Astronomical Coordinate Systems (astropy.coordinates
)¶
Introduction¶
The coordinates
package provides classes for representing a variety
of celestial/spatial coordinates and their velocity components, as well as tools
for converting between common coordinate systems in a uniform way.
Getting Started¶
The simplest way to use coordinates
is to use the SkyCoord
class. SkyCoord
objects are instantiated by passing in positions (and
optional velocities) with specified units and a coordinate frame. Commonly sky
positions are passed in as Quantity
objects and the frame is
specified with the string name. As an example of creating a SkyCoord
to
represent an ICRS (Right ascension [RA], Declination [Dec]) sky position:
>>> from astropy import units as u
>>> from astropy.coordinates import SkyCoord
>>> c = SkyCoord(ra=10.625*u.degree, dec=41.2*u.degree, frame='icrs')
The initializer for SkyCoord
is very flexible and supports inputs provided in
a number of convenient formats. The following ways of initializing a coordinate
are all equivalent to the above:
>>> c = SkyCoord(10.625, 41.2, frame='icrs', unit='deg')
>>> c = SkyCoord('00h42m30s', '+41d12m00s', frame='icrs')
>>> c = SkyCoord('00h42.5m', '+41d12m')
>>> c = SkyCoord('00 42 30 +41 12 00', unit=(u.hourangle, u.deg))
>>> c = SkyCoord('00:42.5 +41:12', unit=(u.hourangle, u.deg))
>>> c
<SkyCoord (ICRS): (ra, dec) in deg
(10.625, 41.2)>
The examples above illustrate a few simple rules to follow when creating a coordinate object:
 Coordinate values can be provided either as unnamed positional arguments or
via keyword arguments like
ra
anddec
, orl
andb
(depending on the frame).  The coordinate
frame
keyword is optional because it defaults toICRS
.  Angle units must be specified for all components, either by passing in a
Quantity
object (e.g.,10.5*u.degree
), by including them in the value (e.g.,'+41d12m00s'
), or via theunit
keyword.
SkyCoord
and all other coordinates
objects also support
array coordinates. These work the same as singlevalue coordinates, but
they store multiple coordinates in a single object. When you’re going
to apply the same operation to many different coordinates (say, from a
catalog), this is a better choice than a list of SkyCoord
objects,
because it will be much faster than applying the operation to each
SkyCoord
in a for
loop. Like the underlying ndarray
instances
that contain the data, SkyCoord
objects can be sliced, reshaped, etc.:
>>> c = SkyCoord(ra=[10, 11, 12, 13]*u.degree, dec=[41, 5, 42, 0]*u.degree)
>>> c
<SkyCoord (ICRS): (ra, dec) in deg
[(10., 41.), (11., 5.), (12., 42.), (13., 0.)]>
>>> c[1]
<SkyCoord (ICRS): (ra, dec) in deg
(11., 5.)>
>>> c.reshape(2, 2)
<SkyCoord (ICRS): (ra, dec) in deg
[[(10., 41.), (11., 5.)],
[(12., 42.), (13., 0.)]]>
Coordinate access¶
Once you have a coordinate object you can access the components of that coordinate (e.g., RA, Dec) and get string representations of the full coordinate.
The component values are accessed using (typically lowercase) named attributes
that depend on the coordinate frame (e.g., ICRS, Galactic, etc.). For the
default, ICRS, the coordinate component names are ra
and dec
:
>>> c = SkyCoord(ra=10.68458*u.degree, dec=41.26917*u.degree)
>>> c.ra
<Longitude 10.68458 deg>
>>> c.ra.hour
0.7123053333333335
>>> c.ra.hms
hms_tuple(h=0.0, m=42.0, s=44.299200000000525)
>>> c.dec
<Latitude 41.26917 deg>
>>> c.dec.degree
41.26917
>>> c.dec.radian
0.7202828960652683
Coordinates can be converted to strings using the
to_string()
method:
>>> c = SkyCoord(ra=10.68458*u.degree, dec=41.26917*u.degree)
>>> c.to_string('decimal')
'10.6846 41.2692'
>>> c.to_string('dms')
'10d41m04.488s 41d16m09.012s'
>>> c.to_string('hmsdms')
'00h42m44.2992s +41d16m09.012s'
For additional information see the section on Working with Angles.
Transformation¶
The simplest way to transform to a new coordinate frame is by accessing
the appropriatelynamed attribute. For instance to get the coordinate in
the Galactic
frame use:
>>> c_icrs = SkyCoord(ra=10.68458*u.degree, dec=41.26917*u.degree, frame='icrs')
>>> c_icrs.galactic
<SkyCoord (Galactic): (l, b) in deg
(121.17424181, 21.57288557)>
For more control, you can use the transform_to
method, which accepts a frame name, frame class, or frame instance:
>>> c_fk5 = c_icrs.transform_to('fk5') # c_icrs.fk5 does the same thing
>>> c_fk5
<SkyCoord (FK5: equinox=J2000.000): (ra, dec) in deg
(10.68459154, 41.26917146)>
>>> from astropy.coordinates import FK5
>>> c_fk5.transform_to(FK5(equinox='J1975')) # precess to a different equinox
<SkyCoord (FK5: equinox=J1975.000): (ra, dec) in deg
(10.34209135, 41.13232112)>
This form of transform_to
also makes it
straightforward to convert from celestial coordinates to
AltAz
coordinates, allowing the use of SkyCoord
as a tool for planning observations. For a more complete example of
this, see Determining and plotting the altitude/azimuth of a celestial object.
Some coordinate frames such as AltAz
require Earth
rotation information (UT1UTC offset and/or polar motion) when transforming
to/from other frames. These Earth rotation values are automatically downloaded
from the International Earth Rotation and Reference Systems (IERS) service when
required. See IERS data access (astropy.utils.iers) for details of this process.
Representation¶
So far we have been using a spherical coordinate representation in the all the
examples, and this is the default for the builtin frames. Frequently it is
convenient to initialize or work with a coordinate using a different
representation such as cartesian or cylindrical. This can be done by setting
the representation
for either SkyCoord
objects or lowlevel frame
coordinate objects:
>>> c = SkyCoord(x=1, y=2, z=3, unit='kpc', representation_type='cartesian')
>>> c
<SkyCoord (ICRS): (x, y, z) in kpc
(1., 2., 3.)>
>>> c.x, c.y, c.z
(<Quantity 1. kpc>, <Quantity 2. kpc>, <Quantity 3. kpc>)
>>> c.representation_type = 'cylindrical'
>>> c
<SkyCoord (ICRS): (rho, phi, z) in (kpc, deg, kpc)
(2.23606798, 63.43494882, 3.)>
For all the details see Representations.
Distance¶
SkyCoord
and the individual frame classes also support specifying a distance
from the frame origin. The origin depends on the particular coordinate frame;
this can be, e.g., centered on the earth, centered on the solar system
barycenter, etc. Two angles and a distance specify a unique point in 3D space,
which also allows converting the coordinates to a Cartesian representation:
>>> c = SkyCoord(ra=10.68458*u.degree, dec=41.26917*u.degree, distance=770*u.kpc)
>>> c.cartesian.x
<Quantity 568.71286542 kpc>
>>> c.cartesian.y
<Quantity 107.3008974 kpc>
>>> c.cartesian.z
<Quantity 507.88994292 kpc>
With distances assigned, SkyCoord
convenience methods are more powerful, as
they can make use of the 3D information. For example, to compute the physical,
3D separation between two points in space:
>>> c1 = SkyCoord(ra=10*u.degree, dec=9*u.degree, distance=10*u.pc, frame='icrs')
>>> c2 = SkyCoord(ra=11*u.degree, dec=10*u.degree, distance=11.5*u.pc, frame='icrs')
>>> c1.separation_3d(c2)
<Distance 1.52286024 pc>
Convenience methods¶
SkyCoord
defines a number of convenience methods that support, for example,
computing onsky (i.e. angular) and 3D separations between two coordinates:
>>> c1 = SkyCoord(ra=10*u.degree, dec=9*u.degree, frame='icrs')
>>> c2 = SkyCoord(ra=11*u.degree, dec=10*u.degree, frame='fk5')
>>> c1.separation(c2) # Differing frames handled correctly
<Angle 1.40453359 deg>
crossmatching catalog coordinates (detailed in Matching Catalogs):
>>> target_c = SkyCoord(ra=10*u.degree, dec=9*u.degree, frame='icrs')
>>> # read in coordinates from a catalog...
>>> catalog_c = ...
>>> idx, sep, _ = target_c.match_to_catalog_sky(catalog_c)
The astropy.coordinates
subpackage also provides a quick way to get
coordinates for named objects assuming you have an active internet
connection. The from_name
method of SkyCoord
uses Sesame to retrieve coordinates
for a particular named object:
>>> SkyCoord.from_name("PSR J1012+5307")
<SkyCoord (ICRS): (ra, dec) in deg
(153.1393271, 53.117343)>
For sites (primarily observatories) on the Earth, astropy.coordinates
provides
a quick way to get an EarthLocation
:
>>> from astropy.coordinates import EarthLocation
>>> EarthLocation.of_site('Apache Point Observatory')
<EarthLocation (1463969.30185172, 5166673.34223433, 3434985.71204565) m>
To see the list of site names available, use
astropy.coordinates.EarthLocation.get_site_names()
.
For arbitrary Earth addresses (e.g., not observatory sites), use the
of_address
classmethod. Any address passed
to this function uses Google maps to retrieve the latitude and longitude and can
also (optionally) query Google maps to get the height of the location. As with
Google maps, this works with fully specified addresses, location names, city
names, and etc.:
.. doctestskip::
>>> EarthLocation.of_address('1002 Holy Grail Court, St. Louis, MO')
<EarthLocation (26726.98216371, 4997009.8604809, 3950271.16507911) m>
>>> EarthLocation.of_address('1002 Holy Grail Court, St. Louis, MO',
... get_height=True)
<EarthLocation (26727.6272786, 4997130.47437768, 3950367.15622108) m>
>>> EarthLocation.of_address('Danbury, CT')
<EarthLocation ( 1364606.64511651, 4593292.9428273, 4195415.93695139) m>
Note
from_name
,
of_site
, and
of_address
are for convenience, and
hence are by design rather simple. If you need precise coordinates for an
object you should find the appropriate reference and input the coordinates
manually, or use more specialized functionality like that in the astroquery or astroplan affiliated packages.
Also note that these methods retrieve data from the internet to determine the celestial or Earth coordinates. The online data may be updated, so if you need to guarantee that your scripts are reproducible in the long term, see the Usage tips/suggestions for methods that access remote resources section.
This functionality can be combined to do more complicated tasks like computing
barycentric corrections to radial velocity observations (also a supported
highlevel SkyCoord
method  see Radial Velocity Corrections):
>>> from astropy.time import Time
>>> obstime = Time('2017214')
>>> target = SkyCoord.from_name('M31')
>>> keck = EarthLocation.of_site('Keck')
>>> target.radial_velocity_correction(obstime=obstime, location=keck).to('km/s')
<Quantity 22.359784554780255 km / s>
Velocities (Proper Motions and Radial Velocities)¶
In addition to positional coordinates, coordinates
supports storing
and transforming velocities. These are available both via the lowerlevel
coordinate frame classes, and (new in v3.0) via SkyCoord
objects:
>>> sc = SkyCoord(1*u.deg, 2*u.deg, radial_velocity=20*u.km/u.s)
>>> sc
<SkyCoord (ICRS): (ra, dec) in deg
( 1., 2.)
(radial_velocity) in km / s
( 20.,)>
For more details on velocity support (and limitations), see the Working with velocities in Astropy coordinates page.
Overview of astropy.coordinates
concepts¶
Note
The coordinates
package from v0.4 onward builds from
previous versions of the package, and more detailed information and
justification of the design is available in APE (Astropy Proposal for Enhancement) 5.
Here we provide an overview of the package and associated framework.
This background information is not necessary for simply using
coordinates
, particularly if you use the SkyCoord
high
level class, but it is helpful for more advanced usage, particularly
creating your own frame, transformations, or representations. Another
useful piece of background information are some
Important Definitions as they are used in
coordinates
.
coordinates
is built on a threetiered system of objects:
representations, frames, and a highlevel class. Representations
classes are a particular way of storing a threedimensional data point
(or points), such as Cartesian coordinates or spherical polar
coordinates. Frames are particular reference frames like FK5 or ICRS,
which may store their data in different representations, but have well
defined transformations between each other. These transformations are
all stored in the astropy.coordinates.frame_transform_graph
, and new
transformations can be created by users. Finally, the highlevel class
(SkyCoord
) uses the frame classes, but provides a more accessible
interface to these objects as well as various convenience methods and
more stringparsing capabilities.
Separating these concepts makes it easier to extend the functionality of
coordinates
. It allows representations, frames, and
transformations to be defined or extended separately, while still
preserving the highlevel capabilities and simplicity of the SkyCoord
class.
Examples:
See Determining and plotting the altitude/azimuth of a celestial object for an
example of using the coordinates
functionality to prepare for an
observing run.
Using astropy.coordinates
¶
More detailed information on using the package is provided on separate pages, listed below.
 Working with Angles
 Using the SkyCoord Highlevel Class
 Transforming Between Systems
 Solar System Ephemerides
 Formatting Coordinate Strings
 Separations, Catalog Matching, and Related Functionality
 Using and Designing Coordinate Representations
 Using and Designing Coordinate Frames
 Working with velocities in Astropy coordinates
 Accounting for space motion
 Description of Galactocentric coordinates transformation
 Usage tips/suggestions for methods that access remote resources
 Important Definitions
 In Place Modification of Coordinates
In addition, another resource for the capabilities of this package is the
astropy.coordinates.tests.test_api_ape5
testing file. It showcases most of
the major capabilities of the package, and hence is a useful supplement to
this document. You can see it by either looking at it directly if you
downloaded a copy of the astropy source code, or typing the following in an
IPython session:
In [1]: from astropy.coordinates.tests import test_api_ape5
In [2]: test_api_ape5??
See Also¶
Some references particularly useful in understanding subtleties of the coordinate systems implemented here include:
 USNO Circular 179
 A useful guide to the IAU 2000/2003 work surrounding ICRS/IERS/CIRS and related problems in precision coordinate system work.
 Standards Of Fundamental Astronomy
 The definitive implementation of IAUdefined algorithms. The “SOFA Tools for Earth Attitude” document is particularly valuable for understanding the latest IAU standards in detail.
 IERS Conventions (2010)
 An exhaustive reference covering the ITRS, the IAU2000 celestial coordinates framework, and other related details of modern coordinate conventions.
 Meeus, J. “Astronomical Algorithms”
 A valuable text describing details of a wide range of coordinaterelated problems and concepts.
Reference/API¶
astropy.coordinates Package¶
This subpackage contains classes and functions for celestial coordinates of astronomical objects. It also contains a framework for conversions between coordinate systems.
The diagram below shows all of the coordinate systems built into the
coordinates
package, their aliases (useful for converting
other coordinates to them using attributestyle access) and the
predefined transformations between them. The user is free to
override any of these transformations by defining new transformations
between these systems, but the predefined transformations should be
sufficient for typical usage.
The color of an edge in the graph (i.e. the transformations between two frames) is set by the type of transformation; the legend box defines the mapping from transform class name to color.

AffineTransform: ➝

FunctionTransform: ➝

FunctionTransformWithFiniteDifference: ➝

StaticMatrixTransform: ➝

DynamicMatrixTransform: ➝
Note
The ecliptic coordinate systems (added in Astropy v1.1) have not been extensively tested for accuracy or consistency with other implementations of ecliptic coordinates. We welcome contributions to add such testing, but in the meantime, users who depend on consistency with other implementations may wish to check test inputs against good datasets before using Astropy’s ecliptic coordinates.
Functions¶
cartesian_to_spherical (x, y, z) 
Converts 3D rectangular cartesian coordinates to spherical polar coordinates. 
concatenate (coords) 
Combine multiple coordinate objects into a single SkyCoord . 
get_body (body, time[, location, ephemeris]) 
Get a SkyCoord for a solar system body as observed from a location on Earth in the GCRS reference system. 
get_body_barycentric (body, time[, ephemeris]) 
Calculate the barycentric position of a solar system body. 
get_body_barycentric_posvel (body, time[, …]) 
Calculate the barycentric position and velocity of a solar system body. 
get_constellation (coord[, short_name, …]) 
Determines the constellation(s) a given coordinate object contains. 
get_icrs_coordinates (name) 
Retrieve an ICRS object by using an online name resolving service to retrieve coordinates for the specified name. 
get_moon (time[, location, ephemeris]) 
Get a SkyCoord for the Earth’s Moon as observed from a location on Earth in the GCRS reference system. 
get_sun (time) 
Determines the location of the sun at a given time (or times, if the input is an array Time object), in geocentric coordinates. 
match_coordinates_3d (matchcoord, catalogcoord) 
Finds the nearest 3dimensional matches of a coordinate or coordinates in a set of catalog coordinates. 
match_coordinates_sky (matchcoord, catalogcoord) 
Finds the nearest onsky matches of a coordinate or coordinates in a set of catalog coordinates. 
search_around_3d (coords1, coords2, distlimit) 
Searches for pairs of points that are at least as close as a specified distance in 3D space. 
search_around_sky (coords1, coords2, seplimit) 
Searches for pairs of points that have an angular separation at least as close as a specified angle. 
spherical_to_cartesian (r, lat, lon) 
Converts spherical polar coordinates to rectangular cartesian coordinates. 
Classes¶
AffineTransform (transform_func, fromsys, tosys) 
A coordinate transformation specified as a function that yields a 3 x 3 cartesian transformation matrix and a tuple of displacement vectors. 
AltAz (*args, **kwargs) 
A coordinate or frame in the AltitudeAzimuth system (Horizontal coordinates). 
Angle 
One or more angular value(s) with units equivalent to radians or degrees. 
Attribute ([default, secondary_attribute]) 
A nonmutable data descriptor to hold a frame attribute. 
BarycentricTrueEcliptic (*args[, copy, …]) 
Barycentric ecliptic coordinates. 
BaseAffineTransform (fromsys, tosys[, …]) 
Base class for common functionality between the AffineTransform type subclasses. 
BaseCoordinateFrame (*args[, copy, …]) 
The base class for coordinate frames. 
BaseDifferential (*args, **kwargs) 
A base class representing differentials of representations. 
BaseEclipticFrame (*args[, copy, …]) 
A base class for frames that have names and conventions like that of ecliptic frames. 
BaseRADecFrame (*args[, copy, …]) 
A base class that defines default representation info for frames that represent longitude and latitude as Right Ascension and Declination following typical “equatorial” conventions. 
BaseRepresentation (*args[, differentials]) 
Base for representing a point in a 3D coordinate system. 
BaseRepresentationOrDifferential (*args, **kwargs) 
3D coordinate representations and differentials. 
BaseSphericalCosLatDifferential (*args, **kwargs) 
Differtials from points on a spherical base representation. 
BaseSphericalDifferential (*args, **kwargs) 

BoundsError 
Raised when an angle is outside of its userspecified bounds. 
CIRS (*args[, copy, representation_type, …]) 
A coordinate or frame in the Celestial Intermediate Reference System (CIRS). 
CartesianDifferential (d_x[, d_y, d_z, unit, …]) 
Differentials in of points in 3D cartesian coordinates. 
CartesianRepresentation (x[, y, z, unit, …]) 
Representation of points in 3D cartesian coordinates. 
CartesianRepresentationAttribute ([default, …]) 
A frame attribute that is a CartesianRepresentation with specified units. 
CartesianRepresentationFrameAttribute (*args, …) 

CompositeTransform (transforms, fromsys, tosys) 
A transformation constructed by combining together a series of singlestep transformations. 
ConvertError 
Raised if a coordinate system cannot be converted to another 
CoordinateAttribute (frame[, default, …]) 
A frame attribute which is a coordinate object. 
CoordinateTransform (fromsys, tosys[, …]) 
An object that transforms a coordinate from one system to another. 
CylindricalDifferential (d_rho, d_phi, d_z[, …]) 
Differential(s) of points in cylindrical coordinates. 
CylindricalRepresentation (rho, phi, z[, …]) 
Representation of points in 3D cylindrical coordinates. 
DifferentialAttribute ([default, …]) 
A frame attribute which is a differential instance. 
Distance 
A onedimensional distance. 
DynamicMatrixTransform (matrix_func, fromsys, …) 
A coordinate transformation specified as a function that yields a 3 x 3 cartesian transformation matrix. 
EarthLocation 
Location on the Earth. 
EarthLocationAttribute ([default, …]) 
A frame attribute that can act as a EarthLocation . 
FK4 (*args[, copy, representation_type, …]) 
A coordinate or frame in the FK4 system. 
FK4NoETerms (*args[, copy, …]) 
A coordinate or frame in the FK4 system, but with the Eterms of aberration removed. 
FK5 (*args[, copy, representation_type, …]) 
A coordinate or frame in the FK5 system. 
FunctionTransform (func, fromsys, tosys[, …]) 
A coordinate transformation defined by a function that accepts a coordinate object and returns the transformed coordinate object. 
FunctionTransformWithFiniteDifference (func, …) 
A coordinate transformation that works like a FunctionTransform , but computes velocity shifts based on the finitedifference relative to one of the frame attributes. 
GCRS (*args[, copy, representation_type, …]) 
A coordinate or frame in the Geocentric Celestial Reference System (GCRS). 
Galactic (*args[, copy, representation_type, …]) 
A coordinate or frame in the Galactic coordinate system. 
GalacticLSR (*args[, copy, …]) 
A coordinate or frame in the Local Standard of Rest (LSR), axisaligned to the Galactic frame. 
Galactocentric (*args, **kwargs) 
A coordinate or frame in the Galactocentric system. 
GenericFrame (frame_attrs) 
A frame object that can’t store data but can hold any arbitrary frame attributes. 
GeocentricTrueEcliptic (*args[, copy, …]) 
Geocentric ecliptic coordinates. 
HCRS (*args[, copy, representation_type, …]) 
A coordinate or frame in a Heliocentric system, with axes aligned to ICRS. 
HeliocentricTrueEcliptic (*args[, copy, …]) 
Heliocentric ecliptic coordinates. 
ICRS (*args[, copy, representation_type, …]) 
A coordinate or frame in the ICRS system. 
ITRS (*args[, copy, representation_type, …]) 
A coordinate or frame in the International Terrestrial Reference System (ITRS). 
IllegalHourError (hour) 
Raised when an hour value is not in the range [0,24). 
IllegalHourWarning (hour[, alternativeactionstr]) 
Raised when an hour value is 24. 
IllegalMinuteError (minute) 
Raised when an minute value is not in the range [0,60]. 
IllegalMinuteWarning (minute[, …]) 
Raised when a minute value is 60. 
IllegalSecondError (second) 
Raised when an second value (time) is not in the range [0,60]. 
IllegalSecondWarning (second[, …]) 
Raised when a second value is 60. 
LSR (*args[, copy, representation_type, …]) 
A coordinate or frame in the Local Standard of Rest (LSR). 
Latitude 
Latitudelike angle(s) which must be in the range 90 to +90 deg. 
Longitude 
Longitudelike angle(s) which are wrapped within a contiguous 360 degree range. 
PhysicsSphericalDifferential (d_phi, d_theta, d_r) 
Differential(s) of 3D spherical coordinates using physics convention. 
PhysicsSphericalRepresentation (phi, theta, r) 
Representation of points in 3D spherical coordinates (using the physics convention of using phi and theta for azimuth and inclination from the pole). 
PrecessedGeocentric (*args[, copy, …]) 
A coordinate frame defined in a similar manner as GCRS, but precessed to a requested (mean) equinox. 
QuantityAttribute ([default, …]) 
A frame attribute that is a quantity with specified units and shape (optionally). 
QuantityFrameAttribute (*args, **kwargs) 

RadialDifferential (*args, **kwargs) 
Differential(s) of radial distances. 
RadialRepresentation (distance[, …]) 
Representation of the distance of points from the origin. 
RangeError 
Raised when some part of an angle is out of its valid range. 
RepresentationMapping 
This namedtuple is used with the frame_specific_representation_info attribute to tell frames what attribute names (and default units) to use for a particular representation. 
SkyCoord (*args[, copy]) 
Highlevel object providing a flexible interface for celestial coordinate representation, manipulation, and transformation between systems. 
SkyCoordInfo ([bound]) 
Container for meta information like name, description, format. 
SkyOffsetFrame (*args, **kwargs) 
A frame which is relative to some specific position and oriented to match its frame. 
SphericalCosLatDifferential (d_lon_coslat, …) 
Differential(s) of points in 3D spherical coordinates. 
SphericalDifferential (d_lon, d_lat, d_distance) 
Differential(s) of points in 3D spherical coordinates. 
SphericalRepresentation (lon, lat, distance) 
Representation of points in 3D spherical coordinates. 
StaticMatrixTransform (matrix, fromsys, tosys) 
A coordinate transformation defined as a 3 x 3 cartesian transformation matrix. 
Supergalactic (*args[, copy, …]) 
Supergalactic Coordinates (see Lahav et al. 
TimeAttribute ([default, secondary_attribute]) 
Frame attribute descriptor for quantities that are Time objects. 
TimeFrameAttribute (*args, **kwargs) 

TransformGraph () 
A graph representing the paths between coordinate frames. 
UnitSphericalCosLatDifferential (…[, copy]) 
Differential(s) of points on a unit sphere. 
UnitSphericalDifferential (d_lon, d_lat[, copy]) 
Differential(s) of points on a unit sphere. 
UnitSphericalRepresentation (lon, lat[, …]) 
Representation of points on a unit sphere. 
UnknownSiteException (site, attribute[, …]) 

solar_system_ephemeris () 
Default ephemerides for calculating positions of SolarSystem bodies. 