314:
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.
515:, 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.
113:. 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).
1953:
2003:
2027:
1979:
2015:
1991:
305:
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.
281:
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
236:
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
220:
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
108:
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
321:. 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.
313:
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.
273:
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
463:
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
304:
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
190:
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.)
100:
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
289:
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
255:
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
224:
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
416:
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
189:
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
324:
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
518:
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.
399:. 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.
333:
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:
260:
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
80:
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
905:
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".
175:
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
121:
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 "
610:, 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
650:
508:
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.
1024:
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".
413:
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.
252:
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
511:
Different astronomers or groups of astronomers used to define individually, but today standard epochs are generally defined by international agreements through the
141:
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.
490:
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
468:, 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
294:
specified appropriately. In that case, their period of validity may stretch over several centuries or even millennia on either side of the stated epoch.
591:, 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
371:
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).
193:
The equinox with equator/ecliptic of a given date defines which coordinate system is used. Most standard coordinates in use today refer to 2000
1830:
1056:
1014:
993:
970:
89:(for predicting orbital paths and positions for bodies in motion under the gravitational effects of other bodies) can be used to generate an
1890:
576:
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
182:
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.
618:
and in
Medieval Western Europe in reckoning the dates of religious festivals, while in others a morning epoch was followed, e.g. the
888:
395:
and measured from the mean equinox of the date, is exactly 280 degrees. This moment falls near the beginning of the corresponding
1885:
1765:
1184:
298:
317:
Additionally, stars move relative to each other through space. Apparent motion across the sky relative to other stars is called
1850:
1604:
580:
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
257:
186:
156:
122:
1923:
1562:
1553:
1290:
1096:
Standish, E. M. Jr. (November 1982). "Conversion of positions and proper motions from B1950.0 to the IAU system at J2000.0".
1140:
1153:
367:
Besselian years, used mostly for star positions, can be encountered in older catalogs but are now becoming obsolete. The
1969:
290:
polynomials in interval of time from the epoch, and they will also be accompanied by trigonometrical terms of periodical
2047:
1870:
1340:
148:
1815:
1127:
486:
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
225:
expressions giving the values, and the other date is that of the coordinate system in which the values are expressed.
176:
144:
93:, a table of values giving the positions and velocities of astronomical objects in the sky at a given time or times.
568:
Over shorter timescales, there are a variety of practices for defining when each day begins. In ordinary usage, the
421:
The IAU constellation boundaries are defined in the equatorial coordinate system relative to the equinox of B1875.0.
1795:
1622:
556:
152:
1933:
549:
179:, nowadays often resolved into precessional components, separate precessions of the equator and of the ecliptic.
1918:
1443:
291:
283:
50:
774:
1928:
1236:
495:
353:
70:
297:
Some data and some epochs have a long period of use for other reasons. For example, the boundaries of the
1790:
1392:
1312:
1300:
494:
date of
January 1, 2000, at 12h TT (about 64 seconds before noon UTC on the same calendar day). (See also
1913:
1855:
1825:
1613:
1490:
1458:
1428:
1387:
1372:
1251:
38:
432:
101:
specified in some other way—for example, by a table, as was common during the 17th and 18th centuries.
584:
at noon. This is still reflected in the definition of J2000, which started at noon, Terrestrial Time.
1938:
1760:
1544:
1433:
1402:
1330:
1305:
1280:
1241:
1222:
1177:
1105:
1075:
1033:
944:
915:
581:
522:
The currently used standard epoch "J2000" is defined by international agreement to be equivalent to:
425:
37:
in time used as a reference point for some time-varying astronomical quantity. It is useful for the
2031:
1800:
1595:
1335:
737:
392:
275:
233:
206:
82:
46:
960:
498:.) Like the Besselian epoch, an arbitrary Julian epoch is therefore related to the Julian date by
2019:
2007:
1473:
1362:
1260:
607:
491:
460:
405:, p. 282 says that a "Besselian epoch" can be calculated from the Julian date according to
983:
935:
Lieske, J.H. (1979). "Precession Matrix Based on IAU (1976) System of Astronomical Constants".
347:
53:
and vary with time. These time-varying astronomical quantities might include, for example, the
1840:
1668:
1423:
1377:
1295:
1052:
1010:
989:
966:
923:
884:
655:
623:
86:
752:
1983:
1820:
1752:
1516:
1478:
1352:
1322:
1275:
1109:
1037:
948:
919:
615:
542:
531:
469:
380:
361:
342:
229:
198:
42:
1860:
1453:
1357:
1347:
1246:
1170:
1157:
1144:
1131:
692:
This article uses a 24-hour clock, so 11:59:27.816 is equivalent to 11:59:27.816 a.m.
611:
592:
456:
62:
475:
In addition, an epoch optionally prefixed by "J" and designated as a year with decimals (
133:" – when these are needed for fully specifying astronomical data of the considered type.
1079:
1956:
1908:
1900:
1895:
1780:
1775:
1706:
1686:
1677:
1270:
1256:
1232:
1227:
1202:
640:
619:
603:
527:
396:
388:
201:
scale on January 1, 2000, see below), which occurred about 64 seconds sooner than noon
54:
387:, p. 125 defines the beginning of a Besselian year to be the moment at which the
2041:
1810:
1805:
1724:
1367:
1285:
883:, 5, trans. Faith Wallis, (Liverpool: Liverpool University Press, 2004), pp. 22–24.
588:
318:
301:
793:(Report). C programming language. International Astronomical Union. October 9, 2017.
209:). Before about 1984, coordinate systems dated to 1950 or 1900 were commonly used.
1995:
1875:
1785:
1659:
1642:
1500:
1397:
1265:
238:
96:
Astronomical quantities can be specified in any of several ways, for example, as a
58:
1137:
1046:
1004:
185:
The difference between reference to an epoch alone, and a reference to a certain
1880:
1715:
1485:
1465:
1382:
1150:
538:
464:
noon (midday) on January 1, 2000, and J1900 refers to the instant of 12 noon on
459:, i.e. 365.25 days. This interval measure does not itself define any epoch: the
242:
1448:
956:
635:
569:
338:
262:
249:
217:
168:
97:
74:
927:
764:"The Hipparcos and Tycho Catalogues", ESA SP-1200, Vol. 1, page XV. ESA, 1997
212:
There is a special meaning of the expression "equinox (and ecliptic/equator)
1865:
1217:
775:
NASA Jet Propulsion Laboratory 'spice' toolkit documentation, function J1900
465:
368:
90:
22:
1124:
573:
172:
130:
379:
A Besselian year is named after the German mathematician and astronomer
1770:
1162:
787:
126:
34:
350:
years (see below), e.g., 1950.0 or B1950.0 for January 0.9235, 1950 TT
325:
equinox/equator, than to keep applying corrections to the older data.
596:
587:
In traditional cultures and in antiquity other epochs were used. In
66:
680:
1990:
455:
A Julian year is an interval with the length of a mean year in the
439:
According to Meeus, and also according to the formula given above,
1575:
1194:
645:
160:
245:, orbital elements have been given including the following data:
1151:
IERS Conventions 2003 (defines ICRS and other related standards)
876:
577:
159:
position, which itself is determined by the orientations of the
1166:
512:
202:
164:
651:
International Celestial Reference System and its realizations
599:, a phenomenon which occurs in the morning just before dawn.
409:
B = 1900.0 + (Julian date − 2415020.31352) / 365.242198781
726:
Jean le Rond d'Alembert, Oeuvres Complètes: Ser.1, Vol.6
804:
167:. Their orientations vary (though slowly, e.g. due to
1967:
1066:
Wilson, H. C. (1925). "Change of astronomical time".
16:
Moment in time used as a reference point in astronomy
1839:
1751:
1695:
1631:
1584:
1524:
1515:
1411:
1321:
1210:
1201:
446:
B1950.0 = JDE 2433282.4235 = 1950 January 0.9235 TT
443:
B1900.0 = JDE 2415020.3135 = 1900 January 0.8135 TT
1006:Explanatory Supplement to the Astronomical Almanac
237:epoch of the data. An example is as follows: For
1138:International Celestial Reference System, or ICRS
341:, e.g., JD 2433282.4235 for January 0.9235, 1950
61:of a body, the node of its orbit relative to a
286:which will change the values of the elements.
155:. These are defined relative to the (moving)
1178:
831:, Glossary, s.v. Terrestrial Dynamical Time..
503:J = 2000 + (Julian date − 2451545.0) ÷ 365.25
8:
1009:. Sausalito, CA: University Science Books.
985:A History of Ancient Mathematical Astronomy
111:of those time-varying quantities themselves
1952:
1521:
1207:
1185:
1171:
1163:
864:
852:
828:
816:
360:All three of these are expressed in TT =
356:, e.g., J2000.0 for January 1.5, 2000 TT
1974:
705:
672:
309:Changing the standard equinox and epoch
1831:Transposition, docking, and extraction
840:
738:Harvard Minor Planet Center, data for
402:
163:'s rotation axis and orbit around the
137:Date-references for coordinate systems
384:
216:". When coordinates are expressed as
7:
1003:Seidelmann, P. Kenneth, ed. (2006).
712:
679:Examples of this usage are seen in:
391:of the Sun, including the effect of
147:most commonly used in astronomy are
728:, Paris (CNRS) (2002), p.xxx, n.50.
555:January 1, 2000, 11:58:55.816 UTC (
548:January 1, 2000, 11:59:27.816 TAI (
788:SOFA Time Scale and Calendar Tools
417:beginning of Besselian year 1950.
14:
1891:Kepler's laws of planetary motion
282:do not show the effect of future
73:of its orbit, or the size of the
2025:
2013:
2001:
1989:
1977:
1951:
1886:Interplanetary Transport Network
1766:Collision avoidance (spacecraft)
1048:Handbook of Geostationary Orbits
1851:Astronomical coordinate systems
1605:Longitude of the ascending node
753:Explanation of Orbital Elements
258:longitude of the ascending node
248:Epoch 2010 Jan. 4.0 TT . . . =
1924:Retrograde and prograde motion
530:January 1, 2000, at 12:00 TT (
329:Specifying an epoch or equinox
269:Epochs and periods of validity
1:
602:In some cultures following a
274:temporary approximation (see
1871:Equatorial coordinate system
937:Astronomy & Astrophysics
435:used B1925.0 as its equinox.
145:Celestial coordinate systems
197:(i.e. to 12h (noon) on the
177:precession of the equinoxes
2064:
1623:Longitude of the periapsis
1156:December 13, 2013, at the
1098:Astronomy and Astrophysics
1026:Astronomy and Astrophysics
908:Astronomy and Astrophysics
557:Coordinated Universal Time
1947:
1934:Specific angular momentum
1125:What is Terrestrial Time?
550:International Atomic Time
431:The classical star atlas
428:uses the equinox B1900.0.
49:, as they are subject to
1147:– U.S. Naval Observatory
1134:– U.S. Naval Observatory
795:(Document revision 1.5.)
724:M Chapront-Touzé (ed.),
256:argument of perihelion,
1929:Specific orbital energy
1143:August 5, 2006, at the
1130:August 6, 2006, at the
1110:1982A&A...115...20S
1038:1994A&A...282..663S
982:Neugebauer, O. (2004).
962:Astronomical Algorithms
949:1979A&A....73..282L
920:1983A&A...128..263A
496:Julian year (astronomy)
65:, the direction of the
1341:Geostationary transfer
451:Julian years and J2000
205:on the same date (see
149:equatorial coordinates
1914:Orbital state vectors
1856:Characteristic energy
1826:Trans-lunar injection
1614:Argument of periapsis
1291:Prograde / Retrograde
1252:Hyperbolic trajectory
881:The Reckoning of Time
867:, pp. 1067–1069.
39:celestial coordinates
1761:Bi-elliptic transfer
1281:Parabolic trajectory
426:Henry Draper Catalog
153:ecliptic coordinates
117:Epoch versus equinox
2048:Astronomical epochs
1801:Low-energy transfer
1080:1925PA.....33....1W
1045:Soop, E.M. (1994).
807:, pp. 263–267.
683:, pp. 663–683
572:is reckoned by the
276:Osculating elements
234:osculating elements
171:), and there is an
129:", or "equinox and
125:", or "equinox and
109:that date and time
83:celestial mechanics
1796:Inclination change
1444:Distant retrograde
624:Buddhist calendars
608:lunisolar calendar
492:Gregorian calendar
461:Gregorian calendar
1965:
1964:
1939:Two-line elements
1747:
1746:
1669:Eccentric anomaly
1511:
1510:
1378:Orbit of the Moon
1237:Highly elliptical
1068:Popular Astronomy
1058:978-0-7923-3054-7
1016:978-1-891389-45-0
995:978-3-540-06995-9
972:978-0-943396-35-4
965:. Willmann-Bell.
681:Simon et al. 1994
656:Time in astronomy
616:Islamic calendars
433:Tabulae Caelestes
87:orbital mechanics
2055:
2030:
2029:
2028:
2018:
2017:
2016:
2006:
2005:
2004:
1994:
1993:
1982:
1981:
1980:
1973:
1955:
1954:
1896:Lagrangian point
1791:Hohmann transfer
1736:
1722:
1713:
1704:
1684:
1675:
1666:
1657:
1653:
1649:
1640:
1620:
1611:
1602:
1593:
1573:
1569:
1560:
1551:
1542:
1522:
1491:Heliosynchronous
1440:Lagrange points
1393:Transatmospheric
1208:
1187:
1180:
1173:
1164:
1113:
1083:
1062:
1041:
1020:
999:
976:
952:
931:
891:
874:
868:
862:
856:
850:
844:
838:
832:
826:
820:
814:
808:
805:Aoki et al. 1983
802:
796:
794:
792:
784:
778:
771:
765:
762:
756:
749:
743:
735:
729:
722:
716:
710:
693:
690:
684:
677:
564:Epoch of the day
543:Terrestrial Time
532:Terrestrial Time
504:
481:
470:Terrestrial Time
381:Friedrich Bessel
362:Terrestrial Time
230:orbital elements
221:to (epoch + t).
199:Terrestrial Time
85:or its subfield
43:orbital elements
2063:
2062:
2058:
2057:
2056:
2054:
2053:
2052:
2038:
2037:
2036:
2026:
2024:
2014:
2012:
2002:
2000:
1988:
1978:
1976:
1968:
1966:
1961:
1943:
1861:Escape velocity
1842:
1835:
1816:Rocket equation
1743:
1735:
1729:
1720:
1711:
1702:
1691:
1682:
1673:
1664:
1655:
1651:
1647:
1638:
1627:
1618:
1609:
1600:
1591:
1580:
1571:
1567:
1563:Semi-minor axis
1558:
1554:Semi-major axis
1549:
1540:
1534:
1507:
1429:Areosynchronous
1413:
1407:
1388:Sun-synchronous
1373:Near-equatorial
1317:
1197:
1191:
1158:Wayback Machine
1145:Wayback Machine
1132:Wayback Machine
1121:
1116:
1095:
1091:
1089:Further reading
1086:
1065:
1059:
1044:
1023:
1017:
1002:
996:
981:
973:
955:
934:
904:
900:
895:
894:
875:
871:
865:Neugebauer 2004
863:
859:
855:, p. 1067.
853:Neugebauer 2004
851:
847:
843:, pp. 1–2.
839:
835:
829:Seidelmann 2006
827:
823:
817:Seidelmann 2006
815:
811:
803:
799:
790:
786:
785:
781:
772:
768:
763:
759:
750:
746:
736:
732:
723:
719:
711:
707:
702:
697:
696:
691:
687:
678:
674:
669:
664:
632:
593:heliacal rising
566:
502:
489:
485:
480:
476:
457:Julian calendar
453:
377:
375:Besselian years
331:
311:
271:
253:
139:
119:
63:reference plane
31:reference epoch
17:
12:
11:
5:
2061:
2059:
2051:
2050:
2040:
2039:
2035:
2034:
2022:
2010:
1998:
1986:
1963:
1962:
1960:
1959:
1957:List of orbits
1948:
1945:
1944:
1942:
1941:
1936:
1931:
1926:
1921:
1916:
1911:
1909:Orbit equation
1906:
1898:
1893:
1888:
1883:
1878:
1873:
1868:
1863:
1858:
1853:
1847:
1845:
1837:
1836:
1834:
1833:
1828:
1823:
1818:
1813:
1808:
1803:
1798:
1793:
1788:
1783:
1781:Gravity assist
1778:
1776:Delta-v budget
1773:
1768:
1763:
1757:
1755:
1749:
1748:
1745:
1744:
1742:
1741:
1733:
1727:
1718:
1709:
1707:Orbital period
1699:
1697:
1693:
1692:
1690:
1689:
1687:True longitude
1680:
1678:Mean longitude
1671:
1662:
1645:
1635:
1633:
1629:
1628:
1626:
1625:
1616:
1607:
1598:
1588:
1586:
1582:
1581:
1579:
1578:
1565:
1556:
1547:
1537:
1535:
1533:
1532:
1529:
1525:
1519:
1513:
1512:
1509:
1508:
1506:
1505:
1504:
1503:
1495:
1494:
1493:
1488:
1483:
1482:
1481:
1468:
1463:
1462:
1461:
1456:
1451:
1446:
1438:
1437:
1436:
1434:Areostationary
1431:
1426:
1417:
1415:
1409:
1408:
1406:
1405:
1403:Very low Earth
1400:
1395:
1390:
1385:
1380:
1375:
1370:
1365:
1360:
1355:
1350:
1345:
1344:
1343:
1338:
1331:Geosynchronous
1327:
1325:
1319:
1318:
1316:
1315:
1313:Transfer orbit
1310:
1309:
1308:
1303:
1293:
1288:
1283:
1278:
1273:
1271:Lagrange point
1268:
1263:
1254:
1249:
1244:
1239:
1230:
1225:
1220:
1214:
1212:
1205:
1199:
1198:
1193:Gravitational
1192:
1190:
1189:
1182:
1175:
1167:
1161:
1160:
1148:
1135:
1120:
1119:External links
1117:
1115:
1114:
1092:
1090:
1087:
1085:
1084:
1063:
1057:
1042:
1021:
1015:
1000:
994:
978:
977:
971:
953:
943:(3): 282–284.
932:
914:(3): 263–267.
901:
899:
896:
893:
892:
869:
857:
845:
833:
821:
809:
797:
779:
766:
757:
744:
730:
717:
704:
703:
701:
698:
695:
694:
685:
671:
670:
668:
665:
663:
660:
659:
658:
653:
648:
643:
641:Ephemeris time
638:
631:
628:
565:
562:
561:
560:
553:
546:
541:2451545.0 TT (
535:
528:Gregorian date
506:
505:
487:
483:
478:
452:
449:
448:
447:
444:
437:
436:
429:
422:
411:
410:
397:Gregorian year
389:mean longitude
376:
373:
358:
357:
351:
345:
330:
327:
310:
307:
302:constellations
270:
267:
247:
157:vernal equinox
138:
135:
118:
115:
77:of its orbit.
55:mean longitude
47:celestial body
15:
13:
10:
9:
6:
4:
3:
2:
2060:
2049:
2046:
2045:
2043:
2033:
2023:
2021:
2011:
2009:
1999:
1997:
1992:
1987:
1985:
1975:
1971:
1958:
1950:
1949:
1946:
1940:
1937:
1935:
1932:
1930:
1927:
1925:
1922:
1920:
1917:
1915:
1912:
1910:
1907:
1905:
1904:-body problem
1903:
1899:
1897:
1894:
1892:
1889:
1887:
1884:
1882:
1879:
1877:
1874:
1872:
1869:
1867:
1864:
1862:
1859:
1857:
1854:
1852:
1849:
1848:
1846:
1844:
1838:
1832:
1829:
1827:
1824:
1822:
1819:
1817:
1814:
1812:
1809:
1807:
1806:Oberth effect
1804:
1802:
1799:
1797:
1794:
1792:
1789:
1787:
1784:
1782:
1779:
1777:
1774:
1772:
1769:
1767:
1764:
1762:
1759:
1758:
1756:
1754:
1750:
1740:
1732:
1728:
1726:
1725:Orbital speed
1719:
1717:
1710:
1708:
1701:
1700:
1698:
1694:
1688:
1681:
1679:
1672:
1670:
1663:
1661:
1646:
1644:
1637:
1636:
1634:
1630:
1624:
1617:
1615:
1608:
1606:
1599:
1597:
1590:
1589:
1587:
1583:
1577:
1566:
1564:
1557:
1555:
1548:
1546:
1539:
1538:
1536:
1530:
1527:
1526:
1523:
1520:
1518:
1514:
1502:
1499:
1498:
1496:
1492:
1489:
1487:
1484:
1480:
1479:Earth's orbit
1477:
1476:
1475:
1472:
1471:
1469:
1467:
1464:
1460:
1457:
1455:
1452:
1450:
1447:
1445:
1442:
1441:
1439:
1435:
1432:
1430:
1427:
1425:
1422:
1421:
1419:
1418:
1416:
1410:
1404:
1401:
1399:
1396:
1394:
1391:
1389:
1386:
1384:
1381:
1379:
1376:
1374:
1371:
1369:
1366:
1364:
1361:
1359:
1356:
1354:
1351:
1349:
1346:
1342:
1339:
1337:
1336:Geostationary
1334:
1333:
1332:
1329:
1328:
1326:
1324:
1320:
1314:
1311:
1307:
1304:
1302:
1299:
1298:
1297:
1294:
1292:
1289:
1287:
1284:
1282:
1279:
1277:
1274:
1272:
1269:
1267:
1264:
1262:
1258:
1255:
1253:
1250:
1248:
1245:
1243:
1240:
1238:
1234:
1231:
1229:
1226:
1224:
1221:
1219:
1216:
1215:
1213:
1209:
1206:
1204:
1200:
1196:
1188:
1183:
1181:
1176:
1174:
1169:
1168:
1165:
1159:
1155:
1152:
1149:
1146:
1142:
1139:
1136:
1133:
1129:
1126:
1123:
1122:
1118:
1111:
1107:
1103:
1099:
1094:
1093:
1088:
1081:
1077:
1073:
1069:
1064:
1060:
1054:
1050:
1049:
1043:
1039:
1035:
1031:
1027:
1022:
1018:
1012:
1008:
1007:
1001:
997:
991:
987:
986:
980:
979:
974:
968:
964:
963:
958:
954:
950:
946:
942:
938:
933:
929:
925:
921:
917:
913:
909:
903:
902:
897:
890:
889:0-85323-693-3
886:
882:
878:
873:
870:
866:
861:
858:
854:
849:
846:
842:
837:
834:
830:
825:
822:
818:
813:
810:
806:
801:
798:
789:
783:
780:
776:
770:
767:
761:
758:
754:
748:
745:
742:
741:
734:
731:
727:
721:
718:
714:
709:
706:
699:
689:
686:
682:
676:
673:
666:
661:
657:
654:
652:
649:
647:
644:
642:
639:
637:
634:
633:
629:
627:
625:
621:
617:
613:
609:
605:
600:
598:
594:
590:
589:ancient Egypt
585:
583:
579:
575:
571:
563:
558:
554:
551:
547:
544:
540:
536:
533:
529:
525:
524:
523:
520:
516:
514:
509:
501:
500:
499:
497:
493:
473:
471:
467:
462:
458:
450:
445:
442:
441:
440:
434:
430:
427:
423:
420:
419:
418:
414:
408:
407:
406:
404:
400:
398:
394:
390:
386:
383:(1784–1846).
382:
374:
372:
370:
365:
363:
355:
352:
349:
346:
344:
340:
337:
336:
335:
328:
326:
322:
320:
319:proper motion
315:
308:
306:
303:
300:
295:
293:
292:perturbations
287:
285:
284:perturbations
279:
277:
268:
266:
264:
259:
251:
246:
244:
240:
235:
232:, especially
231:
228:For example,
226:
222:
219:
215:
210:
208:
204:
200:
196:
191:
188:
183:
180:
178:
174:
170:
166:
162:
158:
154:
150:
146:
142:
136:
134:
132:
128:
124:
116:
114:
112:
107:
102:
99:
94:
92:
88:
84:
78:
76:
72:
68:
64:
60:
56:
52:
51:perturbations
48:
44:
40:
36:
32:
28:
24:
19:
2032:Solar System
1919:Perturbation
1901:
1876:Ground track
1786:Gravity turn
1738:
1737:
1730:
1723:
1714:
1705:
1685:
1676:
1667:
1660:True anomaly
1658:
1643:Mean anomaly
1641:
1621:
1612:
1603:
1594:
1574:
1561:
1552:
1545:Eccentricity
1543:
1501:Lunar cycler
1474:Heliocentric
1414:other points
1363:Medium Earth
1261:Non-inclined
1104:(1): 20–22.
1101:
1097:
1071:
1067:
1051:. Springer.
1047:
1029:
1025:
1005:
988:. Springer.
984:
961:
940:
936:
911:
907:
880:
872:
860:
848:
836:
824:
819:, p. 8.
812:
800:
782:
769:
760:
747:
739:
733:
725:
720:
708:
688:
675:
601:
595:of the star
586:
567:
521:
517:
510:
507:
474:
454:
438:
415:
412:
401:
378:
366:
359:
354:Julian years
332:
323:
316:
312:
296:
288:
280:
272:
254:
239:minor planet
227:
223:
213:
211:
194:
192:
184:
181:
143:
140:
120:
110:
105:
103:
95:
79:
59:mean anomaly
30:
26:
20:
18:
2020:Outer space
2008:Spaceflight
1881:Hill sphere
1716:Mean motion
1596:Inclination
1585:Orientation
1486:Mars cycler
1424:Areocentric
1296:Synchronous
1032:: 663–683.
957:Meeus, Jean
841:Wilson 1925
539:Julian date
403:Lieske 1979
339:Julian days
265:2451545.0.
218:polynomials
1821:Rendezvous
1517:Parameters
1353:High Earth
1323:Geocentric
1276:Osculating
1233:Elliptical
662:References
636:Astrometry
393:aberration
385:Meeus 1991
169:precession
98:polynomial
75:major axis
1984:Astronomy
1866:Ephemeris
1843:mechanics
1753:Maneuvers
1696:Variation
1459:Libration
1454:Lissajous
1358:Low Earth
1348:Graveyard
1247:Horseshoe
928:0004-6361
713:Soop 1994
700:Citations
570:civil day
482:), where
466:January 0
369:Hipparcos
348:Besselian
104:The word
91:ephemeris
23:astronomy
2042:Category
1632:Position
1257:Inclined
1228:Circular
1154:Archived
1141:Archived
1128:Archived
959:(1991).
630:See also
582:meridian
574:midnight
173:infinity
131:ecliptic
71:aphelion
1970:Portals
1841:Orbital
1811:Phasing
1771:Delta-v
1576:Apsides
1570:,
1368:Molniya
1286:Parking
1223:Capture
1211:General
1106:Bibcode
1076:Bibcode
1074:: 1–2.
1034:Bibcode
945:Bibcode
916:Bibcode
898:Sources
477:2000 +
241:(5145)
214:of date
187:equinox
127:equator
123:equinox
1497:Other
1398:Tundra
1266:Kepler
1242:Escape
1195:orbits
1055:
1013:
992:
969:
926:
887:
740:Pholus
612:Jewish
597:Sirius
243:Pholus
67:apogee
35:moment
1996:Stars
1739:Epoch
1528:Shape
1466:Lunar
1420:Mars
1412:About
1383:Polar
1203:Types
791:(PDF)
667:Notes
646:Epoch
620:Hindu
604:lunar
161:Earth
106:epoch
45:of a
33:is a
27:epoch
25:, an
1531:Size
1470:Sun
1449:Halo
1301:semi
1053:ISBN
1011:ISBN
990:ISBN
967:ISBN
924:ISSN
885:ISBN
877:Bede
773:See
751:See
622:and
614:and
578:noon
537:The
526:The
424:The
151:and
1306:sub
1218:Box
1102:115
1030:282
912:128
606:or
513:IAU
299:IAU
278:).
250:JDT
203:UT1
165:Sun
69:or
57:or
41:or
29:or
21:In
2044::
1654:,
1650:,
1259:/
1235:/
1100:.
1072:33
1070:.
1028:.
941:73
939:.
922:.
910:.
879:,
626:.
559:).
552:).
545:).
534:).
472:.
364:.
343:TT
263:JD
207:ΔT
195:TT
1972::
1902:n
1734:0
1731:t
1721:v
1712:n
1703:T
1683:l
1674:L
1665:E
1656:f
1652:θ
1648:ν
1639:M
1619:ϖ
1610:ω
1601:Ω
1592:i
1572:q
1568:Q
1559:b
1550:a
1541:e
1186:e
1179:t
1172:v
1112:.
1108::
1082:.
1078::
1061:.
1040:.
1036::
1019:.
998:.
975:.
951:.
947::
930:.
918::
777:.
755:.
715:.
488:x
484:x
479:x
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