Coordinates can also have line-of-sight distances. If these are provided, a coordinate object becomes a full-fledged point in three-dimensional space. If not (i.e., the distance attribute of the coordinate object is None), the point is interpreted as lying on the (dimensionless) unit sphere.
The Distance class is provided to represent a line-of-sight distance for a coordinate. It must include a length unit to be valid.:
>>> from astropy.coordinates import Distance
>>> d = Distance(770)
UnitsError: A unit must be provided for distance.
>>> d = Distance(770, u.kpc)
>>> c = ICRSCoordinates('00h42m44.3s +41d16m9s', distance=d)
>>> c
<ICRSCoordinates RA=10.68458 deg, Dec=41.26917 deg, Distance=7.7e+02 kpc>
If a distance is available, the coordinate can be converted into cartesian coordinates using the x/y/z attributes:
>>> c.x
568.7128882165681
>>> c.y
107.3009359688103
>>> c.z
507.8899092486349
Note
The location of the origin is different for different coordinate systems, but for common celestial coordinate systems it is often the Earth center (or for precision work, the Earth/Moon barycenter).
The cartesian coordinates can also be accessed via the CartesianCoordinates object, which has additional capabilities like arithmetic operations:
>>> cp = c.cartesian
>>> cp
<CartesianPoints (568.712888217, 107.300935969, 507.889909249) kpc>
>>> cp.x
568.7128882165681
>>> cp.y
107.3009359688103
>>> cp.z
507.8899092486349
>>> cp.unit
Unit("kpc")
>>> cp + cp
<CartesianPoints (1137.42577643, 214.601871938, 1015.7798185) kpc>
>>> cp - cp
<CartesianPoints (0.0, 0.0, 0.0) kpc>
This cartesian representation can also be used to create a new coordinate object, either directly or through a CartesianPoints object:
>>> ICRSCoordinates(x=568.7129, y=107.3009, z=507.8899, unit=u.kpc)
<ICRSCoordinates RA=10.68458 deg, Dec=41.26917 deg, Distance=7.7e+02 kpc>
>>> cp = CartesianPoints(x=568.7129, y=107.3009, z=507.8899, unit=u.kpc)
>>> ICRSCoordinates(cp)
<ICRSCoordinates RA=10.68458 deg, Dec=41.26917 deg, Distance=7.7e+02 kpc>
Finally, two coordinates with distances can be used to derive a real-space distance (i.e., non-projected separation):
>>> c1 = ICRSCoordinates('5h23m34.5s -69d45m22s', distance=Distance(49, u.kpc))
>>> c2 = ICRSCoordinates('0h52m44.8s -72d49m43s', distance=Distance(61, u.kpc))
>>> sep3d = c1.separation_3d(c2)
>>> sep3d
<Distance 23.05685 kpc>
>>> sep3d.kpc
23.05684814695706
>>> sep3d.Mpc
0.02305684814695706
>>> sep3d.au
4755816315.663559