Astrometry

Astrometry literally means measuring the stars. Within astronomy, astrometry is defined as the measurement of real and apparent motions, distances, and positions of stars and other astronomical bodies. This type of measurement determines a specific star’s location in the sky with great precision. German astronomer Friedrich Wilhelm Bessel (1784–1846)) established modern astrometry when he published his book Fundamenta astronomiae, which was a collection of star positions observed by English astronomer James Bradley (1693–1762) between 1750 and 1762 that Bessel corrected with respect to the motions of the Earth.

In order to establish a star’s location, it is necessary to first establish a coordinate system in which the location can be specified. Traditionally, very distant stars, which show very little motion as viewed from Earth, have been used to establish that coordinate system. However, since the accuracy of the coordinate system is dependent on the accuracy of the positions of the defining stars, effort has been made to use the extremely distant point-like objects known as quasars to establish an improved standard coordinate system. Because quasars give off radio waves, their positions can be determined with extreme accuracy, but the implementation of this system has yet to be accomplished.

Astrometry is of fundamental importance to the study of the stars. Astronomers can use the distance of the star to help determine its other properties. The annual motion of the Earth around the Sun causes nearby stars to appear to move about in the sky with respect to distant background stars. The amplitude of this apparent motion determines the distance of the star from the sun, which is known as its trigonometric parallax. The angular rate of change of the star’s position is called its proper motion. If the distance to the star is also known, the proper motion can be converted into a transverse velocity relative to the sun, which is the apparent speed of the star across the line of sight. For most stars, this motion is extremely small and may require positional determinations 50 years or longer for accurate measurement. The transverse velocity may be combined with the radial velocity determined from the star’s spectra to yield the true space velocity with respect to the sun.

Occasionally the proper motion will be found to vary in a periodic manner, suggesting that the target star is orbiting another object in addition to its steady motion across the sky. Such stars are called astrometric binary stars. Stars that are orbited by planets, which are too faint to be directly observed, show this motion. However, the motion is liable to be extremely small unless the star is quite small and the planet rather large.

Often, astronomers cannot determine the distance of the star directly from the coordinate system. In this case, a method called statistical parallax is used. For example, if one independently knew the transverse velocity of a star, one could use the proper motion to obtain a distance. While it is impossible to determine the transverse velocity of a specific star without knowledge of its distance and proper motion, an estimation can be obtained by using the transverse velocity for a collection of similar stars. In addition, the radial velocity of the star can be obtained directly from its spectra without knowledge of its distance or proper motion. This information can then be combined with the observed proper motions to yield distances to the similar stars of a particular type and average values for their intrinsic properties.

A similar technique can be used on a group of stars that move together through space on more-or-less parallel tracks. Such groups of stars are called galactic, or open, clusters. Just as the parallel tracks of a railroad appear to converge to a point in the distance, so the stellar motions will appear to point to a distant convergent point in the sky. The location of this point with respect to each star specifies the angle between the radial velocity and the space velocity for that star. Knowledge of that angle allows the tangential velocity of the star to be obtained from the directly measured radial velocity. Again, knowledge of the individual proper motion and tangential velocity allows for a determination of the distance to each star of the cluster. This scheme is known as the moving cluster method.

Adaptive optics have greatly improved the accuracy of stellar positions made from the ground. Since the mid-twentieth century, astronomers have known that it was possible in principle to undo the distortions of astronomical images generated by the atmosphere. First, one had to measure those distortions, then construct a lens with characteristics that could be changed as fast as the atmosphere itself changed. Theoretically such a lens could then undo the distortions of the atmosphere, leaving the astronomer with the steady image of the star beyond the atmosphere. This technique seemed impossible to accomplish until very recently. Powerful lasers have now been used to produce artificial stars high in the atmosphere, enabling astronomers to measure the atmospheric distortions. Remarkable increases in computer speed have allowed the analysis of those distortions to be completed in milliseconds so that a thin mirror can be adjusted to correct for atmospheric distortions. Such systems are generally referred to as adaptive optics and, in principle, they allow observations of stellar positions to be made from the ground.

However, while adaptive optics systems were being developed, several satellites and satellite programs addressed the fundamental problems of astrometry. The pointing accuracy of the Hubble Space Telescope required a greatly increased catalogue of stars and their positions so that guide stars could be found for all potential targets of the telescope. A number of ground surveys that provided positions of several million stars were undertaken expressly to provide those guide stars. Partly in response to these surveys, machines were developed that could automatically measure star positions on the thousands of

KEY TERMS

Moving cluster method —A method of determining the distances to stars in a cluster, which are assumed to share a similar direction of motion in space. The accuracy of the method depends largely on the extent to which the cluster is spread across the sky and, therefore, has only been applied successfully to the nearest clusters.

Parallax —A generic term used to denote the distance to an astronomical object.

Proper motion —Measures the angular motion of an object across the line of sight.

Quasar —Originally stood for Quasi-Stellar Radio Source. However, the term is now commonly used to refer to any quasi-stellar source exhibiting large recessional velocities associated with the expansion of the universe.

Radial velocity —Motion of an object along the line of sight generally determined from the spectrum of the object. By convention, a positive radial velocity denotes motion away from the observer while a negative radial velocity indicates motion toward the observer.

Space velocity —The vector combination of the radial velocity (vr) and transverse velocity (vt) of an object. The magnitude of the space velocity, vs, is given by vs² = vr² + vt².

Statistical parallax —A method for determining the distance to a class of similar objects assumed to have the same random motion with respect to the Sun. Transverse velocity—That component of the space velocity representing motion across the line of sight.

Trigonometric parallax —The parallax of a stellar object determined from the angular shift of the object with respect to the distant stars resulting from the orbital motion of the Earth about the sun.

photographic glass plates that were taken for the projects. Now, the determination of stellar positions can be accomplished directly by an electronic detector much like those found in a video camera, thereby replacing the photographic plate. This development also allowed the design of satellites dedicated to the determination of stellar positions. The most notable of these is the Hipparcos Space Astrometry Mission, developed by the European Space Agency (ESA). Hipparcos was designed to measure the positions of more than 100,000 stars with an accuracy of between two and four milliarc-seconds. This is easily more than ten times the accuracy readily achievable from the ground. After nearly a decade of development, Hipparcos was launched aboard the Ariane spacecraft in 1989. Unfortunately, due to a failure of the final stage of the rocket, the satellite never achieved the geostationary orbit approximately 25,000 mi (40,250 km) above the Earth. Instead, its orbit is highly elliptical, with its furthest point near the desired distance, but dipping down close to the Earth’s atmosphere at its low point. This problem greatly reduced the efficiency of the satellite.

Eventually satellites like Hipparcos, along with improved ground observations, will significantly enhance the number of stars for which good positions, and other astrometrical data will be obtained. Not only will this clarify the view of the local stellar neighborhood within the Milky Way galaxy, it will also increase the fundamental knowledge of stars themselves. As of October 2006, several astrometry missions are in various stages of planning and development. Some of them include Full-sky Astrometric Mapping Explorer (FAME, currently cancelled by NASA in 2002; future development pending budgetary considerations), Space Interferometry Mission (SIM, currently scheduled to launch by NASA no earlier than 2014), and Gaia probe (to be launched as a successor to Hipparcos by the ESA in 2011).

See also Celestial coordinates.