WEIGHING STARS WITH GENERAL RELATIVITY
Session 24 -- Star Clusters/General Relativity
Oral presentation, Wednesday, January 12, 10:15-11:45, Salon V Room (Crystal Gateway)

## [24.04] WEIGHING STARS WITH GENERAL RELATIVITY

Irwin Shapiro (CfA), Steven Shapiro (MIT), Marc Gorenstein (Millipore Corp.)

The deflection of light by mass offers the possibility to apply this general relativity effect to the weighing of stars and smaller objects. This effect changes the apparent position of a distant, background star (B) when a relatively nearby, foreground object (F) passes by on the sky. The effect of F's motion is to cause the position of B to appear to move in a circle of radius $r=(2GM/{c^2} \theta D)$ if B has negligible proper motion. The center (C) of the circle is a distance r from the true position of B on the extension of the line from F to B at the epoch of closest approach on the sky of F to B. This apparent position has a time dependence given by $\phi(t)=2\arctan(vt/\theta D)$, where $\phi$ is measured from the line from C to the apparent position of B at this epoch ($t\equiv 0$). Aside from the usual constants of nature, $\theta$ represents the impact parameter, M the mass of F, D its distance from us, and v its velocity on the sky. For values of $\theta=1$ arcsec, $M=1$ solar mass, $D=10$ pc, and $\it{v}$=100 kms$^{-1}$, we find $\it{r}= 0.4 mas$, with $\phi$ moving about 180\deg during an interval of under one year surrounding the epoch of closest approach. We will discuss the opportunities for utilizing this technique that will result from an optical interferometer in space, as well as discuss the effects of systems with more than one star. These discussions will be in the context of a parametric analysis of the accuracy with which M can be estimated from astrometric observations of such foreground and background objects.