On October 4, 1957, Homo sapiens crossed a new threshold of technological innovation after constructing an artifact capable of entering Low Earth Orbit and effectively paving the way for a future of space exploration. This artifact was Sputnik 1, launched by the Soviet space program which triggered the "space race" of the mid-20th century. Over the past 65 years, we have continued to explore and populate our solar system with rockets and spacecraft including satellites, probes, landers, and rovers. This expansion into our solar system has left traces of our presence on several planets including the Earth, Mars, Mercury, and Venus along with Earth's Moon, Titan, and several galaxy travelers in the form of asteroids and comets. Today, we have entered the realm of a new privatized and global space race, effectively a "new space race" or "new Space Age." As we expand our material footprint into new extraterrestrial environments, there is a growing need to understand the types of unique site formation processes capable of altering, destroying, or preserving this rapidly increasing archaeological record known as space heritage. Such understandings are germane to the subdiscipline of geoarchaeology, that part of archaeology dedicated to studying the interaction between humans, cultural heritage, and environmental systems from a geoscience perspective. Closely aligned and partially overlapping with the subdisciplines of space archaeology, archaeological science, and planetary geology, we introduce a new subfield we call planetary geoarchaeology to open discussion about how geoarchaeologists can play a role in addressing current and future issues surrounding the preservation and management of space heritage. To demonstrate the potential of the subdiscipline, we focus on the current archaeological record of the Moon, describe lunar site formation processes, and discuss the implications for the current and future preservation of space heritage in the lunar setting. Planetary geoarchaeology can be applied to practically every type of extraterrestrial environment, provided humans have left behind a measurable record. We hope this paper will spur more research studying human-environment interaction in space.