scholarly journals Relativistic Reduction of Astrometric Observations

1986 ◽  
Vol 109 ◽  
pp. 19-42 ◽  
Author(s):  
V. A. Brumberg
Keyword(s):  
Body Problem ◽  
Equations Of Motion ◽  
Satellite Observations ◽  
List Type ◽  
Type Number ◽  
General Technique ◽  
Two Body Problem ◽  
The One ◽  
Relative Measurements ◽  
Relativistic Reduction

The nonuniqueness of the quasi-Galilean coordinates of general relativity leads to the emergence of unmeasurable coordinate-dependent quantities in astronomical practice. One may offer three possible ways to overcome the related difficulties: 1.developing theoretical conclusions only in terms of measurable quantities2.using arbitrary coordinates and developing an unambiguous procedure for comparing measurable and calculated quantities3.agreement to utilize one and only one coordinate system.In this paper we prefer the second way. After formulating the heliocentric planetary and geocentric satellite equations of motion, the general technique for relativistic reduction in astrometry and geodynamics is developed. Specific algorithms for the reduction of absolute and relative measurements are derived for the one- and the two- body problem. For illustration, the relativistic reduction of stellar parallaxes, Doppler satellite observations, navigation measurements with the aid of satellites and radiointerferometric measurements are presented in detail.

scholarly journals RADIATIVE DAMPING AND FUNCTIONAL DIFFERENTIAL EQUATIONS

2011 ◽  
Vol 26 (35) ◽  
pp. 2627-2638 ◽  
Author(s):  
SUVRAT RAJU ◽  
C. K. RAJU
Keyword(s):  
Differential Equations ◽  
Body Problem ◽  
Equations Of Motion ◽  
Functional Differential Equations ◽  
General Technique ◽  
Covariant Model ◽  
Maxwell Electrodynamics ◽  
Functional Differential ◽  
The One ◽  
Radiative Damping

We propose a general technique to solve the classical many-body problem with radiative damping. We modify the short-distance structure of Maxwell electrodynamics. This allows us to avoid runaway solutions as if we had a covariant model of extended particles. The resulting equations of motion are functional differential equations (FDEs) rather than ordinary differential equations (ODEs). Using recently developed numerical techniques for stiff, retarded FDEs, we solve these equations for the one-body central force problem with radiative damping. Our results indicate that locally the magnitude of radiation damping may be well approximated by the standard third-order expression but the global properties of our solutions are dramatically different. We comment on the two-body problem and applications to quantum field theory and quantum mechanics.

The post-Newtonian approximation

2018 ◽  
Author(s):  
Nathalie Deruelle ◽  
Jean-Philippe Uzan
Keyword(s):  
General Relativity ◽  
Gravitational Field ◽  
Body Problem ◽  
Equations Of Motion ◽  
Two Body Problem ◽  
Newtonian Approximation ◽  
Actual Motion ◽  
Law Of Attraction ◽  
Universal Law ◽  
Two Bodies

This chapter embarks on a study of the two-body problem in general relativity. In other words, it seeks to describe the motion of two compact, self-gravitating bodies which are far-separated and moving slowly. It limits the discussion to corrections proportional to v2 ~ m/R, the so-called post-Newtonian or 1PN corrections to Newton’s universal law of attraction. The chapter first examines the gravitational field, that is, the metric, created by the two bodies. It then derives the equations of motion, and finally the actual motion, that is, the post-Keplerian trajectories, which generalize the post-Keplerian geodesics obtained earlier in the chapter.

The two-body problem: an effective-one-body approach

2018 ◽  
Author(s):  
Nathalie Deruelle ◽  
Jean-Philippe Uzan
Keyword(s):  
Body Problem ◽  
Equations Of Motion ◽  
Reaction Force ◽  
Kerr Black Hole ◽  
Radiation Reaction ◽  
Spherically Symmetric ◽  
Geodesic Motion ◽  
Two Body Problem ◽  
Symmetric Spacetime ◽  
Radiation Reaction Force

This chapter presents the basics of the ‘effective-one-body’ approach to the two-body problem in general relativity. It also shows that the 2PN equations of motion can be mapped. This can be done by means of an appropriate canonical transformation, to a geodesic motion in a static, spherically symmetric spacetime, thus considerably simplifying the dynamics. Then, including the 2.5PN radiation reaction force in the (resummed) equations of motion, this chapter provides the waveform during the inspiral, merger, and ringdown phases of the coalescence of two non-spinning black holes into a final Kerr black hole. The chapter also comments on the current developments of this approach, which is instrumental in building the libraries of waveform templates that are needed to analyze the data collected by the current gravitational wave detectors.

scholarly journals 40. Investigation of minor meteor streams

1968 ◽  
Vol 33 ◽  
pp. 408-427 ◽  
Author(s):  
A. K. Terenteva
Keyword(s):  
Numerical Integration ◽  
Electronic Computer ◽  
Equations Of Motion ◽  
Time Interval ◽  
List Type ◽  
Type Number ◽  
Meteor Streams ◽  
Long Period ◽  
The Earth ◽  
Meteor Body

The paper consists of three sections: (1)In continuation of a previous paper by the author, on 154 minor meteor streams, elements of orbits and other data are presented for an additional 95 minor streams (most of them less active). These streams have been found both by the studies of the photographic orbits of meteor bodies known before, and from the visual radiants of faint showers.(2)The problems of a possible family of six minor meteor streams associated with the Lexell comet 1770-I, and the connection between nine other minor streams and long-period comets, are examined. The assumption is made that nearly-parabolic comets may be accompanied by meteor streams of considerable width.(3)Radiants and elements of the orbits for 30 meteor bodies of the Cyclids are described, as were established by photographic data. Perturbed motion of one such meteor body is investigated by numerical integration of differential equations of motion on the electronic computer BESM-2, using Cowell's method of quadratures and taking account of perturbations from six planets (Venus–Uranus) and of high-order terms through to the 4th order. Over the time interval studied of 45 years the orbit of the Cyclids has been stable. Perturbing action of the Earth does not lead to any substantial changes in the elements of the orbits. Even at close approaches of the order of 0–003 AU the changes in the angular elements are not greater than about 1°.

scholarly journals Dust-Embedded AGN in Unusually Warm IRAS Galaxies

1989 ◽  
Vol 134 ◽  
pp. 406-407
Author(s):  
J. P. Vader ◽  
J. A. Frogel ◽  
F. C. Gillett ◽  
M. H. K. de Grijp
Keyword(s):  
Radio Galaxies ◽  
Radio Sources ◽  
List Type ◽  
Broad Line ◽  
Type Number ◽  
Early Type ◽  
Energy Distributions ◽  
Near Ir ◽  
Line Region ◽  
The One

The IRAS Point Source Catalog contains only 61 sources identified as galaxies whose energy distribution peaks at 60 mμ. The scarcity of such galaxies has prompted a search for possible common properties. This sample of ‘60 mμ peakers’, 21 of which are previously identified galaxies, partially overlaps with that of warm IRAS galaxies studied by de Grijp et al. (1987) and contains similar percentages of Seyfert (65%) and starburst galaxies on the one hand, and of strong and weak radio sources on the other hand. A remarkable characteristic is, however, that about half of the 60 mμ peakers seem to be early-type galaxies. The fact that such galaxies are rarely IRAS sources and, if so, have FIR energy distributions peaking at 100 mμ similar to those of spirals, implies that we are sampling active or nuclear starburst early-type galaxies with a very large success rate. The observational data accumulated so far further show that: (i)objects with smaller FIR to near-IR flux ratios have redder J-K colors and warmer 60 to 25 mμ colors, i.e., an infared spectrum dominated by warmer dust and/or a nonthermal source (Figs. 1a,b);(ii)out of 32 objects with radio data, the 5 compact radio sources with luminosities intermediate between those af radio-quiet and radio-loud AGN have among the warmest 60 to 25 mμ colors (Fig. 2). Such warm FIR colors are not a common characteristic of radio galaxies and quasars (Golombek et al. 1987, Neugebauer et al. 1986).(iii)the 60 mμ luminosities range from 109 to 1012 L0, and are largest for Mkn 231, 2306+0505 (Hill et al. 1987) and 2046+1925 (Frogel et al. 1988). The latter 2 objects, along with 0052-7054 (Frogel and Elias 1987) which also belongs to our sample, are Seyfert 2 galaxies with evidence for the presence of a dust-obsured broad line region.

On infinite server queues with batch arrivals

1966 ◽  
Vol 3 (01) ◽  
pp. 274-279 ◽  
Author(s):  
D. N. Shanbhag
Keyword(s):  
Queueing System ◽  
Batch Size ◽  
List Type ◽  
Type Number ◽  
Batch Arrivals ◽  
Batch Sizes ◽  
Infinite Server Queues ◽  
Service Times ◽  
The One ◽  
Independent And Identically Distributed

The queueing system studied in this paper is the one in which (i) there are an infinite number of servers, (ii) initially (at t = 0) all the servers are idle, (iii) one server serves only one customer at a time and the service times are independent and identically distributed with distribution function B(t) (t > 0) and mean β(< ∞), (iv) the arrivals are in batches such that a batch arrives during (t, t + δt) with probability λ(t)δt + o(δt) (λ(t) > 0) and no arrival takes place during (t, t + δt) with the probability 1 –λ(t)δt + o(δt), (v) the batch sizes are independent and identically distributed with mean α(< ∞), and the probability that a batch size equals r is given by a r(r ≧ 1), (vi) the batch sizes, the service times and the arrivals are independent.

Fragments, ellipsis, and PF-repair: New evidence from Indonesian

2013 ◽  
Vol 58 (3) ◽  
pp. 497-505
Author(s):  
Yosuke Sato
Keyword(s):  
List Type ◽  
Type Number ◽  
The One ◽  
New Evidence

Merchant (2004) proposes that a fragmentary response like the one in (1b) to the question in (1a) is derived from its full-fledged sentential counterpart in (1c).(1) a.Who did she see?b.[DP John]c.[TPShe saw John] (Merchant 2004:673)

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