Mathematics A three-dimensional surface, all points of which are equidistant from a fixed point. A spherical object or figure. A celestial body, such as a planet or star. The sky, appearing as a hemisphere to an observer: the sphere of the heavens. Any of a series of concentric, transparent, revolving globes that together were once thought to contain the moon, sun, planets, and stars. The extent of a person's knowledge, interests, or social position. An area of power, control, or influence; domain. See Synonyms at field. To form into a sphere. To put in or within a sphere. To surround or encompass.