183:
1081:
284:
993:
603:
163:
39:
1015:
angle subtended by two straight lines running from both ends of the Earth's radius to the Moon. If they had doubts about the perfection of this method, they were immediately shown that not only did this mean distance amount to a whole two hundred thirty-four thousand three hundred and forty-seven miles (94,330 leagues) but also that the astronomers were not in error by more than seventy miles (≈ 30 leagues).
526:
780:
31:
1077:, and therefore their diameters must be in proportion to their distances from Earth. He thus concluded that the Sun was around 20 times larger than the Moon. This conclusion, although incorrect, follows logically from his incorrect data. It suggests that the Sun is larger than the Earth, which could be taken to support the heliocentric model.
1044:, the difference in position of the Sun as seen from the Earth's center and a point one Earth radius away, i.e., the angle subtended at the Sun by the Earth's mean radius. Knowing the solar parallax and the mean Earth radius allows one to calculate the AU, the first, small step on the long road of establishing the size and
202:
per year, while for halo stars the baseline is 40 AU per year. After several decades, the baseline can be orders of magnitude greater than the Earth–Sun baseline used for traditional parallax. However, secular parallax introduces a higher level of uncertainty because the relative velocity of observed
1014:
Until then, many people had no idea how one could calculate the distance separating the Moon from the Earth. The circumstance was exploited to teach them that this distance was obtained by measuring the parallax of the Moon. If the word parallax appeared to amaze them, they were told that it was the
752:
One of the viewing positions is the place from which the Moon can be seen directly overhead at a given moment. That is, viewed along the vertical line in the diagram. The other viewing position is a place from which the Moon can be seen on the horizon at the same moment. That is, viewed along one of
748:
The diagram for stellar parallax can illustrate lunar parallax as well if the diagram is taken to be scaled right down and slightly modified. Instead of 'near star', read 'Moon', and instead of taking the circle at the bottom of the diagram to represent the size of the Earth's orbit around the Sun,
42:
Parallax is an angle subtended by a line on a point. In the upper diagram, the Earth in its orbit sweeps the parallax angle subtended on the Sun. The lower diagram shows an equal angle swept by the Sun in a geostatic model. A similar diagram can be drawn for a star except that the angle of parallax
818:
Another method is to take two pictures of the Moon at the same time from two locations on Earth and compare the positions of the Moon relative to the stars. Using the orientation of the Earth, those two position measurements, and the distance between the two locations on the Earth, the distance to
1275:
the baseline is 40 AU per year. After several decades, the baseline can be orders of magnitude greater than the Earth–Sun baseline used for traditional parallax. Secular parallax introduces a higher level of uncertainty, because the relative velocity of other stars is an additional unknown. When
814:
The diagram at the right shows how daily lunar parallax arises on the geocentric and geostatic planetary model, in which the Earth is at the center of the planetary system and does not rotate. It also illustrates the important point that parallax need not be caused by any motion of the observer,
798:
equal to the difference between the apparent radii of the Earth and the Sun as seen from the Moon. This radius can be seen to be equal to 0.75 degrees, from which (with the solar apparent radius of 0.25 degrees) we get an Earth apparent radius of 1 degree. This yields for the Earth-Moon distance
265:
which can measure very small angular motions. These combine to provide fundamental distance estimates to supernovae in other galaxies. Though valuable, such cases are quite rare, so they serve as important consistency checks on the distance ladder rather than workhorse steps by themselves.
749:
take it to be the size of the Earth's globe, and a circle around the Earth's surface. Then, the lunar (horizontal) parallax amounts to the difference in angular position, relative to the background of distant stars, of the Moon as seen from two different viewing positions on the Earth.
771:
and similar publications tabulate the lunar horizontal parallax and/or the linear distance of the Moon from the Earth on a periodical e.g. daily basis for the convenience of astronomers (and of celestial navigators), and the study of how this coordinate varies with time forms part of
1032:, with the Earth in revolution around the Sun, it was possible to build a model of the whole Solar System without scale. To ascertain the scale, it is necessary only to measure one distance within the Solar System, e.g., the mean distance from the Earth to the Sun (now called an
1229:
Dynamical parallax has sometimes also been used to determine the distance to a supernova when the optical wavefront of the outburst is seen to propagate through the surrounding dust clouds at an apparent angular velocity, while its true propagation velocity is known to be the
987:
1112:, pass much closer to Earth than Venus. In a favorable opposition, Eros can approach the Earth to within 22 million kilometers. During the opposition of 1900–1901, a worldwide program was launched to make parallax measurements of Eros to determine the
248:
binaries also can have their distance estimated by similar means, and do not suffer from the above geometric uncertainty. The common characteristic to these methods is that a measurement of angular motion is combined with a measurement of the absolute
73:(the distance between the extreme positions of Earth's orbit around the Sun) making the base leg of the triangle and the distance to the star being the long equal-length legs. The amount of shift is quite small, even for the nearest stars, measuring 1
260:
Expansion parallaxes in particular can give fundamental distance estimates for objects that are very far, because supernova ejecta have large expansion velocities and large sizes (compared to stars). Further, they can be observed with radio
1088:
Although
Aristarchus' results were incorrect due to observational errors, they were based on correct geometric principles of parallax, and became the basis for estimates of the size of the Solar System for almost 2000 years, until the
1263:
Two related techniques can determine the mean distances of stars by modelling the motions of stars. Both are referred to as statistical parallaxes, or individually called secular parallaxes and classical statistical parallaxes.
1210:
appear to converge with some precision to a perspective point north of Orion. Combining the observed apparent (angular) proper motion in seconds of arc with the also observed true (absolute) receding motion as witnessed by the
1069:
but inaccurate observational data, Aristarchus concluded that the Sun was slightly less than 20 times farther away than the Moon. The true value of this angle is close to 89° 50', and the Sun is about 390 times farther away.
1250:
generalizing the usual notion of parallax in space only has been developed. Then, event fields in spacetime can be deduced directly without intermediate models of light bending by massive bodies such as the one used in the
756:
The lunar (horizontal) parallax can alternatively be defined as the angle subtended at the distance of the Moon by the radius of the Earth—equal to angle p in the diagram when scaled-down and modified as mentioned above.
584:. Stellar parallax remains the standard for calibrating other measurement methods. Accurate calculations of distance based on stellar parallax require a measurement of the distance from the Earth to the Sun, now based on
764:
around the Earth. The range of the variation in linear distance is from about 56 to 63.7 Earth radii, corresponding to a horizontal parallax of about a degree of arc, but ranging from about 61.4' to about 54'. The
571:
as the Earth moves through its orbit. Measurement of annual parallax was the first reliable way to determine the distances to the closest stars. The first successful measurements of stellar parallax were made by
2418:
Some have suggested that his calculation of the relative size of the earth and sun led
Aristarchus to conclude that it made more sense for the earth to be moving around the much larger sun than the other way
1967:
Benedict, G. Fritz, et al. (1999). "Interferometric
Astrometry of Proxima Centauri and Barnard's Star Using Hubble Space Telescope Fine Guidance Sensor 3: Detection Limits for Substellar Companions".
825:
1438:
Riess, A. G.; Casertano, S.; Anderson, J.; MacKenty, J.; Filippenko, A. V. (2014). "Parallax Beyond a
Kiloparsec from Spatially Scanning the Wide Field Camera 3 on the Hubble Space Telescope".
2787:
Layden, Andrew C; Hanson, Robert B; Hawley, Suzanne L; Klemola, Arnold R; Hanley, Christopher J (1996). "The
Absolute Magnitude and Kinematics of RR Lyrae Stars Via Statistical Parallax".
1416:
2033:
139:
of the star's spectrum caused by motion along the line of sight. For a group of stars with the same spectral class and a similar magnitude range, a mean parallax can be derived from
90:
Because parallax becomes smaller for a greater stellar distance, useful distances can be measured only for stars which are near enough to have a parallax larger than a few times the
745:), is a special case of (diurnal) parallax: the Moon, being the nearest celestial body, has by far the largest maximum parallax of any celestial body, at times exceeding 1 degree.
2861:
555:, defined as the difference in position of a star as seen from the Earth and Sun, i.e. the angle subtended at a star by the mean radius of the Earth's orbit around the Sun. The
760:
The lunar horizontal parallax at any time depends on the linear distance of the Moon from the Earth. The Earth-Moon linear distance varies continuously as the Moon follows its
1215:
redshift of the stellar spectral lines, allows estimation of the distance to the cluster (151 light-years) and its member stars in much the same way as using annual parallax.
629:
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
510: metres (based on the IAU 2012 definition of the astronomical unit). This corresponds to the small-angle definition of the parsec found in many astronomical references.
2725:
Panagia, N.; Gilmozzi, R.; MacChetto, F.; Adorf, H.-M.; et al. (1991). "Properties of the SN 1987A circumstellar ring and the distance to the Large
Magellanic Cloud".
1799:
676:, thus mapping nearby stars (and potentially planets) up to a distance of tens of thousands of light-years from Earth. In April 2014, NASA astronomers reported that the
135:(motion toward or away from the Sun). The former is determined by plotting the changing position of the stars over many years, while the latter comes from measuring the
656:
for over 100,000 nearby stars, increasing the reach of the method tenfold. Even so, Hipparcos was only able to measure parallax angles for stars up to about 1,600
591:
The angles involved in these calculations are very small and thus difficult to measure. The nearest star to the Sun (and thus the star with the largest parallax),
421:
in 1913 to simplify astronomers' calculations of astronomical distances from only raw observational data. Partly for this reason, it is the unit preferred in
2092:
65:. As the Earth orbits the Sun, the position of nearby stars will appear to shift slightly against the more distant background. These shifts are angles in an
203:
stars is an additional unknown. When applied to samples of multiple stars, the uncertainty can be reduced; the uncertainty is inversely proportional to the
2463:
257:). The distance estimate comes from computing how far the object must be to make its observed absolute velocity appear with the observed angular motion.
637:
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
224:
Other individual objects can have fundamental distance estimates made for them under special circumstances. If the expansion of a gas cloud, like a
2640:
1252:
1057:
2521:
Determination of the solar parallax from photographs of Eros made with the
Crossley reflector of the Lick Observatory University of California
794:
One way to determine the lunar parallax from one location is by using a lunar eclipse. A full shadow of the Earth on the Moon has an apparent
703:
seen from different viewing positions on the Earth (at one given moment) can appear differently placed against the background of fixed stars.
236:
distance to that cloud can be estimated. Those measurements however suffer from uncertainties in the deviation of the object from sphericity.
2436:
2262:
2180:
2155:
2072:
2025:
1952:
1932:
1911:
1564:
1408:
695:
is a parallax that varies with the rotation of the Earth or with a difference in location on the Earth. The Moon and to a smaller extent the
1303:
In astronomy, the term "parallax" has come to mean a method of estimating distances, not necessarily utilizing a true parallax, such as:
2413:
182:
1878:
982:{\displaystyle \mathrm {distance} _{\mathrm {moon} }={\frac {\mathrm {distance} _{\mathrm {observerbase} }}{\tan(\mathrm {angle} )}}}
2407:
2327:
213:
is a technique where the motions of individual stars in a nearby star cluster can be used to find the distance to the cluster. Only
1097:
in 1716, although he did not live to see the results. The use of Venus transits was less successful than had been hoped due to the
1267:
The motion of the Sun through space provides a longer baseline that will increase the accuracy of parallax measurements, known as
617:
The fact that stellar parallax was so small that it was unobservable at the time was used as the main scientific argument against
190:
The motion of the Sun through space provides a longer baseline that will increase the accuracy of parallax measurements, known as
2762:"Relativistic Pentametric Coordinates from Relativistic Localizing Systems and the Projective Geometry of the Spacetime Manifold"
2119:
460:
1101:, but the resulting estimate, 153 million kilometers, is just 2% above the currently accepted value, 149.6 million kilometers.
544:
to move relative to more distant objects in the sky. In a geostatic model, the movement of the star would have to be taken as
2856:
2621:
Jones, H. Spencer (1941). "The Solar
Parallax and the Mass of the Moon from Observations of Eros at the Opposition of 1931".
2480:"Solar Parallax Papers No. 7: The General Solution from the Photographic Right Ascensions of Eros, at the Opposition of 1900"
2534:
Perrine, C. D. (1906). "The
Measurement and Reduction of the Photographs of Eros Made With the Crossley Reflector in 1900".
1614:
81:), and thereafter decreasing in angular amount as the distance increases. Astronomers usually express distances in units of
1584:
1768:
753:
the diagonal lines, from an Earth-surface position corresponding roughly to one of the blue dots on the modified diagram.
114:
arcseconds, enabling reliable distance measurements up to 5,000 parsecs (16,000 ly) for small numbers of stars. The
1307:
1506:
1295:. The motions of the stars are modelled to statistically reproduce the velocity dispersion based on their distance.
1276:
applied to samples of multiple stars, the uncertainty can be reduced; the precision is inversely proportional to the
1730:"Astrometric Stability and Precision of Fine Guidance Sensor #3: The Parallax and Proper Motion of Proxima Centauri"
1662:
Bartel, N.; et al. (1994). "The shape, expansion rate and distance of supernova 1993J from VLBI measurements".
1143:
and selected 525 for measurement. A similar program was then carried out, during a closer approach, in 1930–1931 by
186:
Hubble Space
Telescope precision stellar distance measurement has been extended 10 times further into the Milky Way.
1380:
1334:
1061:. He noted that the Sun, Moon, and Earth form a right triangle (with the right angle at the Moon) at the moment of
1006:
788:
684:, can precisely measure distances up to 10,000 light-years away, a ten-fold improvement over earlier measurements.
2088:
1051:
A primitive way to determine the distance to the Sun in terms of the distance to the Moon was already proposed by
2234:. [Department of Defense] Navy Department, Naval Observatory, Nautical Almanac Office. 1981. p. M10.
1493:
1440:
166:
Parallax measurements may be an important clue to understanding three of the universe's most elusive components:
2333:. See in particular p. 33: "Almost everything we know about Hipparchus comes down to us by way of Ptolemy."
1133:
634:
296:
74:
2773:
1243:
1729:
210:
61:
815:
contrary to some definitions of parallax that say it is, but may arise purely from motion of the observed.
540:
can be seen, in the Copernican model, as arising from the orbit of the Earth around the Sun: the star only
1329:
1312:
1203:
715:
677:
606:
328:
103:
91:
2245:
United States Naval Observatory. Nautical Almanac Office; Great Britain. Nautical Almanac Office (2006).
1354:
1199:
1193:
665:
218:
1849:, which may be taken as an abbreviated form of "a distance corresponding to a parallax of one second".
402:
are within a few hundred parsecs of the Sun, with the most distant at a few thousand parsecs, and the
2806:
2734:
2691:
2651:
2566:
2491:
2362:
2292:
1987:
1899:
1866:
1808:
1673:
1525:
1459:
1389:
1151:(roughly the Earth-Sun distance) obtained by this program was considered definitive until 1968, when
1144:
1052:
800:
767:
567:. Annual parallax is normally measured by observing the position of a star at different times of the
464:
144:
140:
48:
2218:. [Department of Defense] Navy Department, Naval Observatory, Nautical Almanac Office. 1981.
1641:
Popowski, P.; Gould, A. (1998). "Mathematics of Statistical Parallax and the Local Distance Scale".
463:(IAU) passed Resolution B2 which, as part of the definition of a standardized absolute and apparent
2846:
1842:
1045:
1029:
1025:
795:
418:
312:
288:
107:
2822:
2796:
2707:
2681:
2584:
2378:
2352:
2003:
1977:
1790:
1689:
1642:
1515:
1475:
1449:
1317:
1224:
1156:
1140:
1125:
696:
120:
space mission provided similarly accurate distances to most stars brighter than 15th magnitude.
66:
1707:
1206:
extends over such a large part of the sky, 20 degrees, that the proper motions as derived from
38:
2851:
2403:
2397:
2323:
2258:
2254:
2176:
2151:
2147:
2141:
2068:
1907:
1874:
1560:
1284:
1148:
1098:
1033:
761:
719:
324:
225:
199:
156:
147:
method is useful for measuring the distances of bright stars beyond 50 parsecs and giant
116:
70:
1271:. For stars in the Milky Way disk, this corresponds to a mean baseline of 4 AU per year. For
217:
are near enough for this technique to be useful. In particular the distance obtained for the
2814:
2742:
2699:
2574:
2499:
2370:
2300:
2229:
2213:
2060:
1995:
1816:
1681:
1664:
1535:
1530:
1467:
1393:
1129:
1090:
1080:
661:
642:
595:, has a parallax of 0.7687 ± 0.0003 arcsec. This angle is approximately that
592:
573:
529:
520:
403:
375:
229:
191:
152:
799:
60.27 Earth radii or 384,399 kilometres (238,854 mi) This procedure was first used by
434:
399:
347:
132:
124:
98:
mission obtained parallaxes for over a hundred thousand stars with a precision of about a
27:
Change in the apparent position of celestial bodies when seen from two different positions
2810:
2738:
2695:
2570:
2523:(First ed.). Washington, D. C.: Carnegie Institution of Washington. pp. 1–104.
2495:
2453:
2366:
2296:
1991:
1903:
1870:
1812:
1677:
1463:
1283:
The mean parallaxes and distances of a large group of stars can be estimated from their
992:
283:
34:
Stellar parallax motion from annual parallax. Half the apex angle is the parallax angle.
1231:
1212:
1113:
707:
673:
602:
437:
texts and common usage. Although parsecs are used for the shorter distances within the
371:
308:
262:
254:
162:
127:, about 30,000 light years away. Stars have a velocity relative to the Sun that causes
2374:
2115:
1471:
1139:
Perrine published progress reports in 1906 and 1908. He took 965 photographs with the
2840:
2588:
2458:
2247:
1830:
1288:
1177:
links has solved this old problem. The currently accepted value of solar parallax is
1094:
1037:
653:
618:
441:, multiples of parsecs are required for the larger scales in the universe, including
382:: from that distance, the gap between the Earth and the Sun spans slightly less than
148:
136:
128:
99:
2711:
2343:
Freedman, W.L. (2000). "The Hubble constant and the expansion age of the Universe".
2007:
1479:
2826:
1693:
1117:
773:
723:
669:
426:
343:
316:
214:
2382:
1540:
1497:
1606:
1758:
1277:
1167:
1062:
1001:
630:
414:
245:
241:
237:
204:
171:
167:
17:
2283:
Gutzwiller, Martin C. (1998). "Moon–Earth–Sun: The oldest three-body problem".
1827:
Taking the unit of distance R* to be that corresponding to a parallax of 1″·0
1580:
548:
with the star oscillating across the sky with respect to the background stars.
525:
2304:
2064:
1795:"The distribution in space of the stars in Carrington's Circumpolar Catalogue"
1207:
1171:
804:
672:, launched in December 2013, can measure parallax angles to an accuracy of 10
657:
581:
560:
430:
320:
78:
2504:
1821:
1794:
1272:
1174:
1121:
649:
596:
564:
445:
parsecs (kpc) for the more distant objects within and around the Milky Way,
438:
422:
351:
331:
195:
95:
52:
613:
precisely measures distances up to 10,000 light-years away (10 April 2014).
2602:
Campbell, W. W. (1906). "Reports of the Observatories: Lick Observatory".
779:
467:
scale, mentioned an existing explicit definition of the parsec as exactly
2801:
2686:
2357:
1982:
1763:
1647:
1109:
1105:
1066:
1065:. He then estimated that the Moon–Earth–Sun angle was 87°. Using correct
700:
626:
577:
339:
292:
250:
175:
102:, providing useful distances for stars out to a few hundred parsecs. The
56:
2467:. Vol. 20 (11th ed.). Cambridge University Press. p. 761.
2026:"NASA's Hubble Extends Stellar Tape Measure 10 Times Farther Into Space"
1837:, but if the violence to the Greek language can be overlooked, the word
1409:"NASA's Hubble Extends Stellar Tape Measure 10 Times Farther Into Space"
536:
Stellar parallax created by the relative motion between the Earth and a
808:
83:
30:
1834:
1685:
1093:
was correctly observed in 1761 and 1769. This method was proposed by
638:
622:
563:) is defined as the distance for which the annual parallax is 1
556:
454:
417:
of "parallax of one second" and was coined by the British astronomer
304:
276:
2479:
2197:
Measuring the universe: cosmic dimensions from Aristarchus to Halley
599:
by an object 2 centimeters in diameter located 5.3 kilometers away.
2818:
2761:
2746:
2703:
2579:
2554:
1999:
1520:
1378:
Perryman, M. A. C.; et al. (1999). "The HIPPARCOS Catalogue".
2318:
Webb, Stephen (1999), "3.2 Aristarchus, Hipparchus, and Ptolemy",
1454:
1163:
1152:
1079:
1074:
991:
778:
601:
585:
524:
450:
446:
442:
282:
181:
161:
37:
29:
1170:, have been used for solar parallax determination. Today, use of
1412:
1116:(or distance to the Sun), with the results published in 1910 by
1104:
Much later, the Solar System was "scaled" using the parallax of
1073:
Aristarchus pointed out that the Moon and Sun have nearly equal
711:
568:
537:
335:
221:
has historically been an important step in the distance ladder.
143:
of the proper motions relative to their radial velocities. This
2452:
2668:
Vijay K. Narayanan; Andrew Gould (1999). "A Precision Test of
1502:
Data Release 2: Summary of the contents and survey properties"
996:
Example of lunar parallax: Occultation of Pleiades by the Moon
379:
87:(parallax arcseconds); light-years are used in popular media.
1607:"Hubble stretches the stellar tape measure ten times further"
1581:"Hubble finds Universe may be expanding faster than expected"
652:
was launched primarily for obtaining improved parallaxes and
660:
away, a little more than one percent of the diameter of the
1898:(2nd ed.). Princeton, NJ: Princeton University Press.
1166:
reflections, both off Venus (1958) and off asteroids, like
1829:* There is need for a name for this unit of distance. Mr.
2089:"Soyuz ST-B successfully launches Gaia space observatory"
1357:, ie. 10 (one million million, or billion in long scale).
1084:
Measuring Venus transit times to determine solar parallax
2320:
Measuring the Universe: The Cosmological Distance Ladder
2604:
Publications of the Astronomical Society of the Pacific
2559:
Publications of the Astronomical Society of the Pacific
2536:
Publications of the Astronomical Society of the Pacific
1159:
methods started producing more precise measurements.
828:
110:
has the potential to provide a precision of 20 to 40
641:(then the most distant known planet) and the eighth
2555:"Progress on the Crossley Eros Solar Parallax Work"
1951:
harvnb error: no target: CITEREFZeilikGregory1998 (
1931:
harvnb error: no target: CITEREFZeilikGregory1998 (
1299:
Other methods for distance measurement in astronomy
123:Distances can be measured within 10% as far as the
94:of the measurement. In the 1990s, for example, the
2249:Explanatory Supplement to the Astronomical Almanac
2246:
2143:Explanatory Supplement to the Astronomical Almanac
1496:; et al. (Gaia collaboration) (August 2018).
981:
378:, is about 1.3 parsecs (4.2 light-years) from the
2484:Monthly Notices of the Royal Astronomical Society
1800:Monthly Notices of the Royal Astronomical Society
2057:The Reception of Copernicus' Heliocentric Theory
2024:Harrington, J.D.; Villard, Ray (10 April 2014).
2019:
2017:
1865:(4th ed.). New York: AIP Press / Springer.
1407:Harrington, J. D.; Villard, R. (10 April 2014).
77:for an object at 1 parsec's distance (3.26
346:, and is defined as the distance at which 1 AU
198:disk, this corresponds to a mean baseline of 4
2055:Dobrzycki, J. (1973). Dobrzycki, Jerzy (ed.).
1058:On the Sizes and Distances of the Sun and Moon
621:during the early modern age. It is clear from
551:Stellar parallax is most often measured using
2435:harvnb error: no target: CITEREFWhipple2007 (
2399:Pathfinders: The Golden Age of Arabic Science
2278:
2276:
2274:
1946:
1926:
449:parsecs (Mpc) for mid-distance galaxies, and
338:). The parsec unit is obtained by the use of
8:
2862:Length, distance, or range measuring devices
762:perturbed and approximately elliptical orbit
287:A parsec is the distance from the Sun to an
1737:Proceedings of the HST Calibration Workshop
807:, and later found its way into the work of
787:Parallax can also be used to determine the
1636:
1634:
1632:
681:
610:
2800:
2766:Electronic Journal of Theoretical Physics
2685:
2578:
2503:
2356:
2207:
2205:
2091:. nasaspaceflight.com. 19 December 2013.
1981:
1820:
1646:
1539:
1529:
1519:
1453:
956:
906:
905:
879:
876:
857:
856:
830:
827:
1708:"Cosmic Distance Scales – The Milky Way"
588:reflection off the surfaces of planets.
2430:
1894:Binney, James; Tremaine, Scott (2008).
1370:
1346:
311:used to measure the large distances to
2199:. University of Chicago Press. Ch. 12.
1587:from the original on 11 September 2018
706:The diurnal parallax has been used by
2146:. University Science Books. pp.
2095:from the original on 19 December 2013
1617:from the original on October 30, 2017
1419:from the original on 17 February 2019
232:, can be observed over time, then an
7:
2253:. University Science Books. p.
743:lunar equatorial horizontal parallax
2116:"ESA's Gaia Mission to study stars"
710:in 1672 to measure the distance to
2036:from the original on 12 April 2014
1728:Benedict, G. F.; et al.
1000:This is the method referred to by
969:
966:
963:
960:
957:
940:
937:
934:
931:
928:
925:
922:
919:
916:
913:
910:
907:
901:
898:
895:
892:
889:
886:
883:
880:
867:
864:
861:
858:
852:
849:
846:
843:
840:
837:
834:
831:
25:
2416:from the original on 2015-03-17,
718:and through that to estimate the
2776:from the original on 2015-02-08.
2672:Systematics toward the Hyades".
1863:Allen's Astrophysical Quantities
1559:. PHI Learning Private Limited.
461:International Astronomical Union
275:This section is an excerpt from
131:(transverse across the sky) and
2175:. CRC Press. pp. 132–135.
2140:Seidelmann, P. Kenneth (2005).
2122:from the original on 2008-03-17
1557:An Introduction to Astrophysics
783:Diagram of daily lunar parallax
457:and the most distant galaxies.
47:The most important fundamental
1293:classical statistical parallax
973:
953:
819:the Moon can be triangulated:
400:stars visible to the naked eye
319:, approximately equal to 3.26
1:
2375:10.1016/S0370-1573(00)00013-2
1769:University of Texas at Austin
1040:, this is referred to as the
2553:Perrine, Charles D. (1908).
2519:Perrine, Charles D. (1910).
2322:, Springer, pp. 27–35,
1861:Cox, Arthur N., ed. (2000).
1841:might be adopted. Professor
1507:Astronomy & Astrophysics
398:of one degree of view. Most
2402:, Penguin UK, p. 270,
1541:10.1051/0004-6361/201833051
1472:10.1088/0004-637X/785/2/161
1308:Photometric parallax method
633:'s principal objections to
490: au, or approximately
2878:
1381:Astronomy and Astrophysics
1335:Lunar distance (astronomy)
1222:
1191:
1063:first or last quarter moon
1007:From the Earth to the Moon
518:
274:
253:(usually obtained via the
2727:The Astrophysical Journal
2674:The Astrophysical Journal
2478:Hinks, Arthur R. (1909).
2305:10.1103/RevModPhys.70.589
2285:Reviews of Modern Physics
2173:Fundamentals of astronomy
2171:Barbieri, Cesare (2007).
2065:10.1007/978-94-015-7614-7
1947:Zeilik & Gregory 1998
1927:Zeilik & Gregory 1998
1441:The Astrophysical Journal
1198:The open stellar cluster
1108:, some of which, such as
1048:of the visible Universe.
739:lunar horizontal parallax
406:at over 700,000 parsecs.
2789:The Astronomical Journal
2641:"Astronomical Constants"
2396:Al-Khalili, Jim (2010),
2231:The Astronomical Almanac
2215:The Astronomical Almanac
1970:The Astronomical Journal
1248:spatio-temporal parallax
1244:relativistic positioning
1238:Spatio-temporal parallax
1134:University of California
1036:, or AU). When found by
635:Copernican heliocentrism
55:come from trigonometric
2464:Encyclopædia Britannica
2451:Newcomb, Simon (1911).
2195:Van Helden, A. (2010).
1555:B., Baidyanath (2003).
1531:2018A&A...616A...1G
1394:1997A&A...323L..49P
1188:Moving-cluster parallax
648:In 1989, the satellite
453:parsecs (Gpc) for many
211:Moving cluster parallax
62:stellar parallax method
2505:10.1093/mnras/69.7.544
1822:10.1093/mnras/73.5.334
1330:Cosmic distance ladder
1313:Spectroscopic parallax
1291:. This is known as a
1085:
1075:apparent angular sizes
1017:
997:
983:
784:
678:Hubble Space Telescope
614:
607:Hubble Space Telescope
533:
300:
187:
179:
104:Hubble Space Telescope
44:
35:
2857:Concepts in astronomy
2623:Mem. Roy. Astron. Soc
1353:One trillion here is
1194:Moving cluster method
1083:
1012:
995:
984:
782:
666:European Space Agency
605:
576:in 1838 for the star
528:
433:remains prominent in
374:). The nearest star,
327:(AU), i.e. 30.9
286:
185:
165:
49:distance measurements
41:
33:
2760:Rubin, J.L. (2015).
2648:US Naval Observatory
1280:of the sample size.
1259:Statistical parallax
1145:Harold Spencer Jones
1053:Aristarchus of Samos
826:
801:Aristarchus of Samos
789:distance to the Moon
768:Astronomical Almanac
722:and the size of the
465:bolometric magnitude
459:In August 2015, the
334:(19.2 trillion
313:astronomical objects
207:of the sample size.
145:statistical parallax
141:statistical analysis
59:, as applied in the
2811:1996AJ....112.2110L
2739:1991ApJ...380L..23P
2696:1999ApJ...515..256N
2571:1908PASP...20..184P
2496:1909MNRAS..69..544H
2367:2000PhR...333...13F
2297:1998RvMP...70..589G
2118:. Astronomy Today.
1992:1999AJ....118.1086B
1904:2008gady.book.....B
1871:2000asqu.book.....C
1813:1913MNRAS..73..334D
1678:1994Natur.368..610B
1464:2014ApJ...785..161R
1147:. The value of the
1030:heliocentric system
796:radius of curvature
697:terrestrial planets
645:(the fixed stars).
419:Herbert Hall Turner
289:astronomical object
194:. For stars in the
108:Wide Field Camera 3
43:would be minuscule.
1739:. pp. 380–384
1318:Dynamical parallax
1225:Dynamical parallax
1219:Dynamical parallax
1157:dynamical parallax
1141:Crossley Reflector
1126:Charles D. Perrine
1086:
1004:in his 1865 novel
998:
979:
785:
615:
534:
325:astronomical units
307:(symbol: pc) is a
301:
234:expansion parallax
188:
180:
157:RR Lyrae variables
67:isosceles triangle
45:
36:
2264:978-1-891389-45-0
2182:978-0-7503-0886-1
2157:978-1-891389-45-0
2074:978-90-481-8340-1
1913:978-0-691-13026-2
1896:Galactic Dynamics
1791:Dyson, F. W.
1672:(6472): 610–613.
1611:ESA/Hubble Images
1566:978-81-203-1121-3
1285:radial velocities
1149:Astronomical Unit
1099:black drop effect
1034:astronomical unit
977:
737:(often short for
720:astronomical unit
226:supernova remnant
16:(Redirected from
2869:
2831:
2830:
2804:
2802:astro-ph/9608108
2784:
2778:
2777:
2757:
2751:
2750:
2722:
2716:
2715:
2689:
2687:astro-ph/9808284
2665:
2659:
2658:
2656:
2650:. Archived from
2645:
2637:
2631:
2630:
2618:
2612:
2611:
2599:
2593:
2592:
2582:
2550:
2544:
2543:
2531:
2525:
2524:
2516:
2510:
2509:
2507:
2475:
2469:
2468:
2456:
2454:"Parallax"
2448:
2442:
2440:
2428:
2422:
2421:
2393:
2387:
2386:
2360:
2358:astro-ph/9909076
2340:
2334:
2332:
2315:
2309:
2308:
2280:
2269:
2268:
2252:
2242:
2236:
2235:
2226:
2220:
2219:
2209:
2200:
2193:
2187:
2186:
2168:
2162:
2161:
2137:
2131:
2130:
2128:
2127:
2114:Henney, Paul J.
2111:
2105:
2104:
2102:
2100:
2085:
2079:
2078:
2052:
2046:
2045:
2043:
2041:
2021:
2012:
2011:
1985:
1983:Astro-ph/9905318
1976:(2): 1086–1100.
1964:
1958:
1956:
1944:
1938:
1936:
1924:
1918:
1917:
1891:
1885:
1884:
1858:
1852:
1851:
1824:
1787:
1781:
1780:
1778:
1776:
1759:"Farthest Stars"
1755:
1749:
1748:
1746:
1744:
1734:
1725:
1719:
1718:
1716:
1714:
1704:
1698:
1697:
1686:10.1038/368610a0
1659:
1653:
1652:
1650:
1648:astro-ph/9703140
1638:
1627:
1626:
1624:
1622:
1603:
1597:
1596:
1594:
1592:
1577:
1571:
1570:
1552:
1546:
1545:
1543:
1533:
1523:
1490:
1484:
1483:
1457:
1435:
1429:
1428:
1426:
1424:
1404:
1398:
1397:
1375:
1358:
1351:
1269:secular parallax
1183:
1182:
1130:Lick Observatory
1091:transit of Venus
988:
986:
985:
980:
978:
976:
972:
945:
944:
943:
904:
877:
872:
871:
870:
855:
693:Diurnal parallax
688:Diurnal parallax
682:spatial scanning
662:Milky Way Galaxy
611:Spatial scanning
593:Proxima Centauri
574:Friedrich Bessel
530:Stellar parallax
521:Stellar parallax
515:Stellar parallax
509:
507:
504:
501:
498:
495:
489:
487:
486:
485:
481:
478:
477:
476:
404:Andromeda Galaxy
397:
395:
394:
391:
388:
376:Proxima Centauri
369:
367:
366:
363:
360:
350:an angle of one
230:planetary nebula
192:secular parallax
21:
18:Diurnal parallax
2877:
2876:
2872:
2871:
2870:
2868:
2867:
2866:
2837:
2836:
2835:
2834:
2786:
2785:
2781:
2759:
2758:
2754:
2724:
2723:
2719:
2667:
2666:
2662:
2654:
2643:
2639:
2638:
2634:
2620:
2619:
2615:
2601:
2600:
2596:
2552:
2551:
2547:
2533:
2532:
2528:
2518:
2517:
2513:
2477:
2476:
2472:
2450:
2449:
2445:
2434:
2429:
2425:
2410:
2395:
2394:
2390:
2345:Physics Reports
2342:
2341:
2337:
2330:
2317:
2316:
2312:
2282:
2281:
2272:
2265:
2244:
2243:
2239:
2228:
2227:
2223:
2211:
2210:
2203:
2194:
2190:
2183:
2170:
2169:
2165:
2158:
2139:
2138:
2134:
2125:
2123:
2113:
2112:
2108:
2098:
2096:
2087:
2086:
2082:
2075:
2054:
2053:
2049:
2039:
2037:
2023:
2022:
2015:
1966:
1965:
1961:
1950:
1945:
1941:
1930:
1925:
1921:
1914:
1893:
1892:
1888:
1881:
1860:
1859:
1855:
1828:
1789:
1788:
1784:
1774:
1772:
1757:
1756:
1752:
1742:
1740:
1732:
1727:
1726:
1722:
1712:
1710:
1706:
1705:
1701:
1661:
1660:
1656:
1640:
1639:
1630:
1620:
1618:
1605:
1604:
1600:
1590:
1588:
1579:
1578:
1574:
1567:
1554:
1553:
1549:
1494:Brown, A. G. A.
1492:
1491:
1487:
1437:
1436:
1432:
1422:
1420:
1406:
1405:
1401:
1377:
1376:
1372:
1367:
1362:
1361:
1352:
1348:
1343:
1326:
1301:
1261:
1240:
1227:
1221:
1196:
1190:
1180:
1178:
1022:
946:
878:
829:
824:
823:
732:
690:
674:microarcseconds
553:annual parallax
523:
517:
512:
511:
505:
502:
499:
496:
493:
491:
483:
482:
479:
474:
472:
471:
470:
468:
435:popular science
392:
389:
386:
385:
383:
364:
361:
358:
357:
355:
280:
272:
263:interferometers
240:which are both
133:radial velocity
125:Galactic Center
28:
23:
22:
15:
12:
11:
5:
2875:
2873:
2865:
2864:
2859:
2854:
2849:
2839:
2838:
2833:
2832:
2819:10.1086/118167
2779:
2772:(32): 83–112.
2752:
2747:10.1086/186164
2717:
2704:10.1086/307021
2660:
2657:on 2011-07-20.
2632:
2613:
2594:
2580:10.1086/121816
2545:
2526:
2511:
2470:
2459:Chisholm, Hugh
2443:
2423:
2408:
2388:
2335:
2328:
2310:
2291:(2): 589–639.
2270:
2263:
2237:
2221:
2201:
2188:
2181:
2163:
2156:
2132:
2106:
2080:
2073:
2059:. p. 51.
2047:
2013:
2000:10.1086/300975
1959:
1939:
1919:
1912:
1886:
1880:978-0387987460
1879:
1853:
1833:has suggested
1793:(March 1913).
1782:
1750:
1720:
1699:
1654:
1628:
1598:
1572:
1565:
1547:
1485:
1430:
1399:
1369:
1368:
1366:
1363:
1360:
1359:
1345:
1344:
1342:
1339:
1338:
1337:
1332:
1325:
1322:
1321:
1320:
1315:
1310:
1300:
1297:
1289:proper motions
1260:
1257:
1255:for instance.
1242:From enhanced
1239:
1236:
1232:speed of light
1223:Main article:
1220:
1217:
1192:Main article:
1189:
1186:
1114:solar parallax
1042:solar parallax
1021:
1020:Solar parallax
1018:
990:
989:
975:
971:
968:
965:
962:
959:
955:
952:
949:
942:
939:
936:
933:
930:
927:
924:
921:
918:
915:
912:
909:
903:
900:
897:
894:
891:
888:
885:
882:
875:
869:
866:
863:
860:
854:
851:
848:
845:
842:
839:
836:
833:
735:Lunar parallax
731:
730:Lunar parallax
728:
708:John Flamsteed
689:
686:
654:proper motions
519:Main article:
516:
513:
309:unit of length
299:(not to scale)
281:
273:
271:
268:
255:Doppler effect
149:variable stars
100:milliarcsecond
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
2874:
2863:
2860:
2858:
2855:
2853:
2850:
2848:
2845:
2844:
2842:
2828:
2824:
2820:
2816:
2812:
2808:
2803:
2798:
2794:
2790:
2783:
2780:
2775:
2771:
2767:
2763:
2756:
2753:
2748:
2744:
2740:
2736:
2732:
2728:
2721:
2718:
2713:
2709:
2705:
2701:
2697:
2693:
2688:
2683:
2679:
2675:
2671:
2664:
2661:
2653:
2649:
2642:
2636:
2633:
2628:
2624:
2617:
2614:
2609:
2605:
2598:
2595:
2590:
2586:
2581:
2576:
2572:
2568:
2564:
2560:
2556:
2549:
2546:
2541:
2537:
2530:
2527:
2522:
2515:
2512:
2506:
2501:
2497:
2493:
2490:(7): 544–67.
2489:
2485:
2481:
2474:
2471:
2466:
2465:
2460:
2455:
2447:
2444:
2438:
2432:
2427:
2424:
2420:
2415:
2411:
2409:9780141965017
2405:
2401:
2400:
2392:
2389:
2384:
2380:
2376:
2372:
2368:
2364:
2359:
2354:
2350:
2346:
2339:
2336:
2331:
2329:9781852331061
2325:
2321:
2314:
2311:
2306:
2302:
2298:
2294:
2290:
2286:
2279:
2277:
2275:
2271:
2266:
2260:
2256:
2251:
2250:
2241:
2238:
2233:
2232:
2225:
2222:
2217:
2216:
2208:
2206:
2202:
2198:
2192:
2189:
2184:
2178:
2174:
2167:
2164:
2159:
2153:
2149:
2145:
2144:
2136:
2133:
2121:
2117:
2110:
2107:
2094:
2090:
2084:
2081:
2076:
2070:
2066:
2062:
2058:
2051:
2048:
2035:
2031:
2027:
2020:
2018:
2014:
2009:
2005:
2001:
1997:
1993:
1989:
1984:
1979:
1975:
1971:
1963:
1960:
1954:
1948:
1943:
1940:
1934:
1928:
1923:
1920:
1915:
1909:
1905:
1901:
1897:
1890:
1887:
1882:
1876:
1872:
1868:
1864:
1857:
1854:
1850:
1848:
1844:
1840:
1836:
1832:
1823:
1818:
1814:
1810:
1806:
1802:
1801:
1796:
1792:
1786:
1783:
1771:. 15 May 2021
1770:
1766:
1765:
1760:
1754:
1751:
1738:
1731:
1724:
1721:
1709:
1703:
1700:
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1586:
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1513:
1509:
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1503:
1501:
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1481:
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1447:
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1442:
1434:
1431:
1418:
1414:
1410:
1403:
1400:
1395:
1391:
1387:
1383:
1382:
1374:
1371:
1364:
1356:
1350:
1347:
1340:
1336:
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1328:
1327:
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1316:
1314:
1311:
1309:
1306:
1305:
1304:
1298:
1296:
1294:
1290:
1286:
1281:
1279:
1274:
1270:
1265:
1258:
1256:
1254:
1253:PPN formalism
1249:
1245:
1237:
1235:
1233:
1226:
1218:
1216:
1214:
1209:
1205:
1201:
1195:
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1137:
1135:
1131:
1127:
1123:
1119:
1115:
1111:
1107:
1102:
1100:
1096:
1095:Edmond Halley
1092:
1082:
1078:
1076:
1071:
1068:
1064:
1060:
1059:
1054:
1049:
1047:
1046:expansion age
1043:
1039:
1038:triangulation
1035:
1031:
1028:proposed his
1027:
1019:
1016:
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994:
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947:
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619:heliocentrism
612:
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587:
583:
579:
578:61 Cygni
575:
570:
566:
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531:
527:
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514:
466:
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243:
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137:Doppler shift
134:
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2652:the original
2647:
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2607:
2603:
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2562:
2558:
2548:
2539:
2535:
2529:
2520:
2514:
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2473:
2462:
2446:
2431:Whipple 2007
2426:
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2391:
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2284:
2248:
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2135:
2124:. Retrieved
2109:
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2083:
2056:
2050:
2038:. Retrieved
2029:
1973:
1969:
1962:
1942:
1922:
1895:
1889:
1862:
1856:
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1838:
1826:
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1785:
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1762:
1753:
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1736:
1723:
1713:24 September
1711:. Retrieved
1702:
1669:
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1657:
1619:. Retrieved
1610:
1601:
1589:. Retrieved
1575:
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1402:
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1302:
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1268:
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1262:
1247:
1241:
1228:
1197:
1184:arcseconds.
1161:
1138:
1118:Arthur Hinks
1103:
1087:
1072:
1056:
1055:in his book
1050:
1041:
1023:
1013:
1005:
999:
817:
813:
793:
786:
774:lunar theory
766:
759:
755:
751:
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742:
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734:
733:
724:Solar System
705:
692:
691:
670:Gaia mission
647:
616:
590:
552:
550:
545:
541:
535:
427:astrophysics
410:
408:
344:trigonometry
317:Solar System
315:outside the
302:
259:
238:Binary stars
233:
223:
209:
189:
151:, including
122:
115:
111:
89:
82:
60:
46:
2099:19 December
1775:5 September
1388:: L49–L52.
1355:short scale
1278:square root
1002:Jules Verne
680:, by using
658:light-years
561:light-years
415:portmanteau
323:or 206,265
321:light-years
291:that has a
205:square root
172:dark energy
168:dark matter
79:light-years
2847:Astrometry
2841:Categories
2680:(1): 256.
2610:(113): 92.
2542:(10): 226.
2126:2008-03-08
1835:Siriometer
1807:(5): 342.
1521:1804.09365
1448:(2): 161.
1423:17 October
1365:References
1273:halo stars
1208:astrometry
1172:spacecraft
1026:Copernicus
805:Hipparchus
716:opposition
582:heliometer
431:light-year
332:kilometres
2670:Hipparcos
2589:121782316
1845:suggests
1621:April 12,
1455:1401.0484
1246:systems,
1175:telemetry
1122:Cambridge
1106:asteroids
951:
701:asteroids
650:Hipparcos
597:subtended
565:arcsecond
439:Milky Way
423:astronomy
409:The word
352:arcsecond
297:arcsecond
196:Milky Way
176:neutrinos
96:Hipparcos
92:precision
75:arcsecond
69:, with 2
53:astronomy
2852:Parallax
2795:: 2110.
2774:Archived
2712:15351552
2629:: 11–66.
2414:archived
2120:Archived
2093:Archived
2040:11 April
2034:Archived
2008:18099356
1949:, § 22-3
1831:Charlier
1764:StarDate
1615:Archived
1585:Archived
1480:55928992
1417:Archived
1324:See also
1067:geometry
627:geometry
580:using a
348:subtends
340:parallax
329:trillion
293:parallax
251:velocity
155:and the
153:Cepheids
57:parallax
2827:8732647
2807:Bibcode
2735:Bibcode
2733:: L23.
2692:Bibcode
2567:Bibcode
2492:Bibcode
2461:(ed.).
2433:, p. 47
2363:Bibcode
2293:Bibcode
2148:123–125
1988:Bibcode
1929:, p. 44
1900:Bibcode
1867:Bibcode
1809:Bibcode
1743:11 July
1694:4316734
1674:Bibcode
1526:Bibcode
1460:Bibcode
1390:Bibcode
1213:Doppler
1128:of the
809:Ptolemy
714:at its
542:appears
488:
469:
455:quasars
396:
384:
368:
356:
84:parsecs
2825:
2710:
2587:
2419:round.
2406:
2383:413222
2381:
2326:
2261:
2179:
2154:
2071:
2006:
1910:
1877:
1847:Parsec
1843:Turner
1839:Astron
1692:
1665:Nature
1591:3 June
1563:
1514:. A1.
1478:
1204:Taurus
1200:Hyades
1168:Icarus
1024:After
664:. The
643:sphere
639:Saturn
623:Euclid
559:(3.26
557:parsec
532:motion
411:parsec
372:degree
305:parsec
277:Parsec
270:Parsec
242:visual
219:Hyades
2823:S2CID
2797:arXiv
2708:S2CID
2682:arXiv
2655:(PDF)
2644:(PDF)
2585:S2CID
2457:. In
2379:S2CID
2353:arXiv
2212:"D".
2004:S2CID
1978:arXiv
1733:(PDF)
1690:S2CID
1643:arXiv
1516:arXiv
1476:S2CID
1450:arXiv
1341:Notes
1179:8.794
1164:radar
1162:Also
1153:radar
631:Tycho
586:radar
492:3.085
413:is a
370:of a
336:miles
112:micro
2437:help
2404:ISBN
2324:ISBN
2259:ISBN
2177:ISBN
2152:ISBN
2101:2013
2069:ISBN
2042:2014
2030:NASA
1953:help
1933:help
1908:ISBN
1875:ISBN
1777:2021
1745:2007
1715:2014
1623:2014
1593:2016
1561:ISBN
1500:Gaia
1425:2014
1413:NASA
1287:and
1155:and
1124:and
1110:Eros
803:and
712:Mars
569:year
546:real
538:star
503:3673
451:giga
447:mega
443:kilo
425:and
393:3600
365:3600
342:and
303:The
244:and
174:and
117:Gaia
2815:doi
2793:112
2743:doi
2731:380
2700:doi
2678:515
2575:doi
2500:doi
2371:doi
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2061:doi
1996:doi
1974:118
1817:doi
1682:doi
1670:368
1536:doi
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1468:doi
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1386:323
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1120:of
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