The motions of stars and other astronomical objects, including the radial component of their velocities, can be deduced not only from spectroscopy, but also from astrometric measurements, using second-order effects in the parallaxes and proper motions, or changes in angular size. Some such determinations have already been possible, using data from the Hipparcos satellite, and many more will become possible with future space experiments, expected to reach astrometric accuracies in the microarcsecond range.

This *"astrometric radial velocity"* is conceptually quite different
from the spectroscopic radial-velocity measure. The astrometric radial
velocity refers to the variation of the coordinates of the source, and
therefore depends on the chosen coordinate system and time scale.
By contrast, the spectroscopic measure is in principle a directly measurable
quantity and therefore independent of coordinate systems.

For example, "radial velocity" may be defined as the rate of change in
distance
with respect to "time".
But is this the time of light emission (at the star) or light reception
(at the observer)? The former seems natural if radial velocity is
considered a "property" of the star, while the latter is more natural for
the observer. The finite speed of light, *c*, causes a difference
of second order in velocity (*V*^{2}/*c*),
exceeding 100 m/s for
*V* > 173 km/s, and 1 km/s for *V > *548
km/s. Thus, the geometric concept of a radial velocity requires a
stringent choice of time coordinates.

Not only the concept of "time", but also that of "distance" enters the
definition of "radial velocity". "Distance" must reasonably correspond
to the path followed by a light beam from the object to the [hypothetical]
observer. Gravitational lensing may imply multiple images of a single
object, and therefore multiple distances and multiple radial velocities
of the same object. A stringent definition should allow for such
possibilities, permitting the "barycentric distance" to be a multi-valued
function.

To enable high-accuracy studies of radial velocities, and to permit accurate
comparisons between observers using different methods, a resolution was
adopted by a number of Divisions and Committees of the International Astronomical
Union, at a special session during its XXIVth General Assembly in Manchester
(August 2000). The resolution defines a stringent
*"astrometric
radial velocity"* which defines the coordinate system and timescale
to be used:

**Resolution No. C2 on the Definition of "Astrometric
Radial Velocity"**

Divisions I, IV, V, VI, VII, IX and X, and Commissions 8, 27, 29, 30, 31, 33, 34 and 40 of the International Astronomical Union

*Recognizing*

That recently improved astrometric techniques may permit the accurate determination of stellar radial velocities independent of spectroscopy, thus requiring a definition independent from spectroscopic measures;

*Considering*

That the change in the barycentric direction ** u** to objects
outside of the solar system is customarily expressed by the proper-motion
vector

*Therefore recommend*

That the geometric concept of radial velocity be defined as v_{r}
= dr/d*t*_{B}, where r is the barycentric
coordinate distance to the object and *t*_{B}
the barycentric coordinate time (TCB) for light arrival at the solar system
barycenter.

*Note: *The Barycentric Celestial Reference System (including the
Barycentric Coordinate Time) is defined in Resolutions B1.3 and B1.5 adopted
at the IAU XXIV:th General Assembly in 2000.

(end of resolution text)

In high-accuracy spectroscopic studies, a stringent definition of the *"barycentric
radial velocity"* enables to correct for relativistic velocity effects
and for measurements made inside gravitational fields.

Lennart Lindegren
& Dainis Dravins: **The fundamental definition of 'radial velocity'**

Astron.Astrophys.
**401**, 1185-1201 (2003),
[PDF,
280 kb]

Comments are welcome to Dainis Dravins,

Updated JD 2,455,775