After working at his family furniture store for eleven years, he followed his brother (astronomer Samuel J. Goldstein, Jr.) to California and NASA's Jet Propulsion Laboratory.
As a graduate student at Caltech in 1961, Goldstein used the antenna at the Goldstone Tracking Station to obtain the first realtime radar echos from the planet Venus.
[7] In 1964, Goldstein had analyzed the spectrum of radar echos from Venus to obtain the first images of features on the surface of that planet.
[11] Goldstein began work in the mid-1980s on topographical mapping techniques using synthetic aperture radar.
[13][14] This algorithm simplified the creation of accurate elevation maps,[15] and made possible many new applications for radar interferometry, including satellite detection[16] and quantification of small changes such as land subsidence,[17] ice flow motion,[18] ocean currents,[19] and geological fault shifts.
[22] In the process, he discovered that the Earth has rings of debris (some apparently left over from the West Ford Project).