code: """
  Common solar physics coordinate systems.
  
  This submodule implements various solar physics coordinate frames for use with
  the `astropy.coordinates` module.
  """
  from contextlib import contextmanager
  
  import numpy as np
  
  import astropy.units as u
  from astropy.coordinates import ConvertError, QuantityAttribute
  from astropy.coordinates.baseframe import BaseCoordinateFrame, RepresentationMapping
  from astropy.coordinates.representation import (
      CartesianDifferential,
      CartesianRepresentation,
      CylindricalRepresentation,
      SphericalDifferential,
      SphericalRepresentation,
      UnitSphericalRepresentation,
  )
  from astropy.time import Time
  
  from sunpy.sun.constants import radius as _RSUN
  from sunpy.time.time import _variables_for_parse_time_docstring
  from sunpy.util.decorators import add_common_docstring
  from sunpy.util.exceptions import SunpyUserWarning
  from .frameattributes import ObserverCoordinateAttribute, TimeFrameAttributeSunPy
  
  _J2000 = Time('J2000.0', scale='tt')
  
  __all__ = ['SunPyBaseCoordinateFrame', 'BaseHeliographic',
             'HeliographicStonyhurst', 'HeliographicCarrington',
             'Heliocentric', 'Helioprojective',
             'HeliocentricEarthEcliptic', 'GeocentricSolarEcliptic',
             'HeliocentricInertial', 'GeocentricEarthEquatorial']
  
  
  def _frame_parameters():
      """
      Returns formatting dictionary to use with add_common_docstring to populate frame docstrings
      """
      ret = {}
  
      # Each text block is missing the first indent because it already exists in the frame docstring
      ret['data'] = ("data : `~astropy.coordinates.BaseRepresentation` or ``None``\n"
                     "        A representation object or ``None`` to have no data\n"
                     "        (or use the coordinate component arguments, see below).")
      ret['common'] = (f"obstime : {_variables_for_parse_time_docstring()['parse_time_types']}\n"
                       "        The time of the observation.  This is used to determine the\n"
                       "        position of solar-system bodies (e.g., the Sun and the Earth) as\n"
                       "        needed to define the origin and orientation of the frame.\n"
                       "    representation_type : `~astropy.coordinates.BaseRepresentation`, str, optional\n"
                       "        A representation class or string name of a representation class.\n"
                       "        This may change the valid coordinate component arguments from the\n"
                       "        defaults (see above). For example, passing\n"
                       "        ``representation_type='cartesian'`` will make the frame expect\n"
                       "        Cartesian coordinate component arguments (typically, ``x``, ``y``,\n"
                       "        and ``z``).\n"
                       "    copy : bool, optional\n"
                       "        If `True` (default), make copies of the input coordinate arrays.")
      ret['lonlat'] = ("lon : `~astropy.coordinates.Angle` or `~astropy.units.Quantity`, optional\n"
                       "        The longitude coordinate for this object (``lat`` must also be\n"
                       "        given and ``data`` must be ``None``).\n"
                       "        Not needed if ``data`` is given.\n"
                       "    lat : `~astropy.coordinates.Angle` or `~astropy.units.Quantity`, optional\n"
                       "        The latitude coordinate for this object (``lon`` must also be\n"
                       "        given and ``data`` must be ``None``).\n"
                       "        Not needed if ``data`` is given.")
      ret['radius'] = ("radius : `~astropy.units.Quantity`, optional\n"
                       "        The radial distance coordinate from Sun center for this object.\n"
                       "        Defaults to the radius of the Sun. Not needed if ``data`` is given.")
      ret['distance_sun'] = ("distance : `~astropy.units.Quantity`, optional\n"
                             "        The distance coordinate from Sun center for this object.\n"
                             "        Not needed if ``data`` is given.")
      ret['distance_earth'] = ("distance : `~astropy.units.Quantity`, optional\n"
                               "        The distance coordinate from Earth center for this object.\n"
                               "        Not needed if ``data`` is given.")
      ret['xyz'] = ("x : `~astropy.units.Quantity`, optional\n"
                    "        X-axis coordinate for this object. Not needed if ``data`` is given.\n"
                    "    y : `~astropy.units.Quantity`, optional\n"
                    "        Y-axis coordinate for this object. Not needed if ``data`` is given.\n"
                    "    z : `~astropy.units.Quantity`, optional\n"
                    "        Z-axis coordinate for this object. Not needed if ``data`` is given.")
      ret['observer'] = ("observer : `~sunpy.coordinates.frames.HeliographicStonyhurst`, str\n"
                         "        The location of the observer. If a string is provided,\n"
                         "        it must be a solar system body that can be parsed by\n"
                         "        `~sunpy.coordinates.ephemeris.get_body_heliographic_stonyhurst`\n"
                         "        at the time ``obstime``. Defaults to Earth center.")
      ret['rsun'] = ("rsun : `~astropy.units.Quantity`\n"
                     "        The radius of the Sun in length units. Used to convert a 2D\n"
                     "        coordinate (i.e., no ``radius`` component) to a 3D coordinate by\n"
                     "        assuming that the coordinate is on the surface of the Sun. Defaults\n"
                     "        to the photospheric radius as defined in `sunpy.sun.constants`.")
      ret['equinox'] = (f"equinox : {_variables_for_parse_time_docstring()['parse_time_types']}\n"
                        "        The date for the mean vernal equinox.\n"
                        "        Defaults to the J2000.0 equinox.")
  
      return ret
  
  
  class SunPyBaseCoordinateFrame(BaseCoordinateFrame):
      """
      Base class for sunpy coordinate frames.
  
      This class is not intended to be used directly and has no transformations defined.
  
      * Defines the frame attribute ``obstime`` for observation time.
      * Defines a default wrap angle of 180 degrees for longitude in spherical coordinates,
        which can be overridden via the class variable ``_wrap_angle``.
      * Inject a nice way of representing the object which the coordinate represents.
      """
      obstime = TimeFrameAttributeSunPy()
  
      default_representation = SphericalRepresentation
      default_differential = SphericalDifferential
  
      frame_specific_representation_info = {
          SphericalDifferential: [RepresentationMapping('d_lon', 'd_lon', u.arcsec/u.s),
                                  RepresentationMapping('d_lat', 'd_lat', u.arcsec/u.s),
                                  RepresentationMapping('d_distance', 'd_distance', u.km/u.s)],
      }
  
      _wrap_angle = 180*u.deg  # for longitude in spherical coordinates
  
      def __init__(self, *args, **kwargs):
          self.object_name = None
  
          # If wrap_longitude=False is passed in, do not impose a specific wrap angle for the frame
          if not kwargs.pop('wrap_longitude', True):
              self._wrap_angle = None
  
          super().__init__(*args, **kwargs)
  
          # If obstime is specified, treat the default observer (None) as explicitly set
          if self.obstime is not None and self.is_frame_attr_default('observer'):
              self._attr_names_with_defaults.remove('observer')
  
          return
  
      def represent_as(self, base, s='base', in_frame_units=False):
          data = super().represent_as(base, s, in_frame_units=in_frame_units)
  
          # If a frame wrap angle is set, use that wrap angle for any spherical representations.
          if self._wrap_angle is not None and \
             isinstance(data, (UnitSphericalRepresentation, SphericalRepresentation)):
              data.lon.wrap_angle = self._wrap_angle
          return data
  
      def __str__(self):
          # We override this here so that when you print a SkyCoord it shows the
          # observer as the string and not the whole massive coordinate.
          if getattr(self, "object_name", None):
              return f"<{self.__class__.__name__} Coordinate for '{self.object_name}'>"
          else:
              return super().__str__()
  
      @property
      def _is_2d(self):
          return (self._data is not None and self._data.norm().unit is u.one
                  and u.allclose(self._data.norm(), 1*u.one))
  
      def __init_subclass__(cls, **kwargs):
          super().__init_subclass__(**kwargs)
  
          # TODO: Remove this after the minimum Astropy dependency includes astropy/astropy#12005
          cls._fix_property_docstrings()
  
      @classmethod
      def _fix_property_docstrings(cls):
          # This class method adds docstrings to properties dynamically created by
          # BaseCoordinateFrame.__init_subclass__().  Accordingly, this method needs to itself be
          # called from SunPyBaseCoordinateFrame.__init_subclass__() to work for our subclasses.
          property_docstrings = {
              'default_representation': "Default representation for position data",
              'default_differential': "Default representation for differential data",
              'frame_specific_representation_info': "Mapping for frame-specific component names",
          }
          for prop, docstring in property_docstrings.items():
              if getattr(cls, prop).__doc__ is None:
                  setattr(getattr(cls, prop), '__doc__', docstring)
  
  
  # TODO: Remove this after the minimum Astropy dependency includes astropy/astropy#12005
  SunPyBaseCoordinateFrame._fix_property_docstrings()
  
  
  class BaseHeliographic(SunPyBaseCoordinateFrame):
      """
      Base class for HeliographicCarrington (HGC) and HeliographicStonyhurst (HGS) frames.
  
      This class is not intended to be used directly and has no transformations defined.
      """
      frame_specific_representation_info = {
          SphericalRepresentation: [RepresentationMapping('lon', 'lon', u.deg),
                                    RepresentationMapping('lat', 'lat', u.deg),
                                    RepresentationMapping('distance', 'radius', None)],
          SphericalDifferential: [RepresentationMapping('d_lon', 'd_lon', u.arcsec/u.s),
                                  RepresentationMapping('d_lat', 'd_lat', u.arcsec/u.s),
                                  RepresentationMapping('d_distance', 'd_radius', u.km/u.s)],
      }
  
      rsun = QuantityAttribute(default=_RSUN, unit=u.km)
  
      def make_3d(self):
          """
          Returns a fully 3D coordinate based on this coordinate.
  
          If this coordinate is only 2D (i.e., no ``radius`` component) or is a
          unit vector (i.e., the norm of the coordinate is unity), a new
          coordinate is created that corresponds to the surface of the Sun.
          That is, the 3D coordinate will retain the ``lon`` and ``lat``, and
          ``radius`` will be set to the frame's ``rsun`` frame attribute.
  
          If this coordinate is already fully 3D, it is directly returned, even
          if it does not lie on the surface of the Sun.
  
          Returns
          -------
          frame : `~sunpy.coordinates.frames.BaseHeliographic`
              The fully 3D coordinate
          """
          if self._is_2d:
              return self.realize_frame(self._data * self.rsun)
  
          # The coordinate is already 3D
          return self
  
  
  @add_common_docstring(**_frame_parameters())
  class HeliographicStonyhurst(BaseHeliographic):
      """
      A coordinate or frame in the Stonyhurst Heliographic (HGS) system.
  
      - The origin is the center of the Sun.
      - The Z-axis (+90 degrees latitude) is aligned with the Sun's north pole.
      - The X-axis (0 degrees longitude and 0 degrees latitude) is aligned with the projection of
        the Sun-Earth line onto the Sun's equatorial plane.
  
      This system is also know as the Heliocentric Earth Equatorial (HEEQ) system when
      represented using Cartesian components.
  
      A new instance can be created using the following signatures
      (note that if supplied, ``obstime`` and ``representation_type`` must be
      keyword arguments)::
  
          HeliographicStonyhurst(lon, lat, obstime=obstime)
          HeliographicStonyhurst(lon, lat, radius, obstime=obstime)
          HeliographicStonyhurst(x, y, z, representation_type='cartesian', obstime=obstime)
  
      Parameters
      ----------
      {data}
      {lonlat}
      {radius}
      {rsun}
      {common}
  
      Examples
      --------
      >>> from astropy.coordinates import SkyCoord
      >>> import sunpy.coordinates
      >>> import astropy.units as u
      >>> sc = SkyCoord(1*u.deg, 1*u.deg, 2*u.km,
      ...               frame="heliographic_stonyhurst",
      ...               obstime="2010/01/01T00:00:45")
      >>> sc
      <SkyCoord (HeliographicStonyhurst: obstime=2010-01-01T00:00:45.000, rsun=695700.0 km): (lon, lat, radius) in (deg, deg, km)
          (1., 1., 2.)>
      >>> sc.frame
      <HeliographicStonyhurst Coordinate (obstime=2010-01-01T00:00:45.000, rsun=695700.0 km): (lon, lat, radius) in (deg, deg, km)
          (1., 1., 2.)>
      >>> sc = SkyCoord(HeliographicStonyhurst(-10*u.deg, 2*u.deg))
      >>> sc
      <SkyCoord (HeliographicStonyhurst: obstime=None, rsun=695700.0 km): (lon, lat) in deg
          (-10., 2.)>
      >>> sc = SkyCoord(CartesianRepresentation(0*u.km, 45*u.km, 2*u.km),
      ...               obstime="2011/01/05T00:00:50",
      ...               frame="heliographic_stonyhurst")
      >>> sc
      <SkyCoord (HeliographicStonyhurst: obstime=2011-01-05T00:00:50.000, rsun=695700.0 km): (lon, lat, radius) in (deg, deg, km)
      (90., 2.54480438, 45.04442252)>
      """
      name = "heliographic_stonyhurst"
  
  
  @add_common_docstring(**_frame_parameters())
  class HeliographicCarrington(BaseHeliographic):
      """
      A coordinate or frame in the Carrington Heliographic (HGC) system.
  
      - The origin is the center of the Sun.
      - The Z-axis (+90 degrees latitude) is aligned with the Sun's north pole.
      - The X-axis and Y-axis rotate with a period of 25.38 days.
  
      This system differs from Stonyhurst Heliographic (HGS) in its definition of longitude.  This
      longitude is an "apparent" longitude because it takes into account the time it takes for light
      to travel from the Sun's surface to the observer.  Thus, the observer needs to be specified to
      be able to transform to any other coordinate frame.
  
      A new instance can be created using the following signatures
      (note that if supplied, ``obstime`` and ``observer`` must be a keyword argument)::
  
          HeliographicCarrington(lon, lat, obstime=obstime, observer=observer)
          HeliographicCarrington(lon, lat, radius, obstime=obstime, observer=observer)
  
      If you want to define the location in HGC such that the observer for the coordinate frame is
      the same as that location (e.g., the location of an observatory in its corresponding HGC
      frame), use ``observer='self'``::
  
          HeliographicCarrington(lon, lat, radius, obstime=obstime, observer='self')
  
      Parameters
      ----------
      {data}
      {lonlat}
      {radius}
      {observer}
      {rsun}
      {common}
  
      Examples
      --------
      >>> from astropy.coordinates import SkyCoord
      >>> import sunpy.coordinates
      >>> import astropy.units as u
      >>> sc = SkyCoord(1*u.deg, 2*u.deg, 3*u.km,
      ...               frame="heliographic_carrington",
      ...               observer="earth",
      ...               obstime="2010/01/01T00:00:30")
      >>> sc
      <SkyCoord (HeliographicCarrington: obstime=2010-01-01T00:00:30.000, rsun=695700.0 km, observer=<HeliographicStonyhurst Coordinate for 'earth'>): (lon, lat, radius) in (deg, deg, km)
          (1., 2., 3.)>
  
      >>> sc = SkyCoord([1,2,3]*u.deg, [4,5,6]*u.deg, [5,6,7]*u.km,
      ...               obstime="2010/01/01T00:00:45",
      ...               observer="self",
      ...               frame="heliographic_carrington")
      >>> sc
      <SkyCoord (HeliographicCarrington: obstime=2010-01-01T00:00:45.000, rsun=695700.0 km, observer=self): (lon, lat, radius) in (deg, deg, km)
          [(1., 4., 5.), (2., 5., 6.), (3., 6., 7.)]>
  
      >>> sc = SkyCoord(CartesianRepresentation(0*u.km, 45*u.km, 2*u.km),
      ...               obstime="2011/01/05T00:00:50",
      ...               frame="heliographic_carrington")
      >>> sc
      <SkyCoord (HeliographicCarrington: obstime=2011-01-05T00:00:50.000, rsun=695700.0 km, observer=None): (lon, lat, radius) in (deg, deg, km)
          (90., 2.54480438, 45.04442252)>
      """
      name = "heliographic_carrington"
      _wrap_angle = 360*u.deg
  
      observer = ObserverCoordinateAttribute(HeliographicStonyhurst)
  
      def __init__(self, *args, **kwargs):
          super().__init__(*args, **kwargs)
          if not isinstance(self.observer, BaseCoordinateFrame) and self.observer == 'self' and self._is_2d:
              raise ValueError("Full 3D coordinate (including radius) must be specified "
                               "when observer='self'.")
  
  
  @add_common_docstring(**_frame_parameters())
  class Heliocentric(SunPyBaseCoordinateFrame):
      """
      A coordinate or frame in the Heliocentric system, which is observer-based.
  
      - The origin is the center of the Sun.
      - The Z-axis is aligned with the Sun-observer line.
      - The Y-axis is aligned with the component of the vector to the Sun's north pole that is
        perpendicular to the Z-axis.
  
      This frame defaults to a Cartesian component representation, which is known as Heliocentric
      Cartesian (HCC).  This frame can also be represented using cylindrical components, where
      where ``rho`` is the impact parameter and ``psi`` is the position angle.
      ``psi`` is measured relative to the west limb, rather than solar north, so is shifted
      by 90 degrees compared to the convention of the Heliocentric Radial (HCR) system.
  
      A new instance can be created using the following signatures
      (note that if supplied, ``obstime``, ``observer``, and ``representation_type`` must be
      keyword arguments)::
  
          Heliocentric(x, y, z, obstime=obstime, observer=observer)
          Heliocentric(rho, psi, z, representation_type='cylindrical', obstime=obstime, observer=observer)
  
      Parameters
      ----------
      {data}
      {xyz}
      {observer}
      {common}
  
      Examples
      --------
  
      >>> from astropy.coordinates import SkyCoord, CartesianRepresentation
      >>> import sunpy.coordinates
      >>> import astropy.units as u
  
      >>> sc = SkyCoord(CartesianRepresentation(10*u.km, 1*u.km, 2*u.km),
      ...               obstime="2011/01/05T00:00:50", observer="earth", frame="heliocentric")
      >>> sc
      <SkyCoord (Heliocentric: obstime=2011-01-05T00:00:50.000, observer=<HeliographicStonyhurst Coordinate for 'earth'>): (x, y, z) in km
          (10., 1., 2.)>
  
      >>> sc = SkyCoord([1,2]*u.km, [3,4]*u.m, [5,6]*u.cm,
      ...               obstime="2011/01/01T00:00:54", observer="earth", frame="heliocentric")
      >>> sc
      <SkyCoord (Heliocentric: obstime=2011-01-01T00:00:54.000, observer=<HeliographicStonyhurst Coordinate for 'earth'>): (x, y, z) in (km, m, cm)
          [(1., 3., 5.), (2., 4., 6.)]>
  
      >>> sc = SkyCoord(CylindricalRepresentation(10*u.km, 60*u.deg, 10*u.km),
      ...               obstime="2011/01/05T00:00:50", observer="earth", frame="heliocentric")
      >>> sc
      <SkyCoord (Heliocentric: obstime=2011-01-05T00:00:50.000, observer=<HeliographicStonyhurst Coordinate for 'earth'>): (x, y, z) in km
          (5., 8.66025404, 10.)>
      """
      default_representation = CartesianRepresentation
      default_differential = CartesianDifferential
  
      frame_specific_representation_info = {
          CylindricalRepresentation: [RepresentationMapping('phi', 'psi', u.deg)]
      }
  
      observer = ObserverCoordinateAttribute(HeliographicStonyhurst)
  
      def represent_as(self, base, s='base', in_frame_units=False):
          data = super().represent_as(base, s, in_frame_units=in_frame_units)
  
          # For cylindrical representations, wrap the `psi` component (natively `phi`) at 360 deg
          if isinstance(data, CylindricalRepresentation):
              data.phi.wrap_at(360*u.deg, inplace=True)
          return data
  
  
  @add_common_docstring(**_frame_parameters())
  class Helioprojective(SunPyBaseCoordinateFrame):
      """
      A coordinate or frame in the Helioprojective Cartesian (HPC) system, which is observer-based.
  
      - The origin is the location of the observer.
      - ``Tx`` (aka "theta_x") is the angle relative to the plane containing the Sun-observer line
        and the Sun's rotation axis, with positive values in the direction of the Sun's west limb.
      - ``Ty`` (aka "theta_y") is the angle relative to the Sun's equatorial plane, with positive
        values in the direction of the Sun's north pole.
      - ``distance`` is the Sun-observer distance.
  
      This system is frequently used in a projective form without ``distance`` specified.  For
      observations looking very close to the center of the Sun, where the small-angle approximation
      is appropriate, ``Tx`` and ``Ty`` can be approximated as Cartesian components.
  
      A new instance can be created using the following signatures
      (note that if supplied, ``obstime`` and ``observer`` must be keyword arguments)::
  
          Helioprojective(Tx, Ty, obstime=obstime, observer=observer)
          Helioprojective(Tx, Ty, distance, obstime=obstime, observer=observer)
  
      Parameters
      ----------
      {data}
      Tx : `~astropy.coordinates.Angle` or `~astropy.units.Quantity`
          The theta_x coordinate for this object. Not needed if ``data`` is given.
      Ty : `~astropy.coordinates.Angle` or `~astropy.units.Quantity`
          The theta_y coordinate for this object. Not needed if ``data`` is given.
      distance : `~astropy.units.Quantity`
          The distance coordinate from the observer for this object.
          Not needed if ``data`` is given.
      {observer}
      {rsun}
      {common}
  
      Examples
      --------
      >>> from astropy.coordinates import SkyCoord
      >>> import sunpy.coordinates
      >>> import astropy.units as u
      >>> sc = SkyCoord(0*u.deg, 0*u.deg, 5*u.km,
      ...               obstime="2010/01/01T00:00:00", observer="earth", frame="helioprojective")
      >>> sc
      <SkyCoord (Helioprojective: obstime=2010-01-01T00:00:00.000, rsun=695700.0 km, observer=<HeliographicStonyhurst Coordinate for 'earth'>): (Tx, Ty, distance) in (arcsec, arcsec, km)
          (0., 0., 5.)>
      >>> sc = SkyCoord(0*u.deg, 0*u.deg,
      ...               obstime="2010/01/01T00:00:00", observer="earth", frame="helioprojective")
      >>> sc
      <SkyCoord (Helioprojective: obstime=2010-01-01T00:00:00.000, rsun=695700.0 km, observer=<HeliographicStonyhurst Coordinate for 'earth'>): (Tx, Ty) in arcsec
          (0., 0.)>
      >>> sc = SkyCoord(CartesianRepresentation(1*u.AU, 1e5*u.km, -2e5*u.km),
      ...               obstime="2011/01/05T00:00:50", observer="earth", frame="helioprojective")
      >>> sc
      <SkyCoord (Helioprojective: obstime=2011-01-05T00:00:50.000, rsun=695700.0 km, observer=<HeliographicStonyhurst Coordinate for 'earth'>): (Tx, Ty, distance) in (arcsec, arcsec, AU)
          (137.87948623, -275.75878762, 1.00000112)>
      """
      frame_specific_representation_info = {
          SphericalRepresentation: [RepresentationMapping('lon', 'Tx', u.arcsec),
                                    RepresentationMapping('lat', 'Ty', u.arcsec),
                                    RepresentationMapping('distance', 'distance', None)],
          SphericalDifferential: [RepresentationMapping('d_lon', 'd_Tx', u.arcsec/u.s),
                                  RepresentationMapping('d_lat', 'd_Ty', u.arcsec/u.s),
                                  RepresentationMapping('d_distance', 'd_distance', u.km/u.s)],
          UnitSphericalRepresentation: [RepresentationMapping('lon', 'Tx', u.arcsec),
                                        RepresentationMapping('lat', 'Ty', u.arcsec)],
      }
  
      rsun = QuantityAttribute(default=_RSUN, unit=u.km)
      observer = ObserverCoordinateAttribute(HeliographicStonyhurst)
  
      @property
      def angular_radius(self):
          """
          Angular radius of the Sun as seen by the observer.
  
          The ``rsun`` frame attribute is the radius of the Sun in length units.
          The tangent vector from the observer to the edge of the Sun forms a
          right-angle triangle with the radius of the Sun as the far side and the
          Sun-observer distance as the hypotenuse. Thus, the sine of the angular
          radius of the Sun is ratio of these two distances.
          """
          from sunpy.coordinates.sun import _angular_radius  # avoiding a circular import
  
          if not isinstance(self.observer, HeliographicStonyhurst):
              if self.observer is None:
                  raise ValueError("The observer must be defined, not `None`.")
              raise ValueError("The observer must be fully defined by specifying `obstime`.")
          return _angular_radius(self.rsun, self.observer.radius)
  
      def make_3d(self):
          """
          This method calculates the third coordinate of the Helioprojective
          frame. It assumes that the coordinate point is on the surface of the Sun.
  
          If a point in the frame is off limb then NaN will be returned.
  
          Returns
          -------
          new_frame : `~sunpy.coordinates.frames.Helioprojective`
              A new frame instance with all the attributes of the original but
              now with a third coordinate.
          """
          # Skip if we already are 3D
          if not self._is_2d:
              return self
  
          if not isinstance(self.observer, BaseCoordinateFrame):
              raise ConvertError("Cannot calculate distance to the Sun "
                                 f"for observer '{self.observer}' "
                                 "without `obstime` being specified.")
  
          rep = self.represent_as(UnitSphericalRepresentation)
          lat, lon = rep.lat, rep.lon
  
          # Check for the use of floats with lower precision than the native Python float
          if not set([lon.dtype.type, lat.dtype.type]).issubset([float, np.float64, np.longdouble]):
              raise SunpyUserWarning("The Helioprojective component values appear to be lower "
                                     "precision than the native Python float: "
                                     f"Tx is {lon.dtype.name}, and Ty is {lat.dtype.name}. "
                                     "To minimize precision loss, you may want to cast the values to "
                                     "`float` or `numpy.float64` via the NumPy method `.astype()`.")
  
          # Calculate the distance to the surface of the Sun using the law of cosines
          cos_alpha = np.cos(lat) * np.cos(lon)
          c = self.observer.radius**2 - self.rsun**2
          b = -2 * self.observer.radius * cos_alpha
          # Ignore sqrt of NaNs
          with np.errstate(invalid='ignore'):
              d = ((-1*b) - np.sqrt(b**2 - 4*c)) / 2  # use the "near" solution
  
          if self._spherical_screen:
              sphere_center = self._spherical_screen['center'].transform_to(self).cartesian
              c = sphere_center.norm()**2 - self._spherical_screen['radius']**2
              b = -2 * sphere_center.dot(rep)
              # Ignore sqrt of NaNs
              with np.errstate(invalid='ignore'):
                  dd = ((-1*b) + np.sqrt(b**2 - 4*c)) / 2  # use the "far" solution
  
              d = np.fmin(d, dd) if self._spherical_screen['only_off_disk'] else dd
  
          return self.realize_frame(SphericalRepresentation(lon=lon,
                                                            lat=lat,
                                                            distance=d))
  
      _spherical_screen = None
  
      @classmethod
      @contextmanager
      def assume_spherical_screen(cls, center, only_off_disk=False):
          """
          Context manager to interpret 2D coordinates as being on the inside of a spherical screen.
  
          The radius of the screen is the distance between the specified ``center`` and Sun center.
          This ``center`` does not have to be the same as the observer location for the coordinate
          frame.  If they are the same, then this context manager is equivalent to assuming that the
          helioprojective "zeta" component is zero.
  
          This replaces the default assumption where 2D coordinates are mapped onto the surface of the
          Sun.
  
          Parameters
          ----------
          center : `~astropy.coordinates.SkyCoord`
              The center of the spherical screen
          only_off_disk : `bool`, optional
              If `True`, apply this assumption only to off-disk coordinates, with on-disk coordinates
              still mapped onto the surface of the Sun.  Defaults to `False`.
  
          Examples
          --------
  
          .. minigallery:: sunpy.coordinates.Helioprojective.assume_spherical_screen
  
          >>> import astropy.units as u
          >>> from sunpy.coordinates import Helioprojective
          >>> h = Helioprojective(range(7)*u.arcsec*319, [0]*7*u.arcsec,
          ...                     observer='earth', obstime='2020-04-08')
          >>> print(h.make_3d())
          <Helioprojective Coordinate (obstime=2020-04-08T00:00:00.000, rsun=695700.0 km, observer=<HeliographicStonyhurst Coordinate for 'earth'>): (Tx, Ty, distance) in (arcsec, arcsec, AU)
              [(   0., 0., 0.99660825), ( 319., 0., 0.99687244),
               ( 638., 0., 0.99778472), ( 957., 0., 1.00103285),
               (1276., 0.,        nan), (1595., 0.,        nan),
               (1914., 0.,        nan)]>
  
          >>> with Helioprojective.assume_spherical_screen(h.observer):
          ...     print(h.make_3d())
          <Helioprojective Coordinate (obstime=2020-04-08T00:00:00.000, rsun=695700.0 km, observer=<HeliographicStonyhurst Coordinate for 'earth'>): (Tx, Ty, distance) in (arcsec, arcsec, AU)
              [(   0., 0., 1.00125872), ( 319., 0., 1.00125872),
               ( 638., 0., 1.00125872), ( 957., 0., 1.00125872),
               (1276., 0., 1.00125872), (1595., 0., 1.00125872),
               (1914., 0., 1.00125872)]>
  
          >>> with Helioprojective.assume_spherical_screen(h.observer, only_off_disk=True):
          ...     print(h.make_3d())
          <Helioprojective Coordinate (obstime=2020-04-08T00:00:00.000, rsun=695700.0 km, observer=<HeliographicStonyhurst Coordinate for 'earth'>): (Tx, Ty, distance) in (arcsec, arcsec, AU)
              [(   0., 0., 0.99660825), ( 319., 0., 0.99687244),
               ( 638., 0., 0.99778472), ( 957., 0., 1.00103285),
               (1276., 0., 1.00125872), (1595., 0., 1.00125872),
               (1914., 0., 1.00125872)]>
          """
          try:
              old_spherical_screen = cls._spherical_screen  # nominally None
  
              center_hgs = center.transform_to(HeliographicStonyhurst(obstime=center.obstime))
              cls._spherical_screen = {
                  'center': center,
                  'radius': center_hgs.radius,
                  'only_off_disk': only_off_disk
              }
              yield
          finally:
              cls._spherical_screen = old_spherical_screen
  
  
  @add_common_docstring(**_frame_parameters())
  class HeliocentricEarthEcliptic(SunPyBaseCoordinateFrame):
      """
      A coordinate or frame in the Heliocentric Earth Ecliptic (HEE) system.
  
      - The origin is the center of the Sun.
      - The X-axis (0 degrees longitude and 0 degrees latitude) is aligned with the Sun-Earth line.
      - The Z-axis (+90 degrees latitude) is aligned with the component perpendicular to the X-axis
        of the mean ecliptic pole at the observation time.
  
      Parameters
      ----------
      {data}
      {lonlat}
      {distance_sun}
      {common}
      """
  
  
  @add_common_docstring(**_frame_parameters())
  class GeocentricSolarEcliptic(SunPyBaseCoordinateFrame):
      """
      A coordinate or frame in the Geocentric Solar Ecliptic (GSE) system.
  
      - The origin is the center of the Earth.
      - The X-axis (0 degrees longitude and 0 degrees latitude) is aligned with the Earth-Sun line.
      - The Z-axis (+90 degrees latitude) is aligned with the component perpendicular to the X-axis
        of the mean ecliptic pole at the observation time.
  
      Parameters
      ----------
      {data}
      {lonlat}
      {distance_earth}
      {common}
  
      Notes
      -----
      Aberration due to Earth motion is not included.
      """
  
  
  @add_common_docstring(**_frame_parameters())
  class HeliocentricInertial(SunPyBaseCoordinateFrame):
      """
      A coordinate or frame in the Heliocentric Inertial (HCI) system.
  
      - The origin is the center of the Sun.
      - The Z-axis (+90 degrees latitude) is aligned with the Sun's north pole.
      - The X-axis (0 degrees longitude and 0 degrees latitude) is aligned with the solar ascending
        node on the ecliptic (mean J2000.0).
  
      Parameters
      ----------
      {data}
      {lonlat}
      {distance_sun}
      {common}
  
      Notes
      -----
      The solar ascending node on the ecliptic lies on the intersection of the solar equatorial
      plane with the ecliptic plane, not on the intersection of the celestial equatorial plane with
      the ecliptic plane.
      """
  
  
  @add_common_docstring(**_frame_parameters())
  class GeocentricEarthEquatorial(SunPyBaseCoordinateFrame):
      """
      A coordinate or frame in the Geocentric Earth Equatorial (GEI) system.
  
      - The origin is the center of the Earth.
      - The Z-axis (+90 degrees latitude) is aligned with the Earth's north pole.
      - The X-axis (0 degrees longitude and 0 degrees latitude) is aligned with the mean (not true)
        vernal equinox.
  
      Parameters
      ----------
      {data}
      {lonlat}
      {distance_earth}
      {equinox}
      {common}
  
      Notes
      -----
      Aberration due to Earth motion is not included.
      """
      equinox = TimeFrameAttributeSunPy(default=_J2000)
  
apis: numpy.sqrt numpy.fmin numpy.cos numpy.errstate