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Proper motion is the astronomical measure of the observed changes in apparent positions of stars in the sky as seen from the center of mass of the Solar System, as compared to the imaginary fixed background of the more distant stars. It was first physically measured individually in both seconds of time in right ascension (RA or α) and seconds of arc in declination (Dec. or δ), whose calculated combined value, is the ''total proper motion'' (μ) expressed in seconds of arc per year (arcsec/yr) or per century (arcsec/100yr), where 3600 arcseconds equal one degree. Because most proper motions are much less than one arcsec per year, most modern catalogues, like the Hipparcos Index Catalogue (HIP), now express proper motion in terms of milliarcseconds per year (mas/yr), where 1000 mas equals one arcsecond. This measured sky motion is separate from the radial velocity, measured in kilometres per second (km/s), being the velocity moving toward or away from the observer, as usefully obtained by the small Doppler shifts seen in starlight when using astronomical spectroscopy. Knowledge of the proper motion and Doppler shift allow approximate calculations of a star's true motion in space in respect to the Sun. Proper motion is not entirely "proper" (that is, intrinsic to the star), because it includes a component due to the motion of the Solar System itself. Due to the finite speed of light (that is also constant; without regard to whatever is the velocity of the emanating or reflecting source) the instantaneous velocities of distant stars cannot be observed; the observed proper motion reflects the velocity of a star relative to the Solar System at the time the light was emitted from that star. == Introduction == Over the course of centuries, stars appear to maintain nearly fixed positions with respect to each other, so that they form the same constellations over historical time. Ursa Major or Crux, for example, looks nearly the same now as they did hundreds of years ago. However, precise long-term observations show that the constellations change shape, albeit very slowly, and that each star has an independent motion. This motion is caused by the movement of the stars relative to the Sun and Solar System. The Sun travels in a nearly circular orbit (the ''solar circle'') about the center of the Milky Way at a speed of about 220 km/s at a radius of from the center, which can be taken as the rate of rotation of the Milky Way itself at this radius. The proper motion is a two-dimensional vector (because it excludes the component in the direction of the line of sight) and is thus defined by two quantities: its position angle and its magnitude. The first quantity indicates the direction of the proper motion on the celestial sphere (with 0 degrees meaning the motion is due north, 90 degrees meaning the motion is due east, and so on), and the second quantity is the motion's magnitude, expressed in seconds of arc per year. Proper motion may alternatively be defined by the angular changes per year in the star's right ascension (''μα'') and declination (''μδ''). On the celestial sphere, the coordinate of α corresponds to 'celestial' longitude, where all right ascensions are measured from the vernal equinox ''V'', the point on the sky where the Sun crosses the celestial equator on near March 21. δ corresponds to 'celestial' latitude. The components of proper motion by convention are arrived at as follows. Suppose in a year an object moves from coordinates (α, δ) to coordinates (α1, δ1), with angles measured in seconds of arc. Then the changes of angle in seconds of arc per year are: ::=\delta_1-\delta \ . |} The magnitude of the proper motion ''μ'' is given by vector addition of its components: ::^2 \cdot \cos^2 \delta \ , |- |style="text-align: right;"| | |- |} where ''δ'' is the declination. The factor in ''cos δ'' accounts for the fact that the radius from the axis of the sphere to its surface varies as ''cos δ'', becoming, for example, zero at the pole. Thus, the component of velocity parallel to the equator corresponding to a given angular change in ''α'' is smaller the further north the object's location. The change ''μα '', which must be multiplied by ''cos δ'' to become a component of the proper motion, is sometimes called the "proper motion in right ascension", and ''μδ'' the "proper motion in declination". If the proper motion in right ascension has been converted by ''cos δ'' into either arcsecond or milliarcsecond, the result is expressed as ''μα *'' ('mu alpha asterisk'), i.e. the proper motion results in right ascension within the Hipparcos Catalogue (HIP) are expressed in the right ascension mas/yr, and therefore have already been converted. Hence, the individual proper motions in right ascension and declination are made equivalent for straight forward calculations of various other stellar motions. Position angle ''θ'' is related to these components by:〔〔See 〕 :: 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Proper motion」の詳細全文を読む スポンサード リンク
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