Note on Inversion Formula to Determine Binary Elements by Astrometry

Simplified solutions to determine binary elements by astrometry were obtained in terms of elementary functions (Asada et al. 2004), and therefore require neither iterative nor numerical methods. In the framework of the simplified solution, this paper discusses the remaining two parameters of the time of periastron passage and the longitude of ascending node in order to complete the solution. We thus clarify a difference between the simplified solution and other analytical methods.Comment: 12 pages, 4 figures, 2 tables; accepted for publication in PAS

Observation of Gravitational Lensing in the Clumpy Universe

We discuss how inhomogeneities of the universe affect observations of the gravitational lensing; (1) the bending angle, (2) the lensing statistics and (3) the time delay. In order to take account of the inhomogeneities, the Dyer-Roeder distance is used, which includes a parameter representing the clumpiness of the matter along the line of sight. It is shown analytically that all three combinations of distances appearing in the above observations (1)-(3) are monotonic with respect to the clumpiness in general, for any given set of the density parameter, cosmological constant and redshifts of the lens and the source. Some implications of this result for the observation are presented; the clumpiness decreases both the bending angle and the lensing event rate, while it increases the time delay. We also discuss cosmological tests using the gravitational lensing in the clumpy universe.Comment: 12 pages, LaTeX(aaspp4); accepted for publication in The Astrophysical Journa

The Light-cone Effect on the Shapiro Time Delay

We investigate the light-cone effect on the Shapiro time delay. The extra time delay caused by Jupiter on the 8th of September 2002 can be measured by advanced VLBI (very long baseline interferometry). Our expression for the delay is in complete agreement with that of Kopeikin (2001), in which he argued that the excess time delay was due to the propagation of gravity. The present letter, however, shows that the excess comes from nothing but the propagation of light, namely the light-cone effect. To make a robust confirmation of general relativity by the coming Jupiter event, it is important to take account of the light-cone effect on the Shapiro time delay.Comment: 5 pages; accepted for publication in ApJ Letter

Deflection angle of light in an Ellis wormhole geometry

We reexamine the light deflection by an Ellis wormhole. The bending angle as a function of the ratio between the impact parameter and the throat radius of the wormhole is obtained in terms of a complete elliptic integral of the first kind. This result immediately yields asymptotic expressions in the weak field approximation. It is shown that an expression for the deflection angle derived (and used) in recent papers is valid at the leading order but it breaks down at the next order because of the nontrivial spacetime topology.Comment: 3 pages, accepted by PR