.. note::
    :class: sphx-glr-download-link-note

    Click :ref:`here <sphx_glr_download_generated_examples_coordinates_rv-to-gsr.py>` to download the full example code
.. rst-class:: sphx-glr-example-title

.. _sphx_glr_generated_examples_coordinates_rv-to-gsr.py:


================================================================
Convert a radial velocity to the Galactic Standard of Rest (GSR)
================================================================

Radial or line-of-sight velocities of sources are often reported in a
Heliocentric or Solar-system barycentric reference frame. A common
transformation incorporates the projection of the Sun's motion along the
line-of-sight to the target, hence transforming it to a Galactic rest frame
instead (sometimes referred to as the Galactic Standard of Rest, GSR). This
transformation depends on the assumptions about the orientation of the Galactic
frame relative to the bary- or Heliocentric frame. It also depends on the
assumed solar velocity vector. Here we'll demonstrate how to perform this
transformation using a sky position and barycentric radial-velocity.

-------------------

*By: Adrian Price-Whelan*

*License: BSD*

-------------------



Make print work the same in all versions of Python and import the required
Astropy packages:



.. code-block:: python

    import astropy.units as u
    import astropy.coordinates as coord







For this example, let's work with the coordinates and barycentric radial
velocity of the star HD 155967, as obtained from
`Simbad <http://simbad.harvard.edu/simbad/>`_:



.. code-block:: python

    icrs = coord.ICRS(ra=258.58356362*u.deg, dec=14.55255619*u.deg,
                      radial_velocity=-16.1*u.km/u.s)







We next need to decide on the velocity of the Sun in the assumed GSR frame.
We'll use the same velocity vector as used in the
`~astropy.coordinates.Galactocentric` frame, and convert it to a
`~astropy.coordinates.CartesianRepresentation` object using the
``.to_cartesian()`` method of the
`~astropy.coordinates.CartesianDifferential` object ``galcen_v_sun``:



.. code-block:: python

    v_sun = coord.Galactocentric.galcen_v_sun.to_cartesian()







We now need to get a unit vector in the assumed Galactic frame from the sky
position in the ICRS frame above. We'll use this unit vector to project the
solar velocity onto the line-of-sight:



.. code-block:: python

    gal = icrs.transform_to(coord.Galactic)
    cart_data = gal.data.to_cartesian()
    unit_vector = cart_data / cart_data.norm()







Now we project the solar velocity using this unit vector:



.. code-block:: python

    v_proj = v_sun.dot(unit_vector)







Finally, we add the projection of the solar velocity to the radial velocity
to get a GSR radial velocity:



.. code-block:: python

    rv_gsr = icrs.radial_velocity + v_proj
    print(rv_gsr)





.. rst-class:: sphx-glr-script-out

 Out:

 .. code-block:: none

    114.8831448932284 km / s


We could wrap this in a function so we can control the solar velocity and
re-use the above code:



.. code-block:: python

    def rv_to_gsr(c, v_sun=None):
        """Transform a barycentric radial velocity to the Galactic Standard of Rest
        (GSR).

        The input radial velocity must be passed in as a

        Parameters
        ----------
        c : `~astropy.coordinates.BaseCoordinateFrame` subclass instance
            The radial velocity, associated with a sky coordinates, to be
            transformed.
        v_sun : `~astropy.units.Quantity` (optional)
            The 3D velocity of the solar system barycenter in the GSR frame.
            Defaults to the same solar motion as in the
            `~astropy.coordinates.Galactocentric` frame.

        Returns
        -------
        v_gsr : `~astropy.units.Quantity`
            The input radial velocity transformed to a GSR frame.

        """
        if v_sun is None:
            v_sun = coord.Galactocentric.galcen_v_sun.to_cartesian()

        gal = icrs.transform_to(coord.Galactic)
        cart_data = gal.data.to_cartesian()
        unit_vector = cart_data / cart_data.norm()

        v_proj = v_sun.dot(unit_vector)

        return c.radial_velocity + v_proj

    rv_gsr = rv_to_gsr(icrs)
    print(rv_gsr)




.. rst-class:: sphx-glr-script-out

 Out:

 .. code-block:: none

    114.8831448932284 km / s


**Total running time of the script:** ( 0 minutes  0.019 seconds)


.. _sphx_glr_download_generated_examples_coordinates_rv-to-gsr.py:


.. only :: html

 .. container:: sphx-glr-footer
    :class: sphx-glr-footer-example



  .. container:: sphx-glr-download

     :download:`Download Python source code: rv-to-gsr.py <rv-to-gsr.py>`



  .. container:: sphx-glr-download

     :download:`Download Jupyter notebook: rv-to-gsr.ipynb <rv-to-gsr.ipynb>`


.. only:: html

 .. rst-class:: sphx-glr-signature

    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.readthedocs.io>`_