670:
1362:
1138:
124:
1149:
925:
2036:
2060:
2012:
2048:
2024:
1357:{\displaystyle {\begin{bmatrix}x_{\text{ecliptic}}\\y_{\text{ecliptic}}\\z_{\text{ecliptic}}\\\end{bmatrix}}={\begin{bmatrix}1&0&0\\0&\cos \varepsilon &\sin \varepsilon \\0&-\sin \varepsilon &\cos \varepsilon \\\end{bmatrix}}{\begin{bmatrix}x_{\text{equatorial}}\\y_{\text{equatorial}}\\z_{\text{equatorial}}\\\end{bmatrix}}}
1133:{\displaystyle {\begin{bmatrix}x_{\text{equatorial}}\\y_{\text{equatorial}}\\z_{\text{equatorial}}\\\end{bmatrix}}={\begin{bmatrix}1&0&0\\0&\cos \varepsilon &-\sin \varepsilon \\0&\sin \varepsilon &\cos \varepsilon \\\end{bmatrix}}{\begin{bmatrix}x_{\text{ecliptic}}\\y_{\text{ecliptic}}\\z_{\text{ecliptic}}\\\end{bmatrix}}}
192:
540:
per century, the speed of general precession. However, for stars near the ecliptic poles, the rate of change of ecliptic longitude is dominated by the slight movement of the ecliptic (that is, of the plane of the Earth's orbit), so the rate of change may be anything from minus infinity to plus
897:
790:
1608:
785:
1926:
528:. Because it is a right-handed system, ecliptic longitude is measured positive eastwards in the fundamental plane (the ecliptic) from 0° to 360°. Because of
287:, but may include B1950.0, B1900.0, etc.) is a fixed standard direction, allowing positions established at various dates to be compared directly.
1919:
1984:
1455:
745:
86:
2080:
1912:
268:
In order to reference a coordinate system which can be considered as fixed in space, these motions require specification of the
1587:
1816:
632:
crossed by the ecliptic. Longitudes were specified in signs, degrees, minutes, and seconds. For example, a longitude of
17:
1525:
1500:
343:, or similar. Note that there is no "mean ecliptic", as the ecliptic is not subject to small periodic oscillations.
1716:
1456:
Nautical
Almanac Office, U.S. Naval Observatory; H.M. Nautical Almanac Office, Royal Greenwich Observatory (1961).
1971:
1935:
1402:
757:
697:
147:
105:
331:). This is the actual intersection of the two planes at any particular moment, with all motions accounted for.
1951:
1946:
521:
479:
208:
58:
1826:
1381:
908:
721:
532:, the ecliptic longitude of most "fixed stars" (referred to the equinox of date) increases by about 50.3
117:
113:
46:
892:{\displaystyle {\begin{aligned}x&=r\cos b\cos l\\y&=r\cos b\sin l\\z&=r\sin b\end{aligned}}}
2002:
1966:
31:
1369:
1609:
Expressions for the
Precession Quantities Based upon the IAU (1976) System of Astronomical Constants
1459:
Explanatory
Supplement to the Astronomical Ephemeris and the American Ephemeris and Nautical Almanac
620:
From antiquity through the 18th century, ecliptic longitude was commonly measured using twelve
574:
has a celestial latitude of +90°. Ecliptic latitude for "fixed stars" is not affected by precession.
1683:
234:
1635:
1781:
74:
257:, completing one circuit in about 26,000 years. Superimposed on this is a smaller motion of the
1463:
242:
171:
1831:
1876:
1786:
1490:
524:, the primary direction (0° ecliptic longitude) points from the Earth towards the Sun at the
328:
306:
262:
253:, causes a slow, continuous turning of the coordinate system westward about the poles of the
220:
1677:
1573:
1881:
1791:
1709:
1569:
1438:
729:
677:
90:
8:
2064:
1776:
1391:
1629:
1442:
779:
These rectangular coordinates are related to the corresponding spherical coordinates by
2052:
2040:
1796:
1756:
1751:
1746:
685:
1457:
1989:
1821:
1808:
1771:
1766:
1741:
1733:
1521:
1496:
1489:
U.S. Naval
Observatory, Nautical Almanac Office (1992). P. Kenneth Seidelmann (ed.).
761:
701:
640:. Since Leo begins 120° from the March equinox, the longitude in modern form is
621:
596:
284:
273:
226:
204:
166:
669:
276:, when giving a position in ecliptic coordinates. The three most commonly used are:
2016:
1961:
1857:
1577:
658:
529:
302:
250:
216:
200:
134:
127:
70:
1904:
772:-axis, and the curl of the other fingers points generally in the direction of the
1761:
1702:
1582:
1554:
1142:
918:
637:
517:
109:
661:
to stay synchronized with the seasons, which is crucial for agrarian societies.
1893:
1886:
716:. The reference frame is relatively stationary, aligned with the March equinox.
50:
1688:
2074:
1862:
1407:
713:
673:
629:
571:
567:
525:
246:
211:(blue), being inclined to the ecliptic, appear to wobble as the Sun advances.
156:
102:
1495:. University Science Books, Mill Valley, CA (reprint 2005). pp. 11–13.
305:
to its position at "date", but free from the small periodic oscillations of
191:
2028:
741:
604:
592:
583:
is also necessary for a complete spherical position (symbols: heliocentric
62:
1429:
Cunningham, Clifford J. (June 1985). "Asteroid Pole
Positions: A Survey".
335:
A position in the ecliptic coordinate system is thus typically specified
78:
1836:
737:
654:
648:
591:). Different distance units are used for different objects. Within the
123:
1852:
764:, that is, if one extends their right thumb upward, it simulates the
625:
608:
537:
533:
297:
of "date" (that is, the ecliptic in its position at "date") with the
38:
1866:
1552:
1386:
749:
689:
563:
513:
320:
294:
258:
254:
230:
179:
143:
82:
902:
624:, each of 30° longitude, a practice that continues in modern
1397:
269:
27:
Celestial coordinate system used to describe Solar System objects
1640:; numerous examples of this notation appear throughout the book.
1725:
66:
1143:
Conversion from equatorial coordinates to ecliptic coordinates
919:
Conversion from ecliptic coordinates to equatorial coordinates
725:
600:
310:
238:
175:
98:
54:
1678:
The
Ecliptic: the Sun's Annual Path on the Celestial Sphere
2023:
1462:. H.M. Stationery Office, London (reprint 1974). pp.
1694:
733:
681:
196:
94:
1689:
MEASURING THE SKY A Quick Guide to the
Celestial Sphere
653:
In China, ecliptic longitude is measured using 24
562:), measures the angular distance of an object from the
512:) measures the angular distance of an object along the
1488:
1305:
1215:
1158:
1081:
991:
934:
199:
along the ecliptic (red) as seen on the inside of the
2000:
1152:
928:
788:
541:
infinity depending on the exact position of the star.
249:, is not quite fixed. A slow motion of Earth's axis,
708:-axis 90° to the east on the fundamental plane. The
245:
of the primary direction, their intersection at the
1934:
1520:. Willmann-Bell, Inc., Richmond, VA. p. 137.
1492:Explanatory Supplement to the Astronomical Almanac
1356:
1132:
891:
566:towards the north (positive) or south (negative)
2072:
1555:"Expressions for IAU 2000 precession quantities"
1553:N. Capitaine; P.T. Wallace; J. Chapront (2003).
913:
903:Conversion between celestial coordinate systems
261:, and a small oscillation of the Earth's axis,
174:coordinates are seldom seen except for certain
657:, each of 15° longitude, and are used by
636:is 19.933° east of the start of the sign
628:. The signs approximately corresponded to the
1920:
1710:
1422:
352:Summary of notation for ecliptic coordinates
142: Ecliptic longitude; measured along the
203:. Ecliptic coordinates appear in (red). The
1927:
1913:
1717:
1703:
1684:Equatorial ↔ Ecliptic coordinate converter
1627:
1428:
664:
1581:
728:calculations and simulations. It has its
724:of ecliptic coordinates is often used in
301:equator (that is, the equator rotated by
668:
346:
327:equator (that is, the mean equator plus
190:
122:
1680:Durham University Department of Physics
1415:
768:-axis, their extended index finger the
101:, its primary direction is towards the
14:
2073:
1691:James B. Kaler, University of Illinois
692:plane, and the primary direction (the
1908:
1698:
1515:
1394:, where the ecliptic latitude is ±90°
170:A full globe is shown here, although
341:mean equinox and ecliptic of J2000.0
186:
599:are used, and for objects near the
49:commonly used for representing the
24:
272:of a particular date, known as an
155: Ecliptic latitude; measured
25:
2092:
1671:
615:
516:from the primary direction. Like
337:true equinox and ecliptic of date
2058:
2046:
2034:
2022:
2010:
1593:from the original on 2012-03-25.
280:Mean equinox of a standard epoch
93:can be the center of either the
2081:Astronomical coordinate systems
1936:Astronomical coordinate systems
1655:
1643:
1621:
1403:Equinox (celestial coordinates)
1631:A Compleat System of Astronomy
1597:
1546:
1534:
1509:
1482:
1470:
1449:
712:-axis points toward the north
454:
309:). Commonly used in planetary
13:
1:
1634:. J. Wilcox, London. p.
77:have orbits with only slight
1628:Leadbetter, Charles (1742).
1613:Astronomy & Astrophysics
1562:Astronomy & Astrophysics
914:Converting Cartesian vectors
522:equatorial coordinate system
89:is convenient. The system's
7:
1382:Celestial coordinate system
1375:
909:Celestial coordinate system
659:Chinese lunisolar calendars
319:is the intersection of the
293:is the intersection of the
195:The apparent motion of the
112:. It may be implemented in
47:celestial coordinate system
10:
2097:
1872:Ecliptic coordinate system
1724:
1583:10.1051/0004-6361:20031539
906:
676:ecliptic coordinates. The
646:
214:
43:ecliptic coordinate system
32:Elliptic coordinate system
29:
1980:
1942:
1845:
1805:
1732:
1431:The Minor Planet Bulletin
1370:obliquity of the ecliptic
760:. The coordinates have a
634:♌ 19° 55′ 58″
478:are usually reserved for
450:
361:
358:
356:
233:are slowly moving due to
133:as seen from outside the
75:small Solar System bodies
642:139° 55′ 58″
30:Not to be confused with
1574:2003A&A...412..567C
1518:Astronomical Algorithms
762:right-handed convention
756:-axis toward the March
665:Rectangular coordinates
554:(symbols: heliocentric
504:(symbols: heliocentric
118:rectangular coordinates
1985:Converting coordinates
1662:Explanatory Supplement
1650:Explanatory Supplement
1541:Explanatory Supplement
1477:Explanatory Supplement
1358:
1134:
893:
717:
480:equatorial coordinates
212:
209:equatorial coordinates
183:
65:objects. Because most
1359:
1135:
894:
732:at the center of the
672:
347:Spherical coordinates
221:Astronomical nutation
194:
126:
110:right-hand convention
1882:Planets in astrology
1516:Meeus, Jean (1991).
1416:Notes and references
1150:
926:
786:
696:-axis) is the March
316:True equinox of date
290:Mean equinox of date
131:ecliptic coordinates
1664:(1992), pp. 555-558
1443:1985MPBu...12...13C
722:rectangular variant
572:north ecliptic pole
570:. For example, the
502:celestial longitude
353:
323:of "date" with the
1734:Astrological signs
1652:(1961), pp. 20, 27
1479:(1961), pp. 20, 28
1354:
1348:
1294:
1201:
1130:
1124:
1070:
977:
889:
887:
718:
686:plane of reference
597:astronomical units
552:celestial latitude
536:per year, or 83.8
498:Ecliptic longitude
494:Ecliptic longitude
351:
213:
184:
85:, using it as the
51:apparent positions
18:Ecliptic longitude
1998:
1997:
1990:Coordinate system
1902:
1901:
1809:Western astrology
1343:
1329:
1315:
1196:
1182:
1168:
1119:
1105:
1091:
972:
958:
944:
746:fundamental plane
702:right-handed rule
548:Ecliptic latitude
544:Ecliptic latitude
491:
490:
235:perturbing forces
227:celestial equator
205:celestial equator
187:Primary direction
167:Celestial equator
87:fundamental plane
16:(Redirected from
2088:
2063:
2062:
2061:
2051:
2050:
2049:
2039:
2038:
2037:
2027:
2026:
2015:
2014:
2013:
2006:
1929:
1922:
1915:
1906:
1905:
1858:Axial precession
1719:
1712:
1705:
1696:
1695:
1665:
1659:
1653:
1647:
1641:
1639:
1625:
1619:
1601:
1595:
1594:
1592:
1585:
1559:
1550:
1544:
1538:
1532:
1531:
1513:
1507:
1506:
1486:
1480:
1474:
1468:
1467:
1453:
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1426:
1367:
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1355:
1353:
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1331:
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1184:
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1139:
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1129:
1128:
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888:
775:
771:
767:
755:
711:
707:
695:
643:
635:
590:
586:
561:
557:
530:axial precession
511:
507:
483:
477:
471:
465:
460:Occasional use;
458:
446:
440:
434:
427:
420:
413:
399:
392:
385:
354:
350:
241:, therefore the
217:Axial precession
201:celestial sphere
164:
154:
141:
135:celestial sphere
61:orientations of
21:
2096:
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1656:
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1551:
1547:
1543:(1961), sec. 1G
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684:'s center, the
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207:(blue) and the
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159:to the ecliptic
152:
150:
146:from the March
139:
108:, and it has a
35:
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1863:Constellations
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1672:External links
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630:constellations
622:zodiacal signs
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616:Historical use
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1972:Supergalactic
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1810:
1804:
1798:
1795:
1793:
1790:
1788:
1785:
1783:
1780:
1778:
1775:
1773:
1770:
1768:
1765:
1763:
1760:
1758:
1755:
1753:
1750:
1748:
1745:
1743:
1740:
1739:
1737:
1735:
1731:
1727:
1720:
1715:
1713:
1708:
1706:
1701:
1700:
1697:
1690:
1687:
1685:
1682:
1679:
1676:
1675:
1663:
1658:
1651:
1646:
1637:
1633:
1632:
1624:
1617:
1614:
1610:
1606:
1600:
1589:
1584:
1579:
1575:
1571:
1567:
1563:
1556:
1549:
1542:
1537:
1529:
1527:0-943396-35-2
1523:
1519:
1512:
1504:
1502:1-891389-45-9
1498:
1494:
1493:
1485:
1478:
1473:
1465:
1461:
1460:
1452:
1444:
1440:
1436:
1432:
1425:
1421:
1409:
1408:March equinox
1406:
1404:
1401:
1400:
1399:
1396:
1393:
1392:Ecliptic pole
1390:
1388:
1385:
1383:
1380:
1379:
1373:
1371:
1349:
1337:
1323:
1309:
1302:
1295:
1289:
1286:
1283:
1278:
1275:
1272:
1269:
1264:
1257:
1254:
1251:
1246:
1243:
1240:
1235:
1228:
1223:
1218:
1212:
1207:
1202:
1190:
1176:
1162:
1155:
1140:
1125:
1113:
1099:
1085:
1078:
1071:
1065:
1062:
1059:
1054:
1051:
1048:
1043:
1036:
1033:
1030:
1027:
1022:
1019:
1016:
1011:
1004:
999:
994:
988:
983:
978:
966:
952:
938:
931:
910:
882:
879:
876:
873:
870:
868:
863:
856:
853:
850:
847:
844:
841:
838:
835:
833:
828:
821:
818:
815:
812:
809:
806:
803:
800:
798:
793:
782:
781:
780:
777:
763:
759:
751:
747:
743:
739:
735:
731:
727:
723:
715:
714:ecliptic pole
703:
699:
691:
687:
683:
679:
675:
671:
662:
660:
656:
650:
645:
639:
631:
627:
623:
610:
606:
602:
598:
594:
587:, geocentric
582:
579:
576:
573:
569:
568:ecliptic pole
565:
558:, geocentric
553:
549:
546:
543:
539:
535:
531:
527:
526:March equinox
523:
519:
515:
508:, geocentric
503:
499:
496:
493:
492:
481:
476:
470:
464:
457:
453:
449:
445:
439:
433:
429:
426:
422:
419:
415:
412:
408:
406:Heliocentric
405:
404:
401:
398:
394:
391:
387:
384:
380:
377:
376:
372:
369:
366:
365:
355:
344:
342:
338:
330:
326:
322:
318:
315:
312:
308:
304:
300:
296:
292:
289:
286:
285:J2000.0 epoch
283:(usually the
282:
279:
278:
277:
275:
271:
266:
264:
260:
256:
252:
248:
247:March equinox
244:
240:
236:
232:
228:
222:
218:
210:
206:
202:
198:
193:
181:
177:
173:
172:high-latitude
168:
158:
157:perpendicular
149:
145:
136:
132:
129:
125:
121:
119:
115:
111:
107:
104:
100:
96:
92:
88:
84:
80:
76:
72:
68:
64:
60:
56:
52:
48:
44:
40:
33:
19:
2065:Solar System
1956:
1871:
1806:Concepts in
1661:
1657:
1649:
1645:
1630:
1623:
1615:
1612:
1604:
1603:J.H. Lieske
1599:
1565:
1561:
1548:
1540:
1536:
1517:
1511:
1491:
1484:
1476:
1472:
1458:
1451:
1434:
1430:
1424:
1146:
922:
778:
742:Solar System
719:
704:specifies a
674:Heliocentric
652:
619:
593:Solar System
580:
551:
547:
501:
497:
474:
468:
462:
456:
443:
437:
431:
424:
417:
410:
396:
389:
382:
362:Rectangular
340:
336:
334:
324:
313:calculation.
298:
267:
224:
130:
79:inclinations
63:Solar System
42:
36:
2053:Outer space
2041:Spaceflight
1782:Sagittarius
736:(or at the
655:Solar terms
605:Earth radii
378:Geocentric
243:orientation
73:) and many
1962:Invariable
1952:Equatorial
1947:Horizontal
1837:Triplicity
1618:, pp. 1-16
1568:(2): 581.
1342:equatorial
1328:equatorial
1314:equatorial
971:equatorial
957:equatorial
943:equatorial
738:barycenter
649:solar term
647:See also:
609:kilometers
538:arcminutes
534:arcseconds
367:Longitude
359:Spherical
303:precession
251:precession
215:See also:
2017:Astronomy
1877:Ophiuchus
1853:Astronomy
1787:Capricorn
1607:(1977), "
1437:: 13–16.
1290:ε
1287:
1279:ε
1276:
1270:−
1258:ε
1255:
1247:ε
1244:
1066:ε
1063:
1055:ε
1052:
1037:ε
1034:
1028:−
1023:ε
1020:
880:
854:
845:
819:
810:
626:astrology
611:are used.
373:Distance
370:Latitude
180:asteroids
114:spherical
39:astronomy
2075:Category
1967:Galactic
1957:Ecliptic
1867:Ecliptic
1832:Polarity
1827:Modality
1792:Aquarius
1588:Archived
1387:Ecliptic
1376:See also
1195:ecliptic
1181:ecliptic
1167:ecliptic
1118:ecliptic
1104:ecliptic
1090:ecliptic
750:ecliptic
690:ecliptic
581:Distance
577:Distance
564:ecliptic
514:ecliptic
329:nutation
321:ecliptic
307:nutation
295:ecliptic
263:nutation
259:ecliptic
255:ecliptic
231:ecliptic
229:and the
144:ecliptic
83:ecliptic
69:(except
2003:Portals
1887:symbols
1865:of the
1846:Related
1817:Element
1777:Scorpio
1570:Bibcode
1439:Bibcode
1398:Equinox
1368:is the
776:-axis.
758:equinox
748:on the
744:), its
740:of the
726:orbital
698:equinox
688:is the
680:is the
520:in the
270:equinox
237:on the
148:equinox
106:equinox
81:to the
71:Mercury
67:planets
1797:Pisces
1757:Cancer
1752:Gemini
1747:Taurus
1726:Zodiac
1605:et al.
1524:
1499:
1364:where
730:origin
678:origin
176:comets
165:
163:
153:
140:
91:origin
57:, and
55:orbits
41:, the
2029:Stars
1822:House
1772:Libra
1767:Virgo
1742:Aries
1591:(PDF)
1558:(PDF)
601:Earth
311:orbit
274:epoch
239:Earth
103:March
99:Earth
45:is a
1611:".
1522:ISBN
1497:ISBN
1466:–27.
700:. A
325:true
299:mean
225:The
219:and
178:and
59:pole
1762:Leo
1578:doi
1566:412
1284:cos
1273:sin
1252:sin
1241:cos
1060:cos
1049:sin
1031:sin
1017:cos
877:sin
851:sin
842:cos
816:cos
807:cos
734:Sun
682:Sun
638:Leo
607:or
550:or
500:or
197:Sun
137:.
116:or
97:or
95:Sun
37:In
2077::
1636:94
1616:58
1586:.
1576:.
1564:.
1560:.
1464:24
1435:12
1433:.
1372:.
720:A
644:.
603:,
595:,
472:,
466:,
441:,
435:,
339:,
265:.
120:.
53:,
2005::
1928:e
1921:t
1914:v
1718:e
1711:t
1704:v
1638:.
1580::
1572::
1530:.
1505:.
1445:.
1441::
1366:ε
1350:]
1338:z
1324:y
1310:x
1303:[
1296:]
1265:0
1236:0
1229:0
1224:0
1219:1
1213:[
1208:=
1203:]
1191:z
1177:y
1163:x
1156:[
1126:]
1114:z
1100:y
1086:x
1079:[
1072:]
1044:0
1012:0
1005:0
1000:0
995:1
989:[
984:=
979:]
967:z
953:y
939:x
932:[
883:b
874:r
871:=
864:z
857:l
848:b
839:r
836:=
829:y
822:l
813:b
804:r
801:=
794:x
774:y
770:x
766:z
754:x
710:z
706:y
694:x
589:Δ
585:r
560:β
556:b
510:λ
506:l
482:.
475:z
469:y
463:x
444:z
438:y
432:x
425:r
418:b
411:l
397:Δ
390:β
383:λ
182:.
34:.
20:)
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