Radial velocity
defining the instantaneous relative position of a target with respect to an observer.
Let the instantaneous relative velocity of the target with respect to the observer be The magnitude of the position vector
is defined as in terms of the inner product The quantity range rate is the time derivative of the magnitude (norm) of
In astronomy, radial velocity is often measured to the first order of approximation by Doppler spectroscopy.
The quantity obtained by this method may be called the barycentric radial-velocity measure or spectroscopic radial velocity.
[2] However, due to relativistic and cosmological effects over the great distances that light typically travels to reach the observer from an astronomical object, this measure cannot be accurately transformed to a geometric radial velocity without additional assumptions about the object and the space between it and the observer.
William Huggins ventured in 1868 to estimate the radial velocity of Sirius with respect to the Sun, based on observed redshift of the star's light.
[6] In many binary stars, the orbital motion usually causes radial velocity variations of several kilometres per second (km/s).
As the spectra of these stars vary due to the Doppler effect, they are called spectroscopic binaries.
Radial velocity can be used to estimate the ratio of the masses of the stars, and some orbital elements, such as eccentricity and semimajor axis.
Radial velocity methods alone may only reveal a lower bound, since a large planet orbiting at a very high angle to the line of sight will perturb its star radially as much as a much smaller planet with an orbital plane on the line of sight.
It has been suggested that planets with high eccentricities calculated by this method may in fact be two-planet systems of circular or near-circular resonant orbit.
[7][8] The radial velocity method to detect exoplanets is based on the detection of variations in the velocity of the central star, due to the changing direction of the gravitational pull from an (unseen) exoplanet as it orbits the star.
By regularly looking at the spectrum of a star—and so, measuring its velocity—it can be determined if it moves periodically due to the influence of an exoplanet companion.
