Closed solution of the Hill differential equation for short arcs and a local mass anomaly in the central body

The Hill differential equation describes the relative motion of a satellite w.r.t. a circular reference orbit. The deviations in the orbit are caused by a residual acceleration, which is small compared to the effect of the central gravitational field. In this paper, the acceleration of a local mass anomaly in the central body is considered, which rotates w.r.t. the inertial frame with a constant angular velocity. The mass anomaly is modeled by a superposition of radial base functions. The potential and the gradient of each base function are represented in the orbit by the Keplerian elements, the rotation rate of the central body and the parameters of the base function, i.e. the position of its center, the shape and a scaling factor. The inhomogeneous solution of the Hill differential equation for short arcs is found by means of the Laplace transform. A few lower orders of the solution require an additional Laplace transform, to consider the so-called resonance cases. The final deviations are described in a closed and differentiable formula of the Keplerian elements and the parameters of the base function.     

Substorm related changes in the geomagnetic tail: the growth phase

Changes in the configuration of the geomagnetic tail are known to play a fundamental role in magnetospheric substorms. Observations with the UCLA magnetometer on the eccentric orbiter OGO-5 indicate that the most pronounced changes in the midnight meridian occur in the cusp between 8 and 11 R_e. In order to organize the observations it is necessary to separate effects on the tail due to the solar wind magnetic field and effects due to substorms. Provided there are no changes in the solar wind there are two distinct phases of a substorm in the near tail: a growth phase and an expansion phase. During each phase the observations depend on the location of the satellite relative to the plasma sheet boundaries. Far behind the Earth is the pure tail region which consists of the lobe and the plasma sheet. In the lobe the field magnitude is characteristically enhanced relative to the dipole. Closer to the Earth is a region of transition. The field magnitude is close to that of the dipole but its orientation is distorted forming a cusp-like field line. Near the Earth is a region of depressed field. Here the field magnitude is much less than that of the dipole, but its orientation is similar. The growth phase of a substorm appears to be the direct consequence of the onset of a southward solar wind magnetic field. In the pure tail region the lobe field begins to increase in magnitude and the plasma sheet thins. The transition region moves earthward and the field lines become more tail-like as the field magnitude increases. In the inner region of depressed field, the field magnitude decreases rapidly. The onset of the expansion phase appears to be a process internal to the magnetosphere and independent of the solar wind. In the depressed field region there is a rapid, turbulent increase in field magnitude. In the transition region there is a sudden decrease in the field magnitude and a return to dipolar orientation. In the tail region the plasma sheet expands rapidly with the field becoming quite dipolar, decreasing slowly in the lobe of the tail.     

The solution of Jacobi's virial equation for celestial bodies

A relationship between the potential energy and the moment of the inertia for celestial bodies is heuristically discovered. This relationship consists in the constancy of the product of formfactors for the potential energy and the moment of the inertia. The product is independent of the body mass and its radial mass distribution.We find the exact solution of Jacobi's virial equation for a gravitating spherical body based on the relationship obtained. This solution represents the unharmonic radial oscillations of the body. The solution is valid for a wide class of celestial bodies including variable stars and relativistic objects for which a relativistic analog of Jacob's equation is derived.The period of the radial oscillations of the planets is estimated with the help of the solution found. We note the coincidence of the experimental data and our theoretical calculations for the Sun.We show the important role of the Coulomb forces in the formation of the planets. It is demonstrated that the Coulomb forces result in the relation between the planet masses and their average molecular weight.     

The specific features of the evolution of the viscous protoplanetary circumsolar disk

The problem of angular-momentum and mass transport in the disk is discussed and the disk viscosity is estimated. The evolution of the gas-dust protoplanetary disk at the stage of its formation inside the protostellar (protosolar) accretion envelope is considered. The conditions for the radial growth of the disk are estimated. For the subsequent period, when the central star (young Sun) is in the T Tauri phase, the temporal variations of the radius, mass, and the surface density of the disk, as well as the total mass flux from the disk onto the star (Sun), i.e., the mass accretion rate, are evaluated. The constraints on the initial value of the angular momentum of the protoplanetary circumsolar disk (that is, on the angular momentum of the protosolar cloud) are discussed with due regard for cosmochemical data.Translated from Astronomicheskii Vestnik, Vol. 38, No. 6, 2004, pp. 559–576.Original Russian Text Copyright © 2004 by Makalkin.     

A mechanism for the growth phase of magnetospheric substorms

A mechanism is presented whereby the rate of energy dissipation in the magnetosphere is controlled by the particle density in the plasma sheet in the near geomagnetic tail. The mechanism is based on a model in which the plasma sheet is sustained by injection of solar-wind particles into the dayside magnetosphere. The efficiency of the injection is controlled by solarwind parameters, in particular, the north-south component of the interplanetary magnetic field; the maximum injection rate occurs when the interplanetary field is northward. During geomagnetically quiet times, this source balances the loss of particles from the edges of the tail current sheet. If the dayside source rate is reduced (e.g. by a southward-turning interplanetary magnetic field), then the plasma sheet is depleted and the rate of magnetic merging is enhanced in the earthward portion of the tail current sheet. This period of steadily-enhanced merging is associated with the growth phase, i.e. the period of enhanced magnetospheric convection for about one hour preceding the breakup of a polar magnetic or auroral substorm. The breakup can be understood as the result of the collapse of a portion of the tail current sheet following the local depletion of the plasma sheet.     

太阳表面米粒结构观测对比度分析

分析以观测系统焦面上和探测器测到的太阳表面米粒结构的对比度与观测系统口径，大气湍流相干长度以及系统探测灵敏度的关系，给出了不同口径，不同大气湍流相干长度以及不同系统探测灵敏度时的米粒结构对比值计算结果，此外还给出了实验结果。     

Correlations Between Color Gradients and Structural Parameters of Disks in Late-type Spiral Galaxies

From the second group of the data released by the Sloan numerical patrol survey (SDSS DR2), 395 face-on late-type spiral galaxies brighter than 15-th magnitude in the waveband r are selected as the sample. The relations between the color gradients and structural parameters of disks are studied. The results indicate the following: (1) The color gradient is independent of the absolute magnitude (mass) of the disk. (2) The color gradient of disk is concerned with the size of disk. The larger the disk, the steeper the color gradient. (3) The color gradient of disk is concerned with the color of disk. The bluer the disk color, the steeper the gradient. (4) The color gradient of disk is related with the surface brightness of disk. The brighter the disk, the steeper the color gradient. Moreover, the historical constraint formed by the relations between the color gradients of disks and various structural parameters is briefly discussed.     

Precision of the ephemerides of outer planetary satellites

Ephemerides of planetary satellites are needed to address many problems. These ephemerides are used for subsequent observations. A comparison of the available ephemerides with new observations allows the accuracy of the former to be assessed. However, the precision of the ephemerides must be known a priori when solving the tasks. In this paper we formulate and solve the problem of estimating the precision of the ephemerides of outer planetary satellites derived from observations when applied up to the future moments.The methods of assessing the precision of ephemerides involve producing a set of samples of the same ephemeris inferred from observations with different samples of Monte Carlo generated random errors (RO) superimposed onto it. The statistical parameters of simulated observational errors are based on the results of the reduction of real satellite observations. We compute the deviations of the samples of the ephemeris from the standard ephemeris inferred from real observations and adopt the root-mean-square deviation of the apparent coordinates as the precision of the ephemeris. We also use alternative methods: one based on the matrix of covariances of parameter errors (RP), and another one based on bootstrap samples of observations (BS).We use three methods (RO, RP, and BS) to estimate the precision of the ephemerides of all the 107 outer planetary satellites over the 2010-2020 time interval. The precision of the ephemerides of different satellites varies from 0.05 to 4.0 arcsec. For a number of satellites new observations are of vital importance for maintaining the precision of the ephemerides at a level that would allow identification of satellites during the reduction of observations. For some satellites the precision of their ephemerides is of the order of the sizes of their orbits and such satellites can be considered to have been lost. We show that the method of bootstrap samples (BS) can give doubtful results in the cases where there are few observations, which covered a time interval that is shorter than the orbital period of the satellite.Our results suggest obtaining more precise ephemeris making new observations at the times of maximum estimated errors of the ephemeris.All the inferred estimates of the precision of ephemerides are available from the MULTI-SAT ephemeris server: www.imcce.fr/sat (IMCCE), www.sai.msu.ru/neb/nss/index.htm (SAI).     

The Oscillations of Coronal Loops Including the Shell

We investigate the MHD waves in a double magnetic flux tube embedded in a uniform external magnetic field. The tube consists of a dense hot cylindrical cord surrounded by a co-axial shell. The plasma and the magnetic field are taken to be uniform inside the cord and also inside the shell. Two slow and two fast magnetosonic modes can exist in the thin double tube. The first slow mode is trapped by the cord, the other is trapped by the shell. The oscillations of the second mode have opposite phases inside the cord and shell. The speeds of the slow modes propagating along the tube are close to the tube speeds inside the cord and the shell. The behavior of the fast modes depends on the magnitude of Alfvén speed inside the shell. If it is less than the Alfvén speed inside the cord and in the environment, then the fast mode is trapped by the shell and the other may be trapped under the certain conditions. In the opposite case when the Alfvén speed in the shell is greater than those inside the cord and in the environment, then the fast mode is radiated by the tube and the other may also be radiated under certain conditions. The oscillation of the cord and the shell with opposite phases is the distinctive feature of the process. The proposed model allows to explain the basic phenomena connected to the coronal oscillations: i) the damping of oscillations stipulated in the double tube model by the radiative loss, ii) the presence of two different modes of perturbations propagating along the loop with close speeds, iii) the opposite phases of oscillations of modulated radio emission, coming from the near coronal sources having sharply different densities.     

Capillary action in a crack on the surface of asteroids with an application to 433 Eros

Some asteroids contain water ice, and a space mission landing on an asteroid may take liquid to the surface of the asteroid. Gas pressure is very weak on the surface of asteroids. Here we consider the capillary action in a crack on the surface of irregular asteroids. The crack is modeled as a capillary which has a fixed radius. An asteroid's irregular gravitational potential influences the height of the liquid in the capillary. The height of the liquid in the capillary on the surface of such asteroids is derived from the asteroid's irregular gravitational potential. Capillary mechanisms are expected to produce an inhomogeneaous distribution of emergent liquid on the surface. This result is applied to asteroid 433 Eros, which has an irregular, elongated, and concave shape. Two cases are considered: (1) we calculate the height of the liquid in the capillary when the direction of the capillary is perpendicular to the local surface of the asteroid; (2) we calculate the height of the liquid in the capillary when the direction of the capillary is parallel to the vector from the center of mass to the surface position. The projected height in the capillary on the local surface of the asteroid seems to depend on the assumed direction of the capillary.