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Positional astronomy (aka spherical astronomy) are the rules and mathematical methods for relating an observation in the celestial sphere to the location and trajectory of an astronomical object. This includes conversion from one celestial coordinate system to another, as well as relating an observation within the sky to the location of the object given some frame of reference. Among its results are every prediction known about what astronomical objects and phenomena are visible in the night sky. It invariably involves considerable trigonometry. Some rather sophisticated methods date back to antiquity and it was undoubtedly a motivation in the development of mathematics.