All components of Alpha Centauri display significant proper motions against the background sky, similar to the first magnitude stars Sirius and Arcturus. Over the centuries, this causes the apparent stellar positions to slowly change. Such motions define the high-proper-motion stars. These stellar motions were unknown to ancient astronomers. Most assumed that all stars were immortal and permanently fixed on the celestial sphere, as stated in the works of the philosopher Aristotle.
Edmond Halley in 1718 found that some stars had significantly moved from their ancient astrometric positions. For example, the bright star Arcturus (α Boo) in the constellation of Boötes showed an almost 0.5° difference in 1800 years, as did the brightest star, Sirius, in Canis Major (α CMa). Halley's positional comparison was Ptolemy's catalogue of stars contained in the Almagest whose original data included portions from an earlier catalog by Hipparchos during the 1st century BCE. Halley's proper motions were mostly for northern stars, so the southern star Alpha Centauri was not determined until the early 19th century.
Scottish-born observer Thomas James Henderson in the 1830s at the Royal Observatory at the Cape of Good Hope discovered the true distance to Alpha Centauri. He soon realised this system displayed an unusually high proper motion, and therefore its observed true velocity through space should be much larger. In this case, the apparent stellar motion was found using Abbé Nicolas Louis de Lacaille's astrometric observations of 1751–1752, by the observed differences between the two measured positions in different epochs. Using the Hipparcos Star Catalogue (HIP) data, the mean individual proper motions are −3678 mas/yr or −3.678 arcsec per year in right ascension and +481.84 mas/yr or 0.48184 arcsec per year in declination. As proper motions are cumulative, the motion of Alpha Centauri is about 6.1 arcmin each century, and 61.3 arcmin or 1.02° each millennium. These motions are about one-fifth and twice, respectively, the diameter of the full moon. Using spectroscopy the mean radial velocity has been determined to be 25.1 ± 0.3 km/s towards the Solar System.
As the stars of Alpha Centauri approach us, the measured proper motion and trigonometric parallax slowly increase. Changes are also observed in the size of the semi-major axis 'a' of the orbital ellipse, increasing by 0.03 arcsec per century. This slightly shortens the observed orbital period of Alpha Centauri AB by some 0.006 years per century being caused by the changes in the size of semi-major axis 'a'. This small effect is gradually reducing, until the star system is closest to us, and is then reversed as the distance increases again. Consequently, the observed position angles of the stars are subject to changes in the orbital elements over time, as first determined by W. H. van den Bos in 1926. Some slight differences of about 0.5% in the measured proper motions are caused by Alpha Centauri AB's orbital motion.
Based on these observed proper motions and radial velocities, Alpha Centauri will continue to gradually brighten, passing just north of the Southern Cross or Crux, before moving northwest and up towards the celestial equator and away from the galactic plane. By about 29,700 AD, in the present-day constellation of Hydra, Alpha Centauri will be 1.00 pc or 3.26 ly away. Then it will reach the stationary radial velocity (RVel) of 0.0 km/s and the maximum apparent magnitude of −0.86V (which is comparable to present-day magnitude of Canopus). However, even during the time of this nearest approach, the apparent magnitude of Alpha Centauri will still not surpass that of Sirius (which will brighten incrementally over the next 60,000 years, and will continue to be the brightest star as seen from Earth for the next 210,000 years).
The Alpha Centauri system will then begin to move away from the Solar System, showing a positive radial velocity. Due to visual perspective, about 100,000 years from now, these stars will reach a final vanishing point and slowly disappear among the countless stars of the Milky Way. Here this once bright yellow star will fall below naked-eye visibility somewhere in the faint present day southern constellation of Telescopium (this unusual location results from the fact that Alpha Centauri's orbit around the galactic centre is highly tilted with respect to the plane of the Milky Way galaxy).
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