What is the art and science of determining one's geographic position through astronomical observations called?

The term that accurately describes the art and science of determining one's geographic position through astronomical observations is commonly known as Celestial Navigation. This practice relies on the position of celestial bodies such as stars, planets, the sun, and the moon as referenced against established coordinate systems to determine an observer's latitude and longitude, especially at sea.

While alternative terms like Astrogation or Geospatial Navigation exist, they do not specifically denote the traditional methods associated with celestial navigation techniques. Astrogation is often related to navigation by using celestial bodies but is less frequently used and not as widely recognized as Celestial Navigation. Geospatial Navigation can refer broadly to navigation techniques that incorporate various data sources, including satellite systems, but again does not focus on astronomical methods in the same historical context.

Thus, Celestial Navigation is the most accurate and recognized term for this specific modality of navigation.