A stringent definition for geometric measurements

Radial velocities in astronomy have usually been determined through spectroscopy, applying the Doppler principle.  However, it is also possible to determine radial motion from purely geometric (astrometric) measurements, e.g. from the secular change of a star's proper motion.

   Why the need for a definition?

  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 (V2/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.

   A stringent definition for geometric measurements

  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:

  IAU definition of "astrometric radial velocity"

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


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;


That the change in the barycentric direction u to objects outside of the solar system is customarily expressed by the proper-motion vector µ = du/dtB, where tB is the barycentric coordinate time (TCB) of light arrival at the solar system barycenter;

Therefore recommend

That the geometric concept of radial velocity be defined as vr = dr/dtB, where r is the barycentric coordinate distance to the object and tB 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)

   Definition of the spectroscopic "barycentric radial-velocity measure"

  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.

   Main publication

  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,  dainis@astro.lu.se  and to Lennart Lindegren,  lennart@astro.lu.se

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