Astrometry for Determining the MACHO Mass and Trajectory

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Abstract

We show that a combination of the photometric and astrometric observations of gravitational microlensing enables us to determine the mass and trajectory of the invisible MACHO. The measurement of separation of two images during the event determines the proper motion and the trigonometric parallax of the source and lens, which constitute two basic parameters for the problem at issue. Furthermore, including the effect of the annual parallax to be observed by the terrestrial observer, we find a better fit of the present model to the recent photometric observations, especially those near to the peak (Alcock et al., Nature, 365, 621 1993), and thereby can trace explicitly the trajectories of the MACHO and source images on the celestial sphere.

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