The reason moons are typically not defined by their orbit around the center of mass of both bodies in a binary or “double planet” system hinges on the gravitational dynamics and the traditional criteria used to classify celestial bodies. In a two-body system like a planet and its moon, both bodies actually do orbit around a common center of mass, known as the barycenter. However, the barycenter is often located inside the larger body due to its significantly greater mass.
When differentiating between a planet and a moon, the key factor is usually the nature of their mutual gravitational influence. A moon is typically considered a natural satellite that orbits a more massive body—usually a planet. In contrast, the concept of a “double planet” generally refers to a pair of celestial bodies of similar mass where the barycenter is located outside either body.
Redefining moons to include any celestial object orbiting the mutual center of mass of two closely interacting bodies would blur the distinctions currently used in celestial mechanics and planetary classification. Current definitions also serve practical observational and educational purposes by maintaining simpler and clearer classifications for objects observed within our solar system and beyond. This helps astronomers and educators maintain a consistent framework to describe various kinds of celestial relationships and behaviors.