Motion of the orbital plane of a satellite due to a secular change of the obliquity of its mother planet

At the present state the rotational axes of Uranus and Pluto are nearly perpendicular to their orbital planes and each satellite moves in the vicinity of the equatorial plane of its mother planet. We assume that in the past a planet's equatorial plane was nearly coincident with its orbital plane and then the inclination of the equatorial plane with respect to the orbital plane began to increase secularly. Here we discuss whether a satellite that moves in its mother's equatorial plane continues to move in the equatorial plane or not. When the direct solar perturbation is neglected, the satellite continues to stay in the equatorial plane under the condition that the secular rate of change of the obliquity is slower than the precessional speed of the satellite orbital plane with respect to the equator.     

On the oscillatory motions of the principal plane of the solar corona

We define the principal plane of the solar corona as the equatorial plane of the dipole component of the solar magnetic field at the source surface. The position of this plane defines the orientation of the heliospheric current sheet and the outer solar corona in 3D space, in particular, their inclination with respect to the solar equatorial plane. Their tilt varies from almost zero at solar minimum to almost 90° at solar maximum. But this change is not monotonic; more or less regular oscillations are superimposed onto the average curve. Data on the inclination of the coronal principal plane during 1994–2000 were analyzed. Oscillations with a quasiperiod of 1.3 years were clearly revealed. These oscillations were found to be correlated with variations of the solar rotation rate at the base of the solar convection zone. The latter variations have the same quasi-period of 1.3 years, but they are 1 month out of phase.     

Magnetic Field in Selected Directions of the Galaxy, Direction of the Spiral Arm of Sagittarius

Faraday rotation data on 40 pulsars are used in a detailed study of the magnetic field and its fluctuations in the direction of the spiral arm of Sagittarius. These results mostly agree with standard models for the galactic magnetic field. A magnetic field on the order of 3.2 G is directed from galactic longitude l ₀=55° (toward the sun). However, an asymmetry has been found in the degrees of rotation relative to a plane lying in the southern hemisphere parallel to the galactic plane and at a distance of 50-60 pc from it. All the pulsars with measures of dispersion greater than 30 pc·cm^-3 and lying to the north of this plane have positive measures of rotation which increase linearly with distance, while the pulsars lying to the south of this plane have unusually absolutely low negative measures of rotation. We propose that the spiral arm of Sagittarius lies entirely to the north of this plane, while the negative measures of rotation of the pulsars below this plane are caused by the magnetic field of the halo of the southern hemisphere of the galaxy. The magnetic field in the arm of Sagittarius is regular to a great extent and its fluctuating component is roughly half the regular component.     

Numerical simulation of the gould belt dynamics

The results of numerical simulations of the Gould Belt motion for the 2D (a ring in the Galactic plane) and 3D (a spherical shell outside the Galactic plane) cases are presented. Particles of the expanding shell interact with each other within the framework of the N-body problem. The Galactic potential has been borrowed from Flynn et al. (1996). The total mass of the shell is 1.5 × 10⁶ M_⊙ in accordance with the estimate from Bobylev (2006). The initial mutual distances and velocities of the shell components are chosen in such a way that the shell reaches the present-day sizes of the Gould Belt in 30–60 Myr. In the 2D case, the ring is shown to be stretched with time into a rotating ellipse, which is consistent with the results from Blaauw (1952) obtained by other methods. In the 3D case, the projections of the initially spherical shell onto the Galactic plane are also rotating ellipses. A vertical oscillation of the Gould Belt components relative to the Galactic plane, a flattening of the spherical shell, and its inclination to the Galactic plane after a certain time interval have been revealed.     

On the determination of the north direction of the sun's image

For a perfectly aligned Coudé heliograph the north direction of Sun's image in the image plane of the heliograph changes linearly with the hour angle of the Sun or in a common heliograph it is constant. But if the alignment is not perfect and there are instrumental errors the angle between the north direction of the Sun's image and a direction fixed in the image plane is a complicated function of the hour angle of the Sun. In this paper we derive this dependence.     

The definition of the ecliptic

The ecliptic as a mean orbital plane of the Sun in Le Verrier's theory is a mean orbital plane determined from the secular parts of the longitude of the ascending node and the inclination of the Sun with respect to a reference plane. On the other hand, the ecliptic in Newcomb's theory is so chosen that the latitude with respect to his ecliptic does not have cosg nor sing whereg is the mean anomaly of the Sun. The two definitions are really different in spite of their apparent similarity. Standish (1981) defined the ecliptic from a kinematical point of view, and it is shown that the ecliptic defined by Standish (in the rotating sense) does coincide with the ecliptic defined by Newcomb.     

Determining the Preliminary Orbit in the Non-Coplanar Case

Solar System Research - An algorithm for finding a solution for determining a preliminary orbit in the noncoplanar case, when the plane of the desired orbit does not coincide with the plane of...     

The Structure of Periodic Solutions in the Restricted Problem of the Three Bodies II

In this work we consider four families of plane periodic orbits direct around the Sun which approach Jupiter but they are sufficiently far from it so as to be considered as predominantly two body orbits of the Sun-asteroid system. We study their horizontal and vertical stabilities and we give the exact orbits of bifurcations of these families with three-dimensional families of the same multiplicity or twice the multiplicity of the above families of plane symmetric periodic orbits. Moreover, we give the first segments of the three dimensional families of symmetric periodic orbits which emanate from these plane bifurcations and we study their stability relating it with the stability of the plane bifurcations.     

The periodic orbits of the second kind in terms of Giacaglia's variables with oblateness

Utilizing secular perturbing potential due to oblateness, the existence of periodic orbits of the second kind is established through analytic continuation using Giacaglia's canonical variables in the planar restricted three-body problem when the more massive primary is an oblate spheroid with its equatorial plane coincident with the plane of motion.     

Influence of the gould belt on interstellar extinction

A new analytical 3D model of interstellar extinction within 500 pc of the Sun as a function of the Galactic spherical coordinates is suggested. This model is physically more justified than the widely used Arenou model, since it takes into account the presence of absorbing matter both in the layer along the equatorial Galactic plane and in the Gould Belt. The extinction in the equatorial layer varies as the sine of the Galactic longitude and in the Gould Belt as the sine of twice the longitude in the Belt plane. The extinction across the layers varies according to a barometric law. It has been found that the absorbing layers intersect at an angle of 17° and that the Sun is located near the axial plane of the absorbing layer of the Gould Belt and is probably several parsecs below the axial plane of the equatorial absorbing layer but above the Galactic plane. The model has been tested using the extinction of real stars from three catalogs.     

Qualitative features of the evolution of some polar satellite orbits

Two special cases of the problem of the secular perturbations in the orbital elements of a satellite with a negligible mass produced by the joint influence of the oblateness of the central planet and the attraction by its most massive (or main) satellites and the Sun are considered. These cases are among the integrable ones in the general nonintegrable evolution problem. The first case is realized when the plane of the satellite orbit and the rotation axis of the planet lie in its orbital plane. The second case is realized when the plane of the satellite orbit is orthogonal to the line of intersection between the equatorial and orbital planes of the planet. The corresponding particular solutions correspond to those polar satellite orbits for which the main qualitative features of the evolution of the eccentricity and pericenter argument are described here. Families of integral curves have been constructed in the phase plane of these elements for the satellite systems of Jupiter, Saturn, and Uranus.     

Gravitational collapse in an expanding background and the role of substructure – I. Planar collapse

We study the interplay of clumping at small scales with the collapse and relaxation of perturbations at much larger scales. We present results of our analysis when the large-scale perturbation is modelled as a plane wave. We find that in the absence of substructure, collapse leads to formation of a pancake with multistream regions. Dynamical relaxation of the plane wave is faster in the presence of substructure. Scattering of substructures and the resulting enhancement of transverse motions of haloes in the multistream region lead to a thinner pancake. In turn, collapse of the plane wave leads to formation of more massive collapsed haloes as compared to the collapse of substructure in the absence of the plane wave. The formation of more massive haloes happens without any increase in the total mass in collapsed haloes. A comparison with the Burgers equation approach in the absence of any substructure suggests that the preferred value of effective viscosity depends primarily on the number of streams in a region.     

Mapping of the sodium emission associated with Io and Jupiter

The sodium D-lines are observed in emission in a disklike distribution surrounding Io and extending outward in the orbital plane of the Galilean satellites to at least 23 R_J from Jupiter. A scale length for the sodium emission cloud in the orbital plane and the thickness of the sodium disk perpendicular to the orbital plane are determined. Weak D-line emission is also detected over the poles of Jupiter. Estimates of the apparent emission rates are derived from microdensitometer scans of the spectrograms as a function of position in the satellite orbital plane and perpendicular to the orbital plane. No other emission lines were detected down to a limit of ～50 R over the spectral range from 3500 Å to 9000 Å.     

The Fine Structure of the Spiral-arms

An explanation for filaments inclined to the galactic plane observed in the next-inner spiral-arm is sought in terms of self-consistent z-oscillations. These filaments or „shingles”︁ are observed to be ˜ 1.4 kpc long, 70 pc thick and inclined to the plane by ˜ 12°. In a collisionless axi-symmetric stellar system we simplify the BOLTZMANN and POISSON equations by assuming a constant density normal to the galactic plane up to z ≈︂ 200 pc and by assuming a constant radial component of the spatial coordinates. The condition for selfconsistency in the linear approximation results in shingles 1.3 kpc long, inclined to the plane by 17°. The length of the shingles is independent of the radial distance R from the centre and the inclination depends inversely on R as is observed.     

Excitation of Orbital Inclinations of Asteroids during Depletion of a Protoplanetary Disk: Dependence on the Disk Configuration

The pumping up of orbital inclinations of asteroids caused by sweeping secular resonances associated with depletion of a protoplanetary disk is discussed, focusing on the dependence on the disk inclinations and surface density distribution. The asteroids have large mean inclinations that cannot be explained by present planetary perturbations alone. It has been suggested that the sweeping secular resonances caused by disk depletion are responsible for these high inclinations. Nagasawa et al. (2000, Astron. J.119, 1480-1497) showed that the inclinations of asteroids are pumped up if the disk is depleted in an inside-out manner on a time scale longer than 3×10⁵ years. Their assumed disk midplane is not on the invariant plane. However, it should be affected by the inclination of the disk plane. Here we investigate the dependence on the disk inclinations. We assume a disk depletion model in which the disk inside the jovian orbit has been removed and the residual outer disk is uniformly depleted. We calculate the locations of the secular resonances and the excitation magnitude of the inclinations with analytical methods. We found that the inclinations are pumped up to the observational level for a depletion time scale longer than 10⁶ years in the case of the disk plane that coincides with the invariant plane. The required time scale is longest (3×10⁶ years) if the disk plane coincides with the jovian orbital plane. However, it is still within the observationally inferred depletion time scale. We also studied dependence on a disk surface density gradient and found that the results do not change significantly as long as the inner disk depletion is faster than the outer disk one.     

The masses in a symmetric solution of the four body problem

It is proved that if a non-collinear motion of the four body problem has a symmetry axis (or plane), then the center of mass lies on this axis (plane) and the symmetric masses are equal. We also remark that this result is true for the generalized attraction law given by the inverse (α+1)-power of the distance, with α > 0.     

The warping of the galactic plane and changes of ellipticity

Observational evidence on the widespread occurrence of warping of the outer part of the galactic plane in many galaxies is presented and various hypotheses for its explanation are reviewed. None is found to be able to account for all the cases reported. Other phenomena considered are: (1) deviations from the galactic plane in the innermost nuclear region; (2) differences in orientation of the nucleus and disk in spiral galaxies; (3) changing ellipticity with distance from the center.After discussing the observations available, a theory has been developed which explains the phenomena mentioned as natural consequences of the non-steady nature of galactic systems due to time-dependent metric. This manifests itself in the appearance of tangential acceleration which leads necessarily to variability of the orbital plane and orbital eccentricity in dependence on the radius vector of the orbits.     

方位指向检测系统的参数测定

针对低纬子午环的观测方式和方位定向系统的精度，叙述了配备方位指向检测系统的必要性，介绍了方位指向检测的原理和系统参数的测定方法，分析了在仪器的三个支承螺杆有晃动的情况下，系统参数测定的不可靠性，提出了克服参数测定不可靠性影响的方法。     

The geometric calibration of the Planck satellite using solar system objects

The geometric calibration of the Planck satellite using the planetary transits is investigated, together with the reconstruction of any offsets from the nominal layout of the focal plane. The methods presented here may be applied to a single focal plane transit of a planet, to find the values of the geometric-calibration parameters at the epoch of the transit or all the transits over the course of the mission. The pointing requirements are easily met, with the pointing reconstruction being dominated by the errors due to the star tracker.     

Dissipationless mergers of elliptical galaxies and the evolution of the fundamental plane

We carry out numerical simulations of dissipationless major mergers of elliptical galaxies using initial galaxy models that consist of a dark matter haloes and a stellar bulge with properties consistent with the observed fundamental plane. By varying the density profile of the dark matter haloes [standard Navarro, Frenk & White (NFW) profile versus adiabatically contracted NFW profile], the global stellar to dark matter mass ratio and the orbit of the merging galaxies, we are able to assess the impact of each of these factors on the structure of the merger remnant. Our results indicate that the properties of the remnant bulge depend primarily on the angular momentum and energy of the orbit; for a cosmologically motivated orbit, the effective radius and velocity dispersion of the remnant bulge remain approximately on the fundamental plane. This indicates that the observed properties of elliptical galaxies are consistent with significant growth via late dissipationless mergers. We also find that the dark matter fraction within the effective radius of our remnants increases after the merger, consistent with the hypothesis that the tilt of the fundamental plane from the virial theorem is due to a varying dark matter fraction as a function of galaxy mass.