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Solve the following problem using Python, implementing the functions described below, one line at a time
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Description:
 def reflex_correct(coords, galactocentric_frame=None):
 """Correct the input Astropy coordinate object for solar reflex motion. The input coordinate instance must have distance and radial velocity information. If the radial velocity is not known, fill the Parameters coords : `~astropy.coordinates.SkyCoord` The Astropy coordinate object with position and velocity information. galactocentric_frame : `~astropy.coordinates.Galactocentric` (optional) To change properties of the Galactocentric frame, like the height of the sun above the midplane, or the velocity of the sun in a Galactocentric intertial frame, set arguments of the `~astropy.coordinates.Galactocentric` object and pass in to this function with your coordinates. Returns ------- coords : `~astropy.coordinates.SkyCoord` The coordinates in the same frame as input, but with solar motion removed. """

    c = coord.SkyCoord(coords)

    # If not specified, use the Astropy default Galactocentric frame
    if galactocentric_frame is None:
        galactocentric_frame = coord.Galactocentric()

    v_sun = galactocentric_frame.galcen_v_sun

    observed = c.transform_to(galactocentric_frame)
    rep = observed.cartesian.without_differentials()
    rep = rep.with_differentials(observed.cartesian.differentials['s'] + v_sun)
    fr = galactocentric_frame.realize_frame(rep).transform_to(c.frame)
    return coord.SkyCoord(fr)