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1.
The intervals of possible stability, on the -axis, of the basic families of three-dimensional periodie motions of the restricted three-body problem (determined in an earlier paper) are extended into regions of the -m 3 parameter space of the general three-body problem. Sample three-dimensional periodic motions corresponding to these regions are computed and tested for stability. Six regions, corresponding to the vertical-critical orbitsl1v, m1v,m2v, andilv, survive this preliminary stability test-therefore, emerging as the mass parameters regions allowing the simplest types of stable low inclination three-dimensional motion of three massive bodies.  相似文献   

2.
In the ordinary restricted problem of three bodies, the first-order stability of planar periodic orbits may be determined by means of their characteristic exponents, as derived from the condition of a vanishing determinant for the coefficients of an infinite system of homogenous linear equations associated with the exponential series solutionu, v representing any initially small oscillations about the periodic solutionx, y. In the elliptic restricted problem, periodic solutions are possible only for periods which are equal to, or integral multiples of, the periodP of the elliptic motion of the two primary masses. It is shown that the infinite determinant approach to the determination of the characteristic exponents can be extended to the treatment of superposed free oscillations in the elliptic problem, and that in generaltwo exponents appear in any complete solutionu, v for eachone existing in the corresponding ordinary restricted problem. The value of each exponent depends on a series proceeding in even powers of the eccentricitye of the relative orbit of the two primaries, in addition to its basic dependence on the mass ratio . For stable periodic orbits, the oscillation frequenciesn 1 (,e 2),n 2 (,e 2) associated with these two exponents tend, withe0, to certain limiting valuesn 1 (),n 2(), which differ from each other by the amount of the frequencyN=2/P of the orbital motion of the primaries. One of the two frequencies, sayn 1(), is identical with the frequency of the corresponding oscillations in the ordinary restricted problem, while the second one gives rise to oscillations only in the elliptic restricted problem, withe0.The method will be described in more detail, together with its application to two families of small periodie librations about the equilateral points of the elliptic restricted problem (E. Rabe: Two new Classes of Periodic Trojan Librations in the Elliptic Restricted Problem and their Stabilities) in theProceedings of the Symposium on Periodic Orbits, Stability and Resonances, held at the University of São Paulo, Brasil, 4–12 September, 1969.Presented at the Conference on Celestial Mechanics, Oberwolfach, Germany, August 17–23, 1969.  相似文献   

3.
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   

4.
A comparison between theGeneral Catalogue of Cool Carbon Stars (CCS) and theAFGL Catalogue has been performed.Eighty-five stars have been found in common between the two lists. Eighty-four stars which were present in Baumert's comparison between CCS and the 2 Sky Survey have no counterpart in the AFGL. Four new tentative identifications are given. The analysis of the two colours diagrams K-[4.2 ] vs. I-K and I-[4.2 ] vs. [4.2 ]-[11 ] led to the conclusion that all the infrared emission from the sources seems to come from a single circumstellar shell.  相似文献   

5.
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   

6.
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   

7.
We consider the bifurcation of 3D periodic orbits from the plane of motion of the primaries in the restricted three-body problem with oblateness. The simplest 3D periodic orbits branch-off at the plane periodic orbits of indifferent vertical stability. We describe briefly suitable numerical techniques and apply them to produce the first few such vertical-critical orbits of the basic families of periodic orbits of the problem, for varying mass parameter and fixed oblateness coefficent A1 = 0.005, as well as for varying A1 and fixed = 1/2. The horizontal stability of these orbits is also determined leading to predictions about the stability of the branching 3D orbits.  相似文献   

8.
Surface photometry of the UV continuum galaxy NGC 838 has been carried out in theB, V system using photographic plates obtained with the 74 Kottamia telescope, Egypt. Isophotes, luminosity profiles, integrated photographic magnitudes, effective diameters and other photometric parameters are derived.The photoelectrically calibrated total apparent magnitudes areB T =13.57 with maximum diameters 1.57×1.34 (at threshold m =27.7 mag.//) andV T =12.91 with maximum diameters 1.54×1.32 (at threshold m =27.7 mag./). The integrated colour index(B–V) T =0.66 and the effective surface brightness e (B=19.0 mag./) and e (V=19.7 mag./. The major axis is at position angle =85°±1°.The nucleus of NGC 838 is quite blue (integrated colour(B–V)=0.41 forr *<0.1) compared to normal galaxies while the colour becomes redder from the nucleus outwards. The UV excess, H emission and radio continuum emission previously observed from this galaxy by other investigators may be attributed to a recent burst of star formation in the nucleus of the galaxy of duration slightly greater than 2×107 yr.  相似文献   

9.
Conditions prevalent in dense molecular clouds are shown to favour the polymerization of H2CO molecules and the deposition of formaldehyde co-polymer mantles, with typical radii 10–5 cm, on smaller refractory grains. If a significant fraction of such co-polymer coated grains are expelled with systematic gas flows into the general interstellar medium, these moderately refractory grains may be responsible for the bulk of interstellar extinction and polarization at optical wavelengths. Mie calculations for a mixture consisting of iron, graphite and POM particles are presented as an example where POM grains of radii 0.15 dominate the extinction at optical wavelengths, providing a satisfactory overall fit to a range of extinction data. A size distribution of POM needles with a mean radius 0.15 also provides good agreement with data on interstellar linear as well as circular polarization. Suitably end-capped and stabilized co-polymer-coated grains, with either silicate or graphite cores, may survive at temperatures 450 K under interstellar ambient conditions and be responsible for the 10 emission feature in many sources. Theoretically computed band profiles of the 10 -feature in POM coated grains, in general, provide better agreement with observations than most types of silicate grains considered so far. We also note that an unexplained dip at 10 in the 8–12 feature of the infrared source OH 231.8+4.2 may be a signature of POM grains; likewise, a persistent 3.3 emission feature in many different types of infrared source could be attributed to the CH stretching mode in formaldehyde co-polymer grains.  相似文献   

10.
In the three-dimensional restricted three-body problem, it is known that there exists a near one-to-one commensurability ratio between the planar angular frequencies (s 1, 2, 3) and the corresponding angular frequency (S 2) in thez-direction at the three collinear equilibria (L 1, 2, 3), which is significant for small and practically important values of the mass parameter (). When the more massive primary is treated as an oblate spheroid with its equatorial plane coincident with the plane of motion of the primaries, it is established that oblateness induces a one-to-one commensurability at the exterior pointL 3 (to the right of the more massive primary) and at the interior pointL 2 for 01/2 and that atL 1 no such commensurability exists. However, the values of the oblateness coefficient (A 1) involved atL 2 are too high to have any practical significance, while those atL 3 being small for small values of may be useful for generating periodic orbits of the third kind.  相似文献   

11.
The sunspot models published so far do not reproduce the observed run of the umbral continuum intensities over the entire spectral range 0.5 < < 4 m. Moreover, in several previous models is the temperature gradient smaller than both the adiabatic and the radiative equilibrium gradient.Agreement between intensities computed from acceptable models and measured intensities can be obtained by introducing an additional opacity for 0.8 m, which is probably caused by the crowding of atomic and molecular lines. We present a new umbral model atmosphere with a wavelength dependent opacity enhancement factor which explains the continuum intensities and also reproduces plausible center-to-limb variations and line profiles. This model is in radiative equilibrium down to 0.5 = 1.5, with an effective temperature of 4000 ± 100K. For the deeper superadiabatic layers a small but probably significant departure from radiative equilibrium is indicated by the intensities in the range 1.5 < < 2.4 m.The uncertainties in the present model and the effect of the additional opacity on line profiles are briefly discussed.  相似文献   

12.
In this note we derive an exact solution of transfer equation in a plane-parallel semiinfinite atmosphere with albedo >1, by the method of Laplace transform and Wiener-Hopf technique. The emergent intensityI(0, ) is obtained in terms of theH 0-functionH 0() (Das Gupta, 1978) for which some good approximations are given. Intensity at any depth is also obtained.I(0, )/I(0, 0) is plotted in graphs against [0,1], and shows a maximum which drops and shifts towards the origin as increases.  相似文献   

13.
A supplement to the theory of analytical continuation of circular orbits in the restricted three-body problem is presented. The first order stability is given analytically to the first power of mass parameter . The theory of the Kirkwood gaps is discussed from this point of view. The stability limit which should determine the size of accretion discs in binaries is found to be in good agreement with earlier numerical experiments for < 1/2.  相似文献   

14.
A study of the galactic structure has been made by deriving the brightness distribution of the galactic plane at 2.2 m and 4.2 m near infrared region using infrared objects detected by ground-based sky surveys. The infrared brightness distribution shows distinct peaks at every 8–12° galactic longitude and indicates a periodic structure. The one-to-one positional correlation observed between the periodic structure in 2.2 m infrared brightness and the 2.6 mm CO emission line suggests that the near-infrared sources are strongly associated with dense clouds of molecular hydrogen distributed in the galactic plane.  相似文献   

15.
We show that a 3 extinction feature in galactic infrared sources cannot be due to water-ice grains. Infrared spectra with a resolution of /=0.015 are in remarkably close agreement with the 2.5–4 extinction properties calculated for bacterial grains.  相似文献   

16.
Numerical and analytical comparisons are made between three methods of obtaining stability information on satellite motion using the model of the restricted problem of three bodies. Kuiper's (1961) and Szebehely's (1978) approximate results are compared with computer solutions obtained by successive iterations. The three methods show close agreement regarding the maximum values of the orbital radii for stability. The lowest result and therefore the most conservative estimate is obtained by the simplest formula, max=(/81)1/3 where is the ratio of the satellite's orbital radius to the distance between the primaries with massesm 1>m 2 and is the mass-ratio given bym 2/(m 1+m 2).  相似文献   

17.
Pitch angle scattering of energetic particles (100 MeV) in the interplanetary medium are studied using Helios 1 and 2 magnetometer and plasma data during 1976 near the minimum of solar activity. An IMF configuration was used in the computer experiments which allowed the pitch angle diffusion coefficient, D and hence the parallel mean free path, to be determined. The radial mean free path was found to vary as r r -0.9 between 0.4 and 1 AU, but between 0.3 and 0.4 AU it decreases significantly. To reconcile our value of r at 1 AU, lying between 0.01 and 0.02 AU, with the average prompt solar proton event profile, an increasing value of r at lower radial distances would be required.  相似文献   

18.
We present quiet Sun observations obtained during a rocket flight of the Al i autoionization lines 1932 and 1936 at solar pointings ranging from = 0.73 out to the visible limb. Absolute intensities are estimated to be accurate to approximately ±20%. These lines progressively weaken with decreasing but never go into emission before finally disappearing with the continuum just beyond the visible solar limb. The observations are compared with LTE line profiles computed through the quiet Sun atmosphere of Vernazza et al. (1976). We discuss several areas of disagreement between the synthetic and observed profiles.  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 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   

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