Acceleration of Numerical Integration of the Equations of Motion of Asteroids

Solar System Research - Finding and studying possible collisions of asteroids approaching the Earth requires a significant amount of computation. This paper describes the R0 program created to...     

A survey of orbits of co-orbitals of Mars

Many asteroids with a semimajor axis close to that of Mars have been discovered in the last several years. Potentially some of these could be in 1:1 resonance with Mars, much as are the classic Trojan asteroids with Jupiter, and its lesser-known horseshoe companions with Earth. In the 1990s, two Trojan companions of Mars, 5261 Eureka and 1998 VF₃₁, were discovered, librating about the L₅ Lagrange point, 60° behind Mars in its orbit. Although several other potential Mars Trojans have been identified, our orbital calculations show only one other known asteroid, 1999 UJ₇, to be a Trojan, associated with the L₄ Lagrange point, 60° ahead of Mars in its orbit. We further find that asteroid 36017 (1999 ND₄₃) is a horseshoe librator, alternating with periods of Trojan motion. This asteroid makes repeated close approaches to Earth and has a chaotic orbit whose behavior can be confidently predicted for less than 3000 years. We identify two objects, 2001 HW₁₅ and 2000 TG₂, within the resonant region capable of undergoing what we designate “circulation transition”, in which objects can pass between circulation outside the orbit of Mars and circulation inside it, or vice versa. The eccentricity of the orbit of Mars appears to play an important role in circulation transition and in horseshoe motion. Based on the orbits and on spectroscopic data, the Trojan asteroids of Mars may be primordial bodies, while some co-orbital bodies may be in a temporary state of motion.     

Graphical representation of periodic motion of the line of nodes of the Moon

In the text-books of astronomy, sections generally related to the Moon deal with the orbital elements of the Earth-Moon system such asa, e, i, , and the time of perigee passage. While the MEAN of the first of the three elements do not vary, mean longitude of the ascending node-mean longitude of the lunar perigee and the time of perigee passage undergoes secular as well as periodic changes due predominantly to the action of the Sun's gravitational attraction. While to a certain degree, explanations related to the calculation of the lunar orbit parameters are given, not a single graphical representation of these short- or long-periodic changes are presented. We allow the number of data related to these periodic changes must cover a large span of time; and if regression of the line of nodes or advances of the line of apses are to be graphically seen, data covering 18.61 and 8.85 yr, respectively, are needed. In this work we particularly aim at the graphical representation of the periodic changes of the line of nodes.     

Theory of motion of hyperion

We solve by an appropriate method the difficulty of near-commensurability, $\text{n}\text{n}{}_1$$\text{3}\text{4}$, in the motion of Hyperion (Saturn VII) and give a first-order solution of its motion. Our result explains two interesting observed features, the regression of the apsidal line and the exclusive occurrence of apocentre C conjunction of SVII and SVI.     

Observations of the intensity of the penumbra of sunspots

Observations of the penumbral intensity of sunspots in 13 wavelength regions are presented. In 4 wavelength regions 54 sunspots are measured. In the other wavelength regions the number of sunspots considered ranges from 3–19.The penumbral intensity alters with position within the spot. This intensity variation is found to be comparable with the change in intensity from one spot to another. The penumbral intensity is found to be independent of spot size in the sample considered.The penumbra model of Kjeldseth Moe and Maltby (1969) with = 0.055 is supported by the measurements.     

Equation of state and anisotropy of pressure of magnetars

Magnetars are the neutron stars with the highest magnetic fields up to 10¹⁵–10¹⁶ G. It has been proposed that they are also responsible for a variety of extra-galactic phenomena, ranging from giant flares in nearby galaxies to fast radio bursts. Utilizing a relativistic mean field model and a variable magnetic field configuration, we investigate the effects of strong magnetic fields on the equation of state and anisotropy of pressure of magnetars. It is found that the mass and radius of low-mass magnetars are weakly enhanced under the action of the strong magnetic field, and the anisotropy of pressure can be ignored. Unlike other previous investigations, the magnetic field is unable to violate the mass limit of the neutron stars.     

The accuracy of observations of the Galilean satellites of Jupiter taken at the Abastumani Astrophysical Observatory of the Academy of Sciences of Georgia

The sets of photographic observations of the Galilean satellites of Jupiter taken at the Abastumani Astrophysical Observatory of the Academy of Sciences of Georgia are analyzed here. Positional observations of the system of Jupiter were made in the period from 1985 to 1994 with the use of the double Zeiss astrograph in order to determine the exact coordinates of Jupiter and its satellites. The accurate positions of the satellites and Jupiter itself, as well as their stellar (equatorial) coordinates relative to the stars of the currently available catalogs and the relative ??satellite ?? satellite?? coordinates were obtained from the observations. From the comparison of the observation results with the modern theories of motion of satellites, the accuracy in determining the positions of the satellites and Jupiter was analyzed. The results of observations are presented in the Pulkovo database of observations of Solar System bodies that is accessible to users at http://www.puldb.ru.     

An explanation of the discretization of redshifts of quasars

Published in Astrofizika, Vol. 38, No. 4, pp. 700–702, October–December, 1995.     

Estimation of the Time Scale of Merging of the Components of Contact Binaries of the W UMa Type

Time scales of the transition from contact binary systems of the W UMa type to single stars of the blue straggler type are estimated. A model of one-way mass transfer from the primary component to the companion inside a common envelope (Eggen et al.) and a model of a contact binary lying on the zero-age main sequence with a companion that is losing mass (F. van't Veer) are used to calculate these scales. The merging times of components were calculated for 304 contact systems of the W UMa type from the Catalog of Approximate Photometric and Absolute Elements of Eclipsing Variable Stars on a scale of loss of mass and orbital angular momentum due to magnetic braking, under the assumption of synchronization of the axial rotation and orbital revolution. On the basis of the resulting statistics, the characteristic merging scales are 0.4-0.6 and 0.5-0.7 Gyr, respectively, for the above two models. The results of a comparison with the work of other authors are discussed.     

Distribution of Doppler Redshifts of Associated Absorbers of SDSS Quasars

Doppler redshifts of a sample of Mg II associated absorbers of SDSS DR7 quasars are analysed. We find that there might be three Gaussian components in the distribution of the Doppler redshift. The first Gaussian component, with the peak being located at z _Dopp?=???0.0074, probably arises from absorbers with outflow histories observed in the direction close to jets of quasars. The second Gaussian component, with the peak being located at z _Dopp?=???0.0017, possibly arises from absorbers with outflow histories observed in the direction far away from jets of quasars. Whereas, the third Gaussian component, with the peak being located at z _Dopp?=???0.0004, might arise from the random motion of absorbers with respect to quasars.     

Numerical integration of the equations of motion of celestial mechanics

Recently a number of new techniques have been developed for the numerical solution of the differential equations governing the motion of bodies in the Solar System, moving under their mutual gravitational forces. Some of these new methods are tested against each other and against more traditional methods and conclusions are made as to under what circumstances any of these methods should be used to produce optimum results.     

Properties of the motion of the isolated body of the problem of three bodies

We investigate the condition for the third body of the problem of three bodies to be an “isolated body”, and the properties of its motion, particularly in the case where the system has a negative total angular momentum. We give the permitted regions for the acceleration and radius vector of the isolated body, the law of variation of its velocity and the region of escape of the isolated body.