proper motion

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proper motion,

in astronomy, apparent movement of a star on the celestial spherecelestial sphere,
imaginary sphere of infinite radius with the earth at its center. It is used for describing the positions and motions of stars and other objects. For these purposes, any astronomical object can be thought of as being located at the point where the line of sight
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, usually measured as seconds of arc per year; it is due both to the actual relative motions of the sun and the star through space. Proper motion reflects only transverse motion, i.e., the component of motion across the line of sight to the star; it does not include the component of motion toward or away from the sun. The most distant stars show the least proper motion. Barnard's Star, one of the closest stars, has the largest measured proper motion, 10.27 sec of arc per year. The average proper motion of the stars that can be seen with the naked eye is 0.1" per year.

proper motion

Symbol: μ. The apparent angular motion per year of a star on the celestial sphere, i.e. in a direction perpendicular to the line of sight. It results both from the actual movement of the star in space – its peculiar motion – and from the star's motion relative to the Solar System. It was first detected in 1718 by Halley. The considerable distances of stars reduce their apparent motion to a very small amount, which for most stars is considered negligible. It is only after thousands of years that differences in the directions of proper motion cause groups of stars to change shape appreciably.

The proper motion of a star, usually a nearby star, can be determined if its cumulative effect over many decades produces a measurable change in the star's position. It is quoted in arc seconds per year, often in terms of two components: proper motion in right ascension (μα) and in declination (μδ ). Barnard's star has the greatest proper motion (10″.3 per year). If the distance, d (in parsecs), of the star is known then the velocity along the direction of proper motion – the tangential velocity, v t – can be found:

v t = μd AU/year = 4.74μd km s–1

Proper Motion

(religion, spiritualism, and occult)

Proper motion refers to the motion of a planet or other celestial body in space as opposed to apparent motion caused by such factors as the axial rotation of Earth.

Proper Motion


the apparent angular displacement per year of a star on the celestial sphere. A star’s proper motion is the result of both its actual velocity through space (peculiar velocity) and its apparent displacements, which are caused by the motion of the solar system with the earth through space. The periodic annual change in a star’s position (parallax) caused by the earth’s motion around the sun is not included in the star’s proper motion.

Proper motions are important in plotting fundamental systems of spherical coordinates (fundamental star catalogs) based on the precise positions of stars and in studying the kinematics of star systems (together with radial velocity and parallax). Proper motions usually do not exceed several thousandths of a second of arc; they rarely attain tenths of a second of arc and even more rarely whole seconds of arc. Barnard’s Star, which is of stellar magnitude 9.7 and is located in the constellation Ophiuchus, has the largest known proper motion—10′27.

In ancient times, the stars were believed to be fixed in their positions in the sky. However, the Chinese astronomer I Hsing (683–727 A.D.) compared the relative positions of stars in the constellation Sagittarius with observations recorded by his predecessors and proposed that the angular distances between stars change over time. In the 16th century G. Bruno maintained that stars, like all bodies in the universe, undergo constant motion and change. In 1718, E. Halley first detected the proper motion of three bright stars—Aldebaran, Sirius, and Arcturus—by comparing the coordinates known to him at that time with the coordinates in Ptolemy’s Almagest. In 1742, J. Bradley proposed that the proper motions were due to the sun’s motion through space. Catalogs of the proper motions of stars appeared in the late 18th and early 19th centuries. In later years it was shown that the peculiar velocities and, consequently, proper motions should be considered random (with a certain degree of caution, as there are general factors governing the motion of stars through space, such as the motion of star clusters and galactic rotation).

Determination of proper motions entails considerable difficulty because the motions are so small that a substantial period of time is needed for observations. The visual method of determining proper motions is based on the comparison of the star’s equatorial coordinates, recorded on meridian instruments in different years and usually at different observatories. However, in making such measurements it is difficult to consider all the errors in the catalogs being used, and it is nearly impossible to observe stars fainter than stellar magnitude ten. In the photographic method, suitable for determining proper motions of many stars at once, two or more photographs of the region of the sky under study are compared. The time interval separating the photographs must be sufficient to permit a reliable measurement of the change in the stars’ positions. The photographic method makes it possible to determine proper motions with an average accuracy of ±0.003 second of arc. The proper motions of more than 250,000 stars had been recorded by the 1970’s. Examples of catalogs of proper motions are those of the Astronomischen Gesellschaft (AGK) and the catalog of the Smithsonian Astrophysical Observatory (SAO Star Catalog).

Proper motions obtained by the visual method are plotted in an inertial frame of reference, which is determined by positions of stars contained in the fundamental catalog being used. When proper motions are determined photographically, they are defined relative to a small group of reference stars in the region under examination whose average motion is taken as equal to zero. In order to convert to the inertial coordinate system, the average motion of the set of reference stars is considered parallactic and is calculated from statistical formulations. The photographic images of galaxies may be used in place of reference stars, since the former are nearly motionless on the celestial sphere.


Parenago, P. P. Kurs zvezdnoi astronomii, 3rd ed. Moscow, 1954.


proper motion

[′präp·ər ′mō·shən]
That component of the space motion of a celestial body perpendicular to the line of sight, resulting in the change of a star's apparent position relative to that of other stars; expressed in angular units.
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