# SunPy coordinates¶

The SunPy coordinates submodule is an implementation of the common solar physics coordinate frames using the Astropy coordinates framework.

## Getting Started¶

The easiest interface to the coordinates module is through the `SkyCoord` class:

```>>> import astropy.units as u
>>> from astropy.coordinates import SkyCoord
>>> from sunpy.coordinates import frames

>>> c = SkyCoord(-100*u.arcsec, 500*u.arcsec, frame=frames.Helioprojective)
>>> c = SkyCoord(x=-72241.0*u.km, y=361206.1*u.km, z=589951.4*u.km, frame=frames.Heliocentric)
>>> c = SkyCoord(70*u.deg, -30*u.deg, frame=frames.HeliographicStonyhurst)
>>> c
<SkyCoord (HeliographicStonyhurst: obstime=None): (lon, lat, radius) in (deg, deg, km)
(70., -30., 695700.)>
```

It is also possible to use strings to define the frame but in that case make sure to explicitly import `sunpy.coordinates` as it registers solar coordinate frames with astropy coordinates.:

```>>> import astropy.units as u
>>> from astropy.coordinates import SkyCoord

>>> import sunpy.coordinates
>>> c = SkyCoord(-100*u.arcsec, 500*u.arcsec, frame='helioprojective')
>>> c
<SkyCoord (Helioprojective: obstime=None, rsun=695700.0 km, observer=earth): (Tx, Ty) in arcsec
(-100., 500.)>
```

SunPy implements support for the following solar physics coordinate systems:

for a complete description of these frames see `sunpy.coordinates.frames`, for a more detailed description of the frames see Thompson (2006)

`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, 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.

```>>> c = SkyCoord([-500, 400]*u.arcsec, [100, 200]*u.arcsec, frame=frames.Helioprojective)
>>> c
<SkyCoord (Helioprojective: obstime=None, rsun=695700.0 km, observer=earth): (Tx, Ty) in arcsec
[(-500.,  100.), ( 400.,  200.)]>
>>> c[0]
<SkyCoord (Helioprojective: obstime=None, rsun=695700.0 km, observer=earth): (Tx, Ty) in arcsec
(-500.,  100.)>
```

### Accessing Coordinates¶

Individual coordinates can be accessed via attributes on the SkyCoord object, but the names of the components of the coordinates for each frame differ. For a full description of all the properties of the frames see `sunpy.coordinates.frames`.

#### `Helioprojective`¶

For the helioprojective frame the coordinates are accessed as `Tx` and `Ty` representing theta x and y. These are the same coordinates that are often referred to as ‘solar-x’ and ‘solar-y’.:

```>>> c = SkyCoord(-500*u.arcsec, 100*u.arcsec, frame=frames.Helioprojective)
>>> c.Tx
<Longitude -500. arcsec>
>>> c.Ty
<Latitude 100. arcsec>
```

#### `Heliocentric`¶

Heliocentric normally a Cartesian frame so the coordinates are accessed as `x, y, z`:

```>>> c = SkyCoord(-72241.0*u.km, 361206.1*u.km, 589951.4*u.km, frame=frames.Heliocentric)
>>> c.x
<Quantity -72241. km>
>>> c.y
<Quantity 361206.1 km>
>>> c.z
<Quantity 589951.4 km>
```

#### `HeliographicStonyhurst` and `HeliographicCarrington`¶

Both the heliographic frames use latitude, longitude and radius which are accessed as follows:

```>>> c = SkyCoord(70*u.deg, -30*u.deg, frame=frames.HeliographicStonyhurst)
>>> c.lat
<Latitude -30. deg>
>>> c.lon
<Longitude 70. deg>
<Distance 695700. km>
```

## Transforming Between Coordinate Frames¶

Both `SkyCoord` and `BaseCoordinateFrame` instances have a `transform_to` method. This can be used to transform the frame to any other frame, either implemented in SunPy or in Astropy the astropy documentation for more details. An example of transforming the center of the solar disk to Carrington coordinates is:

```>>> c = SkyCoord(0*u.arcsec, 0*u.arcsec, frame=frames.Helioprojective, obstime="2017-07-26")
>>> c
<SkyCoord (Helioprojective: obstime=2017-07-26T00:00:00.000, rsun=695700.0 km, observer=<HeliographicStonyhurst Coordinate for 'earth'>): (Tx, Ty) in arcsec
(0., 0.)>
>>> c.transform_to(frames.HeliographicCarrington)
<SkyCoord (HeliographicCarrington: obstime=2017-07-26T00:00:00.000): (lon, lat, radius) in (deg, deg, AU)
(283.95274241, 5.31701821, 0.00465047)>
```

It is also possible to transform to any coordinate system implemented in Astropy. This can be used to find the position of the solar limb in AltAz equatorial coordinates:

```>>> from astropy.coordinates import EarthLocation, AltAz
>>> time = '2017-07-11 15:00'
>>> greenbelt = EarthLocation(lat=39.0044*u.deg, lon=-76.8758*u.deg)
>>> greenbelt_frame = AltAz(obstime=time, location=greenbelt)
>>> west_limb = SkyCoord(900*u.arcsec, 0*u.arcsec, frame=frames.Helioprojective, obstime=time)
>>> west_limb.transform_to(greenbelt_frame)
<SkyCoord (AltAz: obstime=2017-07-11 15:00:00.000, location=(1126916.53031967, -4833386.58391627, 3992696.622115747) m, pressure=0.0 hPa, temperature=0.0 deg_C, relative_humidity=0, obswl=1.0 micron): (az, alt, distance) in (deg, deg, m)
(111.40839101, 57.16645715, 1.51860261e+11)>
```

## Observer Location Information¶

Both `Helioprojective` and `Heliocentric` frames are defined by the location of the observer. For example in `Helioprojective` the observer is at the origin of the coordinate system. This information is encoded in the `Helioprojective` and `Heliocentric` frames as the `observer` attribute, which is itself an instance of the `HeliographicStonyhurst` frame. The default observer location is set to the position of the Earth (using `get_body_heliographic_stonyhurst`) as long as the `obstime` attribute is specified. If the `obstime` attribute is not set then you will be unable to transform the frame unless an explicit `observer` is specified, as the time is required to calculate the location of the Earth. The location of the observer is automatically populated from meta data when coordinate frames are created using map.

It is possible to convert from a `Helioprojective` frame with one observer location to another `Helioprojective` frame with a different observer location, by converting through `Heliographic`, this does involve making an assumption of the radius of the Sun to calculate the position on the solar sphere. The conversion can be performed as follows:

```# Input coordinate
>>> hpc1 = SkyCoord(0*u.arcsec, 0*u.arcsec, observer="earth", obstime="2017-07-26", frame=frames.Helioprojective)

Define a new Helioprojective frame with a different observer.
>>> import sunpy.coordinates
>>> hpc_out = sunpy.coordinates.Helioprojective(observer="venus", obstime="2017-07-26")

Perform the transformation from one to the other.
>>> hpc2 = hpc1.transform_to(hpc_out)
```

An example with two maps, named `aia` and `stereo`:

```>>> hpc1 = SkyCoord(0*u.arcsec, 0*u.arcsec, frame=aia.coordinate_frame)
>>> hpc2 = hpc1.transform_to(stereo.coordinate_frame)
```

## Design of the Coordinates Module¶

This module works by defining a collection of `Frames` (`sunpy.coordinates.frames`), which exists on a transformation graph, where the transformations between the coordinate frames are then defined and registered with the transformation graph (`sunpy.coordinates.transformations`). It is also possible to transform SunPy frames to Astropy frames.

Positions within these `Frames` are stored as a `Representation` of a coordinate, a representation being a description of a point in a Cartesian, spherical or cylindrical system (`astropy.coordinates.representation`). A frame that contains a representation of one or many points is said to have been ‘realized’.

For a more in depth look at the design and concepts of the Astropy coordinates system see Overview of astropy.coordinates Concepts

### Frames and SkyCoord¶

The `SkyCoord` class is a high level wrapper around the `astropy.coordinates` package. It provides an easier way to create and transform coordinates, by using string representations for frames rather than the classes themselves and some other usability improvements, for more information see the `SkyCoord` documentation.

The main advantage provided by `SkyCoord` is the support it provides for caching Frame attributes. Frame attributes are extra data specified with a frame, some examples in `sunpy.coordinates` are `obstime` or `observer` for observer location. Only the frames where this data is meaningful have these attributes, i.e. only the Helioprojective frames have `observer`. However, when you transform into another frame and then back to a projective frame using `SkyCoord` it will remember the attributes previously provided, and repopulate the final frame with them. If you were to do transformations using the Frames alone this would not happen.

The most important implication for this in `sunpy.coordinates` is the `rsun` parameter in the projective frames. If you create a projective frame with a `rsun` attribute, if you convert back to a projective frame it will be set correctly. It should also be noted that, if you create a Heliographic frame and then transform to a projective frame with an `rsun` attribute, it will not match the `radius` coordinate in the Heliographic frame. This is because you may mean to be describing a point above the defined ‘surface’ of the Sun.

## Coordinates and WCS¶

The `sunpy.coordinates` package provides a mapping between FITS-WCS CTYPE convention and the coordinate frames as defined in `sunpy.coordinates`. This is used via the `astropy.wcs.utils.wcs_to_celestial_frame` function, with which the SunPy frames are registered upon being imported. This list is used by packages such as `wcsaxes` to convert from `astropy.wcs.WCS` objects to coordinate frames.

The `sunpy.map.GenricMap` class creates `astropy.wcs.WCS` objects as `amap.wcs`, however, it adds some extra attributes to the `WCS` object to be able to fully specify the coordinate frame. It adds `heliographic_observer` and `rsun`.

If you want to obtain a un-realized coordinate frame corresponding to a `GenericMap` object you can do the following:

```>>> import sunpy.map
>>> from sunpy.data.sample import AIA_171_IMAGE
>>> amap = sunpy.map.Map(AIA_171_IMAGE)
>>> amap.observer_coordinate
<SkyCoord (HeliographicStonyhurst: obstime=2011-06-07T06:33:02.770): (lon, lat, radius) in (deg, deg, m)
(-0.00406308, 0.04787238, 1.51846026e+11)>
```

which is equivalent to:

```>>> from astropy.wcs.utils import wcs_to_celestial_frame
>>> wcs_to_celestial_frame(amap.wcs)
<Helioprojective Frame (obstime=2011-06-07T06:33:02.770, rsun=696000000.0 m, observer=<HeliographicStonyhurst Coordinate (obstime=2011-06-07T06:33:02.770): (lon, lat, radius) in (deg, deg, m)
(-0.00406308, 0.04787238, 1.51846026e+11)>)>
```

### sunpy.coordinates Package¶

This subpackage contains:

• A robust framework for working with coordinate systems

• Functions to obtain the locations of solar-system bodies

• Functions to calculate Sun-specific coordinate information (`sunpy.coordinates.sun`)

The diagram below shows all of Sun-based and Earth-based coordinate systems available through `sunpy.coordinates`, as well as the transformations between them. Each frame is labeled with the name of its class and its alias (useful for converting other coordinates to them using attribute-style access).

The frames colored in cyan are implemented in `astropy.coordinates`, and there are other astronomical frames that can be transformed to that are not shown below. See the documentation for `astropy.coordinates` for more information.

• SunPy frames:

• Astropy frames:

• AffineTransform:

• FunctionTransform:

• FunctionTransformWithFiniteDifference:

• StaticMatrixTransform:

• DynamicMatrixTransform:

#### Functions¶

 `get_body_heliographic_stonyhurst`(body[, …]) Return a `HeliographicStonyhurst` frame for the location of a solar-system body at a specified time. `get_earth`([time]) Return a `SkyCoord` for the location of the Earth at a specified time in the `HeliographicStonyhurst` frame. `get_horizons_coord`(body[, time, id_type]) Queries JPL HORIZONS and returns a `SkyCoord` for the location of a solar-system body at a specified time. `get_sun_B0`([time]) Deprecated since version 1.0. `get_sun_L0`([time]) Deprecated since version 1.0. `get_sun_P`([time]) Deprecated since version 1.0. `get_sun_orientation`(location[, time]) Deprecated since version 1.0. `get_sunearth_distance`([time]) Deprecated since version 1.0. `solar_frame_to_wcs_mapping`(frame[, projection]) For a given frame, this function returns the corresponding WCS object. This function registers the coordinates frames to their FITS-WCS coordinate type values in the `astropy.wcs.utils.wcs_to_celestial_frame` registry.

#### Classes¶

 `Heliocentric`(*args, **kwargs) A coordinate or frame in the Heliocentric system, which is observer-based. `HeliographicCarrington`(*args, **kwargs) A coordinate or frame in the Carrington Heliographic (HGC) system. `HeliographicStonyhurst`(*args, **kwargs) A coordinate or frame in the Stonyhurst Heliographic (HGS) system. `Helioprojective`(*args, **kwargs) A coordinate or frame in the Helioprojective Cartesian (HPC) system, which is observer-based. `NorthOffsetFrame` A frame which is relative to some position and another frame.

### sunpy.coordinates.frames Module¶

Common solar physics coordinate systems.

This submodule implements various solar physics coordinate frames for use with the `astropy.coordinates` module.

#### Classes¶

 `HeliographicStonyhurst`(*args, **kwargs) A coordinate or frame in the Stonyhurst Heliographic (HGS) system. `HeliographicCarrington`(*args, **kwargs) A coordinate or frame in the Carrington Heliographic (HGC) system. `Heliocentric`(*args, **kwargs) A coordinate or frame in the Heliocentric system, which is observer-based. `Helioprojective`(*args, **kwargs) A coordinate or frame in the Helioprojective Cartesian (HPC) system, which is observer-based.

### sunpy.coordinates.transformations Module¶

Coordinate Transformation Functions

This module contains the functions for converting one `sunpy.coordinates.frames` object to another.

Warning

The functions in this submodule should never be called directly, transforming between coordinate frames should be done using the `.transform_to` methods on `BaseCoordinateFrame` or `SkyCoord` instances.

#### Functions¶

 `hgs_to_hgc`(hgscoord, hgcframe) Convert from Heliographic Stonyhurst to Heliographic Carrington. `hgc_to_hgs`(hgccoord, hgsframe) Convert from Heliographic Carrington to Heliographic Stonyhurst. `hcc_to_hpc`(helioccoord, heliopframe) Convert from Heliocentric Cartesian to Helioprojective Cartesian. `hpc_to_hcc`(heliopcoord, heliocframe) Convert from Helioprojective Cartesian to Heliocentric Cartesian. `hcc_to_hgs`(helioccoord, heliogframe) Convert from Heliocentric Cartesian to Heliographic Stonyhurst. `hgs_to_hcc`(heliogcoord, heliocframe) Convert from Heliographic Stonyhurst to Heliocentric Cartesian. `hpc_to_hpc`(from_coo, to_frame) This converts from HPC to HPC, with different observer location parameters. `hcrs_to_hgs`(hcrscoord, hgsframe) Convert from HCRS to Heliographic Stonyhurst (HGS). `hgs_to_hcrs`(hgscoord, hcrsframe) Convert from Heliographic Stonyhurst to HCRS. `hgs_to_hgs`(from_coo, to_frame) Convert between two Heliographic Stonyhurst frames. `hgc_to_hgc`(from_coo, to_frame) Convert between two Heliographic Carrington frames. `hcc_to_hcc`(from_coo, to_frame) Convert between two Heliocentric frames.

### sunpy.coordinates.ephemeris Module¶

Ephemeris calculations using SunPy coordinate frames

#### Functions¶

 `get_body_heliographic_stonyhurst`(body[, …]) Return a `HeliographicStonyhurst` frame for the location of a solar-system body at a specified time. `get_earth`([time]) Return a `SkyCoord` for the location of the Earth at a specified time in the `HeliographicStonyhurst` frame. `get_sun_B0`([time]) Deprecated since version 1.0. `get_sun_L0`([time]) Deprecated since version 1.0. `get_sun_P`([time]) Deprecated since version 1.0. `get_sunearth_distance`([time]) Deprecated since version 1.0. `get_sun_orientation`(location[, time]) Deprecated since version 1.0. `get_horizons_coord`(body[, time, id_type]) Queries JPL HORIZONS and returns a `SkyCoord` for the location of a solar-system body at a specified time.

### sunpy.coordinates.sun Module¶

Sun-specific coordinate calculations

#### Functions¶

 Return the angular radius of the Sun as viewed from Earth. `sky_position`([t, equinox_of_date]) Returns the apparent position of the Sun (right ascension and declination) on the celestial sphere using the equatorial coordinate system, referred to the true equinox of date (as default). Return the Carrington rotation number. Returns the Sun’s true geometric longitude, referred to the mean equinox of date. Returns the Sun’s apparent longitude, referred to the true equinox of date. Returns the Sun’s true geometric latitude, referred to the mean equinox of date. Returns the Sun’s apparent latitude, referred to the true equinox of date. Returns the mean obliquity of the ecliptic, using the IAU 2006 definition. `true_rightascension`([t, equinox_of_date]) Returns the Sun’s true geometric right ascension relative to Earth, referred to the mean equinox of date (as default). `true_declination`([t, equinox_of_date]) Returns the Sun’s true geometric declination relative to Earth, referred to the mean equinox of date (as default). Returns the true obliquity of the ecliptic, using the IAU 2006 definition. `apparent_rightascension`([t, equinox_of_date]) Returns the Sun’s apparent right ascension relative to Earth, referred to the true equinox of date (as default). `apparent_declination`([t, equinox_of_date]) Returns the Sun’s apparent declination relative to Earth, referred to the true equinox of date (as default). Print out a summary of solar ephemeris. `B0`([time]) Return the B0 angle for the Sun at a specified time, which is the heliographic latitude of the Sun-disk center as seen from Earth. `L0`([time]) Return the L0 angle for the Sun at a specified time, which is the Carrington longitude of the Sun-disk center as seen from Earth. `P`([time]) Return the position (P) angle for the Sun at a specified time, which is the angle between geocentric north and solar north as seen from Earth, measured eastward from geocentric north. `earth_distance`([time]) Return the distance between the Sun and the Earth at a specified time. `orientation`(location[, time]) Return the orientation angle for the Sun from a specified Earth location and time.

### sunpy.coordinates.offset_frame Module¶

#### Classes¶

 `NorthOffsetFrame` A frame which is relative to some position and another frame.

### sunpy.coordinates.wcs_utils Module¶

#### Functions¶

 This function registers the coordinates frames to their FITS-WCS coordinate type values in the `astropy.wcs.utils.wcs_to_celestial_frame` registry. `solar_frame_to_wcs_mapping`(frame[, projection]) For a given frame, this function returns the corresponding WCS object.