CoordinateTransformation#

class pygaia.astrometry.coordinates.CoordinateTransformation(desired_transformation)#

Bases: object

Provides methods for carrying out transformations between different coordinate (reference) systems. Transformations between the following systems are supported:

  • ICRS or Equatorial (right ascension, declination)

  • Galactic (longitude, latitude)

  • Ecliptic (longitude, latitude)

The transformations can be applied to sky coordinates or Cartesian coordinates.

Note

The transformations here are only intended for systems that represent a rotated version of the ICRS. For transformations from and to non-ICRS systems (such as FK5) refer to Astropy’s coordinates package.

transformation#

The transformation represented by the instance of this class.

Type:

Transformations

rotationMatrix#

Rotation matrix corresponding to the transformation.

Type:

array

Methods Summary

start_coordinates()

Query which is the starting coordinate system of this transformation.

target_coordinates()

Query which is the target coordinate system of this transformation.

transform_cartesian_coordinates(x, y, z)

Rotate Cartesian coordinates from one reference system to another.

transform_covariance_matrix(phi, theta, covmat)

Transform the astrometric covariance matrix to its representation in the new coordinate system.

transform_proper_motion_errors(phi, theta, ...)

Converts the proper motion uncertainties from one reference system to another, including the covariance term.

transform_proper_motions(phi, theta, ...)

Converts proper motions from one reference system to another.

transform_sky_coordinate_errors(phi, theta, ...)

Converts the sky coordinate uncertainties from one reference system to another, including the covariance term.

transform_sky_coordinates(phi, theta)

Convert sky coordinates from one reference system to another.

Methods Documentation

start_coordinates()#

Query which is the starting coordinate system of this transformation.

Returns:

from_sys – String with starting coordinate system.

Return type:

str

target_coordinates()#

Query which is the target coordinate system of this transformation.

Returns:

to_sys – String with target coordinate system.

Return type:

str

transform_cartesian_coordinates(x, y, z)#

Rotate Cartesian coordinates from one reference system to another.

Use the rotation matrix with which the class was initialized. The inputs can be scalars or 1-dimensional numpy arrays. The length scale units of the inputs can be arbitrary but should of course be consistent.

Parameters:

  • x (float or array) – Value of X-coordinate in original reference system.

  • y (float or array) – Value of Y-coordinate in original reference system.

  • z (float or array) – Value of Z-coordinate in original reference system.

Returns:

  • xrot (float or array) – Value of X-coordinate after rotation

  • yrot (float or array) – Value of Y-coordinate after rotation

  • zrot (float or array) – Value of Z-coordinate after rotation

transform_covariance_matrix(phi, theta, covmat)#

Transform the astrometric covariance matrix to its representation in the new coordinate system.

Parameters:

  • phi (float) – The longitude-like angle of the position of the source (radians).

  • theta (float) – The latitude-like angle of the position of the source (radians).

  • covmat (array) – Covariance matrix (5,5) of the astrometric parameters.

Returns:

covmat_rot – Covariance matrix in its representation in the new coordinate system.

Return type:

array

transform_proper_motion_errors(phi, theta, sigmuphistar, sigmutheta, rho_muphi_mutheta=0)#

Converts the proper motion uncertainties from one reference system to another, including the covariance term.

Equations (1.5.4) and (1.5.20) from section 1.5 in the Hipparcos Explanatory Volume 1 are used.

Parameters:

  • phi (float or array) – The longitude-like angle of the position of the source (radians).

  • theta (float or array) – The latitude-like angle of the position of the source (radians).

  • sigmuphistar (float or attay) – Uncertainty in the proper motion in the longitude-like direction (including cos(latitude) factor).

  • sigmutheta (float or array) – Uncertainty in the proper motion in the latitude-like direction.

  • rho_muphi_mutheta (float or array) – Correlation coefficient of the proper motion errors. Zero by default.

Returns:

  • sigMuPhiRotStar (float or array) – The transformed uncertainty in the proper motion in the longitude direction (including np.cos(latitude) factor).

  • sigMuThetaRot (float or array) – The transformed uncertainty in the proper motion in the longitude direction.

  • rhoMuPhiMuThetaRot (float or array) – The transformed correlation coefficient.

transform_proper_motions(phi, theta, muphistar, mutheta)#

Converts proper motions from one reference system to another.

Use the prescriptions in section 1.5.3 of the Hipparcos Explanatory Volume 1 (equations 1.5.18, 1.5.19).

Parameters:

  • phi (float or array) – The longitude-like angle of the position of the source (radians).

  • theta (float or array) – The latitude-like angle of the position of the source (radians).

  • muphistar (float or array) – Value of the proper motion in the longitude-like angle, multiplied by cos(latitude).

  • mutheta (float or array) – Value of the proper motion in the latitude-like angle.

Returns:

  • muphistarrot (float or array) – Value of the transformed proper motion in the longitude-like angle (including the cos(latitude) factor).

  • muthetarot (float or array) – Value of the transformed proper motion in the latitude-like angle.

transform_sky_coordinate_errors(phi, theta, sigphistar, sigtheta, rho_phi_theta=0)#

Converts the sky coordinate uncertainties from one reference system to another, including the covariance term.

Equations (1.5.4) and (1.5.20) from section 1.5 in the Hipparcos Explanatory Volume 1 are used.

Parameters:

  • phi (float or array) – The longitude-like angle of the position of the source (radians).

  • theta (float or array) – The latitude-like angle of the position of the source (radians).

  • sigphistar (float or array) – Uncertainty in the longitude-like angle of the position of the source (radians or sexagesimal units, including cos(latitude) term)

  • sigtheta (float or array) – Uncertainty in the latitude-like angle of the position of the source (radians or sexagesimal units)

  • rho_phi_theta (float or array) – Correlation coefficient of the position uncertainties. Zero by default

Returns:

  • sigPhiRotStar (float or array) – The transformed uncertainty in the longitude-like angle (including cos(latitude) factor)

  • sigThetaRot (float or array) – The transformed uncertainty in the latitude-like angle.

  • rhoPhiThetaRot (float or array) – The transformed correlation coefficient.

transform_sky_coordinates(phi, theta)#

Convert sky coordinates from one reference system to another.

Use of the rotation matrix with which the class was initialized. Inputs can be scalars or 1-dimensional numpy arrays.

Parameters:

  • phi (float or array) – Value of the longitude-like angle (right ascension, longitude) in radians.

  • theta (float or array) – Value of the latitude-like angle (declination, latitude) in radians.

Returns:

  • phirot (float or array) – Value of the transformed longitude-like angle in radians.

  • thetarot (float or array) – Value of the transformed latitude-like angle in radians.