Astrogeometry: Geometry Explains Shapes of Celestial Bodies 1. Our Main Idea: Astroshapes as Geometric Objects 1.1. Physical Background

Celestial bodies such as galaxies, stellar clusters, planetary systems, etc., have diierent geometric shapes (e.g., galaxies can be spiral or circular, etc.). Usually, complicated physical theories are used to explain these shapes; for example, several dozen diierent theories explain why many galaxies are of spiral shape; see, e. Some rare shapes are still unexplained. In the present paper, we show that to explain these \as-troshapes", we do not need to know the details of physical equations: practically all the shapes of celestial bodies can be explained by simple geometric invariance properties. This fact explains, e.g., why so many diierent physical theories lead to the same spiral galaxy shape. To nd out how shapes have been formed, let us start from the beginning of the Universe (for a detailed physical description, see,