The coordinates package provides classes for representing a variety of celestial/spatial coordinates, as well as tools for converting between common coordinate systems in a uniform way.
Note
If you have existing code that uses coordinates functionality from Astropy version 0.3.x or earlier, please see the section on Migrating from pre-v0.4 coordinates. The interface has changed in ways that are not backward compatible in many circumstances.
The simplest way to use coordinates is to use the SkyCoord class. SkyCoord objects are instantiated with a flexible and natural approach that supports inputs provided in a number of convenient formats. The following ways of initializing a coordinate are all equivalent:
>>> from astropy import units as u
>>> from astropy.coordinates import SkyCoord
>>> c = SkyCoord(ra=10.5*u.degree, dec=41.2*u.degree, frame='icrs')
>>> c = SkyCoord(10.5, 41.2, 'icrs', unit='deg')
>>> c = SkyCoord('00h42m00s', '+41d12m00s', 'icrs')
>>> c = SkyCoord('00 42 00 +41 12 00', 'icrs', unit=(u.hourangle, u.deg))
>>> c
<SkyCoord (ICRS): ra=10.5 deg, dec=41.2 deg>
The examples above illustrate a few simple rules to follow when creating a coordinate object:
The individual components of equatorial coordinates are Longitude or Latitude objects, which are specialized versions of the general Angle class. The component values are accessed using aptly named attributes:
>>> 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 easily 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 more control over the string formatting, use the to_string method of the individual components:
>>> c.ra.to_string(decimal=True)
'10.6846'
>>> c.dec.to_string(format='latex')
'$41^\\circ16{}^\\prime09.012{}^{\\prime\\prime}$'
>>> msg = 'My coordinates are: ra="{0}"" dec="{1}"'
>>> msg.format(c.ra.to_string(sep=':'), c.dec.to_string(sep=':'))
'My coordinates are: ra="10:41:04.488"" dec="41:16:09.012"'
Many of the above examples did not explicitly specify the coordinate frame. This is fine if you do not need to transform to other frames or compare with coordinates defined in a different frame. However, to use the full power of coordinates, you should specify the reference frame your coordinates are defined in:
>>> c_icrs = SkyCoord(ra=10.68458*u.degree, dec=41.26917*u.degree, frame='icrs')
Once you’ve defined the frame of your coordinates, you can transform from that frame to another frame. You can do this a few different ways: if you just want the default version of that frame, you can use attribute-style access. For more control, you can use the transform_to method, which accepts a frame name, frame class, or frame instance:
>>> from astropy.coordinates import FK5
>>> c_icrs.galactic
<SkyCoord (Galactic): l=121.174302631 deg, b=-21.5728000618 deg>
>>> c_fk5 = c_icrs.transform_to('fk5') # c_icrs.fk5 does the same thing
>>> c_fk5
<SkyCoord (FK5): equinox=J2000.000, ra=10.6845915393 deg, dec=41.2691714591 deg>
>>> c_fk5.transform_to(FK5(equinox='J1975')) # precess to a different equinox
<SkyCoord (FK5): equinox=J1975.000, ra=10.3420913461 deg, dec=41.1323211229 deg>
SkyCoord and all other coordinates objects also support array coordinates. These work the same as single-value 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.
>>> SkyCoord(ra=[10, 11]*u.degree, dec=[41, -5]*u.degree)
<SkyCoord (ICRS): (ra, dec) in deg
[(10.0, 41.0), (11.0, -5.0)]>
So far we have been using a spherical coordinate representation in the all the examples, and this is the default for the built-in 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 low-level frame coordinate objects:
>>> c = SkyCoord(x=1, y=2, z=3, unit='kpc', frame='icrs', representation='cartesian')
>>> c
<SkyCoord (ICRS): x=1.0 kpc, y=2.0 kpc, z=3.0 kpc>
>>> c.x, c.y, c.z
(<Quantity 1.0 kpc>, <Quantity 2.0 kpc>, <Quantity 3.0 kpc>)
>>> c.representation = 'cylindrical'
>>> c
<SkyCoord (ICRS): rho=2.2360679775 kpc, phi=63.4349488229 deg, z=3.0 kpc>
>>> c.phi
<Angle 63.434948... deg>
>>> c.phi.to(u.radian)
<Angle 1.107148... rad>
>>> c.representation = 'spherical'
>>> c
<SkyCoord (ICRS): ra=63.4349488229 deg, dec=53.3007747995 deg, distance=3.74165738677 kpc>
>>> c.representation = 'unitspherical'
>>> c
<SkyCoord (ICRS): ra=63.4349488229 deg, dec=53.3007747995 deg>
SkyCoord defines a number of convenience methods as well, like on-sky separation between two coordinates and catalog matching (detailed in Matching Catalogs):
>>> 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 1.4045335865905868 deg>
Distance from the origin (which is system-dependent, but often the Earth center) can also be assigned to a SkyCoord. With two angles and a distance, a unique point in 3D space is available, which also allows conversion to the Cartesian representation of this location:
>>> from astropy.coordinates import Distance
>>> c = SkyCoord(ra=10.68458*u.degree, dec=41.26917*u.degree, distance=770*u.kpc)
>>> c.cartesian.x
<Quantity 568.7128654235232 kpc>
>>> c.cartesian.y
<Quantity 107.3008974042025 kpc>
>>> c.cartesian.z
<Quantity 507.88994291875713 kpc>
With distances assigned, SkyCoord convenience methods are more powerful, as they can make use of the 3D information. For example:
>>> 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 1.5228602415117989 pc>
Finally, 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("M42")
<SkyCoord (ICRS): ra=83.82208 deg, dec=-5.39111 deg>
Note
from_name is intended to be a convenience, and is rather simple. If you need precise coordinates for an object you should find the appropriate reference for that measurement and input the coordinates manually.
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 infromation are some Important Definitions as they are used in coordinates.
coordinates is built on a three-tiered system of objects: representations, frames, and a high-level class. Representations classes are a particular way of storing a three-dimensional 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 high-level class (SkyCoord) uses the frame classes, but provides a more accessible interface to these objects as well as various convenience methods and more string-parsing 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 high-level capabilities and simplicity of the SkyCoord class.
More detailed information on using the package is provided on separate pages, listed below.
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??
For typical users, the major change is that the recommended way to use coordinate functionality is via the SkyCoord class, instead of classes like ICRS classes (now called “frame classes”).
For most users of pre-v0.4 coordinates, this means that the best way to adapt old code to the new framework is to change code like:
>>> from astropy import units as u
>>> from astropy.coordinates import ICRS # or FK5, or Galactic, or similar
>>> coordinate = ICRS(123.4*u.deg, 56.7*u.deg)
to instead be:
>>> from astropy import units as u
>>> from astropy.coordinates import SkyCoord
>>> coordinate = SkyCoord(123.4*u.deg, 56.7*u.deg, frame='icrs')
Note that usage like:
>>> coordinate = ICRS(123.4, 56.7, unit=('deg', 'deg')) # NOT RECOMMENDED!
will continue to work in v0.4, but will yield a SkyCoord instead of an ICRS object (the former behaves more like the pre-v0.4 ICRS). This compatibility feature will issue a deprecation warning, and will be removed in the next major version, so you should update your code to use SkyCoord directly by the next release.
Users should also be aware that if they continue to use the first form (directly creating ICRS frame objects), old code may still work if it uses basic coordinate functionality, but many of the convenience functions like catalog matching or attribute-based transforms like coordinate.galactic will no longer work. These features are now all in SkyCoord.
For advanced users or developers who have defined their own coordinates, take note that the extensive internal changes will require re-writing user-defined coordinate frames. The Example: Defining A Coordinate Frame for the Sgr Dwarf document has been updated for the new framework to provide a worked example of how custom coordinates work.
More detailed information about the new framework and using it to define custom coordinates is available at Overview of astropy.coordinates concepts, Important Definitions, Defining a New Frame, and Creating your own representations.
Some references particularly useful in understanding subtleties of the coordinate systems implemented here include:
The definitive implementation of IAU-defined algorithms. The “SOFA Tools for Earth Attitude” document is particularly valuable for understanding the latest IAU standards in detail.
A useful guide to the IAU 2000/2003 work surrounding ICRS/IERS/CIRS and related problems in precision coordinate system work.
A valuable text describing details of a wide range of coordinate-related problems and concepts.
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 attribute-style access) and the pre-defined transformations between them. The user is free to override any of these transformations by defining new transformations between these systems, but the pre-defined transformations should be sufficient for typical usage.
The graph also indicates the priority for each transformation as a number next to the arrow. These priorities are used to decide the preferred order when two transformation paths have the same number of steps. These priorities are defined such that the path with a smaller total priority is favored.
digraph AstropyCoordinateTransformGraph { FK5 [shape=oval label="FK5\n`fk5`"]; ICRS [shape=oval label="ICRS\n`icrs`"]; Galactic [shape=oval label="Galactic\n`galactic`"]; FK4NoETerms [shape=oval label="FK4NoETerms\n`fk4noeterms`"]; FK4 [shape=oval label="FK4\n`fk4`"]; AltAz[ shape=oval ]; FK5 -> FK5[ label = "1.0" ]; FK5 -> ICRS[ label = "1.0" ]; FK5 -> Galactic[ label = "1.0" ]; FK5 -> FK4NoETerms[ label = "1.0" ]; FK4 -> FK4[ label = "1.0" ]; FK4 -> FK4NoETerms[ label = "1.0" ]; Galactic -> FK5[ label = "1.0" ]; Galactic -> FK4NoETerms[ label = "1.0" ]; ICRS -> FK5[ label = "1.0" ]; FK4NoETerms -> FK4NoETerms[ label = "1.0" ]; FK4NoETerms -> FK4[ label = "1.0" ]; FK4NoETerms -> Galactic[ label = "1.0" ]; FK4NoETerms -> FK5[ label = "1.0" ]; overlap=false }
| cartesian_to_spherical(x, y, z) | Converts 3D rectangular cartesian coordinates to spherical polar coordinates. |
| get_icrs_coordinates(name) | Retrieve an ICRS object by using an online name resolving service to retrieve coordinates for the specified name. |
| match_coordinates_3d(matchcoord, catalogcoord) | Finds the nearest 3-dimensional matches of a coordinate or coordinates in a set of catalog coordinates. |
| match_coordinates_sky(matchcoord, catalogcoord) | Finds the nearest on-sky matches of a coordinate or coordinates in a set of catalog coordinates. |
| spherical_to_cartesian(r, lat, lon) | Converts spherical polar coordinates to rectangular cartesian coordinates. |
| AltAz(*args, **kwargs) | A coordinate or frame in the Altitude-Azimuth system (i.e., Horizontal coordinates). |
| Angle | One or more angular value(s) with units equivalent to radians or degrees. |
| BaseCoordinateFrame(*args, **kwargs) | The base class for coordinate frames. |
| BaseRepresentation | Base Representation object, for representing a point in a 3D coordinate system. |
| BoundsError | Raised when an angle is outside of its user-specified bounds. |
| CartesianPoints(*args, **kwargs) | Deprecated since version v0.4. |
| CartesianRepresentation(x[, y, z, copy]) | Representation of points in 3D cartesian coordinates. |
| CompositeTransform(transforms, fromsys, tosys) | A transformation constructed by combining together a series of single-step transformations. |
| ConvertError | Raised if a coordinate system cannot be converted to another |
| CoordinateTransform(fromsys, tosys[, ...]) | An object that transforms a coordinate from one system to another. |
| CylindricalRepresentation(rho, phi, z[, copy]) | Representation of points in 3D cylindrical coordinates. |
| Distance | A one-dimensional distance. |
| DynamicMatrixTransform(matrix_func, fromsys, ...) | A coordinate transformation specified as a function that yields a 3 x 3 cartesian transformation matrix. |
| EarthLocation | Location on Earth. |
| FK4(*args, **kwargs) | A coordinate or frame in the FK4 system. |
| FK4NoETerms(*args, **kwargs) | A coordinate or frame in the FK4 system, but with the E-terms of aberration removed. |
| FK5(*args, **kwargs) | A coordinate or frame in the FK5 system. |
| FrameAttribute([default, secondary_attribute]) | A non-mutable data descriptor to hold a frame attribute. |
| FunctionTransform(func, fromsys, tosys[, ...]) | A coordinate transformation defined by a function that accepts a coordinate object and returns the transformed coordinate object. |
| Galactic(*args, **kwargs) | Galactic Coordinates. |
| GenericFrame(frame_attrs) | A frame object that can’t store data but can hold any arbitrary frame attributes. |
| ICRS(*args, **kwargs) | A coordinate or frame in the ICRS system. |
| 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. |
| Latitude | Latitude-like angle(s) which must be in the range -90 to +90 deg. |
| Longitude | Longitude-like angle(s) which are wrapped within a contiguous 360 degree range. |
| 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). |
| 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, **kwargs) | High-level object providing a flexible interface for celestial coordinate representation, manipulation, and transformation between systems. |
| 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. |
| TimeFrameAttribute([default, ...]) | Frame attribute descriptor for quantities that are Time objects. |
| TransformGraph() | A graph representing the paths between coordinate frames. |
| UnitSphericalRepresentation(lon, lat[, copy]) | Representation of points on a unit sphere. |
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"BaseCoordinateFrame" -> "FK4NoETerms" [arrowsize=0.5,style="setlinewidth(0.5)"]; "FK5" [style="setlinewidth(0.5)",URL="../api/astropy.coordinates.FK5.html#astropy.coordinates.FK5",fontname="Vera Sans, DejaVu Sans, Liberation Sans, Arial, Helvetica, sans",tooltip="A coordinate or frame in the FK5 system.",height=0.25,shape=box,fontsize=10]; "BaseCoordinateFrame" -> "FK5" [arrowsize=0.5,style="setlinewidth(0.5)"]; "FrameAttribute" [style="setlinewidth(0.5)",URL="../api/astropy.coordinates.FrameAttribute.html#astropy.coordinates.FrameAttribute",fontname="Vera Sans, DejaVu Sans, Liberation Sans, Arial, Helvetica, sans",tooltip="A non-mutable data descriptor to hold a frame attribute.",height=0.25,shape=box,fontsize=10]; "FunctionTransform" [style="setlinewidth(0.5)",URL="../api/astropy.coordinates.FunctionTransform.html#astropy.coordinates.FunctionTransform",fontname="Vera Sans, DejaVu Sans, Liberation Sans, Arial, Helvetica, sans",tooltip="A coordinate transformation defined by a function that accepts a",height=0.25,shape=box,fontsize=10]; "CoordinateTransform" -> "FunctionTransform" [arrowsize=0.5,style="setlinewidth(0.5)"]; "Galactic" [style="setlinewidth(0.5)",URL="../api/astropy.coordinates.Galactic.html#astropy.coordinates.Galactic",fontname="Vera Sans, DejaVu Sans, Liberation Sans, Arial, Helvetica, sans",tooltip="Galactic Coordinates.",height=0.25,shape=box,fontsize=10]; "BaseCoordinateFrame" -> "Galactic" [arrowsize=0.5,style="setlinewidth(0.5)"]; "GenericFrame" [style="setlinewidth(0.5)",URL="../api/astropy.coordinates.GenericFrame.html#astropy.coordinates.GenericFrame",fontname="Vera Sans, DejaVu Sans, Liberation Sans, Arial, Helvetica, sans",tooltip="A frame object that can't store data but can hold any arbitrary frame",height=0.25,shape=box,fontsize=10]; "BaseCoordinateFrame" -> "GenericFrame" [arrowsize=0.5,style="setlinewidth(0.5)"]; "ICRS" [style="setlinewidth(0.5)",URL="../api/astropy.coordinates.ICRS.html#astropy.coordinates.ICRS",fontname="Vera Sans, DejaVu Sans, Liberation Sans, Arial, Helvetica, sans",tooltip="A coordinate or frame in the ICRS system.",height=0.25,shape=box,fontsize=10]; "BaseCoordinateFrame" -> "ICRS" [arrowsize=0.5,style="setlinewidth(0.5)"]; "IllegalHourError" [style="setlinewidth(0.5)",URL="../api/astropy.coordinates.IllegalHourError.html#astropy.coordinates.IllegalHourError",fontname="Vera Sans, DejaVu Sans, Liberation Sans, Arial, Helvetica, sans",tooltip="Raised when an hour value is not in the range [0,24).",height=0.25,shape=box,fontsize=10]; "RangeError" -> "IllegalHourError" [arrowsize=0.5,style="setlinewidth(0.5)"]; "IllegalHourWarning" [style="setlinewidth(0.5)",URL="../api/astropy.coordinates.IllegalHourWarning.html#astropy.coordinates.IllegalHourWarning",fontname="Vera Sans, DejaVu Sans, Liberation Sans, Arial, Helvetica, sans",tooltip="Raised when an hour value is 24.",height=0.25,shape=box,fontsize=10]; "AstropyWarning" -> "IllegalHourWarning" [arrowsize=0.5,style="setlinewidth(0.5)"]; "IllegalMinuteError" [style="setlinewidth(0.5)",URL="../api/astropy.coordinates.IllegalMinuteError.html#astropy.coordinates.IllegalMinuteError",fontname="Vera Sans, DejaVu Sans, Liberation Sans, Arial, Helvetica, sans",tooltip="Raised when an minute value is not in the range [0,60].",height=0.25,shape=box,fontsize=10]; "RangeError" -> "IllegalMinuteError" [arrowsize=0.5,style="setlinewidth(0.5)"]; "IllegalMinuteWarning" [style="setlinewidth(0.5)",URL="../api/astropy.coordinates.IllegalMinuteWarning.html#astropy.coordinates.IllegalMinuteWarning",fontname="Vera Sans, DejaVu Sans, Liberation Sans, Arial, Helvetica, sans",tooltip="Raised when a minute value is 60.",height=0.25,shape=box,fontsize=10]; "AstropyWarning" -> "IllegalMinuteWarning" [arrowsize=0.5,style="setlinewidth(0.5)"]; "IllegalSecondError" [style="setlinewidth(0.5)",URL="../api/astropy.coordinates.IllegalSecondError.html#astropy.coordinates.IllegalSecondError",fontname="Vera Sans, DejaVu Sans, Liberation Sans, Arial, Helvetica, sans",tooltip="Raised when an second value (time) is not in the range [0,60].",height=0.25,shape=box,fontsize=10]; "RangeError" -> "IllegalSecondError" [arrowsize=0.5,style="setlinewidth(0.5)"]; "IllegalSecondWarning" [style="setlinewidth(0.5)",URL="../api/astropy.coordinates.IllegalSecondWarning.html#astropy.coordinates.IllegalSecondWarning",fontname="Vera Sans, DejaVu Sans, Liberation Sans, Arial, Helvetica, sans",tooltip="Raised when a second value is 60.",height=0.25,shape=box,fontsize=10]; "AstropyWarning" -> "IllegalSecondWarning" [arrowsize=0.5,style="setlinewidth(0.5)"]; "Latitude" [style="setlinewidth(0.5)",URL="../api/astropy.coordinates.Latitude.html#astropy.coordinates.Latitude",fontname="Vera Sans, DejaVu Sans, Liberation Sans, Arial, Helvetica, sans",tooltip="Latitude-like angle(s) which must be in the range -90 to +90 deg.",height=0.25,shape=box,fontsize=10]; "Angle" -> "Latitude" [arrowsize=0.5,style="setlinewidth(0.5)"]; "Longitude" [style="setlinewidth(0.5)",URL="../api/astropy.coordinates.Longitude.html#astropy.coordinates.Longitude",fontname="Vera Sans, DejaVu Sans, Liberation Sans, Arial, Helvetica, sans",tooltip="Longitude-like angle(s) which are wrapped within a contiguous 360 degree range.",height=0.25,shape=box,fontsize=10]; "Angle" -> "Longitude" [arrowsize=0.5,style="setlinewidth(0.5)"]; "PhysicsSphericalRepresentation" [style="setlinewidth(0.5)",URL="../api/astropy.coordinates.PhysicsSphericalRepresentation.html#astropy.coordinates.PhysicsSphericalRepresentation",fontname="Vera Sans, DejaVu Sans, Liberation Sans, Arial, Helvetica, sans",tooltip="Representation of points in 3D spherical coordinates (using the physics",height=0.25,shape=box,fontsize=10]; "BaseRepresentation" -> "PhysicsSphericalRepresentation" [arrowsize=0.5,style="setlinewidth(0.5)"]; "Quantity" [style="setlinewidth(0.5)",URL="../api/astropy.units.quantity.Quantity.html#astropy.units.quantity.Quantity",fontname="Vera Sans, DejaVu Sans, Liberation Sans, Arial, Helvetica, sans",tooltip="A `Quantity` represents a number with some associated unit.",height=0.25,shape=box,fontsize=10]; "ndarray" -> "Quantity" [arrowsize=0.5,style="setlinewidth(0.5)"]; "RangeError" [style="setlinewidth(0.5)",URL="../api/astropy.coordinates.RangeError.html#astropy.coordinates.RangeError",fontname="Vera Sans, DejaVu Sans, Liberation Sans, Arial, Helvetica, sans",tooltip="Raised when some part of an angle is out of its valid range.",height=0.25,shape=box,fontsize=10]; "RepresentationMapping" [style="setlinewidth(0.5)",URL="../api/astropy.coordinates.RepresentationMapping.html#astropy.coordinates.RepresentationMapping",fontname="Vera Sans, DejaVu Sans, Liberation Sans, Arial, Helvetica, sans",tooltip="RepresentationMapping(reprname, framename, defaultunit)",height=0.25,shape=box,fontsize=10]; "RepresentationMapping" [style="setlinewidth(0.5)",URL="../api/astropy.coordinates.RepresentationMapping.html#astropy.coordinates.RepresentationMapping",fontname="Vera Sans, DejaVu Sans, Liberation Sans, Arial, Helvetica, sans",tooltip="This `~collections.namedtuple` is used with the",height=0.25,shape=box,fontsize=10]; "RepresentationMapping" -> "RepresentationMapping" [arrowsize=0.5,style="setlinewidth(0.5)"]; "SkyCoord" [style="setlinewidth(0.5)",URL="../api/astropy.coordinates.SkyCoord.html#astropy.coordinates.SkyCoord",fontname="Vera Sans, DejaVu Sans, Liberation Sans, Arial, Helvetica, sans",tooltip="High-level object providing a flexible interface for celestial coordinate",height=0.25,shape=box,fontsize=10]; "SphericalRepresentation" [style="setlinewidth(0.5)",URL="../api/astropy.coordinates.SphericalRepresentation.html#astropy.coordinates.SphericalRepresentation",fontname="Vera Sans, DejaVu Sans, Liberation Sans, Arial, Helvetica, sans",tooltip="Representation of points in 3D spherical coordinates.",height=0.25,shape=box,fontsize=10]; "BaseRepresentation" -> "SphericalRepresentation" [arrowsize=0.5,style="setlinewidth(0.5)"]; "StaticMatrixTransform" [style="setlinewidth(0.5)",URL="../api/astropy.coordinates.StaticMatrixTransform.html#astropy.coordinates.StaticMatrixTransform",fontname="Vera Sans, DejaVu Sans, Liberation Sans, Arial, Helvetica, sans",tooltip="A coordinate transformation defined as a 3 x 3 cartesian",height=0.25,shape=box,fontsize=10]; "CoordinateTransform" -> "StaticMatrixTransform" [arrowsize=0.5,style="setlinewidth(0.5)"]; "TimeFrameAttribute" [style="setlinewidth(0.5)",URL="../api/astropy.coordinates.TimeFrameAttribute.html#astropy.coordinates.TimeFrameAttribute",fontname="Vera Sans, DejaVu Sans, Liberation Sans, Arial, Helvetica, sans",tooltip="Frame attribute descriptor for quantities that are Time objects.",height=0.25,shape=box,fontsize=10]; "FrameAttribute" -> "TimeFrameAttribute" [arrowsize=0.5,style="setlinewidth(0.5)"]; "TransformGraph" [style="setlinewidth(0.5)",URL="../api/astropy.coordinates.TransformGraph.html#astropy.coordinates.TransformGraph",fontname="Vera Sans, DejaVu Sans, Liberation Sans, Arial, Helvetica, sans",tooltip="A graph representing the paths between coordinate frames.",height=0.25,shape=box,fontsize=10]; "UnitSphericalRepresentation" [style="setlinewidth(0.5)",URL="../api/astropy.coordinates.UnitSphericalRepresentation.html#astropy.coordinates.UnitSphericalRepresentation",fontname="Vera Sans, DejaVu Sans, Liberation Sans, Arial, Helvetica, sans",tooltip="Representation of points on a unit sphere.",height=0.25,shape=box,fontsize=10]; "BaseRepresentation" -> "UnitSphericalRepresentation" [arrowsize=0.5,style="setlinewidth(0.5)"]; "ndarray" [style="setlinewidth(0.5)",fontname="Vera Sans, DejaVu Sans, Liberation Sans, Arial, Helvetica, sans",tooltip="ndarray(shape, dtype=float, buffer=None, offset=0,",height=0.25,shape=box,fontsize=10]; }