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If the Galactic Coordinate System is made up of two values, angles of longitude and latitude, how is distance measured? If you have those two values, you get a line from the sun in a certain direction. There might be multiple objects on that line, how can you specify one of them in the coordinate?

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You need three coordinates to represent a point in 3-dimensional space. Galactic coordinates are a 2-dimensional coordinate system on the surface of the abstract celestial sphere. Typically it is easier to measure position on the celestial sphere than it is to measure astronomical distances, so usually the systems are given in those terms. For 3D you need to supplement the Galactic coordinate system with distance as a separate coordinate, this is in fact the natural choice for a 3D spherical coordinate system.

Remember that the galactic coordinate system has its origin in the same place as equatorial coordinates (right ascension, declination), so the distance measurement is the same: you don't have to translate it relative to the Galactic Centre. To measure it, you use the usual techniques used to determine the cosmic distance ladder: parallaxes, standard candles (Cepheid variables, etc.), redshifts...

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    $\begingroup$ Good answer. You'd think the galactic coordinate system's origin would be the center of the galaxy, but, since we don't accurately know how far the center of the galaxy, our own coordinates would be inaccurate. Thus, we center galactic coordinates at our solar system's barycenter (SSB) $\endgroup$ – barrycarter Dec 4 at 16:29

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