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Not quite. Instead of being described in Cartesian coordinates such as X, Y, and Z, celestial objects are described in an angular coordinate system sometimes called "rho, theta". These are letters of the Greek alphabet often used to measure angles.

We still use three coordinates representing the number of degrees around the ecliptic a celestial object is, and the number of degrees north or south of the ecliptic plane. The third coordinate is a distance. These are similar to the bearing, elevation and range coordinates that you might use in gunnery.

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