164:
1819:
1169:
666:
36:
435:, the Moon must move a little further to reach the new position having the same angular distance from the Sun, appearing to move with respect to the stars since the previous month. Consequently, at 27 days, 7 hours, 43 minutes and 11.5 seconds, the sidereal month is about 2.2 days shorter than the synodic month. Thus, about 13.37 sidereal months, but about 12.37 synodic months, occur in a
1496:
2124:
In medieval times, the part of the Moon's orbit south of the ecliptic was known as the 'dragon' (which devoured the Moon during eclipses) and from this we get the terminology 'dragon's head' for the ascending node and 'dragon's tail' for the descending node. … The periods between successive nodes
1935:
the numerical conversion factor then becomes 2 × B1 × B1 ÷ B2 = 2 × 1,296,000. This would give a linear term in days change (of the period) per day, which is also an inconvenient unit: for change per year multiply by a factor 365.25, and for change per century multiply by a factor 36,525.
1814:{\displaystyle Q={1 \over A'}={1 \over A_{1}+(2\times A_{2}\times T)}={1 \over A_{1}}\times {1 \over 1+(2\times {A_{2} \over A_{1}}\times T)}={1 \over A_{1}}\times (1-2\times {A_{2} \over A_{1}}\times T)={1 \over A_{1}}-(2\times {A_{2} \over (A_{1}\times A_{1})}\times T)}
1482:
474:
may vary from about 29.27 to about 29.83 days. The average duration in modern times is 29.53059 days with up to seven hours variation about the mean in any given year. (which gives a mean synodic month as 29.53059 days or
132:
This article is about the definitions of a 'month' that are mainly of significance in astronomy. For other definitions, including a description of a month in the calendars of different cultures around the world, see
1380:
588:
is based on the amount of time between perceived rotations of the sun around the earth (based on the Greek word τροπή meaning "turn"), the tropical month is the average time between corresponding
2349:
Elements of
Astronomy: Accompanied with Numerous Illustrations, a Colored Representations of the Solar, Stellar, and Nebular Spectra, and Celestial Charts of the Northern and Southern Hemisphere
304:, a "lunar month" traditionally meant exactly 28 days or four weeks, thus a contract for 12 months ran for exactly 48 weeks. In the United Kingdom, the lunar month was formally replaced by the
730:
approximates an ellipse rather than a circle. However, the orientation (as well as the shape) of this orbit is not fixed. In particular, the position of the extreme points (the line of the
1933:
898:
to that in which the Moon is orbiting Earth, one rotation every 18.6 years. Therefore, the Moon returns to the same node slightly earlier than it returns to meet the same reference star.
592:. It is also the average time between successive moments when the moon crosses from the southern celestial hemisphere to the northern (or vice versa), or successive crossing of a given
746:) in about 3,233 days (8.85 years). It takes the Moon longer to return to the same apsis because it has moved ahead during one revolution. This longer period is called the
2011:
853:
about 5.14° with respect to the ecliptic plane. The line of intersection of these planes passes through the two points at which the Moon's orbit crosses the ecliptic plane: the
408:, is the average period of the Moon's orbit with respect to the line joining the Sun and Earth: 29 (Earth) days, 12 hours, 44 minutes and 2.9 seconds. This is the period of the
572:
days (27 d 7 h 43 min 11.6 s).This type of month has been observed among cultures in the Middle East, India, and China in the following way: they divided the sky into 27 or 28
880:
westward, which means the nodes gradually rotate around Earth. As a result, the time it takes the Moon to return to the same node is shorter than a sidereal month, lasting
784:
as the Moon is orbiting the Earth, one revolution in about 8.85 years. Therefore, the Moon takes a little longer to return to perigee than to return to the same star.
1396:
906:
Regardless of the culture, all lunar calendar months approximate the mean length of the synodic month, the average period the Moon takes to cycle through
470:. The same is true (to an even larger extent) for the Moon's orbit around Earth. Because of these two variations in angular rate, the actual time between
769:), whose extent, duration, and appearance (whether total or annular) depend on the exact apparent diameter of the Moon. The apparent diameter of the
546:
1151:
Apart from the long term (millennial) drift in these values, all these periods vary continually around their mean values because of the complex
2610:
2228:
235:
calendar, widely used in the Indian subcontinent. In India, the month from conjunction to conjunction is divided into thirty parts known as
1144:, which follows the somewhat unpredictable rotation of the Earth, and progressively accumulates a difference with ephemeris time called
525:
corresponds to 1 January AD 2000). The duration of synodic months in ancient and medieval history is itself a topic of scholarly study.
2369:
The nodical month is the time in which the Moon accomplishes a revolution with respect to her nodes, the line of which is also movable.
777:, which is the beat period of the synodic and anomalistic month, as well as the period after which the apsides point to the Sun again.
2620:
345:
Most of the following types of lunar month, except the distinction between the sidereal and tropical months, were first recognized in
1216:
713:
119:
2601:
1295:
2681:
163:
2486:
1194:
838:. A solar or lunar eclipse is possible only when the Moon is at or near either of the two points where its orbit crosses the
691:
57:
2181:
2125:
has, over time, been termed the dracontic, draconic and draconitic month, the words deriving from the Greek for 'dragon'.
484:
100:
2353:
1190:
687:
72:
53:
2531:
Chapront-Touzé, M; Chapront, J (1988). "ELP 2000-85: a semi-analytical lunar ephemeris adequate for historical times".
412:, because the Moon's appearance depends on the position of the Moon with respect to the Sun as seen from Earth. Due to
2652:
1179:
676:
212:, the lunar month began on the day when the waning moon could no longer be seen just before sunrise. Others run from
171:
as it cycles through its phases, as seen from the
Northern Hemisphere. The apparent wobbling of the Moon is known as
2729:
2635:
2498:"A new determination of lunar orbital parameters, precession constant and tidal acceleration from LLR measurements"
1879:
1842:
1 revolution (rev) is 360 × 60 × 60" = 1,296,000"; to convert the unit of the velocity to revolutions/day, divide A
1230:
864:
The draconic or nodical month is the average interval between two successive transits of the Moon through the same
620:
227:. Calendars count integer days, so months may be 29 or 30 days in length, in some regular or irregular sequence.
79:
2246:, p. 577: For convenience, it is common to speak of a lunar year of twelve synodic months, or 354.36707 days.
1198:
1183:
695:
680:
46:
1251:
to the sidereal angular velocity, we get the angular velocity w.r.t. the
Equinox of the Date: its period is the
2724:
1152:
309:
201:
1140:
of 36,525 days. For calendrical calculations, one would probably use days measured in the time scale of
86:
1137:
313:
1964:
2719:
2672:
2668:
431:
While the Moon is orbiting Earth, Earth is progressing in its orbit around the Sun. After completing its
394:
68:
2662:
2185:
926:
motion around the Sun, the Moon does not yet finish a synodic cycle until it has reached the point in
2639:
2568:
2540:
2509:
604:
316:(Schedule 1 read with sections 5 and 23 and with Schedule 2 paragraph 4(1)(a)) and its predecessors.
2664:
Explanatory
Supplement to the Astronomical Ephemeris and the American Ephemeris and Nautical Almanac
2497:
2060:
1145:
931:
850:
2584:
2325:
2045:
2036:= 94,672,800,000 × −6.8498 ÷ (1,602,961,601.0312 × 1,602,961,601.0312) = −0.00000025238 days/cy.
743:
655:
597:
436:
404:, meaning "pertaining to a synod, i.e., a meeting"; in this case, of the Sun and the Moon), also
149:
922:. The Moon completes one orbit around Earth every 27.3 days (a sidereal month), but due to
2616:
2415:
2256:
2224:
949:
942:
927:
895:
887: days (27 d 5 h 5 min 35.8 s). The line of nodes of the Moon's orbit
758:
727:
600:. The moon rises at the North Pole once every tropical month, and likewise at the South Pole.
534:
518:
421:
209:
937:
This table lists the average lengths of five types of astronomical lunar month, derived from
2576:
2544:
2517:
2513:
2357:
2075:
2070:
2050:
1477:{\displaystyle \operatorname {d} \!A/\operatorname {d} \!t=A'=A_{1}+(2\times A_{2}\times T)}
1248:
1122:
956:
923:
888:
873:
797:
793:
651:
612:
538:
459:
443:
205:
761:
of the Moon varies with this period, so this type has some relevance for the prediction of
479:
A more precise figure of the average duration may be derived for a specific date using the
2734:
2055:
1243:
W1 is the ecliptic longitude of the Moon w.r.t. the fixed ICRS equinox: its period is the
781:
774:
593:
220:
93:
2643:
2572:
2441:
2065:
1141:
1118:
839:
558:
451:
447:
385:
358:
325:
305:
141:
780:
An anomalistic month is longer than a sidereal month because the perigee moves in the
2713:
2588:
2462:
639:
608:
585:
573:
455:
420:(sunrise to sunrise on the Moon) equals the time that the Moon takes to complete one
413:
2396:
1234:
894:
A draconic month is shorter than a sidereal month because the nodes precess in the
843:
801:
553:
because it is the time it takes the Moon to return to a similar position among the
480:
346:
228:
219:
Yet others use calculation, of varying degrees of sophistication, for example, the
185:
2437:
2347:
416:, the same hemisphere of the Moon always faces the Earth and thus the length of a
2522:
2488:
A Treatise on the
Limitations of Actions at Law and Suits in Equity and Admiralty
1168:
907:
766:
665:
624:
542:
425:
409:
368:
339:
189:
35:
2580:
1283:
877:
865:
831:
576:, one for each day of the month, identified by the prominent star(s) in them.
301:
232:
17:
2553:
603:
It is customary to specify positions of celestial bodies with respect to the
915:
770:
463:
417:
364:
213:
172:
160:. The precise definition varies, especially for the beginning of the month.
157:
2326:"Questions and Answers: What does the period "tropical month" represent?"
941:. These are not constant, so a first-order (linear) approximation of the
911:
616:
471:
467:
374:
224:
197:
153:
458:
of Earth's progression around the Sun varies during the year. Thus, the
231:
are prominent, and calculated with great precision in the ancient Hindu
952:
835:
762:
735:
589:
1129:
869:
827:
739:
193:
2496:
Chapront, Jean; Chapront-Touzé, Michelle; Francou, George (2002).
731:
238:
162:
134:
2466:
2202:
2200:
2198:
2196:
2194:
554:
168:
2032:= 47,336,400,000 ÷ 1,602,961,601.0312 = 29.530588860986 days; C
204:
with the Sun one or two days before that evening (e.g., in the
1862:
is then the period (in days/revolution) at the epoch J2000.0.
1275:
is the elongation of the Moon from the Sun: its period is the
1162:
919:
876:
of the Earth–Moon system, the plane of the Moon's orbit
757: days (27 d 13 h 18 min 33.2 s). The
659:
308:
for deeds and other written contracts by section 61(a) of the
29:
2632:
From
Eudoxus to Einstein: a history of mathematical astronomy
1238:
938:
249:
is between 19 and 26 hours long. The date is named after the
1375:{\displaystyle A=A_{0}+(A_{1}\times T)+(A_{2}\times T^{2})}
1126:
291:
is associated with two consecutive days. This is known as
2667:. London: Her Majesty's Stationery Office. 1961. pp.
619:. Therefore, it takes the Moon less time to return to an
2554:"Ancient and Medieval Values for the Mean Synodic Month"
1839:
is expressed in cy/" which is a very inconvenient unit.
1229:
The periods are derived from polynomial expressions for
634:
days (27 d 7 h 43 min 4.7 s), is commonly known as the
2704:. The Royal Astronomical Society of Canada. p. 14.
2491:. Boston: Charles C Little and James Brown. p. 52.
2379:
2377:
2273:
2308:
2306:
1967:
1882:
1499:
1399:
1388:
in centuries (cy) is 36,525 days from epoch J2000.0.
1298:
2016:
Example for synodic month, from
Delaunay's argument
399:
60:. Unsourced material may be challenged and removed.
2683:Explanatory Supplement to the Astronomical Almanac
2005:
1927:
1813:
1476:
1374:
1136:is centuries since the epoch (2000), expressed in
842:; i.e., the satellite is at or near either of its
1415:
1403:
891:360° in about 6,798 days (18.6 years).
330:There are several types of lunar month. The term
2330:Journal of the British Astronomical Association
2020:: D′ = 1602961601.0312 − 2 × 6.8498 × T "/cy; A
1267:is the argument of latitude: its period is the
373:"Lunation" redirects here. For the number, see
1873:= 1,296,000 × 36,525 = 1,728,962,010,000,000.
1391:The angular velocity is the first derivative:
849:The orbit of the Moon lies in a plane that is
1928:{\displaystyle A_{2}\div (A_{1}\times A_{1})}
1155:of the Sun and planets affecting its motion.
8:
918:, last quarter) and back again: 29–30
2416:"Length of the Synodic Month: 2001 to 2100"
2257:"Length of the Synodic Month: 2001 to 2100"
2223:. Richmond, VA: Willmann-Bell. p. 23.
1239:Chapront, Chapront-Touzé & Francou 2002
1197:. Unsourced material may be challenged and
939:Chapront, Chapront-Touzé & Francou 2002
694:. Unsourced material may be challenged and
292:
286:
280:
274:
268:
262:
256:
250:
244:
236:
2285:
2243:
2206:
2107:in July. In 2004 the variations were from
1491:) is the inverse of the angular velocity:
2567:(114). Science History Publications: 65.
2521:
2297:
1991:
1978:
1966:
1916:
1903:
1887:
1881:
1790:
1777:
1763:
1757:
1737:
1728:
1708:
1698:
1692:
1666:
1657:
1634:
1624:
1618:
1597:
1586:
1577:
1556:
1534:
1524:
1506:
1498:
1459:
1437:
1407:
1398:
1363:
1350:
1325:
1309:
1297:
1217:Learn how and when to remove this message
714:Learn how and when to remove this message
615:, this point moves back slowly along the
200:first becomes visible, at evening, after
120:Learn how and when to remove this message
2099:In 2001, the synodic months varied from
1850:= 1,296,000 × 36,525 = 47,336,400,000; C
961:
285:may 'stall' as well, that is – the same
2657:. Chicago: University of Chicago Press.
2138:
2092:
1259:is the mean anomaly: its period is the
547:International Celestial Reference Frame
338:because it is the cycle of the visible
2383:
2157:
2145:
623:of 0° than to the same point amid the
196:traditions, the month starts when the
2598:Astrophysical Data: Planets and Stars
2221:Astronomical formulae for calculators
2006:{\displaystyle P=C_{1}-C_{2}\times T}
326:Orbital period § Related periods
312:and for post-1850 legislation by the
7:
2680:Seidelmann, P. Kenneth, ed. (1992).
2561:Journal for the History of Astronomy
2312:
2274:Chapront-Touzé & Chapront (1988)
1195:adding citations to reliable sources
1117:In this table, time is expressed in
872:exerted by the Sun's gravity on the
692:adding citations to reliable sources
58:adding citations to reliable sources
2169:
432:
148:is the time between two successive
1412:
1400:
834:and eat the Sun or Moon during an
485:Chapront-Touzé and Chapront (1988)
335:
25:
627:. This slightly shorter period,
27:Time between successive new moons
2485:Angell, Joseph Kinnicut (1846).
1167:
664:
34:
2630:Linton, Christopher M. (2004).
2463:"Eclipses and the Moon's Orbit"
2436:Fraser Cain (24 October 2008).
2184:, volume 27: "Time", paragraph
537:as defined with respect to the
375:New moon § Lunation number
45:needs additional citations for
2654:The Calendars of Ancient Egypt
1922:
1896:
1808:
1796:
1770:
1748:
1722:
1677:
1648:
1609:
1568:
1543:
1471:
1446:
1369:
1343:
1337:
1318:
1282:Derivation of a period from a
1255:month (which is rarely used).
511:= (JD − 2451545.0)/36525
267:may jump. This case is called
1:
1824:ignoring higher-order terms.
930:where the Sun is in the same
750:and has an average length of
490:29.5305888531 + 0.00000021621
261:is shorter than the day, the
225:ecclesiastical lunar calendar
2700:Bishop, Roy L., ed. (1991).
2502:Astronomy & Astrophysics
2346:Lockyer, Sir Norman (1870).
1940:= 2 × 1,296,000 × 36,525 × A
255:ruling at sunrise. When the
2651:Parker, Richard A. (1950).
2615:. Oxford University Press.
2609:Law, Jonathan, ed. (1983).
2552:Goldstein, Bernard (2003).
613:precession of the equinoxes
400:
293:
287:
281:
275:
269:
263:
257:
251:
245:
237:
2751:
2636:Cambridge University Press
2581:10.1177/002182860303400104
2533:Astronomy and Astrophysics
2523:10.1051/0004-6361:20020420
2182:Halsbury's Laws of England
1237:, as listed in Table 4 of
791:
649:
372:
362:
356:
347:Babylonian lunar astronomy
323:
131:
2024:= 1602961601.0312 "/cy; A
389:
638:by analogy with Earth's
424:, returning to the same
310:Law of Property Act 1925
2545:1988A&A...190..342C
2514:2002A&A...387..700C
2401:Encyclopedia Britannica
1835:in "/cy; so the result
607:(Sun's location at the
314:Interpretation Act 1978
2596:Lang, Kenneth (2012).
2007:
1929:
1815:
1478:
1376:
1125:) with days of 86,400
955:(1 January 2000 12:00
830:, said to live in the
611:). Because of Earth's
562:
549:; ICRF) is known as a
334:usually refers to the
176:
2354:American Book Company
2008:
1930:
1816:
1479:
1377:
1247:month. If we add the
826:refers to a mythical
477:29 d 12 h 44 min 3 s)
433:§ Sidereal month
357:Further information:
166:
2219:Meeus, Jean (2002).
2209:, pp. 107, 488.
1965:
1880:
1865:For rev/day divide A
1497:
1397:
1296:
1191:improve this section
688:improve this section
605:First Point of Aries
54:improve this article
2702:Observer's handbook
2644:2004fete.book.....L
2612:A Dictionary of Law
2573:2003JHA....34...65G
2061:Babylonian calendar
814:is also known as a
198:young crescent moon
2263:. 8 November 2019.
2046:Lunisolar calendar
2003:
1925:
1811:
1474:
1372:
1249:rate of precession
1233:arguments used in
896:opposite direction
744:apsidal precession
656:Apsidal precession
621:ecliptic longitude
598:ecliptic longitude
533:The period of the
446:around the Sun is
422:orbit around Earth
340:phases of the Moon
177:
152:of the same type:
2730:Orbit of the Moon
2324:John Guy Porter,
2286:Seidelmann (1992)
2244:Seidelmann (1992)
2230:978-0-9433-9674-3
2207:Supplement (1961)
1800:
1743:
1714:
1672:
1652:
1640:
1592:
1572:
1519:
1227:
1226:
1219:
1112:
1111:
932:relative position
914:, first quarter,
878:gradually rotates
868:. Because of the
759:apparent diameter
748:anomalistic month
742:), rotates once (
724:
723:
716:
646:Anomalistic month
519:Julian day number
462:is faster nearer
398:
167:Animation of the
130:
129:
122:
104:
16:(Redirected from
2742:
2705:
2687:
2676:
2658:
2647:
2626:
2605:
2592:
2558:
2548:
2527:
2525:
2492:
2471:
2470:
2459:
2453:
2452:
2450:
2448:
2433:
2427:
2426:
2424:
2422:
2411:
2405:
2404:
2397:"Draconic month"
2393:
2387:
2381:
2372:
2371:
2366:
2364:
2343:
2337:
2322:
2316:
2310:
2301:
2295:
2289:
2283:
2277:
2271:
2265:
2264:
2253:
2247:
2241:
2235:
2234:
2216:
2210:
2204:
2189:
2179:
2173:
2167:
2161:
2155:
2149:
2148:, pp. 9–23.
2143:
2126:
2122:
2116:
2114:
2113:29 d 10 h 34 min
2110:
2109:29 d 15 h 35 min
2106:
2102:
2101:29 d 19 h 14 min
2097:
2076:Tibetan calendar
2071:Islamic calendar
2051:Chinese calendar
2028:= −6.8498"/cy; C
2012:
2010:
2009:
2004:
1996:
1995:
1983:
1982:
1934:
1932:
1931:
1926:
1921:
1920:
1908:
1907:
1892:
1891:
1831:in "/cy ; A
1820:
1818:
1817:
1812:
1801:
1799:
1795:
1794:
1782:
1781:
1768:
1767:
1758:
1744:
1742:
1741:
1729:
1715:
1713:
1712:
1703:
1702:
1693:
1673:
1671:
1670:
1658:
1653:
1651:
1641:
1639:
1638:
1629:
1628:
1619:
1598:
1593:
1591:
1590:
1578:
1573:
1571:
1561:
1560:
1539:
1538:
1525:
1520:
1518:
1507:
1483:
1481:
1480:
1475:
1464:
1463:
1442:
1441:
1429:
1411:
1381:
1379:
1378:
1373:
1368:
1367:
1355:
1354:
1330:
1329:
1314:
1313:
1286:for an argument
1222:
1215:
1211:
1208:
1202:
1171:
1163:
1138:Julian centuries
1123:Terrestrial Time
1121:(more precisely
1104:
1102:
1096:
1095:
1092:
1076:
1074:
1068:
1067:
1064:
1048:
1046:
1040:
1039:
1036:
1020:
1018:
1012:
1011:
1008:
992:
990:
984:
983:
980:
962:
886:
885:
874:angular momentum
812:draconitic month
798:Nodal precession
794:Lunar precession
773:varies with the
756:
755:
719:
712:
708:
705:
699:
668:
660:
652:Lunar precession
633:
632:
571:
570:
539:celestial sphere
524:
516:
512:
505:
501:
499:
478:
466:and slower near
460:angular velocity
403:
393:
391:
296:
290:
284:
278:
272:
266:
260:
254:
248:
242:
206:Islamic calendar
125:
118:
114:
111:
105:
103:
62:
38:
30:
21:
2750:
2749:
2745:
2744:
2743:
2741:
2740:
2739:
2725:Lunar calendars
2710:
2709:
2708:
2699:
2695:
2693:Further reading
2690:
2679:
2661:
2650:
2629:
2623:
2608:
2595:
2556:
2551:
2530:
2495:
2484:
2480:
2475:
2474:
2461:
2460:
2456:
2446:
2444:
2435:
2434:
2430:
2420:
2418:
2414:Espenak, Fred.
2413:
2412:
2408:
2395:
2394:
2390:
2382:
2375:
2362:
2360:
2345:
2344:
2340:
2323:
2319:
2311:
2304:
2296:
2292:
2284:
2280:
2272:
2268:
2261:astropixels.com
2255:
2254:
2250:
2242:
2238:
2231:
2218:
2217:
2213:
2205:
2192:
2180:
2176:
2168:
2164:
2156:
2152:
2144:
2140:
2135:
2130:
2129:
2123:
2119:
2112:
2108:
2105:29 d 7 h 11 min
2104:
2100:
2098:
2094:
2089:
2084:
2056:Hebrew calendar
2042:
2035:
2031:
2027:
2023:
1987:
1974:
1963:
1962:
1951:
1947:
1943:
1939:
1912:
1899:
1883:
1878:
1877:
1872:
1868:
1861:
1857:
1853:
1849:
1845:
1834:
1830:
1786:
1773:
1769:
1759:
1733:
1704:
1694:
1662:
1630:
1620:
1602:
1582:
1552:
1530:
1529:
1511:
1495:
1494:
1455:
1433:
1422:
1395:
1394:
1359:
1346:
1321:
1305:
1294:
1293:
1223:
1212:
1206:
1203:
1188:
1172:
1161:
1153:orbital effects
1100:
1098:
1093:
1090:
1088:
1072:
1070:
1065:
1062:
1060:
1044:
1042:
1037:
1034:
1032:
1016:
1014:
1009:
1006:
1004:
988:
986:
981:
978:
976:
968:Length in days
924:Earth's orbital
904:
883:
881:
859:descending node
804:
790:
775:full moon cycle
753:
751:
720:
709:
703:
700:
685:
669:
658:
648:
630:
628:
594:right ascension
582:
568:
566:
531:
522:
514:
507:
497:
495:
489:
488:
476:
378:
371:
361:
355:
328:
322:
279:. Conversely a
221:Hebrew calendar
182:
142:lunar calendars
138:
126:
115:
109:
106:
63:
61:
51:
39:
28:
23:
22:
15:
12:
11:
5:
2748:
2746:
2738:
2737:
2732:
2727:
2722:
2712:
2711:
2707:
2706:
2696:
2694:
2691:
2689:
2688:
2686:. p. 576.
2677:
2659:
2648:
2627:
2622:978-0198802525
2621:
2606:
2593:
2549:
2528:
2508:(2): 700–709.
2493:
2481:
2479:
2476:
2473:
2472:
2454:
2442:Universe Today
2428:
2406:
2388:
2373:
2338:
2317:
2302:
2298:Goldstein 2003
2290:
2288:, p. 576.
2278:
2266:
2248:
2236:
2229:
2211:
2190:
2174:
2172:, p. 405.
2162:
2150:
2137:
2136:
2134:
2131:
2128:
2127:
2117:
2103:in January to
2091:
2090:
2088:
2085:
2083:
2080:
2079:
2078:
2073:
2068:
2066:Hindu calendar
2063:
2058:
2053:
2048:
2041:
2038:
2033:
2029:
2025:
2021:
2002:
1999:
1994:
1990:
1986:
1981:
1977:
1973:
1970:
1949:
1945:
1941:
1937:
1924:
1919:
1915:
1911:
1906:
1902:
1898:
1895:
1890:
1886:
1870:
1866:
1859:
1855:
1851:
1847:
1843:
1832:
1828:
1810:
1807:
1804:
1798:
1793:
1789:
1785:
1780:
1776:
1772:
1766:
1762:
1756:
1753:
1750:
1747:
1740:
1736:
1732:
1727:
1724:
1721:
1718:
1711:
1707:
1701:
1697:
1691:
1688:
1685:
1682:
1679:
1676:
1669:
1665:
1661:
1656:
1650:
1647:
1644:
1637:
1633:
1627:
1623:
1617:
1614:
1611:
1608:
1605:
1601:
1596:
1589:
1585:
1581:
1576:
1570:
1567:
1564:
1559:
1555:
1551:
1548:
1545:
1542:
1537:
1533:
1528:
1523:
1517:
1514:
1510:
1505:
1502:
1473:
1470:
1467:
1462:
1458:
1454:
1451:
1448:
1445:
1440:
1436:
1432:
1428:
1425:
1421:
1418:
1414:
1410:
1406:
1402:
1371:
1366:
1362:
1358:
1353:
1349:
1345:
1342:
1339:
1336:
1333:
1328:
1324:
1320:
1317:
1312:
1308:
1304:
1301:
1225:
1224:
1175:
1173:
1166:
1160:
1157:
1142:Universal Time
1119:Ephemeris Time
1110:
1109:
1086:
1082:
1081:
1058:
1054:
1053:
1030:
1026:
1025:
1002:
998:
997:
974:
970:
969:
966:
948:Valid for the
943:secular change
903:
900:
855:ascending node
840:ecliptic plane
808:draconic month
789:
788:Draconic month
786:
782:same direction
722:
721:
672:
670:
663:
647:
644:
636:tropical month
581:
580:Tropical month
578:
574:lunar mansions
551:sidereal month
541:of apparently
530:
529:Sidereal month
527:
437:Gregorian year
359:Synodic period
354:
351:
321:
318:
306:calendar month
216:to full moon.
190:Middle Eastern
181:
178:
128:
127:
42:
40:
33:
26:
24:
18:Sidereal month
14:
13:
10:
9:
6:
4:
3:
2:
2747:
2736:
2733:
2731:
2728:
2726:
2723:
2721:
2720:Units of time
2718:
2717:
2715:
2703:
2698:
2697:
2692:
2685:
2684:
2678:
2674:
2670:
2666:
2665:
2660:
2656:
2655:
2649:
2645:
2641:
2638:. p. 7.
2637:
2633:
2628:
2624:
2618:
2614:
2613:
2607:
2604:. p. 57.
2603:
2599:
2594:
2590:
2586:
2582:
2578:
2574:
2570:
2566:
2562:
2555:
2550:
2546:
2542:
2538:
2534:
2529:
2524:
2519:
2515:
2511:
2507:
2503:
2499:
2494:
2490:
2489:
2483:
2482:
2477:
2468:
2464:
2458:
2455:
2443:
2439:
2438:"Lunar Month"
2432:
2429:
2417:
2410:
2407:
2402:
2398:
2392:
2389:
2385:
2380:
2378:
2374:
2370:
2359:
2355:
2351:
2350:
2342:
2339:
2335:
2331:
2327:
2321:
2318:
2315:, p. 57.
2314:
2309:
2307:
2303:
2300:, p. 65.
2299:
2294:
2291:
2287:
2282:
2279:
2275:
2270:
2267:
2262:
2258:
2252:
2249:
2245:
2240:
2237:
2232:
2226:
2222:
2215:
2212:
2208:
2203:
2201:
2199:
2197:
2195:
2191:
2188:(1st edition)
2187:
2183:
2178:
2175:
2171:
2166:
2163:
2160:, p. 52.
2159:
2158:Angell (1846)
2154:
2151:
2147:
2146:Parker (1950)
2142:
2139:
2132:
2121:
2118:
2096:
2093:
2086:
2081:
2077:
2074:
2072:
2069:
2067:
2064:
2062:
2059:
2057:
2054:
2052:
2049:
2047:
2044:
2043:
2039:
2037:
2019:
2014:
2000:
1997:
1992:
1988:
1984:
1979:
1975:
1971:
1968:
1960:
1958:
1953:
1917:
1913:
1909:
1904:
1900:
1893:
1888:
1884:
1874:
1863:
1840:
1838:
1825:
1822:
1805:
1802:
1791:
1787:
1783:
1778:
1774:
1764:
1760:
1754:
1751:
1745:
1738:
1734:
1730:
1725:
1719:
1716:
1709:
1705:
1699:
1695:
1689:
1686:
1683:
1680:
1674:
1667:
1663:
1659:
1654:
1645:
1642:
1635:
1631:
1625:
1621:
1615:
1612:
1606:
1603:
1599:
1594:
1587:
1583:
1579:
1574:
1565:
1562:
1557:
1553:
1549:
1546:
1540:
1535:
1531:
1526:
1521:
1515:
1512:
1508:
1503:
1500:
1492:
1490:
1485:
1468:
1465:
1460:
1456:
1452:
1449:
1443:
1438:
1434:
1430:
1426:
1423:
1419:
1416:
1408:
1404:
1392:
1389:
1387:
1383:
1364:
1360:
1356:
1351:
1347:
1340:
1334:
1331:
1326:
1322:
1315:
1310:
1306:
1302:
1299:
1291:
1289:
1285:
1280:
1278:
1274:
1270:
1266:
1262:
1258:
1254:
1250:
1246:
1241:
1240:
1236:
1232:
1221:
1218:
1210:
1200:
1196:
1192:
1186:
1185:
1181:
1176:This section
1174:
1170:
1165:
1164:
1158:
1156:
1154:
1149:
1148:("delta-T").
1147:
1143:
1139:
1135:
1131:
1128:
1124:
1120:
1116:
1108:
1087:
1084:
1083:
1080:
1059:
1056:
1055:
1052:
1031:
1028:
1027:
1024:
1003:
1000:
999:
996:
975:
972:
971:
967:
964:
963:
960:
958:
954:
951:
946:
945:is provided.
944:
940:
935:
933:
929:
925:
921:
917:
913:
909:
902:Cycle lengths
901:
899:
897:
892:
890:
879:
875:
871:
867:
862:
860:
856:
852:
847:
845:
844:orbital nodes
841:
837:
833:
829:
825:
821:
820:nodical month
817:
813:
809:
803:
799:
795:
787:
785:
783:
778:
776:
772:
768:
764:
760:
749:
745:
741:
737:
733:
729:
718:
715:
707:
697:
693:
689:
683:
682:
678:
673:This section
671:
667:
662:
661:
657:
653:
645:
643:
641:
640:tropical year
637:
626:
622:
618:
614:
610:
609:March equinox
606:
601:
599:
595:
591:
587:
586:tropical year
579:
577:
575:
564:
560:
556:
552:
548:
544:
540:
536:
528:
526:
520:
510:
504:
493:
486:
482:
473:
469:
465:
461:
457:
453:
449:
445:
444:Earth's orbit
440:
438:
434:
429:
427:
423:
419:
415:
414:tidal locking
411:
407:
402:
396:
387:
383:
382:synodic month
376:
370:
366:
360:
353:Synodic month
352:
350:
348:
343:
341:
337:
336:synodic month
333:
327:
319:
317:
315:
311:
307:
303:
298:
295:
289:
283:
277:
271:
265:
259:
253:
247:
241:
240:
234:
230:
226:
222:
217:
215:
211:
210:ancient Egypt
207:
203:
199:
195:
191:
187:
179:
174:
170:
165:
161:
159:
155:
151:
147:
143:
136:
124:
121:
113:
102:
99:
95:
92:
88:
85:
81:
78:
74:
71: –
70:
69:"Lunar month"
66:
65:Find sources:
59:
55:
49:
48:
43:This article
41:
37:
32:
31:
19:
2701:
2682:
2663:
2653:
2631:
2611:
2597:
2564:
2560:
2536:
2532:
2505:
2501:
2487:
2457:
2445:. Retrieved
2431:
2419:. Retrieved
2409:
2400:
2391:
2386:, p. 7.
2368:
2361:. Retrieved
2348:
2341:
2336:(1952), 180.
2333:
2329:
2320:
2293:
2281:
2269:
2260:
2251:
2239:
2220:
2214:
2177:
2165:
2153:
2141:
2120:
2115:in December.
2095:
2017:
2015:
1961:
1956:
1955:Then period
1954:
1875:
1864:
1841:
1836:
1826:
1823:
1493:
1488:
1487:The period (
1486:
1393:
1390:
1385:
1384:
1292:
1287:
1281:
1276:
1272:
1268:
1264:
1260:
1256:
1252:
1244:
1242:
1235:lunar theory
1228:
1213:
1204:
1189:Please help
1177:
1150:
1133:
1114:
1113:
1106:
1078:
1057:anomalistic
1050:
1022:
994:
947:
936:
905:
893:
863:
858:
854:
848:
823:
819:
815:
811:
807:
805:
802:Nodal period
779:
747:
728:Moon's orbit
725:
710:
701:
686:Please help
674:
635:
602:
584:Just as the
583:
550:
535:Moon's orbit
532:
523:JD = 2451545
508:
502:
491:
481:lunar theory
441:
430:
410:lunar phases
405:
381:
379:
344:
331:
329:
299:
229:Lunar cycles
218:
183:
145:
139:
116:
107:
97:
90:
83:
76:
64:
52:Please help
47:verification
44:
2384:Linton 2004
2363:10 February
1261:anomalistic
973:draconitic
832:lunar nodes
822:. The name
816:nodal month
625:fixed stars
543:fixed stars
426:lunar phase
369:Synodic day
332:lunar month
300:In English
202:conjunction
146:lunar month
2714:Categories
2356:. p.
2170:Law (1983)
2111:in May to
2082:References
1284:polynomial
1231:Delaunay's
1159:Derivation
965:Month type
908:its phases
792:See also:
650:See also:
448:elliptical
363:See also:
324:See also:
302:common law
233:Panchangam
180:Variations
158:full moons
80:newspapers
2589:121983695
2313:Lang 2012
2133:Citations
1998:×
1985:−
1959:in days:
1910:×
1894:÷
1803:×
1784:×
1755:×
1746:−
1717:×
1690:×
1684:−
1675:×
1643:×
1616:×
1595:×
1563:×
1550:×
1466:×
1453:×
1357:×
1332:×
1290:(angle):
1178:does not
1029:sidereal
1001:tropical
928:its orbit
889:precesses
771:full moon
675:does not
590:equinoxes
472:lunations
464:periapsis
418:lunar day
401:synodikós
395:romanized
390:συνοδικός
365:Lunar day
214:full moon
173:libration
154:new moons
2602:Springer
2447:18 April
2040:See also
1516:′
1427:′
1269:draconic
1253:tropical
1245:sidereal
1207:May 2024
1085:synodic
857:and the
851:inclined
824:draconic
763:eclipses
704:May 2024
617:ecliptic
494:−
468:apoapsis
452:circular
450:and not
406:lunation
194:European
150:syzygies
110:May 2024
2640:Bibcode
2569:Bibcode
2541:Bibcode
2539:: 342.
2510:Bibcode
2478:Sources
2421:4 April
1279:month.
1277:synodic
1271:month.
1263:month.
1199:removed
1184:sources
1130:seconds
953:J2000.0
836:eclipse
736:perigee
732:apsides
696:removed
681:sources
517:is the
397::
294:vriddhi
223:or the
94:scholar
2735:Months
2619:
2587:
2227:
1089:29.530
1061:27.554
1033:27.321
1005:27.321
977:27.212
882:27.212
870:torque
828:dragon
800:, and
752:27.554
740:apogee
629:27.321
567:27.321
563:sidera
506:where
454:, the
442:Since
208:). In
192:, and
96:
89:
82:
75:
67:
2585:S2CID
2557:(PDF)
2087:Notes
1115:Note:
1071:1.007
950:epoch
767:Saros
765:(see
559:Latin
555:stars
545:(the
521:(and
456:speed
386:Greek
320:Types
288:tithi
282:tithi
270:kṣaya
264:tithi
258:tithi
252:tithi
246:tithi
239:tithi
186:Shona
135:month
101:JSTOR
87:books
2617:ISBN
2467:NASA
2449:2012
2423:2014
2365:2014
2225:ISBN
1944:÷ (A
1876:For
1869:by B
1846:by B
1182:any
1180:cite
1099:2.52
1043:2.17
1015:1.82
987:4.14
920:days
916:full
866:node
738:and
726:The
679:any
677:cite
654:and
513:and
496:3.64
380:The
367:and
276:lopa
243:. A
169:Moon
144:, a
73:news
2673:488
2669:107
2577:doi
2537:190
2518:doi
2506:387
2358:223
2186:866
1952:).
1948:× A
1858:÷ A
1854:= B
1193:by
1132:.
1094:861
1091:588
1066:886
1063:549
1038:554
1035:661
1010:252
1007:582
982:815
979:220
959:):
912:new
884:220
818:or
810:or
754:551
690:by
631:582
596:or
569:661
565:):
483:of
273:or
184:In
156:or
140:In
56:by
2716::
2671:,
2634:.
2600:.
2583:.
2575:.
2565:34
2563:.
2559:.
2535:.
2516:.
2504:.
2500:.
2465:.
2440:.
2399:.
2376:^
2367:.
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