Starting in the 1960s, astronomers’ view of the sky shifted from an analog perspective in which data was recorded using photographic plates and strip charts to one wholly mediated by digital technologies. By the early 1980s, astronomers expressed growing concern about having to deal with a deluge of data that was increasingly “born digital.” Data management became one of the modern astronomers’ necessary tasks as astronomy itself transformed into a particular form of “information science.” This transition presaged today’s debates about Big Data and the archiving of massive data sets in astronomy and other sciences which researchers mine. This paper explore two episodes in this historical process using astronomy as an example. Both center around scientists’ wish to share data and data processing tools with their colleagues. The first episode concerns the emergence of the Flexible Image Transport System or FITS. This is a common data format developed by scientists at national observatories in the U.S. and the Netherlands and accepted as an international standard in 1982. The second example is STARLINK, a sophisticated computer network for sharing and manipulating digital astronomical images that debuted in the United Kingdom in 1980. In both cases, astronomers’ desire to share digital data speaks to broader changes in researchers’ moral economy as the availability of new technologies challenged traditional norms and encouraged the formation of common formats, standards, and tools.