The destruction of a continuous ring revolving around a gravitating center

In article by Morozov and Fridman (1984) the general equation of motion of an elastic thread in an external gravitational field was formulated and also instability of an elastic thread rotating around a gravitating center was established.On this basis, in the present article we show that the classical model of a hypothetical continous ice ring around Saturn, proposed by Laplace and Maxwell, was incorrectly interpreted by them. Specifically, supposing the ring to be infinitely hard and firm, they came to the conclusion that it will fall on the planet's surface. However, in reality such a ring would be destroyed due to internal stresses under displacements which are three orders of magnitude smaller than the distance between the ring and the planet. We also note that accounting for this effect is important under discussions of cosmogonical models.In conclusion, estimates are given which show that the steel ring (thread) revolving the Earth and rotating around it at the distance of 200 km from the surface would be torn, due to its instability before it falls on the Earth. Meanwhile, for threads of firm aluminium fusions the opposite picture is to be expected. It is noted that the instabilities indicated may be stabilized by using follow-up (cybernetic) systems with power plants.     

引力坍缩能形成环星系吗?

大部分环星系是由星系相互作用、引力响应的演化形成．但是，这并不是形成环星系的唯一方式．孤立星系的引力坍缩也可能形成环星系．本文进行引力坍缩的数值模拟试验，计算结果也显示出较好的环形结构．     

The polar stellar ring and dark halo of NGC 5907

Numerical simulations of the disruption of a dwarf companion moving in the polar plane of a massive galaxy are presented. The constructed model is compared with observational data on the recently discovered low-surface-brightness stellar ring around the galaxy NGC 5907. Constraints on the ring lifetime (≤ 1.5 Gyr after the first approach of the galaxies), on the structure of the companion—the ring precursor, and on the mass of the dark halo of the main galaxy in whose gravitational field the companion moves are provided. The dark-halo mass within 50 kpc of the NGC 5907 center cannot exceed 3 or 4 “visible” masses.     

黑洞发光环谱线轮廓的精确解

围绕黑洞作开普勒运动的环状发光物所发射的光，将受到多普勒颇移和引力的综合作用．本文用光子输运方程方法，针对洛仑兹型发射谱线，求出在Schwarzschild度规下谱线轮廓的精确解，并讨论了Hercules星系团中类星体1604＋179光谱的认证．     

A complete infrared Einstein ring in the gravitational lens system B1938 + 666

We report the discovery, using NICMOS on the Hubble Space Telescope , of an arcsec-diameter Einstein ring in the gravitational lens system B1938+666. The lensing galaxy is also detected, and is most likely an early-type galaxy. Modelling of the ring is presented and compared with the radio structure from MERLIN maps. We show that the Einstein ring is consistent with the gravitational lensing of an extended infrared component, centred between the two radio components.     

Numerical simulations of collisions in self-gravitating systems

The influence of partially elastic collisions, gravitational encounters, and different gravitational potentials is studied in terms of computer simulations involving a ring of 200 identical particles. If the masses of the particles are small, their mutual gravitational attraction is found to produce a decrease in the dispersion of velocities below the collisional equilibrium value, but for heavier particles the dispersion again begins to increase. The vertical component of the force which is produced by the self-gravitation of the ring reduces its thickness. The results of the simulations are in good agreement with the predictions of the collisional theory.     

Theoretical profile of Saturn's rings

Steady-state solutions for the optical thickness of Saturn's rings are studied in terms of Hämeen-Anttila's (1983) theory of bimodal gravitating systems. The elastic properties of particles determine the behaviour of the rarefied mode (gaps), while the dense mode (ringlets) depends on the size and the internal density of the particles. In the outer parts of the rings the dense mode is unstable against the growth of gravitational perturbations. Inside the Roche distance this produces only very narrow ring-shaped configurations with helical orbits around them, and the system is not destroyed. The outer boundary of the rings corresponds to the distance beyond which the gravitational instability transforms the dense mode into strictly local condensations (moons). The inner boundary of the ring system is caused by the absence of dense mode near Saturn. The rarefied mode is stable in a larger region.     

Expectations for Cassini observations of ring material with nearby moons

This paper describes N-body simulations of two regions of the saturnian ring system and examines what we might expect the Cassini orbiter to see in those areas. The first region is the edge of the Encke gap in the A ring that is perturbed by the satellite, Pan. Our previous simulations of this region neglected particle self-gravity [Lewis and Stewart, 2000a, Bull. Am. Astron. Soc. 34, 883]. Here we examine the interactions of the wakes caused by Pan with the wakes that form from local gravitational instabilities. We find that the two phenomena do not normally coexist and predict that measurements of particle sizes between the moon wakes should reflect the true particle size distribution of the region and not what is caused by gravitational aggregation. The region between the Encke gap edge and the first wake peak is an exception to this rule because our simulations exhibit the formation of exceptionally large gravity-induced wakes in this region. We also describe simulations of the F ring and explain the nature of braid-like structures that form naturally when the ring is perturbed by a single moon on an eccentric orbit. Finally, we discuss the very dynamic nature of the F ring system and how this should be taken into account when interpreting observations and even when planning future observations of this system.     

Mars geodesy, rotation and gravity

This review provides explanations of how geodesy, rotation and gravity can be addressed using radioscience data of an orbiter around a planet or of the lander on its surface.The planet Mars is the center of the discussion.The information one can get from orbitography and radioscience in general concerns the global static gravitational field, the time variation of the gravitational field induced by mass exchange between the atmosphere and the ice caps, the time variation of the gravitational field induced by...     

A new Wolf–Rayet star and its ring nebula: PCG 11

In a search for new Galactic planetary nebulae from our systematic scans of the Anglo-Australian Observatory/United Kingdom Schmidt Telescope (AAO/UKST) Hα Survey of the Southern Galactic Plane, we have identified a Population I Wolf–Rayet star of type WN7h associated with an unusual ring nebula that has a fractured rim. We present imagery in Hα, the 843-MHz continuum from the Molonglo Observatory Synthesis Telescope (MOST), the mid-infrared from the Midcourse Space Experiment ( MSX ), and confirmatory optical spectroscopy of the character of the nebula and of its central star. The inner edge of the Hα shell shows gravitational instabilities with a well-defined wavelength around its complete circumference.     

Analytical method for the effects of the asteroid belt on planetary orbits

Analytic expressions are derived for the perturbation of planetary orbits due to a thick constant density asteroid belt. The derivations include extensions and adaptations of Plakhov's analytic expressions for the perturbations in five of the orbital elements for closed orbits around Saturn's rings. The equations of Plakhov are modified to include the effect of ring thickness and additional equations are derived for the perturbations in the sixth orbital element, the mean anomaly. The gravitational potential and orbital perturbations are derived for the asteroid belt with and without thickness, and for a hoop approximation to the belt. The procedures are also applicable to Saturn's rings and the newly discovered rings of Uranus.The effects of the asteroid belt thickness on the gravitational potential coefficients and the orbital motions are demonstrated. Comparisons between the Mars orbital perturbations obtained using the analytic expressions and those obtained using numerical integration are discussed. The effects of the asteroid belt on the Earth based ranging to Mars are also demonstrated.     

The secular stability of a gravitating stellar ring

The problem of secular stability of a homogeneous and cold differentially rotating gravitating stellar ring in an external gravitational field is considered. For the analysis of stability we use the method of variation of the system energy in the frames of the local hydrodynamical approximation. We show that the considered stellar system is always characterized by secular instability for all non–zero values of the density. This conclusion is valid also in the case of solid–body rotation of the ring.     

Ring dynamics

In this paper I review the dynamical phenomena occurring in a planetary ring under the influence of the non-spherical gravitational potential in which the particles orbit, the self-gravity of the ring, the collisions between particles, and the perturbations by satellites.     

Formation and evolution of rings in disk-shaped protostellar clouds

Numerical simulation of the evolution of a disc-like system of protostellar clouds is made by means of N gravitating bodies. It is shown that the ring structure is physically present in the course of the gravitational collapse, that the ring structure represents only one stage of the cloud's evolution, and that it will eventually break up into new structures.     

Spiral structure and hydrodynamic gravitational resonance

A persistent and large scale galactic spiral structure might be the result of resonant excitation of density waves, forced in the low viscosity interstellar gas, by the gravitational field of an asymmetric stellar structure (galactic nucleus, condensation, companion galaxy, etc.) rotating like a rigid body around the galactic centre. This paper deals with this problem in the simple case of a homogeneous plane viscous medium of infinite extent, in a state of rigid body rotation. Numerical estimates are given in the case of density waves excited by the gravitational field of a central dumb-bell. They show that the mechanism of hydrodynamic gravitational resonance is worthy of a further, more realistic, treatment.     

A model for the formation of spokes in Saturn's ring

We suggest that spokes consist of charged micron-sized dust particles elevated from the rings by radially moving dense plasma columns created by meteor impacts on the ring. Dense plasma causes electrostatic wall-sheaths at the ring and charging of the ring with electric fields strong enough to overcome the gravitational force on small dust particles. Under “ordinary” conditions only very few dust particles will be elevated as the probability of a dust particle having at least one excess electronic charge is very low. Dense plasma raises this probability significantly. The radial motion of the plasma column is due to an azimuthal polarization electric field built up by the relative motion between the corotating plasma and the negatively charged dust particles which move with a Keplerian speed.     

The three-dimensional structure of Saturn’s E ring

Saturn’s diffuse E ring consists of many tiny (micron and sub-micron) grains of water ice distributed between the orbits of Mimas and Titan. Various gravitational and non-gravitational forces perturb these particles’ orbits, causing the ring’s local particle density to vary noticeably with distance from the planet, height above the ring-plane, hour angle and time. Using remote-sensing data obtained by the Cassini spacecraft in 2005 and 2006, we investigate the E-ring’s three-dimensional structure during a time when the Sun illuminated the rings from the south at high elevation angles (>15°). These observations show that the ring’s vertical thickness grows with distance from Enceladus’ orbit and its peak brightness density shifts from south to north of Saturn’s equator plane with increasing distance from the planet. These data also reveal a localized depletion in particle density near Saturn’s equatorial plane around Enceladus’ semi-major axis. Finally, variations are detected in the radial brightness profile and the vertical thickness of the ring as a function of longitude relative to the Sun. Possible physical mechanisms and processes that may be responsible for some of these structures include solar radiation pressure, variations in the ambient plasma, and electromagnetic perturbations associated with Saturn’s shadow.     

Application of the Gauss' Method to the Stellar Three Body Problem

In this paper, we deal with the stellar three body problem, that is one star is far away from the other two stars. The outer orbit is assumed to be Keplerian. To analyze the effect of the distant star on the orbit of the close stars, we use the Gauss method; this method consist in replacing the gravitational attraction of the third star by the gravitational attraction of an infinitesimal non-homogeneous elliptic ring. We obtain the force vector for the Gauss method in terms of elliptic integrals. Finally we compare the results obtained by this model with the classical third body model. This revised version was published online in August 2006 with corrections to the Cover Date.     

A small mass,large image separation gravitational lens model

It is shown that gravitational lensing could produce images of comparable brightness which are separated by an angular distance larger than the angular size of the Einstein ring of the lens distribution. Hence, specific lens configurations allow given image separations to be derived with significantly less mass than a standard single lens model. A specific example is supplied, a simple case of two properly positioned lenses acting instead of one. Observational consequences are discussed that would result if such a model was used to explain the candidate gravitational lens systems Hazard 1146+111 B, C and PKS 1145–071. Such a lens distribution might, in many cases, be verifiable with VLBI techniques.     

Precession of the orbital nodes of Jupiter and Saturn triggered by the mutual perturbation: A model of two rings

The problem of the precession of the orbital planes of Jupiter and Saturn under the influence of mutual gravitational perturbations was formulated and solved using a simple dynamical model. Using the Gauss method, the planetary orbits are modeled by material circular rings, intersecting along the diameter at a small angle α. The planet masses, semimajor axes and inclination angles of orbits correspond to the rings. What is new is that each ring has an angular momentum equal to the orbital angular momentum of the planet. Contrary to popular belief, it was proved that the orbital resonance 5: 2 does not preclude the use of the ring model. Moreover, the period of averaging of the disturbing force (T ≈ 1332 yr) proves to be appreciably greater than a conventionally used period (≈900 yr). The mutual potential energy of rings and the torque of gravitational forces between the rings were calculated. We compiled and solved the system of differential equations for the spatial motion of rings. It was established that a perturbing torque causes the precession and simultaneous rotation of the orbital planes of Jupiter and Saturn. Moreover, the opposite orbit nodes on the Laplace plane coincide and perform a secular movement in retrograde direction with the same velocity of 25.6″/yr and the period T _J = T _S ≈ 50687 yr. These results are close to those obtained in the general theory (25.93″/yr), which confirms the adequacy of the developed model. It was found that the vectors of the angular velocity of orbital rings move counterclockwise over circular cones and describe circles on the celestial sphere with radii β₁ ≈ 0.8403504° (Saturn) and β₂ ≈ 0.3409296° (Jupiter) around the point which is located at an angular distance of 1.647607° from the ecliptic pole.