Periodic solutions around the collinear langrangian points in the photo gravitational restricted three-body problem: Sun-Jupiter case

The evolution of the periodic orbits around the collinear equilibrium positions, belonging to the Strömgren families a, b and c, with the radiation pressure parameter of the more massive body is studied in the Sun-Jupiter system. These families are determined for a single value of the radiation pressure parameter and particularly when the radiation force of the more massive body is equal to one half of the gravitational attraction. Then the critical stability orbits of each family are transferred with the radiation parameter. The stability of each periodic solution is also studied.     

Dynamics of a satellite orbiting a planet with an inhomogeneous gravitational field

We study the dynamics of a satellite (artificial or natural) orbiting an Earth-like planet at low altitude from an analytical point of view. The perturbation considered takes into account the gravity attraction of the planet and in particular it is caused by its inhomogeneous potential. We begin by truncating the equations of motion at second order, that is, incorporating the zonal and the tesseral harmonics up to order two. The system is formulated as an autonomous Hamiltonian and has three degrees of freedom. After three successive Lie transformations, the system is normalised with respect to two angular co-ordinates up to order five in a suitable small parameter given by the quotient between the angular velocity of the planet and the mean motion of the satellite. Our treatment is free of power expansions of the eccentricity and of truncated Fourier series in the anomalies. Once these transformations are performed, the truncated Hamiltonian defines a system of one degree of freedom which is rewritten as a function of two variables which generate a phase space which takes into account all of the symmetries of the problem. Next an analysis of the system is achieved obtaining up to six relative equilibria and three types of bifurcations. The connection with the original system is established concluding the existence of various families of invariant 3-tori of it, as well as quasiperiodic and periodic trajectories. This is achieved by using KAM theory techniques.     

The accelerated Kepler problem

The accelerated Kepler problem (AKP) is obtained by adding a constant acceleration to the classical two-body Kepler problem. This setting models the dynamics of a jet-sustaining accretion disk and its content of forming planets as the disk loses linear momentum through the asymmetric jet-counterjet system it powers. The dynamics of the accelerated Kepler problem is analyzed using physical as well as parabolic coordinates. The latter naturally separate the problem’s Hamiltonian into two unidimensional Hamiltonians. In particular, we identify the origin of the secular resonance in the AKP and determine analytically the radius of stability boundary of initially circular orbits that are of particular interest to the problem of radial migration in binary systems as well as to the truncation of accretion disks through stellar jet acceleration.     

The stellar-disk electric (short) circuit: observational predictions for a YSO jet flow

We discuss the star-disk electric circuit for a young stellar object (YSO) and calculate the expected torques on the star and the disk. We obtain the same disk magnetic field and star-disk torques as given by standard magnetohydrodynamic (MHD) analysis. We show how a short circuit in the star-disk electric circuit may produce a magnetically-driven jet flow from the inner edge of a disk surrounding a young star. An unsteady bipolar jet flow is produced that flows perpendicular to the disk plane. Jet speeds of order hundreds of kilometers per second are possible, while the outflow mass loss rate is proportional to the mass accretion rate and is a function of the disk inner radius relative to the disk co-rotation radius.     

High-performance direct gravitational N-body simulations on graphics processing units

We present the results of gravitational direct N-body simulations using the commercial graphics processing units (GPU) NVIDIA Quadro FX1400 and GeForce 8800GTX, and compare the results with GRAPE-6Af special purpose hardware. The force evaluation of the N-body problem was implemented in Cg using the GPU directly to speed-up the calculations. The integration of the equations of motions were, running on the host computer, implemented in C using the 4th order predictor–corrector Hermite integrator with block time steps. We find that for a large number of particles (N  10⁴) modern graphics processing units offer an attractive low cost alternative to GRAPE special purpose hardware. A modern GPU continues to give a relatively flat scaling with the number of particles, comparable to that of the GRAPE. The GRAPE is designed to reach double precision, whereas the GPU is intrinsically single-precision. For relatively large time steps, the total energy of the N-body system was conserved better than to one in 10⁶ on the GPU, which is impressive given the single-precision nature of the GPU. For the same time steps, the GRAPE gave somewhat more accurate results, by about an order of magnitude. However, smaller time steps allowed more energy accuracy on the grape, around 10⁻¹¹, whereas for the GPU machine precision saturates around 10⁻⁶ For N  10⁶ the GeForce 8800GTX was about 20 times faster than the host computer. Though still about a factor of a few slower than GRAPE, modern GPUs outperform GRAPE in their low cost, long mean time between failure and the much larger onboard memory; the GRAPE-6Af holds at most 256k particles whereas the GeForce 8800GTX can hold 9 million particles in memory.     

Absolute Magnitudes of Be Stars Based on Hipparcos Parallaxes

The absolute visual magnitudes of 457 Be stars are determined from Hipparcos parallaxes, subsequently the mean absolute visual magnitudes of Be stars for luminosity classes III, IV and V are obtained. The new Mv calibration is compared with existing calibrations. It is found that Be stars are generally brighter than B stars of the corresponding spectral types, and that there is no direct correlation between absolute magnitudes and the stellar rotational velocity, these results are in agreement with some earlier results. A new and interesting result is that there is no direct correlation between near infrared excess and absolute visual magnitudes for Be stars. Moreover, possible biases, such as the Malmquist bias and the Lutz–Kelker bias, are also discussed.     

Differential rotation of some HK-Project stars and the butterfly diagrams

We analyze the long-term variability of the chromospheric radiation of 20 stars monitored in the course of the HK-Project at the Mount Wilson Observatory. We apply the modified wavelet algorithm for this set of gapped time series. Besides the mean rotational periods for all these stars, we find reliable changes of the rotational periods from year to year for a few stars. Epochs of slower rotation occur when the activity level of the star is high, and the relationship repeats again during the next maximum of an activity cycle. Such an effect is traced in two stars with activity cycles that are not perfectly regular (but labeled “Good” under the classification in [Baliunas, S.L., Donahue, R.A., Soon, W.H., Horne, J.H., Frazer, J., Woodard-Eklund, L., Bradford, M., Rao, L.M., Wilson, O.C., Zhang, Q. et al., 1995. ApJ 438, 269.]) but the two stars have mean activity levels exceed that of the Sun. The averaged rotational period of HD 115404 is 18.5 days but sometimes the period increases up to 21.5 days. The sign of the differential rotation is the same as the Sun’s, and the value ΔΩ/Ω=-0.14. For the star HD 149661, this ratio is −0.074. Characteristic changes of rotational periods occur over around three years when the amplitude of the rotational modulation is large. These changes can be transformed into latitude-time butterfly diagrams with minimal a priori assumptions. We compare these results with those for the Sun as a star and conclude that epochs when surface inhomogeneities rotate slower are synchronous with the reversal of the global magnetic dipole.     

Dynamics of two satellites in the 2/1 Mean–Motion resonance: application to the case of Enceladus and Dione

The dynamics of a pair of satellites similar to Enceladus–Dione is investigated with a two-degrees-of-freedom model written in the domain of the planar general three-body problem. Using surfaces of section and spectral analysis methods, we study the phase space of the system in terms of several parameters, including the most recent data. A detailed study of the main possible regimes of motion is presented, and in particular we show that, besides the two separated resonances, the phase space is replete of secondary resonances.     

The manifolds of families of 3D periodic orbits associated to Sitnikov motions in the restricted three-body problem

This paper deals with the Sitnikov family of straight-line motions of the circular restricted three-body problem, viewed as generator of families of three-dimensional periodic orbits. We study the linear stability of the family, determine several new critical orbits at which families of three dimensional periodic orbits of the same or double period bifurcate and present an extensive numerical exploration of the bifurcating families. In the case of the same period bifurcations, 44 families are determined. All these families are computed for equal as well as for nearly equal primaries (μ = 0.5, μ = 0.4995). Some of the bifurcating families are determined for all values of the mass parameter μ for which they exist. Examples of families of three dimensional periodic orbits bifurcating from the Sitnikov family at double period bifurcations are also given. These are the only families of three-dimensional periodic orbits presented in the paper which do not terminate with coplanar orbits and some of them contain stable parts. By contrast, all families bifurcating at single-period bifurcations consist entirely of unstable orbits and terminate with coplanar orbits.     

Spectroscopic binaries near the north Galactic Pole

Orbits based principally on radial-velocity measurements made with the Haute-Provence Coravel spectrometer are presented for eight binary systems which include some of the faintest HD stars in the Galactic-Pole field. They are HD 103418 (which is double-lined), 105021, 108151, 113169, 113323, 113650, 113714, and 116514. Their periods range from 3.7 to 15.1 days. Very little else is known about any of them.