Uniqueness of collinear solutions for the relativistic three-body problem
Continuing work initiated in an earlier publication [Yamada, Asada,  104019 (2010)], we investigate collinear solutions to the general relativistic three-body problem. We prove the uniqueness of the configuration for given system parameters (the masses and the end-to-end length). First, we show that the equation determining the distance ratio among the three masses, which has been obtained as a seventh-order polynomial in the previous paper, has at most three positive roots, which apparently provide three cases of the distance ratio. It is found, however, that, even for such cases, there exists one physically reasonable root and only one, because the remaining two positive roots do not satisfy the slow-motion assumption in the post-Newtonian approximation and are thus discarded. This means that, especially for the restricted three-body problem, exactly three positions of a third body are true even at the post-Newtonian order. They are relativistic counterparts of the Newtonian Lagrange points L{sub 1}, L{sub 2}, and L{sub 3}. We show also that, for the same masses and full length, the angular velocity of the post-Newtonian collinear configuration is smaller than that for the Newtonian case. Provided that the masses and angular rate are fixed, the relativistic end-to-end lengthmore » is shorter than the Newtonian one.« less

title: Moment Approach to Determining the Orbital Elements of an Astrometric Binary with a Low Signal-to-Noise Ratio
abstract: A moment approach to the orbit determination of an astrometric binary with a low signal-to-noise ratio from astrometric observations alone is proposed, especially aiming at a close binary system with a short orbital period, such as Cyg X-1, and also at a star wobbled by planets. As an exact solution to the nonlinearly coupled equation, the orbital elements are written in terms of the second and third moments of projected positions that are measured by astrometry. This may hold the possibility of the true orbit estimate.

title: Collinear solution to the general relativistic three-body problem
abstract: The three-body problem is reexamined in the framework of general relativity. The Newtonian three-body problem admits Euler's collinear solution, where three bodies move around the common center of mass with the same orbital period and always line up. The solution is unstable. Hence, it is unlikely that such a simple configuration would exist owing to general relativistic forces dependent not only on the masses but also on the velocity of each body. However, we show that the collinear solution remains true with a correction to the spatial separation between masses. Relativistic corrections to the Sun-Jupiter Lagrange points L{sub 1}, L{sub 2}, and L{sub 3} are also evaluated.

title: Post-Newtonian effects of planetary gravity on the perihelion shift
abstract: We consider a coplanar system comprising of a massive central body (a star), a less massive secondary (a planet) on a circular orbit, and a test particle on a bound orbit exterior to that of the secondary. The gravitational pull exerted on the test particle by the secondary acts as a small perturbation, wherefore the trajectory of the particle can be described as an ellipse of a precessing perihelion. While the apsidal motion is defined overwhelmingly by the Newtonian portion of the secondary’s gravity, the post-Newtonian portion, too, brings its tiny input. We explore whether this input may be of any astrophysical relevance in the next few decades. We demonstrate that the overall post-Newtonian input of the secondary’s gravity can be split into two parts. One can be expressed via the orbital angular momentum of the secondary and another via its orbital radius. Despite some moderately large numerical factors showing up in the expressions for these two parts, the resulting post-Newtonian contributions from the secondary’s gravity into the apsidal motion of the test particle turn out to be small enough to be neglected in the near-future measurements.

title: Triangular solution to the general relativistic three-body problem for general masses
abstract: Continuing work initiated in an earlier publication [Ichita, Yamada and Asada,  (2011)], we reexamine the post-Newtonian effects on Lagrange's equilateral triangular solution for the three-body problem. For three finite masses, it is found that a triangular configuration satisfies the post-Newtonian equation of motion in general relativity, if and only if it has the relativistic corrections to each side length. This post-Newtonian configuration for three finite masses is not always equilateral and it recovers previous results for the restricted three-body problem when one mass goes to zero. For the same masses and angular velocity, the post-Newtonian triangular configuration is always smaller than the Newtonian one.

title: Three-body-interaction effects on the relativistic perihelion precession for the Sun-Jupiter-Saturn system
abstract: The relativistic perihelion precession due to the three-body interaction is derived. We consider a hierarchical coplanar three-body system, such as the Sun, Jupiter and Saturn, in which both the secondary object as the largest planet corresponding to Jupiter (mass $m_2$) and the third one corresponding to Saturn (mass $m_3$) orbit around the primary object corresponding to Sun (mass $m_1 \gg m_2 \gg m_3$), where the mean orbital radius of the third body is larger than that of the secondary one (denoted as $\ell$). We investigate the post-Newtonian effects on the motion of the third body (semimajor axis a, eccentricity e for the Keplerian orbital elements). Under some assumptions with a certain averaging, the relativistic perihelion precession of the third mass by the post-Newtonian three-body interaction is expressed as $6 G m_2 \ell^2 c^{-2} a^{-3} n (1+9e^2/16) (1-e^2)^{-3} $, where G and c denote the gravitational constant and the speed of light, respectively, and the mean motion for the third body is denoted as $n = 2\pi a^{3/2} G^{-1/2} (m_1+m_2)^{-1/2}$. For the Sun-Jupiter-Saturn system, it is $7.8 \times 10^{-6}$ arcsec/cy. This is larger than the Lense-Thirring effect by Sun but it cannot yet explain the recently reported value for the anomalous perihelion precession of Saturn as $-0.006 \pm 0.002$ arcsec/cy by Iorio (2009) based on the analyses by Pitjeva with the EPM2008 ephemerides.

title: Radiative Decays of Ground-State Mesons in the Covariant Quark Model

title: Possible Evidence for a Chiral Axial‐Vector State in the D Meson System
abstract: We reanalyze the D⋅+π− mass spectrum from CLEO II by the VMW method in order to examine the existence of a chiral axial‐vector state, which is predicted in a covariant level‐classification scheme recently proposed, other than normal orbitally‐excited P‐wave states in the D meson system. A result of the present analysis seems to suggest that there exists an extra axial‐vector meson, in addition to the two normal ones, in a similar mass region.

title: Light-quark meson spectrum in the covariant oscillator quark model with one-gluon-exchange effects
abstract: The covariant oscillator quark model, which was extended recently to include one-gluon-exchange effects, is applied to investigate the mass spectrum of light-quark mesons. In the meson rest frame our effective potential due to one-gluon exchange is given as the sum of a Coulomb-type, orbit-orbit-like, spin-orbit, and hyperfine interaction, and has similar general features as in the standard nonrelativistic quark model. However, there are essential differences between them. First, our scheme is manifestly covariant and the potential is concerned with the squared masses of hadrons. Second, our effective one-gluon-exchange potential is greatly modified due to the covariant nature and the retardation effect. Owing to these modifications our model reproduces quite well the experimental behavior of the spectra of radially excited states as well as orbitally excited states.

title: Radiative decays of charmed mesons in the covariant oscillator quark model
abstract: We report on a study of the radiative decays for the ground S -wave and the excited P -wave charmed ( c u ¯ , c d ¯ ) mesons applying the covariant oscillator quark model. The obtained results are compared with experimental data including a recently reported D 1 ( 2420 ) 0 → D 0 γ , and other quark-model predictions. These predictions could provide a useful clue as to search for the radiative decays of excited D mesons in the foreseeable future experiments at the B-factories.

title: Possible evidence for a chiral particle D1**chi, axial vector in the D meson system
abstract: In the covariant level-classification scheme of hadrons proposed recently, the existence of "chiral particles", scalar and axial-vector mesons as the partners of the ground-state pseudo-scalar and vector mesons, respectively, were predicted in the D and B meson systems, realizing a linear representation of chiral symmetry. In this work we reanalyze the D* pi mass spectra obtained through the Upsilon (4S) and Z0 decays to show a possibility for the D_1chi.