Orbits and Relative Motion in the Gravitational Field of an Oblate Body

2008 ◽  
Vol 31 (3) ◽  
pp. 522-532 ◽  
Author(s):  
Mayer Humi ◽  
Thomas Carter
Keyword(s):  
Gravitational Field ◽  
Relative Motion ◽  
Oblate Body

scholarly journals The Split Comets: Gravitational Interaction Between the Fragments

1979 ◽  
Vol 81 ◽  
pp. 311-314
Author(s):  
Z. Sekanina
Keyword(s):  
Gravitational Field ◽  
Computer Program ◽  
Numerical Integration ◽  
Relative Motion ◽  
Gravitational Interaction ◽  
Parent Nucleus ◽  
The Other ◽  
Comet Nucleus

The n-body computer program by Schubart and Stumpff (1966) has been slightly modified to study the gravitational interaction between two fragments of a split comet nucleus in the sun's gravitational field. All calculations refer to the orbit of Comet West (1976 VI), the velocity of separation of the fragments is assumed to be equal in magnitude to the velocity of escape from the parent nucleus, and the numerical integration of the relative motion of one fragment (called the companion) with respect to the other (principal fragment) is carried over the period of 200 days from separation.

scholarly journals A scalar geodesic deviation equation and a phase theorem

1983 ◽  
Vol 6 (4) ◽  
pp. 795-802 ◽  
Author(s):  
P. Choudhury ◽  
P. Dolan ◽  
N. S. Swaminarayan
Keyword(s):  
Gravitational Field ◽  
Phase Shift ◽  
Relative Motion ◽  
Plane Waves ◽  
Relative Energy ◽  
Positive Definite ◽  
Geodesic Deviation ◽  
Deviation Equation ◽  
Test Particles ◽  
Geodesic Deviation Equation

A scalar equation is derived forη, the distance between two structureless test particles falling freely in a gravitational field:η¨+(K−Ω2)η=0. An amplitude, frequency and a phase are defined for the relative motion. The phases are classed as elliptic, hyperbolic and parabolic according asK−Ω2>0,<0,=0.In elliptic phases we deduce a positive definite relative energyEand a phase-shift theorem. The relevance of the phase-shift theorem to gravitational plane waves is discussed.

scholarly journals Figures of Pluto and Charon and their relative motion

2021 ◽  
Vol 8 (3) ◽  
pp. 533-546
Author(s):  
Konstantin V. Kholshevnikov ◽  
◽  
Denis V. Mikryukov ◽  
Mohammad S. Jazmati ◽  
◽  
...  
Keyword(s):  
Gravitational Field ◽  
Gravitational Potential ◽  
Relative Motion ◽  
Tidal Effect ◽  
The Body ◽  
Surface Shape ◽  
The Sun ◽  
Comparative Effect ◽  
Translatory Motion ◽  
Two Factors

The comparative effect of two factors on the translatory motion of the centres of mass of the Pluto-Charon system is investigated. The first important factor is the non-sphericity of the shape and gravitational field of the bodies in the system. The second is the gravitation of the Sun. As a measure of the influence of both factors we use the ratio of the corresponding perturbing acceleration to the main one. The main acceleration is caused by the mutual Newtonian attraction of Pluto and Charon. It has been established that for the first factor this measure is of the order of 10^−6, while for the second factor it is two orders of magnitude smaller. This explains why the Lidov-Kozai effect (despite a large mutual slope of 96 between the planes of the satellite’s orbit around the planet, and the barycentre of the system around the Sun) does not appear. The situation is similar to the case with the satellites of Uranus. As a result, the Pluto-Charon system remains stable at least on a timescale of millions of years. The tidal effect of the Sun on the surface shape of the bodies under study is also estimated. The ratio of the tidal potential of the Sun at a point on the surface of the body to the gravitational potential of the body itself at this point is taken as a measure of impact. It turned out to be of the order of 3 · 10^−12, which is more than six orders less than the influence of rotation and mutual attraction of Pluto and Charon. In fact, the Sun does not affect the figures of the bodies of the system.

scholarly journals Note on the harmonic oscillator in general relativity

1961 ◽  
Vol 2 (2) ◽  
pp. 206-208 ◽  
Author(s):  
N. W. Taylor
Keyword(s):  
General Relativity ◽  
Gravitational Field ◽  
Harmonic Oscillator ◽  
Relative Motion ◽  
Interior Solution ◽  
Theory Of Relativity ◽  
Harmonic Motion ◽  
Static Gravitational Field ◽  
The Times ◽  
Gravitational Equations

The theory of relativity shows that the times measured by two observers will in general be different if they are in relative motion, so that their respective times between any two coincidences will differ. Bergmann [1] has investigated the problem of a particle moving in a small simple harmonic motion in a static gravitational field, and has found that the time difference for this particle and an observer at rest becomes zero whenever the particle passes through the centre and limits of its swing. This problem will now be dealt with in a different manner, using Schwarzschild's interior solution of the gravitational equations. The exterior solution for a point mass is not suitable in the present case, due to the singularity of the field at a point in the path of the particle.

Detection of relative motion in a gravitational field

1979 ◽  
Vol 72 (2) ◽  
pp. 69-70
Author(s):  
F.I. Cooperstock ◽  
D.W. Hobill
Keyword(s):  
Gravitational Field ◽  
Relative Motion

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.

The restoration of blurred electron micrographs

1986 ◽  
Vol 44 ◽  
pp. 180-181
Author(s):  
Bridget Carragher ◽  
David A. Bluemke ◽  
Michael J. Potel ◽  
Robert Josephs
Keyword(s):  
Cross Section ◽  
Electron Micrographs ◽  
Relative Motion ◽  
Finite Thickness ◽  
Image Plane ◽  
Helical Axis ◽  
Thin Sections ◽  
Structural Details

We have investigated the feasibility of restoring blurred electron micrographs. Two related problems have been considered; the restoration of images blurred as a result of relative motion between the specimen and the image plane, and the restoration of images which are rotationally blurred about an axis. Micrographs taken while the specimen is drifting result in images which are blurred in the direction of motion. An example of rotational blurring arises in micrographs of thin sections of helical particles viewed in cross section. The twist of the particle within the finite thickness of the section causes the image to appear rotationally blurred about the helical axis. As a result, structural details, particularly at large distances from the helical axis, will be obscured.

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