325:
The magnitude of those errors increases with the time difference between the date and time of observation and the date of the coordinate system used, because of the precession of the equinoxes. If the time difference is small, then fairly easy and small corrections for the precession may well suffice. If the time difference gets large, then fuller and more accurate corrections must be applied. For this reason, a star position read from a star atlas or catalog based on a sufficiently old equinox and equator cannot be used without corrections if reasonable accuracy is required.
526:, so astronomers worldwide can collaborate more effectively. It is inefficient and error-prone if data or observations of one group have to be translated in non-standard ways so that other groups could compare the data with information from other sources. An example of how this works: if a star's position is measured by someone today, they then use a standard transformation to obtain the position expressed in terms of the standard reference frame of J2000, and it is often then this J2000 position which is shared with others.
1964:
2014:
2038:
1990:
124:. In accordance with that alternative historical usage, an expression such as 'correcting the epochs' would refer to the adjustment, usually by a small amount, of the values of the tabulated astronomical quantities applicable to a fixed standard date and time of reference (and not, as might be expected from current usage, to a change from one date and time of reference to a different date and time).
2026:
2002:
316:
comet must be expressed in the coordinate system of 1875 (equinox/equator of 1875). Thus that coordinate system can still be used today, even though most comet predictions made originally for 1875 (epoch = 1875) would no longer, because of the lack of information about their time-dependence and perturbations, be useful today.
292:
Thus a particular coordinate system (equinox and equator/ecliptic of a particular date, such as J2000.0) could be used forever, but a set of osculating elements for a particular epoch may only be (approximately) valid for a rather limited time, because osculating elements such as those exampled above
247:
for minor planets, are routinely given with reference to two dates: first, relative to a recent epoch for all of the elements: but some of the data are dependent on a chosen coordinate system, and then it is usual to specify the coordinate system of a standard epoch which often is not the same as the
231:
in time relative to a reference frame defined in this way, that means the values obtained for the coordinates in respect of any interval t after the stated epoch, are in terms of the coordinate system of the same date as the obtained values themselves, i.e. the date of the coordinate system is equal
119:
was often used in a different way in older astronomical literature, e.g. during the 18th century, in connection with astronomical tables. At that time, it was customary to denote as "epochs", not the standard date and time of origin for time-varying astronomical quantities, but rather the values at
332:. Most stars have very small proper motions, but a few have proper motions that accumulate to noticeable distances after a few tens of years. So, some stellar positions read from a star atlas or catalog for a sufficiently old epoch require proper motion corrections as well, for reasonable accuracy.
324:
To calculate the visibility of a celestial object for an observer at a specific time and place on the Earth, the coordinates of the object are needed relative to a coordinate system of the current date. If coordinates relative to some other date are used, then that will cause errors in the results.
284:
In the particular set of coordinates exampled above, much of the elements has been omitted as unknown or undetermined; for example, the element n allows an approximate time-dependence of the element M to be calculated, but the other elements and n itself are treated as constant, which represents a
474:
is in general use for dating. But, standard conventional epochs which are not
Besselian epochs have been often designated nowadays with a prefix "J", and the calendar date to which they refer is widely known, although not always the same date in the year: thus "J2000" refers to the instant of 12
315:
are specified relative to an equinox from near the beginning of the year 1875. This is a matter of convention, but the convention is defined in terms of the equator and ecliptic as they were in 1875. To find out in which constellation a particular comet stands today, the current position of that
201:
coordinate system in terms of which those astronomical variables are expressed. (Sometimes the word 'equinox' may be used alone, e.g. where it is obvious from the context to users of the data in which form the considered astronomical variables are expressed, in equatorial form or ecliptic form.)
111:
function of the time interval, with an epoch as a temporal point of origin (this is a common current way of using an epoch). Alternatively, the time-varying astronomical quantity can be expressed as a constant, equal to the measure that it had at the epoch, leaving its variation over time to be
300:
Nevertheless, the period of validity is a different matter in principle and not the result of the use of an epoch to express the data. In other cases, e.g. the case of a complete analytical theory of the motion of some astronomical body, all of the elements will usually be given in the form of
266:
where the epoch is expressed in terms of
Terrestrial Time, with an equivalent Julian date. Four of the elements are independent of any particular coordinate system: M is mean anomaly (deg), n: mean daily motion (deg/d), a: size of semi-major axis (AU), e: eccentricity (dimensionless). But the
235:
It can be seen that the date of the coordinate system need not be the same as the epoch of the astronomical quantities themselves. But in that case (apart from the "equinox of date" case described above), two dates will be associated with the data: one date is the epoch for the time-dependent
427:
To distinguish between calendar years and
Besselian years, it became customary to add ".0" to the Besselian years. Since the switch to Julian years in the mid-1980s, it has become customary to prefix "B" to Besselian years. So, "1950" is the calendar year 1950, and "1950.0" = "B1950.0" is the
200:
with equator or ecliptic, is therefore that the reference to the epoch contributes to specifying the date of the values of astronomical variables themselves; while the reference to an equinox along with equator/ecliptic, of a certain date, addresses the identification of, or changes in, the
335:
Due to precession and proper motion, star data become less useful as the age of the observations and their epoch, and the equinox and equator to which they are referred, get older. After a while, it is easier or better to switch to newer data, generally referred to as a newer epoch and
529:
On the other hand, there has also been an astronomical tradition of retaining observations in just the form in which they were made, so that others can later correct the reductions to standard if that proves desirable, as has sometimes occurred.
410:. The definition depended on a particular theory of the orbit of the Earth around the Sun, that of Newcomb (1895), which is now obsolete; for that reason among others, the use of Besselian years has also become or is becoming obsolete.
344:
Epochs and equinoxes are moments in time, so they can be specified in the same way as moments that indicate things other than epochs and equinoxes. The following standard ways of specifying epochs and equinoxes seem the most popular:
271:
and the inclination are all coordinate-dependent, and are specified relative to the reference frame of the equinox and ecliptic of another date "2000.0", otherwise known as J2000, i.e. January 1.5, 2000 (12h on
January 1) or
91:
The main use of astronomical quantities specified in this way is to calculate other relevant parameters of motion, in order to predict future positions and velocities. The applied tools of the disciplines of
916:
Aoki, S.; Soma, M.; Kinoshita, H.; Inoue, K. (December 1983). "Conversion matrix of epoch B 1950.0 FK 4-based positions of stars to epoch J 2000.0 positions in accordance with the new IAU resolutions".
186:
of such coordinate systems possible. Thus the coordinate systems most used in astronomy need their own date-reference because the coordinate systems of that type are themselves in motion, e.g. by the
132:
Astronomical data are often specified not only in their relation to an epoch or date of reference but also in their relations to other conditions of reference, such as coordinate systems specified by "
621:, in which the beginning of the month is determined by the appearance of the New Moon in the evening, the beginning of the day was reckoned from sunset to sunset, following an evening epoch, e.g. the
519:
The IAU decided at their
General Assembly of 1976 that the new standard equinox of J2000.0 should be used starting in 1984. Before that, the equinox of B1950.0 seems to have been the standard.
1035:
Simon, J. L.; Bretagnon, P.; Chapront, J.; Chapront-Touze, M.; Francou, G.; Laskar, J (1994). "Numerical expressions for precession formulae and mean elements for the Moon and the planets".
424:
Lieske's definition is not exactly consistent with the earlier definition in terms of the mean longitude of the Sun. When using
Besselian years, specify which definition is being used.
661:
263:
2455200.5 M 72.00071 . . . . . . . .(2000.0) n. 0.01076162 .. . . . Peri . 354.75938 a 20.3181594 . . . . . Node . 119.42656 e. 0.5715321 . . . . . Incl .. 24.66109
522:
Different astronomers or groups of astronomers used to define individually, but today standard epochs are generally defined by international agreements through the
152:
When the data are dependent for their values on a particular coordinate system, the date of that coordinate system needs to be specified directly or indirectly.
501:
Julian years of 365.25 days away from the epoch J2000 = JD 2451545.0 (TT), still corresponding (in spite of the use of the prefix "J" or word "Julian") to the
479:, 1900, equal to December 31, 1899. It is also usual now to specify on what time scale the time of day is expressed in that epoch-designation, e.g. often
305:
specified appropriately. In that case, their period of validity may stretch over several centuries or even millennia on either side of the stated epoch.
443:
602:, days were reckoned from sunrise to sunrise, following a morning epoch. This may be related to the fact that the Egyptians regulated their year by the
382:
catalog summary, for example, defines the "catalog epoch" as "J1991.25" (8.75 Julian years before
January 1.5, 2000 TT, e.g., April 2.5625, 1991 TT).
204:
The equinox with equator/ecliptic of a given date defines which coordinate system is used. Most standard coordinates in use today refer to 2000
100:(for predicting orbital paths and positions for bodies in motion under the gravitational effects of other bodies) can be used to generate an
358:
587:
epoch, that is, the civil day begins at midnight. But in older astronomical usage, it was usual, until
January 1, 1925, to reckon by a
193:
The epoch of the coordinate system need not be the same, and often in practice is not the same, as the epoch for the data themselves.
629:
and in
Medieval Western Europe in reckoning the dates of religious festivals, while in others a morning epoch was followed, e.g. the
406:
and measured from the mean equinox of the date, is exactly 280 degrees. This moment falls near the beginning of the corresponding
328:
Additionally, stars move relative to each other through space. Apparent motion across the sky relative to other stars is called
1841:
591:
epoch, 12 hours after the start of the civil day of the same denomination, so that the day began when the mean sun crossed the
1107:
Standish, E. M. Jr. (November 1982). "Conversion of positions and proper motions from B1950.0 to the IAU system at J2000.0".
1067:
1025:
1004:
981:
1151:
1901:
1164:
378:
Besselian years, used mostly for star positions, can be encountered in older catalogs but are now becoming obsolete. The
301:
polynomials in interval of time from the epoch, and they will also be accompanied by trigonometrical terms of periodical
1138:
497:
is either positive or negative and is quoted to 1 or 2 decimal places, has come to mean a date that is an interval of
236:
expressions giving the values, and the other date is that of the coordinate system in which the values are expressed.
899:
104:, a table of values giving the positions and velocities of astronomical objects in the sky at a given time or times.
579:
Over shorter timescales, there are a variety of practices for defining when each day begins. In ordinary usage, the
432:
The IAU constellation boundaries are defined in the equatorial coordinate system relative to the equinox of B1875.0.
1896:
1776:
1195:
309:
1861:
1615:
268:
197:
190:, nowadays often resolved into precessional components, separate precessions of the equator and of the ecliptic.
167:
133:
1934:
1573:
1564:
1301:
785:
2058:
1881:
1351:
308:
Some data and some epochs have a long period of use for other reasons. For example, the boundaries of the
159:
505:
date of
January 1, 2000, at 12h TT (about 64 seconds before noon UTC on the same calendar day). (See also
1826:
187:
155:
1980:
1806:
1633:
567:
163:
112:
specified in some other way—for example, by a table, as was common during the 17th and 18th centuries.
595:
at noon. This is still reflected in the definition of J2000, which started at noon, Terrestrial Time.
1944:
560:
533:
The currently used standard epoch "J2000" is defined by international agreement to be equivalent to:
48:
in time used as a reference point for some time-varying astronomical quantity. It is useful for the
1929:
1454:
748:
302:
294:
61:
971:
509:.) Like the Besselian epoch, an arbitrary Julian epoch is therefore related to the Julian date by
1939:
1247:
506:
364:
81:
17:
833:
416:, p. 282 says that a "Besselian epoch" can be calculated from the Julian date according to
1801:
1403:
1323:
1311:
994:
946:
Lieske, J.H. (1979). "Precession Matrix Based on IAU (1976) System of Astronomical Constants".
64:
and vary with time. These time-varying astronomical quantities might include, for example, the
1924:
1866:
1836:
1624:
1501:
1469:
1439:
1398:
1383:
1262:
763:
49:
1120:
1048:
959:
930:
1949:
1771:
1555:
1444:
1413:
1341:
1316:
1291:
1252:
1233:
1188:
1116:
1086:
1044:
955:
926:
592:
436:
703:
This article uses a 24-hour clock, so 11:59:27.816 is equivalent to 11:59:27.816 a.m.
8:
2042:
1811:
1606:
1346:
486:
In addition, an epoch optionally prefixed by "J" and designated as a year with decimals (
403:
286:
244:
144:" – when these are needed for fully specifying astronomical data of the considered type.
93:
57:
1090:
217:
2030:
2018:
1484:
1373:
1271:
618:
502:
471:
212:
scale on January 1, 2000, see below), which occurred about 64 seconds sooner than noon
398:, p. 125 defines the beginning of a Besselian year to be the moment at which the
1851:
1679:
1434:
1388:
1306:
1063:
1021:
1000:
977:
934:
895:
894:, 5, trans. Faith Wallis, (Liverpool: Liverpool University Press, 2004), pp. 22–24.
666:
634:
97:
804:(Report). C programming language. International Astronomical Union. October 9, 2017.
220:). Before about 1984, coordinate systems dated to 1950 or 1900 were commonly used.
1994:
1831:
1763:
1527:
1489:
1363:
1333:
1286:
626:
553:
542:
480:
391:
372:
353:
240:
209:
107:
Astronomical quantities can be specified in any of several ways, for example, as a
53:
1871:
1464:
1368:
1358:
1257:
1181:
1168:
1155:
1148:
1142:
1057:
1015:
622:
603:
467:
196:
The difference between reference to an epoch alone, and a reference to a certain
73:
1161:
475:
noon (midday) on January 1, 2000, and J1900 refers to the instant of 12 noon on
470:, i.e. 365.25 days. This interval measure does not itself define any epoch: the
1967:
1919:
1911:
1906:
1791:
1786:
1717:
1697:
1688:
1281:
1267:
1243:
1238:
1213:
651:
630:
614:
538:
407:
399:
65:
2052:
1821:
1816:
1735:
1378:
1296:
938:
775:"The Hipparcos and Tycho Catalogues", ESA SP-1200, Vol. 1, page XV. ESA, 1997
599:
329:
312:
223:
There is a special meaning of the expression "equinox (and ecliptic/equator)
786:
NASA Jet Propulsion Laboratory 'spice' toolkit documentation, function J1900
2006:
1886:
1796:
1670:
1653:
1511:
1408:
1276:
1135:
249:
69:
1891:
1726:
1496:
1476:
1393:
549:
253:
809:
390:
A Besselian year is named after the German mathematician and astronomer
1459:
1173:
967:
798:
646:
580:
349:
273:
260:
228:
179:
108:
85:
361:
years (see below), e.g., 1950.0 or B1950.0 for January 0.9235, 1950 TT
336:
equinox/equator, than to keep applying corrections to the older data.
1876:
1228:
598:
In traditional cultures and in antiquity other epochs were used. In
476:
379:
101:
33:
1034:
691:
584:
466:
A Julian year is an interval with the length of a mean year in the
450:
According to Meeus, and also according to the formula given above,
183:
141:
1781:
256:, orbital elements have been given including the following data:
137:
45:
1162:
IERS Conventions 2003 (defines ICRS and other related standards)
170:
position, which itself is determined by the orientations of the
869:
607:
77:
1586:
1205:
662:
International Celestial Reference System and its realizations
656:
610:, a phenomenon which occurs in the morning just before dawn.
171:
887:
588:
2001:
857:
420:
B = 1900.0 + (Julian date − 2415020.31352) / 365.242198781
319:
523:
213:
175:
147:
737:
Jean le Rond d'Alembert, Oeuvres Complètes: Ser.1, Vol.6
821:
915:
815:
178:. Their orientations vary (though slowly, e.g. due to
1978:
1077:
Wilson, H. C. (1925). "Change of astronomical time".
845:
27:
Moment in time used as a reference point in astronomy
457:
B1950.0 = JDE 2433282.4235 = 1950 January 0.9235 TT
454:
B1900.0 = JDE 2415020.3135 = 1900 January 0.8135 TT
1017:Explanatory Supplement to the Astronomical Almanac
248:epoch of the data. An example is as follows: For
1149:International Celestial Reference System, or ICRS
352:, e.g., JD 2433282.4235 for January 0.9235, 1950
339:
279:
2050:
717:
72:of a body, the node of its orbit relative to a
297:which will change the values of the elements.
166:. These are defined relative to the (moving)
1189:
842:, Glossary, s.v. Terrestrial Dynamical Time..
514:J = 2000 + (Julian date − 2451545.0) ÷ 365.25
1020:. Sausalito, CA: University Science Books.
996:A History of Ancient Mathematical Astronomy
122:of those time-varying quantities themselves
1963:
1196:
1182:
1013:
992:
875:
863:
839:
827:
461:
371:All three of these are expressed in TT =
1203:
1106:
367:, e.g., J2000.0 for January 1.5, 2000 TT
697:
320:Changing the standard equinox and epoch
127:
14:
2051:
1842:Transposition, docking, and extraction
1076:
945:
851:
749:Harvard Minor Planet Center, data for
413:
174:'s rotation axis and orbit around the
148:Date-references for coordinate systems
1177:
966:
684:
395:
227:". When coordinates are expressed as
1055:
1014:Seidelmann, P. Kenneth, ed. (2006).
723:
690:Examples of this usage are seen in:
402:of the Sun, including the effect of
158:most commonly used in astronomy are
739:, Paris (CNRS) (2002), p.xxx, n.50.
574:
566:January 1, 2000, 11:58:55.816 UTC (
559:January 1, 2000, 11:59:27.816 TAI (
24:
1099:
799:SOFA Time Scale and Calendar Tools
428:beginning of Besselian year 1950.
385:
25:
2070:
1902:Kepler's laws of planetary motion
1129:
293:do not show the effect of future
84:of its orbit, or the size of the
2036:
2024:
2012:
2000:
1988:
1962:
1897:Interplanetary Transport Network
1777:Collision avoidance (spacecraft)
1059:Handbook of Geostationary Orbits
1862:Astronomical coordinate systems
1616:Longitude of the ascending node
881:
764:Explanation of Orbital Elements
269:longitude of the ascending node
259:Epoch 2010 Jan. 4.0 TT . . . =
1935:Retrograde and prograde motion
791:
778:
769:
756:
742:
729:
541:January 1, 2000, at 12:00 TT (
340:Specifying an epoch or equinox
280:Epochs and periods of validity
13:
1:
672:
613:In some cultures following a
285:temporary approximation (see
1882:Equatorial coordinate system
948:Astronomy & Astrophysics
710:
446:used B1925.0 as its equinox.
156:Celestial coordinate systems
7:
640:
208:(i.e. to 12h (noon) on the
188:precession of the equinoxes
10:
2075:
1634:Longitude of the periapsis
1167:December 13, 2013, at the
1109:Astronomy and Astrophysics
1037:Astronomy and Astrophysics
919:Astronomy and Astrophysics
908:
568:Coordinated Universal Time
1958:
1945:Specific angular momentum
1850:
1762:
1706:
1642:
1595:
1535:
1526:
1422:
1332:
1221:
1212:
1136:What is Terrestrial Time?
561:International Atomic Time
442:The classical star atlas
439:uses the equinox B1900.0.
60:, as they are subject to
1158:– U.S. Naval Observatory
1145:– U.S. Naval Observatory
806:(Document revision 1.5.)
735:M Chapront-Touzé (ed.),
677:
267:argument of perihelion,
1940:Specific orbital energy
1154:August 5, 2006, at the
1141:August 6, 2006, at the
1121:1982A&A...115...20S
1049:1994A&A...282..663S
993:Neugebauer, O. (2004).
973:Astronomical Algorithms
960:1979A&A....73..282L
931:1983A&A...128..263A
507:Julian year (astronomy)
76:, the direction of the
1352:Geostationary transfer
462:Julian years and J2000
216:on the same date (see
160:equatorial coordinates
1925:Orbital state vectors
1867:Characteristic energy
1837:Trans-lunar injection
1625:Argument of periapsis
1302:Prograde / Retrograde
1263:Hyperbolic trajectory
892:The Reckoning of Time
878:, pp. 1067–1069.
50:celestial coordinates
1772:Bi-elliptic transfer
1292:Parabolic trajectory
437:Henry Draper Catalog
164:ecliptic coordinates
128:Epoch versus equinox
2059:Astronomical epochs
1812:Low-energy transfer
1091:1925PA.....33....1W
1056:Soop, E.M. (1994).
818:, pp. 263–267.
694:, pp. 663–683
583:is reckoned by the
287:Osculating elements
245:osculating elements
182:), and there is an
140:", or "equinox and
136:", or "equinox and
120:that date and time
94:celestial mechanics
1807:Inclination change
1455:Distant retrograde
635:Buddhist calendars
619:lunisolar calendar
503:Gregorian calendar
472:Gregorian calendar
1976:
1975:
1950:Two-line elements
1758:
1757:
1680:Eccentric anomaly
1522:
1521:
1389:Orbit of the Moon
1248:Highly elliptical
1079:Popular Astronomy
1069:978-0-7923-3054-7
1027:978-1-891389-45-0
1006:978-3-540-06995-9
983:978-0-943396-35-4
976:. Willmann-Bell.
692:Simon et al. 1994
667:Time in astronomy
627:Islamic calendars
444:Tabulae Caelestes
98:orbital mechanics
16:(Redirected from
2066:
2041:
2040:
2039:
2029:
2028:
2027:
2017:
2016:
2015:
2005:
2004:
1993:
1992:
1991:
1984:
1966:
1965:
1907:Lagrangian point
1802:Hohmann transfer
1747:
1733:
1724:
1715:
1695:
1686:
1677:
1668:
1664:
1660:
1651:
1631:
1622:
1613:
1604:
1584:
1580:
1571:
1562:
1553:
1533:
1532:
1502:Heliosynchronous
1451:Lagrange points
1404:Transatmospheric
1219:
1218:
1198:
1191:
1184:
1175:
1174:
1124:
1094:
1073:
1052:
1031:
1010:
987:
963:
942:
902:
885:
879:
873:
867:
861:
855:
849:
843:
837:
831:
825:
819:
816:Aoki et al. 1983
813:
807:
805:
803:
795:
789:
782:
776:
773:
767:
760:
754:
746:
740:
733:
727:
721:
704:
701:
695:
688:
575:Epoch of the day
554:Terrestrial Time
543:Terrestrial Time
515:
492:
481:Terrestrial Time
392:Friedrich Bessel
373:Terrestrial Time
241:orbital elements
232:to (epoch + t).
210:Terrestrial Time
96:or its subfield
54:orbital elements
21:
2074:
2073:
2069:
2068:
2067:
2065:
2064:
2063:
2049:
2048:
2047:
2037:
2035:
2025:
2023:
2013:
2011:
1999:
1989:
1987:
1979:
1977:
1972:
1954:
1872:Escape velocity
1853:
1846:
1827:Rocket equation
1754:
1746:
1740:
1731:
1722:
1713:
1702:
1693:
1684:
1675:
1666:
1662:
1658:
1649:
1638:
1629:
1620:
1611:
1602:
1591:
1582:
1578:
1574:Semi-minor axis
1569:
1565:Semi-major axis
1560:
1551:
1545:
1518:
1440:Areosynchronous
1424:
1418:
1399:Sun-synchronous
1384:Near-equatorial
1328:
1208:
1202:
1169:Wayback Machine
1156:Wayback Machine
1143:Wayback Machine
1132:
1127:
1102:
1100:Further reading
1097:
1070:
1028:
1007:
984:
911:
906:
905:
886:
882:
876:Neugebauer 2004
874:
870:
866:, p. 1067.
864:Neugebauer 2004
862:
858:
854:, pp. 1–2.
850:
846:
840:Seidelmann 2006
838:
834:
828:Seidelmann 2006
826:
822:
814:
810:
801:
797:
796:
792:
783:
779:
774:
770:
761:
757:
747:
743:
734:
730:
722:
718:
713:
708:
707:
702:
698:
689:
685:
680:
675:
643:
604:heliacal rising
577:
513:
500:
496:
491:
487:
468:Julian calendar
464:
388:
386:Besselian years
342:
322:
282:
264:
150:
130:
74:reference plane
42:reference epoch
28:
23:
22:
15:
12:
11:
5:
2072:
2062:
2061:
2046:
2045:
2033:
2021:
2009:
1997:
1974:
1973:
1971:
1970:
1968:List of orbits
1959:
1956:
1955:
1953:
1952:
1947:
1942:
1937:
1932:
1927:
1922:
1920:Orbit equation
1917:
1909:
1904:
1899:
1894:
1889:
1884:
1879:
1874:
1869:
1864:
1858:
1856:
1848:
1847:
1845:
1844:
1839:
1834:
1829:
1824:
1819:
1814:
1809:
1804:
1799:
1794:
1792:Gravity assist
1789:
1787:Delta-v budget
1784:
1779:
1774:
1768:
1766:
1760:
1759:
1756:
1755:
1753:
1752:
1744:
1738:
1729:
1720:
1718:Orbital period
1710:
1708:
1704:
1703:
1701:
1700:
1698:True longitude
1691:
1689:Mean longitude
1682:
1673:
1656:
1646:
1644:
1640:
1639:
1637:
1636:
1627:
1618:
1609:
1599:
1597:
1593:
1592:
1590:
1589:
1576:
1567:
1558:
1548:
1546:
1544:
1543:
1540:
1536:
1530:
1524:
1523:
1520:
1519:
1517:
1516:
1515:
1514:
1506:
1505:
1504:
1499:
1494:
1493:
1492:
1479:
1474:
1473:
1472:
1467:
1462:
1457:
1449:
1448:
1447:
1445:Areostationary
1442:
1437:
1428:
1426:
1420:
1419:
1417:
1416:
1414:Very low Earth
1411:
1406:
1401:
1396:
1391:
1386:
1381:
1376:
1371:
1366:
1361:
1356:
1355:
1354:
1349:
1342:Geosynchronous
1338:
1336:
1330:
1329:
1327:
1326:
1324:Transfer orbit
1321:
1320:
1319:
1314:
1304:
1299:
1294:
1289:
1284:
1282:Lagrange point
1279:
1274:
1265:
1260:
1255:
1250:
1241:
1236:
1231:
1225:
1223:
1216:
1210:
1209:
1204:Gravitational
1201:
1200:
1193:
1186:
1178:
1172:
1171:
1159:
1146:
1131:
1130:External links
1128:
1126:
1125:
1103:
1101:
1098:
1096:
1095:
1074:
1068:
1053:
1032:
1026:
1011:
1005:
989:
988:
982:
964:
954:(3): 282–284.
943:
925:(3): 263–267.
912:
910:
907:
904:
903:
880:
868:
856:
844:
832:
820:
808:
790:
777:
768:
755:
741:
728:
715:
714:
712:
709:
706:
705:
696:
682:
681:
679:
676:
674:
671:
670:
669:
664:
659:
654:
652:Ephemeris time
649:
642:
639:
576:
573:
572:
571:
564:
557:
552:2451545.0 TT (
546:
539:Gregorian date
517:
516:
498:
494:
489:
463:
460:
459:
458:
455:
448:
447:
440:
433:
422:
421:
408:Gregorian year
400:mean longitude
387:
384:
369:
368:
362:
356:
341:
338:
321:
318:
313:constellations
281:
278:
258:
168:vernal equinox
149:
146:
129:
126:
88:of its orbit.
66:mean longitude
58:celestial body
26:
9:
6:
4:
3:
2:
2071:
2060:
2057:
2056:
2054:
2044:
2034:
2032:
2022:
2020:
2010:
2008:
2003:
1998:
1996:
1986:
1985:
1982:
1969:
1961:
1960:
1957:
1951:
1948:
1946:
1943:
1941:
1938:
1936:
1933:
1931:
1928:
1926:
1923:
1921:
1918:
1916:
1915:-body problem
1914:
1910:
1908:
1905:
1903:
1900:
1898:
1895:
1893:
1890:
1888:
1885:
1883:
1880:
1878:
1875:
1873:
1870:
1868:
1865:
1863:
1860:
1859:
1857:
1855:
1849:
1843:
1840:
1838:
1835:
1833:
1830:
1828:
1825:
1823:
1820:
1818:
1817:Oberth effect
1815:
1813:
1810:
1808:
1805:
1803:
1800:
1798:
1795:
1793:
1790:
1788:
1785:
1783:
1780:
1778:
1775:
1773:
1770:
1769:
1767:
1765:
1761:
1751:
1743:
1739:
1737:
1736:Orbital speed
1730:
1728:
1721:
1719:
1712:
1711:
1709:
1705:
1699:
1692:
1690:
1683:
1681:
1674:
1672:
1657:
1655:
1648:
1647:
1645:
1641:
1635:
1628:
1626:
1619:
1617:
1610:
1608:
1601:
1600:
1598:
1594:
1588:
1577:
1575:
1568:
1566:
1559:
1557:
1550:
1549:
1547:
1541:
1538:
1537:
1534:
1531:
1529:
1525:
1513:
1510:
1509:
1507:
1503:
1500:
1498:
1495:
1491:
1490:Earth's orbit
1488:
1487:
1486:
1483:
1482:
1480:
1478:
1475:
1471:
1468:
1466:
1463:
1461:
1458:
1456:
1453:
1452:
1450:
1446:
1443:
1441:
1438:
1436:
1433:
1432:
1430:
1429:
1427:
1421:
1415:
1412:
1410:
1407:
1405:
1402:
1400:
1397:
1395:
1392:
1390:
1387:
1385:
1382:
1380:
1377:
1375:
1372:
1370:
1367:
1365:
1362:
1360:
1357:
1353:
1350:
1348:
1347:Geostationary
1345:
1344:
1343:
1340:
1339:
1337:
1335:
1331:
1325:
1322:
1318:
1315:
1313:
1310:
1309:
1308:
1305:
1303:
1300:
1298:
1295:
1293:
1290:
1288:
1285:
1283:
1280:
1278:
1275:
1273:
1269:
1266:
1264:
1261:
1259:
1256:
1254:
1251:
1249:
1245:
1242:
1240:
1237:
1235:
1232:
1230:
1227:
1226:
1224:
1220:
1217:
1215:
1211:
1207:
1199:
1194:
1192:
1187:
1185:
1180:
1179:
1176:
1170:
1166:
1163:
1160:
1157:
1153:
1150:
1147:
1144:
1140:
1137:
1134:
1133:
1122:
1118:
1114:
1110:
1105:
1104:
1092:
1088:
1084:
1080:
1075:
1071:
1065:
1061:
1060:
1054:
1050:
1046:
1042:
1038:
1033:
1029:
1023:
1019:
1018:
1012:
1008:
1002:
998:
997:
991:
990:
985:
979:
975:
974:
969:
965:
961:
957:
953:
949:
944:
940:
936:
932:
928:
924:
920:
914:
913:
901:
900:0-85323-693-3
897:
893:
889:
884:
877:
872:
865:
860:
853:
848:
841:
836:
829:
824:
817:
812:
800:
794:
787:
781:
772:
765:
759:
753:
752:
745:
738:
732:
725:
720:
716:
700:
693:
687:
683:
668:
665:
663:
660:
658:
655:
653:
650:
648:
645:
644:
638:
636:
632:
628:
624:
620:
616:
611:
609:
605:
601:
600:ancient Egypt
596:
594:
590:
586:
582:
569:
565:
562:
558:
555:
551:
547:
544:
540:
536:
535:
534:
531:
527:
525:
520:
512:
511:
510:
508:
504:
484:
482:
478:
473:
469:
456:
453:
452:
451:
445:
441:
438:
434:
431:
430:
429:
425:
419:
418:
417:
415:
411:
409:
405:
401:
397:
394:(1784–1846).
393:
383:
381:
376:
374:
366:
363:
360:
357:
355:
351:
348:
347:
346:
337:
333:
331:
330:proper motion
326:
317:
314:
311:
306:
304:
303:perturbations
298:
296:
295:perturbations
290:
288:
277:
275:
270:
262:
257:
255:
251:
246:
243:, especially
242:
239:For example,
237:
233:
230:
226:
221:
219:
215:
211:
207:
202:
199:
194:
191:
189:
185:
181:
177:
173:
169:
165:
161:
157:
153:
145:
143:
139:
135:
125:
123:
118:
113:
110:
105:
103:
99:
95:
89:
87:
83:
79:
75:
71:
67:
63:
62:perturbations
59:
55:
51:
47:
43:
39:
35:
30:
19:
2043:Solar System
1930:Perturbation
1912:
1887:Ground track
1797:Gravity turn
1749:
1748:
1741:
1734:
1725:
1716:
1696:
1687:
1678:
1671:True anomaly
1669:
1654:Mean anomaly
1652:
1632:
1623:
1614:
1605:
1585:
1572:
1563:
1556:Eccentricity
1554:
1512:Lunar cycler
1485:Heliocentric
1425:other points
1374:Medium Earth
1272:Non-inclined
1115:(1): 20–22.
1112:
1108:
1082:
1078:
1062:. Springer.
1058:
1040:
1036:
1016:
999:. Springer.
995:
972:
951:
947:
922:
918:
891:
883:
871:
859:
847:
835:
830:, p. 8.
823:
811:
793:
780:
771:
758:
750:
744:
736:
731:
719:
699:
686:
612:
606:of the star
597:
578:
532:
528:
521:
518:
485:
465:
449:
426:
423:
412:
389:
377:
370:
365:Julian years
343:
334:
327:
323:
307:
299:
291:
283:
265:
250:minor planet
238:
234:
224:
222:
205:
203:
195:
192:
154:
151:
131:
121:
116:
114:
106:
90:
70:mean anomaly
41:
37:
31:
29:
2031:Outer space
2019:Spaceflight
1892:Hill sphere
1727:Mean motion
1607:Inclination
1596:Orientation
1497:Mars cycler
1435:Areocentric
1307:Synchronous
1043:: 663–683.
968:Meeus, Jean
852:Wilson 1925
550:Julian date
414:Lieske 1979
350:Julian days
276:2451545.0.
229:polynomials
1832:Rendezvous
1528:Parameters
1364:High Earth
1334:Geocentric
1287:Osculating
1244:Elliptical
673:References
647:Astrometry
404:aberration
396:Meeus 1991
180:precession
109:polynomial
86:major axis
1995:Astronomy
1877:Ephemeris
1854:mechanics
1764:Maneuvers
1707:Variation
1470:Libration
1465:Lissajous
1369:Low Earth
1359:Graveyard
1258:Horseshoe
939:0004-6361
724:Soop 1994
711:Citations
581:civil day
493:), where
477:January 0
380:Hipparcos
359:Besselian
115:The word
102:ephemeris
34:astronomy
2053:Category
1643:Position
1268:Inclined
1239:Circular
1165:Archived
1152:Archived
1139:Archived
970:(1991).
641:See also
593:meridian
585:midnight
184:infinity
142:ecliptic
82:aphelion
1981:Portals
1852:Orbital
1822:Phasing
1782:Delta-v
1587:Apsides
1581:,
1379:Molniya
1297:Parking
1234:Capture
1222:General
1117:Bibcode
1087:Bibcode
1085:: 1–2.
1045:Bibcode
956:Bibcode
927:Bibcode
909:Sources
488:2000 +
252:(5145)
225:of date
198:equinox
138:equator
134:equinox
18:B1875.0
1508:Other
1409:Tundra
1277:Kepler
1253:Escape
1206:orbits
1066:
1024:
1003:
980:
937:
898:
751:Pholus
623:Jewish
608:Sirius
254:Pholus
78:apogee
46:moment
2007:Stars
1750:Epoch
1539:Shape
1477:Lunar
1431:Mars
1423:About
1394:Polar
1214:Types
802:(PDF)
678:Notes
657:Epoch
631:Hindu
615:lunar
172:Earth
117:epoch
56:of a
44:is a
38:epoch
36:, an
1542:Size
1481:Sun
1460:Halo
1312:semi
1064:ISBN
1022:ISBN
1001:ISBN
978:ISBN
935:ISSN
896:ISBN
888:Bede
784:See
762:See
633:and
625:and
589:noon
548:The
537:The
435:The
162:and
1317:sub
1229:Box
1113:115
1041:282
923:128
617:or
524:IAU
310:IAU
289:).
261:JDT
214:UT1
176:Sun
80:or
68:or
52:or
40:or
32:In
2055::
1665:,
1661:,
1270:/
1246:/
1111:.
1083:33
1081:.
1039:.
952:73
950:.
933:.
921:.
890:,
637:.
570:).
563:).
556:).
545:).
483:.
375:.
354:TT
274:JD
218:ΔT
206:TT
1983::
1913:n
1745:0
1742:t
1732:v
1723:n
1714:T
1694:l
1685:L
1676:E
1667:f
1663:θ
1659:ν
1650:M
1630:ϖ
1621:ω
1612:Ω
1603:i
1583:q
1579:Q
1570:b
1561:a
1552:e
1197:e
1190:t
1183:v
1123:.
1119::
1093:.
1089::
1072:.
1051:.
1047::
1030:.
1009:.
986:.
962:.
958::
941:.
929::
788:.
766:.
726:.
499:x
495:x
490:x
20:)
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