric version of general relativity, and for the Kasner cosmological model (Bianchi type I) we find a non-trivial solution (for the metric and spinor-vector) under the most simple assumption =11 + 22; 12+21=0 and for a special choosed gaugeN=1,N j=0, 0=0. This method could be also applied to other cosmological metrics and extended to enlarged Grassmann basis.O. Obregón was partially supported by the Alexander von Humboldt Stiftung.  相似文献   

12.
This paper deals with the stationary solutions of the planar restricted three-body problem when the more massive primary is a source of radiation and the smaller primary is an oblate spheroid with its equatorial plane coincident with the plane of motion. The collinear equilibria have conditional retrograde elliptical periodic orbits around them in the linear sense, while the triangular points have long- or short-periodic retrograde elliptical orbits for the mass parameter 0 < crit, the critical mass parameter, which decreases with the increase in oblateness and radiation force. Through special choice of initial conditions, retrograde elliptical periodic orbits exist for the case = crit, whose eccentricity increases with oblateness and decreases with radiation force for non-zero oblateness.  相似文献   

13.
The exact calculation of scattering and absorption by various sub-micron sized silicate spheres is presented here, using accurately determined optical constants in the wavelength range from 50 m to 0.21 m. The extinction features near 10 m and 20 m for various samples are discussed. It is found that the ratio of peak extinction at 20 m to that at 10 m is constant for small particles up tor=0.4 m, but is less for particles of radius 1 m. The ratio of maximum extinction in the ultraviolet to that at 10 m decreases with increasing particle size.  相似文献   

14.
We have produced high-resolution images of the nuclear region of M82 with SpectroCam-10, a mid-infrared instrument at the Palomar 5 m telescope. These images were taken at 11.7 m and 9.8 m with a 1m filter bandpass at the diffraction limit of 0.6 arcsec, making them the highest resolution maps yet available of M82. In addition, we have obtained high-resolution (/=2000) maps of the velocity field of the nuclear disk of M82 in the 12.81 m line emission of [NeII]. In these proceedings we present the 11.7 m image, which will appear together with the 9.8 m map and the [Ne II] spectra in a subsequent paper, now in preparation. This image shows very clearly a bridge structure joining the eastern and western clusters.  相似文献   

15.
Ahern  Sean  Chapman  G.A. 《Solar physics》2000,191(1):71-84
Full-disk images from the Cartesian Full-Disk Telescope no. 2 (CFDT2) were used to study the center-to-limb (CLV) variation of facular contrast in two colors. The CFDT2 images, which have 2.5 arc sec pixels, were obtained during the summer months of 1993, 1994 and 1995. In order to minimize the bias in finding faint facular features in continuum images, we have used coaligned images obtained in the Ca K-line to identify faculae. Faculae were sorted into 20 annular bins of equal width. To reduce the effects of seeing, faculae were not identified closer to the limb than =0.2. The facular pixel contrasts were fitted to various trial functions. The contrast in the blue filter (470.6 nm) rose from 0.122% at disk center to 12.2% at =0.2. The contrast in the red filter (672.3 nm) rose from 0.13% at disk center to 8.16% at =0.2. We have also analyzed the facular contrasts multiplied by their -value to obtain an estimate of facular flux tube contrasts. These flux tube contrasts increased roughly linearly from =0.95 to 0.25. The blue flux tube contrast reached a maximum of 2.48% near =0.25. The red flux tube contrast reached a maximum of 1.59% at =0.2. These contrast values are not corrected for the filling factor. The blue curve leveled off slightly betwen =0.25 and 0.2 while the red curve showed no deviation from its linear trend. These results may provide some support for the hot wall model of facular flux tubes.  相似文献   

16.
Since the average relation between the angular momentaP and the massesM of galaxies can be represented by a power lawPM , we can define a relative angular momentum =P/M (or a constant timeP/M ). For a random motion picture within protogalaxies, should follow a Maxwellian distribution and consequently the dispersion of log should be 0.210.For the reasonable range of ( to 2), the limited sample of galaxies with known dynamical parameters gives between and 1 times the Maxwellian value. For the plausible special case =2 the reciprocal of the maximum rotational velocityv m is already a measure of and the larger sample ofv m-values not only yields the Maxwellian but, moreover, shows the shape of the distribution.
PM , =constP/M . , (lg )=0.210. 7/42, . =2 v m- .
  相似文献   

17.
Near-infrared photometric and low-resolution spectroscopic observations of Aurigae at two phases during the current eclipse are presented. The eclipse depths are found to be wavelength-independent in the infrared right up to 2.5 m. There is no infrared excess at wavelengths shorter than 2.5 m. The light absorbing particles in the eclipsing body must be larger than 10 m in size.  相似文献   

18.
We compare families of simple periodic orbits of test particles in the Newtonian and relativistic problems of two fixed centers (black holes). The Newtonian problem is integrable, while the relativistic problem is highly non-integrable.The orbits are calculated on the meridian plane through the fixed centersM 1 (atz=+1) andM 2 (atz=–1) for energies smaller than the escape energyE=1. We use prolate spheroidal coordinates (, , =const) and also the variables =cosh and =–cos . The orbits are inside a curve of zero velocity (CZV). The Newtonian orbits are also limited by an ellipse and a hyperbola, or by two eillipses. There are 3 main types of periodic orbits (1) elliptic type (around both centers), (2) hyperbolic-type, and (3) resonant-type.The elliptic type orbits are stable in the Newtonian case and both stable and unstable in the relativistic case. From the stable orbits bifurcate double period orbits both symmetric and asymmetric with respect to thez-axis. There are also higher order bifurcations. The hyperbolic-type orbits are unstable. The Newtonian resonant orbits are defined by the ratiot µ/t =n/m of oscillations along and during one period, and they are all marginally unstable. The corresponding relativistic orbits are stable, or unstable. The main families are figure eight orbits aroundM 1, or aroundM 2 (3/1 orbits); gamma, or inverse gamma orbits (4/2); higher resonant families 5/1,7/1,...,8/2,12/2,...;, more complicated orbits, like 5/3, and bifurcations from the above orbits. Satellite orbits aroundM 1, orM 2, and their bifurcations (e.g. double period) exist in the relativistic case but not in the Newtonian case. The characteristics of the various families are quite different in the Newtonian and the relativistic cases. The sizes of the orbits and their stabilities are also quite different in general. In the Appendix we study the various types of straight line orbits and prove that some subcases introduced by Charlier (1902) are impossible.  相似文献   

19.
The purpose of this paper is to study, for small values of , the three-dimensional p–q resonant orbits that are close to periodic second species solutions (SSS) of the restricted three-body problem. The work is based on an analytic study of the in- and out-maps. These maps are associated to follow, under the flow of the problem, initial conditions on a sphere of radius around the small primary, and consider the images of those initial points on the same sphere. The out-map is associated to follow the flow forward in time and the in-map backwards. For both mappings we give analytical expressions in powers of the mass parameter. Once these expressions are obtained, we proceed to the study of the matching equations between both, obtaining initial conditions of orbits that will be 'periodic' with an error of the order 1–, for some (1/3,1/2). Since, as 0, the inner solution and the outer solution will collide with the small primary, these orbits will be close to SSS.  相似文献   

20.
The concept of velocity correlation functions is introduced and applied to the calculation of cosmic ray spatial diffusion coefficients. It is assumed that the pitch angle scattering coefficient is already known from some other theory, and is reasonably well-behaved. Previous results for the coefficient for diffusion parallel to the mean field are recovered when the velocity-changing mechanism is artificially restricted to pitch angle scattering. The velocity correlation method is then applied to the more general case where there are fluctuations in the local mean field. It is found that the parallel diffusion coefficient is reduced in proportion to the amplitude of the field fluctuations, and that the ratio of the perpendicular to parallel diffusion coefficients cannot be greater than B x 2 /B 0 2 . It is shown in the appendix that the Liouville form of the scattering equation implies that the Fokker-Planck coefficients 2/t=2D and /t=D /, and that all higher-order coefficients are identically zero.  相似文献   

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