Velocities in spherical coordinates

Hi, I’m converting some positions and velocities from ICRS to Galactocentric, and then turning that into a spherical representation. The velocities are given as angular velocities, which is a little strange since I would have expected them in km/s.

c = coord.SkyCoord(
        ra = ra * u.deg, 
        dec = dec * u.deg, 
        pm_ra_cosdec = pmracosdec * u.mas/u.yr, 
        pm_dec = pmdec * u.mas / u.yr, 
        radial_velocity = vrad * u.km / u.s, 
        distance = dist * u.kpc,
        frame = 'icrs',
    )
cg = c.transform_to(coord.Galactocentric())
cgs = cg.represent_as('spherical')
diffs = cgs.differentials['s']
diffs
<SphericalDifferential (d_lon, d_lat, d_distance) in (mas / yr, mas / yr, kpc mas / (rad yr))
    (-0.17801241, -0.06221044, -12.62912254)>

How can I get these in km/s? For d_distance I can do

cgs.differentials['s'].d_distance.to(u.km/u.s)

but for d_lon and d_lat I can’t do the conversion, even when I multiply by the distance:

(cgs.differentials['s'].d_lon * dist * u.kpc).to(u.km/u.s)

gives the following error:

UnitConversionError: 'kpc mas / yr' and 'km / s' (speed) are not convertible

Thanks.

[adrn]

Coming back to this because of velocity conversion headaches the students are facing at our Galactic Dynamics summer school — we should really just implement your proposed solution @mhvk (and same for PhysicsSpherical, Cylindrical, etc.)!

[mhvk]

Sounds good! Mostly just needs agreement on the name! Also for the attributes: v_ra, v_dec, radial_velocity, I guess?