Goldberg grew up in financially straitened circumstances in an immigrant family in New York and New Bedford on. In 1930 he received a scholarship to Harvard University. First, he studied engineering, but then changed her soon under the influence of Donald Menzel to astronomy. In 1938 he received his doctorate in on line intensities in the spectrum of helium and thereafter remained first in Harvard. In 1941 he went to the well-known for solar observation McMath - Hulbert Observatory, where he worked during the war in a project for submarine combat. In 1946 he began as head of the Department of Astronomy and Observatory Director at the University of Michigan a successful career in management positions in astronomy.
Starting with the cooperation with Menzel Goldberg dealt with atomic physics, the calculation of line strengths and their application for the determination of elemental abundances from spectra of the sun in the visible and near infrared. In the late 1950s he recognized the potential of space observatories for the solar observation and began experiments to image the sun and its corona prepare in high spectral lines of ionized elements. After overcoming many difficulties, the satellite IV and VI of the Orbiting Solar Observatory series and solar observations from Skylab made great achievements were.
Goldberg's excellent organizational skills earned him leading positions in science management. He was director of the observatories of the University of Michigan (1946-1960) and Harvard University (1960-1971) and the Kitt Peak National Observatory (1971-1977) and on the foundation of the Kitt Peak National Observatory and the National Radio Astronomy Observatory involved. From 1964 to 1966 he was president of the American Astronomical Society and 1971-1976 President of the International Astronomical Union.