Kei Yamada

Triangular solution to the general relativistic three-body problem for general masses

Continuing work initiated in an earlier publication [Ichita, Yamada and Asada, Phys. Rev. D 83, 084026 (2011)], we reexamine the post-Newtonian effects on Lagranges 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.

Post-Newtonian effects of planetary gravity on the perihelion shift

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.

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 Eulers 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.

Post-Newtonian effects on the stability of the triangular solution in the three-body problem for general masses

Continuing work initiated in earlier publications [T. Ichita et al., Phys. Rev. D 83, 084026 (2011); K. Yamada and H. Asada, Phys. Rev. D 86, 124029 (2012)], we examine the post-Newtonian (PN) effects on the stability of the triangular solution in the relativistic three-body problem for general masses. For three finite masses, a condition for stability of the triangular solution is obtained at the first post-Newtonian (1PN) order, and it recovers previous results for the PN restricted three-body problem when one mass goes to zero. The stability regions still exist even at the 1PN order, though the PN triangular configuration for general masses is less stable than the PN restricted three-body case as well as the Newtonian one.

Possible daily and seasonal variations in quantum interference induced by Chern-Simons gravity

Possible effects of Chern-Simons (CS) gravity on a quantum interferometer turn out to be dependent on the latitude and direction of the interferometer on Earth in orbital motion around the Sun. Daily and seasonal variations in phase shifts are predicted with an estimate of the size of the effects, wherefore neutron interferometry with ~5 m arm length and ~10(-4) phase measurement accuracy would place a bound on a CS parameter comparable to the Gravity Probe B satellite.

Post-Newtonian effects on Lagrange's equilateral triangular solution for the three-body problem

Continuing work initiated in earlier publications [Yamada, Asada, Phys. Rev. D 82, 104019 (2010); ibid.83, 024040 (2011)], we investigate the post-Newtonian effects on Lagranges 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.

Moment Approach to Determining the Orbital Elements of an Astrometric Binary with a Low Signal-to-Noise Ratio

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.

Possible altitudinal, latitudinal, and directional dependence of the relativistic Sagnac effect in Chern-Simons modified gravity

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, Phys. Rev. Lett. 109, 231101 (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

Possible latitude effects of Chern-Simons gravity on quantum interference

m_{CS}

Improving the moment approach for astrometric binaries: possible application to Cygnus X-1

. Therefore, the international space station site as well as a ground-based experiment is also discussed.