Collinear solution to the general relativistic three-body problem
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: 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: 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: Possible altitudinal, latitudinal, and directional dependence of the relativistic Sagnac effect in Chern-Simons modified gravity
abstract: Toward a test of parity violation in a gravity theory, possible effects of Chern-Simons (CS) gravity on an interferometer have been recently discussed. Continuing work initiated in an earlier publication [Okawara, Yamada and Asada,  (2012)], we study possible altitudinal and directional dependence of relativistic Sagnac effect in CS modified gravity. We compare the CS effects on Sagnac interferometers with the general relativistic Lense-Thirring (LT) effects. Numerical calculations show that the eastbound Sagnac interferometer might be preferred for testing CS separately, because LT effects on this interferometer cancel out. The size of the phase shift induced in the CS model might have an oscillatory dependence also on the altitude of the interferometer through the CS mass parameter $m_{CS}$. Therefore, the international space station site as well as a ground-based experiment is also discussed.

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: Post-Newtonian effects on Lagrange's equilateral triangular solution for the three-body problem
abstract: Continuing work initiated in earlier publications [Yamada, Asada,  104019 (2010); ibid.83, 024040 (2011)], we investigate the post-Newtonian effects on Lagrange's equilateral triangular solution for the three-body problem. For three finite masses, it is found that the equilateral triangular configuration satisfies the post-Newtonian equation of motion in general relativity, if and only if all three masses are equal. When a test mass is included, the equilateral configuration is possible for two cases: (1) one mass is finite and the other two are zero, or (2) two of the masses are finite and equal, and the third one is zero, namely, a symmetric binary with a test mass. The angular velocity of the post-Newtonian equilateral triangular configuration is always smaller than the Newtonian one, provided that the masses and the side length are the same.

title: Hybrids and gluonia in the covariant oscillator quark model with massive constituent gluons

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: Electromagnetic transitions of light-through-heavy mesons and the covariant oscillator quark model

title: Properties of the Ground-State q bar q Mesons and Possible Classification of Observed Mesons in the U~(12)_SF X O(3,1)_L Scheme
abstract: We examine possible assignments for known mesons to the predicted ground-state q bar q multiplets in the U~(12)_SF-classification scheme of hadrons, based on their observed properties. The masses of missing members of the ground-state multiplets are estimated, using a phenomenological mixing scheme for the normal- and extra-spin wave functions specific to this classification scheme. We also examine experimental candidates for the excited 1P, 1D and 2S multiplets in a framework of the U~(12)_SF X O(3,1)_L-classification scheme, based on the analysis of the ground-state masses. Then we see that the two exotic mesons pi_1(1400) and pi_1(1600) with J^PC=1^-+ have suitable masses to be assigned to the P-wave excitation and also there are a number of observed mesonic states which could be classified in terms of the U~(12)_SF X O(3,1)_L scheme.

title: Candidates for Chiral Particles
abstract: We find possible candidates for the new type of q bar q meson, mesonic chiralons, whose existence is predicted in the covariant level-classification scheme of hadrons with U(12)_SF * O(3,1)_L symmetry, by assigning all the known light-unflavored and strange mesons, with masses below about 1.8 GeV, to U(12)_SF * O(3,1)_L multiplets.