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We describe plans for several science programs in crowded fields using the faint object spectrograph (FOS) which rely critically on the enhanced angular resolution provided by the COSTAR corrective optics. Based on ground-based calibration of the COSTAR and on-orbit performance of the FOS, the anticipated performance of the COSTAR+/FOS should allow many important scientific studies to be completed which have had to be postponed due to the spherical aberration in the HST primary mirror. Particularly impacted by spherical aberration, and thus able to benefit most dramatically from the installation of COSTAR, are spectroscopic observations with FOS in crowded fields. Many of the most important science goals for the FOS instrument involve observations of crowded fields, for which the restored high- angular resolution of HST is essential - not only to isolate features of small angular extent, but also to eliminate optical contamination from the surrounding luminous regions. Spectroscopy of the nuclei of galaxies to obtain rotation curves and velocity dispersions which might reveal the presence of central black holes benefits dramatically from the enhanced angular resolution of HST as restored by COSTAR. We present models based on our current understanding of the dynamics of galaxy nuclei to illustrate the dramatic improvement in sensitivity in searching for black holes made possible by restoring HST's image quality. Two other categories of scientific investigations in crowded fields which will benefit greatly from restoring HST's image quality are spectroscopy of the luminous material (presumably distant galaxies) surrounding quasistellar objects, and spectroscopy of individual stars in globular clusters. The promise of finally being able to carry out these exciting scientific programs with the FOS on the restored HST explains why our team of scientists, along with many other astronomers, look forward to using the restored HST to carry out the scientific investigations for which it was originally intended.
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