Existence and Stability of Libration Points in the Restricted Three-Body Problem When the Primaries are Triaxial Rigid Bodies

This paper deals with the stationary solutions of the planar restricted three-body problem when the primaries are triaxial rigid bodies with one of the axes as the axis of symmetry and its equatorial plane coinciding with the plane of motion. It is seen that there are five libration points, two triangular and three collinear. It is further observed that the collinear points are unstable, while the triangular points are stable for the mass parameter 0 < _crit(the critical mass parameter). It is further seen that the triangular points have long or short periodic elliptical orbits in the same range of .This revised version was published online in October 2005 with corrections to the Cover Date.     

Stability of and motion aboutL 4 at three-to-one commensurability

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.     

Bifurcations of Plane to 3d Periodic Orbits in the Restricted Three-Body Problem with Oblateness

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.     

On the restrited three-body problem when the mass parameter is small

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.     

Three-dimensional,periodic, ‘halo’ orbits

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 .     

Comparison of analytical and numerical calculations of the first class periodic orbits

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 .     

On periodic flybys of the moon

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).     

Stability of periodic resonance-orbits in the elliptic restricted 3-body problem

Results of families of periodic orbits in the elliptic restricted problem are shown. They are calculated for the mass ratios =0.5 and =0.1 for the primary bodies and for different values of the eccentricity of the orbit of the primaries which is the second parameter. The case =0.5 is also a good model for planetary orbits in binaries. Finally we show detailed stability diagrams and give results according to the stability classification of Contopoulos.     

A high resolution mid-infrared image of the Starburst Galaxy M82

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.     

Ejection and collision orbits of the spatial restricted three-body problem

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.     

A case of commensurability induced by oblateness

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.     

On the evolution of families of periodic orbits approaching a small primary

A network of families of periodic orbits is obtained approximately for the case =0.1 of the restricted problem using a direct grid search. Only such orbits of the third body are considered that cross the synodical line of the primaries outside the smaller of the two, perpendicularly, and in the direction of rotation of the system.     

Three-Dimensional p–q Resonant Orbits Close to Second Species Solutions

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.     

Extinction and scattering by several types of silicate sphere of radius 0.05–1.0μm,for the wavelength range 0.21–50μm

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.     

The evaluation of the interplanetary diffusion coefficient for energetic particles employing real magnetic field data

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.     

Laboratory simulation of infrared astrophysical features

Laboratory infrared emission and absorption spectra have been taken of terrestrial silicates, meteorites and lunar soils in the form of micrometer and sub-micrometer grains. The emission spectra were taken in a way that imitates telescopic observations. The purpose was to see which materials best simulate the 10 m astrophysical feature.The emission spectra of dunite, fayalite and Allende give a good fit to the 10 m broadband emission feature of comets Bennett and Kohoutek. A study of the effect of grain size on the presence of the 10 m emission feature of dunite shows that for particles larger than 37 m no feature is seen.The emission spectrum of the Murray meteorite, a Type 2 carbonaceous chondrite, is quite similar to the intermediate resolution spectrum of comet Kohoutek in the 10 m region. Hydrous silicates or amorphous magnesium silicates in combination with high-temperature condensates, such as olivine or anorthite, would yield spectra that match the intermediate resolution spectrum of comet Kohoutek in the 10 m region. Glassy olivine and glassy anorthite in approximately equal proportions would also give a spectrum that is a good fit to the cometary 10 m feature.Invited contribution to the Proceedings of a Workshop onThermodynamics and Kinetics of Dust Formation in the Space Medium held at the Lunar and Planetary Institute, Houston, 6 8 September, 1978.     

Interstellar absorptions at λ=3.2 μm and 3.3 μm

Unidentified interstellar absorption bands at =3.2 m and 3.3 m might be due to amino-acids in bacterial grains.     

Stability of outer planetary orbits around binary stars: A comparison of Hill's and Laplace's stability criteria

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 .     

Astronomical imaging with InSb arrays

Ten years ago, Forrest presented the first astronomical images with an SBRC 32×32 InSb array camera at the first NASA-Ames Infrared Detector Technology Workshop. Soon after, SBRC began development of 58×62 InSb arrays, both for ground-based astronomy and for SIRTF. By the time of the 1987 Hilo workshop Ground-based Astronomical Observations with Infrared Array Detectors astronomical results from cameras based on SBRC 32×32 and 58×62 InSb arrays, a CE linear InSb array, and a French 32×32 InSb CID array were presented. And at the Tucson 1990 meeting Astrophysics with Infrared Arrays, it was clear that this new technology was no longer the province of IR pundits, but provided a tool for all astronomers. At this meeting, the first astronomical observations with SBRC's new, gateless passivation 256×256 InSb arrays will be presented: they perform spectacularly!In this review, I can only broadly brush on the interesting science completed with InSb array cameras. Because of the broad wavelength coverage (1–5.5 m) of InSb, and the extremely high performance levels throughout the band, InSb cameras are used not only in the near IR, but also from 3–5.5 m, where unique science is achieved. For example, the point-like central engines of AGNs are delineated at L and M, and Br and 3.29 m dust emission images of galactic and extragalactic objects yield excitation conditions. Examples of imaging spectroscopy, high spatial resolution imaging, as well as deep, broad-band imaging with InSb cameras at this meeting illustrate the power of InSb array cameras.     

A search for carbon stars in the AFGL Catalogue

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.