Жұлдыздық параллакс: Астрономиялық қашықтықтарды өлшеу әдісі

Concept in astronomy

Stellar parallax is the apparent shift of position (parallax) of any nearby star (or other object) against the background of distant stars. By extension, it is a method for determining the distance to the star through trigonometry, the stellar parallax method. Created by the different orbital positions of Earth, the extremely small observed shift is largest at time intervals of about six months, when Earth arrives at opposite sides of the Sun in its orbit, giving a baseline distance of about two astronomical units between observations. The parallax itself is considered to be half of this maximum, about equivalent to the observational shift that would occur due to the different positions of Earth and the Sun, a baseline of one astronomical unit (AU). Stellar parallax is so difficult to detect that its existence was the subject of much debate in astronomy for hundreds of years. Thomas Henderson, Friedrich Georg Wilhelm von Struve, and Friedrich Bessel made first successful parallax measurements in 1832–1838, for the stars Alpha Centauri, Vega, and 61 Cygni.

Stellar parallax is most often measured using annual parallax, defined as the difference in position of a star as seen from Earth and Sun, i. e. the angle subtended at a star by the mean radius of Earth's orbit around the Sun. The parsec (3.26 light years) is defined as the distance for which the annual parallax is 1 arcsecond. Annual parallax is normally measured by observing the position of a star at different times of the year as Earth moves through its orbit. The angles involved in these calculations are very small and thus difficult to measure. The nearest star to the Sun (and also the star with the largest parallax), Proxima Centauri, has a parallax of 0.7685 ± 0.0002 arcsec.

Stellar parallax is so small that it was unobservable until the 19th century, and its apparent absence was used as a scientific argument against heliocentrism during the early modern age. It is clear from Euclid's geometry that the effect would be undetectable if the stars were far enough away, but for various reasons, such gigantic distances involved seemed entirely implausible: it was one of Tycho Brahe's principal objections to Copernican heliocentrism that for it to be compatible with the lack of observable stellar parallax, there would have to be an enormous and unlikely void between the orbit of Saturn and the eighth sphere (the fixed stars). James Bradley first tried to measure stellar parallaxes in 1729. The stellar movement proved too insignificant for his telescope, but he instead discovered the aberration of light and the nutation of Earth's axis, and catalogued 3,222 stars.

Measurement of annual parallax was the first reliable way to determine the distances to the closest stars. In the second quarter of the 19th century, technological progress reached to the level which provided sufficient accuracy and precision for stellar parallax measurements. Giuseppe Calandrelli noted stellar parallax in 1805 6 and came up with a 4 second value for the star Vega which was a gross overestimate. The first successful stellar parallax measurements were done by Thomas Henderson in Cape Town South Africa in 1832–1833, where he measured parallax of one of the closest stars, Alpha Centauri. Between 1835 and 1836, astronomer Friedrich Georg Wilhelm von Struve at the Dorpat university observatory measured the distance of Vega, publishing his results in 1837. Friedrich Bessel, a friend of Struve, carried out an intense observational campaign in 1837–1838 at Koenigsberg Observatory for the star 61 Cygni using a heliometer, and published his results in 1838. Henderson published his results in 1839, after returning from South Africa. Those three results, two of which were measured with the best instruments at the time (Fraunhofer great refractor used by Struve and Fraunhofer heliometer by Bessel) were the first ones in history to establish the reliable distance scale to the stars. A large heliometer was installed at Kuffner Observatory (In Vienna) in 1896, and was used for measuring the distance to other stars by trigonometric parallax. By 1910 it had computed 16 parallax distances to other stars, out of only 108 total known to science at that time. and more sophisticated computer technology of the 1960s allowed more efficient compilation of star catalogues. In the 1980s, charge coupled devices (CCDs) replaced photographic plates and reduced optical uncertainties to one milliarcsecond. Stellar parallax remains the standard for calibrating other measurement methods (see Cosmic distance ladder). Accurate calculations of distance based on stellar parallax require a measurement of the distance from Earth to the Sun, now known to exquisite accuracy based on radar reflection off the surfaces of planets.

In 1989, the satellite Hipparcos was launched primarily for obtaining parallaxes and proper motions of nearby stars, increasing the number of stellar parallaxes measured to milliarcsecond accuracy a thousandfold. Even so, Hipparcos is only able to measure parallax angles for stars up to about 1,600 light years away, a little more than one percent of the diameter of the Milky Way Galaxy. The Hubble telescope WFC3 now has a precision of 20 to 40 microarcseconds, enabling reliable distance measurements up to for a small number of stars. This gives more accuracy to the cosmic distance ladder and improves the knowledge of distances in the Universe, based on the dimensions of the Earth's orbit. As distances between the two points of observation are increased, the visual effect of the parallax is likewise rendered more visible. NASA's New Horizons spacecraft performed the first interstellar parallax measurement on 22 April 2020, taking images of Proxima Centauri and Wolf 359 in conjunction with earth based observatories. The relative proximity of the two stars combined with the 6.5 billion kilometer (about 43 AU) distance of the spacecraft from Earth yielded a discernible parallax of arcminutes, allowing the parallax to be seen visually without instrumentation. The European Space Agency's Gaia mission, launched 19 December 2013, is expected to measure parallax angles to an accuracy of 10 microarcseconds for all moderately bright stars, thus mapping nearby stars (and potentially planets) up to a distance of tens of thousands of light years from Earth. Data Release 2 in 2018 claims mean errors for the parallaxes of 15th magnitude and brighter stars of 20–40 microarcseconds.

Very long baseline interferometry in the radio band can produce images with angular resolutions of about 1 milliarcsecond, and hence, for bright radio sources, the precision of parallax measurements made in the radio can easily exceed those of optical telescopes like Gaia. These measurements tend to be sensitivity limited, and need to be made one at a time, so the work is generally done only for sources like pulsars and X ray binaries, where the radio emission is strong relative to the optical emission.