The equatorial coordinate system is a widely-used method of specifying the positions of celestial objects. It may be implemented in spherical or rectangular coordinates, both defined by an origin at the center of the Earth, a fundamental plane consisting of the projection of the Earth's equator onto the celestial sphere (forming the celestial equator), a primary direction towards the vernal equinox, and a right-handed convention.
The origin at the center of the Earth means the coordinates are geocentric, that is, as seen from the center of the Earth as if it were transparent and nonrefracting. The fundamental plane and the primary direction mean that the coordinate system, while aligned with the Earth's equator and pole, does not rotate with the Earth, but remains relatively fixed against the background stars. A right-handed convention means that coordinates are positive toward the north and toward the east in the fundamental plane.
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“He is not a true man of science who does not bring some sympathy to his studies, and expect to learn something by behavior as well as by application. It is childish to rest in the discovery of mere coincidences, or of partial and extraneous laws. The study of geometry is a petty and idle exercise of the mind, if it is applied to no larger system than the starry one.”
—Henry David Thoreau (1817–1862)