Surface of zero relative velocity in the gravitational field of a pair of interacting galaxies

1980 ◽  
Vol 67 (2) ◽  
pp. 503-510 ◽  
Author(s):  
P. V. Subrahmanyam
Keyword(s):  
Gravitational Field ◽  
Relative Velocity ◽  
Interacting Galaxies

scholarly journals Transient Annular Structures in Exploding Galaxies

1972 ◽  
Vol 44 ◽  
pp. 313-313
Author(s):  
J. L. Sěrsic
Keyword(s):  
Gravitational Field ◽  
Test Particle ◽  
Relative Velocity ◽  
Symmetry Axis ◽  
Equations Of Motion ◽  
Variable Mass ◽  
Physical Space ◽  
Space Time ◽  
High Mass ◽  
New Variables

The explosive events going on in the central parts of some galaxies are related to a very high mass concentration. As an explosion is actually a drastic rearrangement of the concerned masses with energy release, the binding energy of the central core will change and, correspondingly, its effective gravitational mass. A test particle far from the nuclear region, although within the galaxy, will be moving accordingly in a variable-mass Newtonian gravitational field.On the other hand the observations suggest that explosions in galaxies have axial symmetry, so we are concerned with the global properties of the motion of a particle in a variable mass axisymmetric gravitational field. In order to get rid of the mass variation a space-time conformal transformation is made, which, after imposing some not very restrictive conditions, leads to a conservative potential in the new variables. This new potential has additional terms due to the elimination of the variable mass. The equations of motion in the new variables provide the motion of the test particle relative to an expanding or contracting background which depends on the choice of the transformation and the law of the mass variability. The problem is, at this point, formally similar to Hill's. It is possible to write an equation for the relative energy (a generalization of Jacobi's integral) and also to define surfaces of zero relative velocity for the infinitesimal particle. The general topological properties of these surfaces require singular points along the symmetry axis (analogous to the collinear Eulerian points) and also a dense set in a circumference on a plane perpendicular to the symmetry axis (analogous to the Lagrangian points). The latter one is the main feature characterizing the topology of the zero relative velocity surfaces. Even when we lift some of the restrictive conditions, the Lagrangian ring preserves its properties, as for example, the one of being the only region where zero-velocity curves and equi-potentials coincide when the configuration evolves in time (in the transformed space-time).It is easy to understand that the topology of the surfaces is kept when we reverse the transformation and go back to physical space-time. If the dust, gas or stars in the system has definite upper limits for its Jacobian constants, spatial segregation of them will arise, as is the case in radio-galaxies such as NGC 5128, NGC 1316, etc. where ringlike dust structures are observed.

scholarly journals Gravitational Fields and Gravitational Waves

2021 ◽  
Author(s):  
Tony Yuan
Keyword(s):  
Gravitational Field ◽  
Gravitational Waves ◽  
Doppler Effect ◽  
Relative Velocity ◽  
Gravitational Force ◽  
Speed Of Light ◽  
Finite Velocity ◽  
Gravitational Fields ◽  
Light Waves ◽  
The Doppler Effect

Abstract For any object with finite velocity, the relative velocity between them will affect the effect between them. This effect can be called the chasing effect (general Doppler effect). LIGO discovered gravitational waves and measured the speed of gravitational waves equal to the speed of light c. Gravitational waves are generated due to the disturbance of the gravitational field, and the gravitational waves will affect the gravitational force on the object. We know that light waves have the Doppler effect, and gravitational waves also have this characteristic. The article studies the following questions around gravitational waves: What is the spatial distribution of gravitational waves? Can the speed of the gravitational wave represent the speed of the gravitational field (the speed of the action of the gravitational field on the object)? What is the speed of the gravitational field? Will gravitational waves caused by the revolution of the sun affect planetary precession?

scholarly journals Gravitational Fields and Gravitational Waves

2021 ◽  
Author(s):  
Tony Yuan
Keyword(s):  
Gravitational Field ◽  
Gravitational Waves ◽  
Doppler Effect ◽  
Relative Velocity ◽  
Gravitational Force ◽  
Gravitational Equation ◽  
Speed Of Light ◽  
Gravitational Fields ◽  
Light Waves ◽  
The Doppler Effect

Abstract For any object with finite velocity, the relative velocity between them will affect the effect between them. This effect can be called the chasing effect (general Doppler effect). LIGO discovered gravitational waves and measured the speed of gravitational waves equal to the speed of light c. Gravitational waves are generated due to the disturbance of the gravitational field, and the gravitational waves will affect the gravitational force on the object. We know that light waves have the Doppler effect, and gravitational waves also have this characteristic. The article studies the following questions around gravitational waves: What is the spatial distribution of gravitational waves? Can the speed of the gravitational wave represent the speed of the gravitational field (the speed of the action of the gravitational field on the object)? What is the speed of the gravitational field? Will gravitational waves caused by the revolution of the sun affect planetary precession? Can we modify Newton’s gravitational equation through the influence of gravitational waves?

scholarly journals Secular evolutionary trends in ellipticals and bulges due to mergers

1993 ◽  
Vol 153 ◽  
pp. 399-400
Author(s):  
Tapan K. Chatterjee
Keyword(s):  
Relative Velocity ◽  
Structural Changes ◽  
Gravitational Interaction ◽  
Orbital Evolution ◽  
Interacting Galaxies ◽  
Evolutionary Trends ◽  
Dynamical Friction ◽  
Initial Separation ◽  
Impulsive Approximation

Using basically the impulsive approximation and a modification of the method used by Alladin S.M., (1965, Ap.J.,141, 768), and described in detail in Chatterjee T.K., (1990, IAU Col.,124, 519, 569) we study the evolution of binary interacting galaxies, leading ultimately to mergers. Each collision is characterised by the initial separation between the galaxies and the relative velocity therein. In each case the orbital evolution and largescale structural changes in the galaxies are studied by taking into account the change in relative velocity due to dynamical friction, leading ultimately to mergers. The evolution is considered from a time when the gravitational interaction between the progenitor pairs is physically significant (Chatterjee, 1992, Astroph. Sp.Sc., in press).

A one-dimensional self-gravitating stellar gas

1966 ◽  
Vol 25 ◽  
pp. 46-48 ◽  
Author(s):  
M. Lecar
Keyword(s):  
Gravitational Field ◽  
Phase Space ◽  
Motion Picture ◽  
Space Distribution ◽  
Two Dimensional ◽  
One Dimensional ◽  
Phase Space Distribution ◽  
Dimensional Phase Space ◽  
The Mean

“Dynamical mixing”, i.e. relaxation of a stellar phase space distribution through interaction with the mean gravitational field, is numerically investigated for a one-dimensional self-gravitating stellar gas. Qualitative results are presented in the form of a motion picture of the flow of phase points (representing homogeneous slabs of stars) in two-dimensional phase space.

Evolution of collisional systems

1984 ◽  
Vol 75 ◽  
pp. 361-362
Author(s):  
André Brahic
Keyword(s):  
Gravitational Field ◽  
Dynamical Evolution ◽  
Oblate Planet

AbstractThe dynamical evolution of planetary discs in the gravitational field of an oblate planet and a satellite is numerically simulated.

Rapid Freezing of Freeze-Etch Specimens

1980 ◽  
Vol 38 ◽  
pp. 752-755
Author(s):  
A. Elgsaeter ◽  
T. Espevik ◽  
G. Kopstad
Keyword(s):  
Low Temperature ◽  
Metal Surface ◽  
Relative Velocity ◽  
Thermal Contact ◽  
High Rate ◽  
Rapid Freezing ◽  
Temperature Decrease ◽  
Freeze Etching

The importance of a high rate of temperature decrease (“rapid freezing”) when freezing specimens for freeze-etching has long been recognized1. The two basic methods for achieving rapid freezing are: 1) dropping the specimen onto a metal surface at low temperature, 2) bringing the specimen instantaneously into thermal contact with a liquid at low temperature and subsequently maintaining a high relative velocity between the liquid and the specimen. Over the last couple of years the first method has received strong renewed interest, particularily as the result of a series of important studies by Heuser and coworkers 2,3. In this paper we will compare these two freezing methods theoretically and experimentally.

Sedimentation of charged colloids in the gravitational field : Relaxation toward equilibrium

2000 ◽  
Vol 10 (PR5) ◽  
pp. Pr5-109-Pr5-112
Author(s):  
J.-F. Dufrêche ◽  
J.-P. Simonin ◽  
P. Turq
Keyword(s):  
Gravitational Field ◽  
Charged Colloids
Sign in / Sign up

Export Citation Format

Share Document