# Accounting for Space Motion¶

The SkyCoord object supports updating the position of a source given its space motion and a time at which to evaluate the new position (or a difference between the coordinate’s current time and a new one). This is done using the apply_space_motion() method. As an example, first we’ll create a SkyCoord object with a specified obstime:

>>> import astropy.units as u
>>> from astropy.time import Time
>>> from astropy.coordinates import SkyCoord
>>> c = SkyCoord(l=10*u.degree, b=45*u.degree, distance=100*u.pc,
...              pm_l_cosb=34*u.mas/u.yr, pm_b=-117*u.mas/u.yr,
...              frame='galactic',
...              obstime=Time('1988-12-18 05:11:23.5'))


We can now find the position at some other time, taking the space motion into account. We can either specify the time difference between the observation time and the desired time:

>>> c.apply_space_motion(dt=10. * u.year)
<SkyCoord (Galactic): (l, b, distance) in (deg, deg, pc)
( 10.00013356,  44.999675,  99.99999994)
(pm_l_cosb, pm_b, radial_velocity) in (mas / yr, mas / yr, km / s)
( 33.99980714, -117.00005604,  0.00034117)>
>>> c.apply_space_motion(dt=-10. * u.year)
<SkyCoord (Galactic): (l, b, distance) in (deg, deg, pc)
( 9.99986643,  45.000325,  100.00000006)
(pm_l_cosb, pm_b, radial_velocity) in (mas / yr, mas / yr, km / s)
( 34.00019286, -116.99994395, -0.00034117)>


Or, we can specify the new time to evaluate the position at:

>>> c.apply_space_motion(new_obstime=Time('2017-12-18 01:12:07.3'))
<SkyCoord (Galactic): (l, b, distance) in (deg, deg, pc)
( 10.00038732,  44.99905754,  99.99999985)
(pm_l_cosb, pm_b, radial_velocity) in (mas / yr, mas / yr, km / s)
( 33.99944073, -117.00016248,  0.00098937)>


If the SkyCoord object has no specified radial velocity (RV), the RV is assumed to be 0. The new position of the source is determined assuming the source moves in a straight line with constant velocity in an inertial frame. There are no plans to support more complex evolution (e.g., non-inertial frames or more complex evolution), as that is out of scope for the astropy core package (although it may well be in-scope for a variety of affiliated packages).

## Example: Use velocity to compute sky position at different epochs¶

In this example, we’ll use Gaia TGAS astrometry for a nearby star to compute the sky position of the source on the date that the 2MASS survey observed that region of the sky. The TGAS astrometry is provided on the reference epoch J2015.0, whereas the 2MASS survey occurred in the late 1990’s. For the star of interest, the proper motion is large enough that there are appreciable differences in the sky position between the two surveys.

After computing the previous position of the source, we’ll then cross-match the source with the 2MASS catalog to compute Gaia-2MASS colors for this object source.

Note

This example requires accessing data from the Gaia TGAS and 2MASS catalogs. For convenience and speed below, we have created dictionary objects that contain the data. We retrieved the data using the Astropy affiliated package astroquery using the following queries:

import astropy.coordinates as coord
import astropy.units as u
from astroquery.gaia import Gaia
from astroquery.vizier import Vizier

job = Gaia.launch_job("SELECT TOP 1 * FROM gaiadr1.tgas_source \
WHERE parallax_error < 0.3  AND parallax > 5 AND pmra > 100 \
ORDER BY random_index")
result_tgas = job.get_results()[0]

c_tgas = coord.SkyCoord(ra=result_tgas['ra'] * u.deg,
dec=result_tgas['dec'] * u.deg)
v = Vizier(columns=["**"], catalog="II/246/out")
result_2mass = v.query_region(c, radius=1*u.arcmin)['II/246/out']


The TGAS data from relevant columns for this source (see queries in Note above):

>>> result_tgas = dict(ra=66.44280212823296,
...                    dec=-69.99366255906372,
...                    parallax=22.764078749733947,
...                    pmra=144.91354358297048,
...                    pmdec=5.445648092997134,
...                    ref_epoch=2015.0,
...                    phot_g_mean_mag=7.657174523348196)


The 2MASS data for all sources within 1 arcminute around the above position (see queries in Note above):

>>> result_2mass = dict(RAJ2000=[66.421970000000002, 66.433521999999996,
...                              66.420564999999996, 66.485068999999996,
...                              66.467928999999998, 66.440815000000001,
...                              66.440454000000003],
...                     DEJ2000=[-70.003722999999994, -69.990768000000003,
...                              -69.992255999999998, -69.994881000000007,
...                              -69.994926000000007, -69.993613999999994,
...                              -69.990836999999999],
...                     Jmag=[16.35, 13.663, 16.171, 16.184, 16.292,
...                           6.6420002, 12.275],
...                     Hmag=[15.879, 13.955, 15.154, 15.856, 15.642,
...                           6.3660002, 12.185],
...                     Kmag=[15.581, 14.238, 14.622, 15.398, 15.123,
...                           6.2839999, 12.106],
...                     Date=['1998-10-24', '1998-10-24', '1998-10-24',
...                           '1998-10-24', '1998-10-24', '1998-10-24',
...                           '1998-10-24'])


We’ll first create a SkyCoord object from the information provided in the TGAS catalog. Note that we set the obstime of the object to the reference epoch provided by the TGAS catalog (J2015.0):

>>> import astropy.units as u
>>> from astropy.coordinates import SkyCoord, Distance
>>> from astropy.time import Time
>>> c = SkyCoord(ra=result_tgas['ra'] * u.deg,
...              dec=result_tgas['dec'] * u.deg,
...              distance=Distance(parallax=result_tgas['parallax'] * u.mas),
...              pm_ra_cosdec=result_tgas['pmra'] * u.mas/u.yr,
...              pm_dec=result_tgas['pmdec'] * u.mas/u.yr,
...              obstime=Time(result_tgas['ref_epoch'], format='decimalyear'))


We next create a SkyCoord object with the sky positions from the 2MASS catalog, and an Time object for the date of the 2MASS observations provided in the 2MASS catalog (for the data in this region the observation date is the same, so we take only the 0th value):

>>> catalog_2mass = SkyCoord(ra=result_2mass['RAJ2000'] * u.deg,
...                          dec=result_2mass['DEJ2000'] * u.deg)
>>> epoch_2mass = Time(result_2mass['Date'][0])


We can now use the apply_space_motion() method to compute the position of the TGAS source at another epoch. This uses the proper motion and parallax information to evolve the position of the source assuming straight-line motion:

>>> c_2mass_epoch = c.apply_space_motion(epoch_2mass)


Now that we have the coordinates of the TGAS source at the 2MASS epoch, we can do the cross-match (see also Separations, Offsets, Catalog Matching, and Related Functionality):

>>> idx, sep, _ = c_2mass_epoch.match_to_catalog_sky(catalog_2mass)
>>> sep[0].to_string()
'0d00m00.2818s'
>>> idx
array(5)


The closest source it found is 0.2818 arcseconds away and corresponds to row index 5 in the 2MASS catalog. We can then, for example, compute Gaia-2MASS colors:

>>> G = result_tgas['phot_g_mean_mag']
>>> J = result_2mass['Jmag'][idx]
>>> K = result_2mass['Kmag'][idx]
>>> G - J, G - K
(1.0151743233481962, 1.3731746233481958)