325:
281:
157:
125:
231:
31:
1757:
953:
431:, at which point the spacecraft was traveling at approximately 10.4 km/s (34150 ft/s) relative to the Earth. The Apollo 8 TLI was spectacularly observed from the Hawaiian Islands in the pre-dawn sky south of Waikiki, photographed and reported in the papers the next day. In 1969, the Apollo 10 pre-dawn TLI was visible from
147:
missions, since the spacecraft will return to Earth "for free" after the initial TLI burn. The
Apollos 8, 10 and 11 began on a free return trajectory, while the later missions used a functionally similar hybrid trajectory, in which a midway course correction is required to reach the Moon.
105:
near to the radius of the Moon's orbit. The TLI burn is sized and timed to precisely target the Moon as it revolves around the Earth. The burn is timed so that the spacecraft nears apogee as the Moon approaches. Finally, the spacecraft enters the Moon's
477:
became the first commercial satellite to reach the Moon's sphere of influence when, after a launch failure, it swung by the Moon twice as a low delta-v way to reach its desired geostationary orbit. It passed within 6200 km of the Moon's surface.
201:
from many bodies. Gravitation from Earth and Moon dominate the spacecraft's acceleration, and since the spacecraft's own mass is negligible in comparison, the spacecraft's trajectory may be better approximated as a
372:
on
January 2, 1959 which was designed to impact the Moon. The burn however didn't go exactly as planned and the spacecraft missed the Moon by more than three times its radius and was sent into a heliocentric orbit.
489:(GTO), it used solar powered ion engines for propulsion. As a result of its extremely low delta-v TLI maneuver, the spacecraft took over 13 months to reach a lunar orbit and 17 months to reach its desired orbit.
940:
214:
More detailed simulation involves modeling the Moon's true orbital motion; gravitation from other astronomical bodies; the non-uniformity of the Earth's and Moon's
961:
537:
377:
performed the same maneuver more accurately on
September 12, 1959 and crashed into the Moon two days later. The Soviets repeated this success with 22 more
841:
470:
spacecraft, designed to showcase lightweight technologies, used a 3 week long TLI with two intermediate Earth flybys before entering a lunar orbit.
439:. It was described as resembling car headlights coming over a hill in fog, with the spacecraft appearing as a bright comet with a greenish tinge.
324:
1634:
900:
1694:
181:. The spacecraft is assumed to accelerate only under classical 2 body dynamics, being dominated by the Earth until it reaches the Moon's
182:
107:
101:. As the spacecraft begins coasting on the lunar transfer arc, its trajectory approximates an elliptical orbit about the Earth with an
280:
868:"The TLI firing was begun at PST while the craft was over Hawaii and it was reported there that the burn was visible from the ground."
722:
1796:
1689:
1569:
988:
883:
186:
1654:
1408:
222:; and so on. Propagating spacecraft motion in such a model is numerically intensive, but necessary for true mission accuracy.
1786:
1727:
1366:
1357:
1094:
185:. Motion in a patched-conic system is deterministic and simple to calculate, lending itself for rough mission design and "
203:
177:, which may be approximated in various ways. The simplest way to explore lunar transfer trajectories is by the method of
1674:
1144:
888:
604:
486:
454:
335:
1619:
513:
485:
technology demonstrator satellite became the first
European satellite to orbit the Moon. After being launched into a
1791:
1599:
1426:
396:, on April 23, 1962. Another 27 US missions to the Moon were launched from 1962 to 1973, including five successful
496:
spacecraft in a lunar orbit. It used multiple burns to slowly raise its apogee to reach the vicinity of the Moon.
1737:
1722:
1247:
820:
523:
satellites used a low delta-v route to the Moon, passing by the Sun-Earth L1 point, and taking over 3 months.
1801:
1732:
1040:
591:
466:
1781:
1594:
1196:
1116:
1104:
133:
119:
59:
849:
751:
572:
206:. This model is a closer approximation but lacks an analytic solution, requiring numerical calculation.
1717:
1659:
1417:
1294:
1262:
1232:
1191:
1176:
1055:
934:
547:
401:
161:
156:
124:
1742:
1564:
1348:
1237:
1206:
1134:
1109:
1084:
1045:
1026:
981:
552:
137:
1604:
1399:
1139:
542:
427:
lasted approximately 350 seconds, providing 3.05 to 3.25 km/s (10,000 to 10,600 ft/s) of
412:
230:
215:
198:
71:
63:
619:
392:, on January 26, 1962, which failed to reach the Moon. This was followed by the first US success,
1277:
1166:
1064:
447:
74:
from sources outside the Earth-Moon system, a fast
Hohmann transfer is typically more practical.
67:
892:
863:
655:
1644:
1542:
1472:
1227:
1181:
1099:
896:
689:
144:
769:
1624:
1556:
1320:
1282:
1156:
1126:
1079:
705:
397:
98:
86:
47:
787:
503:
into a GTO and, like the
Chinese spacecraft, increasing its apogee over a number of burns.
1664:
1257:
1161:
1151:
1050:
974:
730:
637:
140:
around behind the Moon and return to Earth without need for further propulsive maneuvers.
94:
1760:
1712:
1704:
1699:
1584:
1579:
1510:
1490:
1481:
1074:
1060:
1036:
1031:
1006:
405:
378:
178:
174:
30:
1775:
1614:
1609:
1528:
1171:
1089:
922:
672:
532:
500:
317:
78:
957:
17:
1679:
1589:
1463:
1446:
1304:
1201:
1069:
382:
365:
493:
1684:
1519:
1289:
1269:
1186:
93:
engine, increases the spacecraft's velocity, changing its orbit from a circular
1252:
424:
219:
51:
1669:
1021:
593:
Trajectories in the Earth-Moon Space with
Symmetrical Free Return Properties
508:
474:
450:
436:
432:
923:"A Review of Technical Requirements for Lunar Structures – Present Status"
461:
TLI method with a 6-month transfer time (compared to 3 days for Apollo).
420:
393:
389:
77:
A spacecraft performs TLI to begin a lunar transfer from a low circular
1574:
966:
482:
458:
428:
34:
Lunar transfer, perspective view. TLI occurs at the red dot near Earth.
374:
369:
90:
411:
For the Apollo lunar missions, TLI was performed by the restartable
173:
TLI targeting and lunar transfers are a specific application of the
1379:
998:
520:
443:
416:
323:
279:
273:
245:
229:
155:
123:
102:
82:
29:
845:
827:
791:
726:
600:
576:
259:
55:
970:
388:
The United States launched its first lunar impactor attempt,
128:
Sketch of a circumlunar free return trajectory (not to scale)
492:
China launched its first Moon mission in 2007, placing the
457:
in a lunar orbit. Following that, it explored a novel low
197:
More realistically, however, the spacecraft is subject to
132:
In some cases it is possible to design a TLI to target a
710:
Theory of Orbits, The
Restricted Problem of Three Bodies
143:
Such free return trajectories add a margin of safety to
70:
probe. For short duration missions without significant
516:, used this maneuver in 2019, but crashed on the Moon.
385:
missions travelling to the Moon between 1959 and 1976.
876:
874:
408:
missions, which landed the first humans on the Moon.
1643:
1555:
1499:
1435:
1388:
1328:
1319:
1215:
1125:
1014:
1005:
864:"Independent Star News, Sunday, December 22, 1968"
58:. Typical lunar transfer trajectories approximate
921:Alexander M. Jablonski1a; Kelly A. Ogden (2006).
164:stack performing the trans-lunar injection burn
66:have also been used in some cases, as with the
815:
813:
811:
809:
807:
805:
803:
801:
599:. Technical Note D-1833. Huntsville, Alabama:
27:Propulsive maneuver used to arrive at the Moon
982:
962:National Aeronautics and Space Administration
538:Comparison of super heavy lift launch systems
364:The first space probe to attempt TLI was the
8:
446:launched its first lunar mission, using the
939:: CS1 maint: numeric names: authors list (
696:, Paris, Gauthier-Villars et fils, 1892-99.
694:Les MĂ©thodes Nouvelles de MĂ©canique CĂ©leste
1756:
1325:
1011:
989:
975:
967:
453:to fly by the Moon and place the Hagoromo
712:, Yale University, Academic Press, 1967.
881:French, Francis; Colin Burgess (2007).
564:
1635:Transposition, docking, and extraction
932:
916:
914:
912:
752:"NASA - NSSDCA - Spacecraft - Details"
499:India followed in 2008, launching the
618:Mansfield, Cheryl L. (May 18, 2017).
193:Restricted circular three body (RC3B)
110:, making a hyperbolic lunar swingby.
7:
960:from websites or documents of the
89:, usually performed by a chemical
25:
1695:Kepler's laws of planetary motion
1755:
1690:Interplanetary Transport Network
1570:Collision avoidance (spacecraft)
956: This article incorporates
951:
927:Journal of Aerospace Engineering
1655:Astronomical coordinate systems
1409:Longitude of the ascending node
590:Schwaninger, Arthur J. (1963).
1728:Retrograde and prograde motion
404:surveillance probes, and nine
136:, so that the spacecraft will
1:
770:"Soviet Missions to the Moon"
423:rocket. This particular TLI
204:restricted three-body problem
1675:Equatorial coordinate system
889:University of Nebraska Press
605:Marshall Space Flight Center
487:geostationary transfer orbit
336:Lunar Reconnaissance Orbiter
514:Israel Aerospace Industries
328:Animation of LRO trajectory
160:Artist's concept of NASA's
1818:
1427:Longitude of the periapsis
284:Animation of Chandrayaan-2
117:
50:, which is used to send a
1751:
1738:Specific angular momentum
884:In the Shadow of the Moon
220:solar radiation pressure
1797:Exploration of the Moon
1733:Specific orbital energy
842:"Apollo By the Numbers"
1145:Geostationary transfer
958:public domain material
673:"Launch Windows Essay"
361:
321:
277:
165:
134:free return trajectory
129:
120:Free return trajectory
35:
1787:Spacecraft propulsion
1718:Orbital state vectors
1660:Characteristic energy
1630:Trans-lunar injection
1418:Argument of periapsis
1095:Prograde / Retrograde
1056:Hyperbolic trajectory
661:(Report). p. 93.
548:Trans-Earth injection
327:
283:
233:
159:
127:
40:trans-lunar injection
33:
1565:Bi-elliptic transfer
1085:Parabolic trajectory
553:Trans-Mars injection
234:Animation of GRAIL-A
199:gravitational forces
187:back of the envelope
64:low-energy transfers
18:Lunar Transfer Orbit
1605:Low-energy transfer
866:. 22 December 1968.
774:nssdc.gsfc.nasa.gov
756:nssdc.gsfc.nasa.gov
543:Low energy transfer
419:third stage of the
400:soft landers, five
183:sphere of influence
108:sphere of influence
48:propulsive maneuver
1600:Inclination change
1248:Distant retrograde
429:change in velocity
362:
322:
278:
166:
130:
36:
1792:Orbital maneuvers
1769:
1768:
1743:Two-line elements
1551:
1550:
1473:Eccentric anomaly
1315:
1314:
1182:Orbit of the Moon
1041:Highly elliptical
902:978-0-8032-1128-5
519:In 2011 the NASA
145:human spaceflight
85:. The large TLI
60:Hohmann transfers
16:(Redirected from
1809:
1759:
1758:
1700:Lagrangian point
1595:Hohmann transfer
1540:
1526:
1517:
1508:
1488:
1479:
1470:
1461:
1457:
1453:
1444:
1424:
1415:
1406:
1397:
1377:
1373:
1364:
1355:
1346:
1326:
1295:Heliosynchronous
1244:Lagrange points
1197:Transatmospheric
1012:
991:
984:
977:
968:
955:
954:
945:
944:
938:
930:
918:
907:
906:
878:
869:
867:
860:
854:
853:
848:. Archived from
838:
832:
831:
825:
817:
796:
795:
784:
778:
777:
766:
760:
759:
748:
742:
741:
739:
738:
729:. Archived from
719:
713:
706:Victor Szebehely
703:
697:
687:
681:
680:
677:history.nasa.gov
669:
663:
662:
660:
656:Ways to the Moon
652:
646:
645:
642:history.nasa.gov
634:
628:
627:
615:
609:
608:
598:
587:
581:
580:
569:
506:The soft lander
360:
358:
349:
347:
338:
333:
320:
315:
306:
304:
295:
293:
287:
276:
271:
262:
257:
248:
243:
237:
210:Further accuracy
21:
1817:
1816:
1812:
1811:
1810:
1808:
1807:
1806:
1772:
1771:
1770:
1765:
1747:
1665:Escape velocity
1646:
1639:
1620:Rocket equation
1547:
1539:
1533:
1524:
1515:
1506:
1495:
1486:
1477:
1468:
1459:
1455:
1451:
1442:
1431:
1422:
1413:
1404:
1395:
1384:
1375:
1371:
1367:Semi-minor axis
1362:
1358:Semi-major axis
1353:
1344:
1338:
1311:
1233:Areosynchronous
1217:
1211:
1192:Sun-synchronous
1177:Near-equatorial
1121:
1001:
995:
952:
949:
948:
931:
920:
919:
910:
903:
880:
879:
872:
862:
861:
857:
840:
839:
835:
823:
819:
818:
799:
786:
785:
781:
768:
767:
763:
750:
749:
745:
736:
734:
721:
720:
716:
704:
700:
688:
684:
671:
670:
666:
658:
654:
653:
649:
636:
635:
631:
617:
616:
612:
596:
589:
588:
584:
571:
570:
566:
561:
529:
381:missions and 5
356:
355:
345:
344:
331:
330:
329:
313:
312:
302:
301:
291:
290:
289:
285:
269:
268:
255:
254:
241:
240:
239:
235:
228:
212:
195:
171:
154:
122:
116:
99:eccentric orbit
95:low Earth orbit
28:
23:
22:
15:
12:
11:
5:
1815:
1813:
1805:
1804:
1802:Apollo program
1799:
1794:
1789:
1784:
1774:
1773:
1767:
1766:
1764:
1763:
1761:List of orbits
1752:
1749:
1748:
1746:
1745:
1740:
1735:
1730:
1725:
1720:
1715:
1713:Orbit equation
1710:
1702:
1697:
1692:
1687:
1682:
1677:
1672:
1667:
1662:
1657:
1651:
1649:
1641:
1640:
1638:
1637:
1632:
1627:
1622:
1617:
1612:
1607:
1602:
1597:
1592:
1587:
1585:Gravity assist
1582:
1580:Delta-v budget
1577:
1572:
1567:
1561:
1559:
1553:
1552:
1549:
1548:
1546:
1545:
1537:
1531:
1522:
1513:
1511:Orbital period
1503:
1501:
1497:
1496:
1494:
1493:
1491:True longitude
1484:
1482:Mean longitude
1475:
1466:
1449:
1439:
1437:
1433:
1432:
1430:
1429:
1420:
1411:
1402:
1392:
1390:
1386:
1385:
1383:
1382:
1369:
1360:
1351:
1341:
1339:
1337:
1336:
1333:
1329:
1323:
1317:
1316:
1313:
1312:
1310:
1309:
1308:
1307:
1299:
1298:
1297:
1292:
1287:
1286:
1285:
1272:
1267:
1266:
1265:
1260:
1255:
1250:
1242:
1241:
1240:
1238:Areostationary
1235:
1230:
1221:
1219:
1213:
1212:
1210:
1209:
1207:Very low Earth
1204:
1199:
1194:
1189:
1184:
1179:
1174:
1169:
1164:
1159:
1154:
1149:
1148:
1147:
1142:
1135:Geosynchronous
1131:
1129:
1123:
1122:
1120:
1119:
1117:Transfer orbit
1114:
1113:
1112:
1107:
1097:
1092:
1087:
1082:
1077:
1075:Lagrange point
1072:
1067:
1058:
1053:
1048:
1043:
1034:
1029:
1024:
1018:
1016:
1009:
1003:
1002:
997:Gravitational
996:
994:
993:
986:
979:
971:
947:
946:
908:
901:
870:
855:
852:on 2004-11-18.
833:
821:"Beyond Earth"
797:
779:
761:
743:
714:
698:
690:Henri Poincaré
682:
664:
647:
629:
610:
582:
563:
562:
560:
557:
556:
555:
550:
545:
540:
535:
528:
525:
455:microsatellite
415:engine in the
227:
224:
211:
208:
194:
191:
179:patched conics
175:n body problem
170:
169:Patched conics
167:
153:
150:
118:Main article:
115:
112:
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
1814:
1803:
1800:
1798:
1795:
1793:
1790:
1788:
1785:
1783:
1782:Astrodynamics
1780:
1779:
1777:
1762:
1754:
1753:
1750:
1744:
1741:
1739:
1736:
1734:
1731:
1729:
1726:
1724:
1721:
1719:
1716:
1714:
1711:
1709:
1708:-body problem
1707:
1703:
1701:
1698:
1696:
1693:
1691:
1688:
1686:
1683:
1681:
1678:
1676:
1673:
1671:
1668:
1666:
1663:
1661:
1658:
1656:
1653:
1652:
1650:
1648:
1642:
1636:
1633:
1631:
1628:
1626:
1623:
1621:
1618:
1616:
1613:
1611:
1610:Oberth effect
1608:
1606:
1603:
1601:
1598:
1596:
1593:
1591:
1588:
1586:
1583:
1581:
1578:
1576:
1573:
1571:
1568:
1566:
1563:
1562:
1560:
1558:
1554:
1544:
1536:
1532:
1530:
1529:Orbital speed
1523:
1521:
1514:
1512:
1505:
1504:
1502:
1498:
1492:
1485:
1483:
1476:
1474:
1467:
1465:
1450:
1448:
1441:
1440:
1438:
1434:
1428:
1421:
1419:
1412:
1410:
1403:
1401:
1394:
1393:
1391:
1387:
1381:
1370:
1368:
1361:
1359:
1352:
1350:
1343:
1342:
1340:
1334:
1331:
1330:
1327:
1324:
1322:
1318:
1306:
1303:
1302:
1300:
1296:
1293:
1291:
1288:
1284:
1283:Earth's orbit
1281:
1280:
1279:
1276:
1275:
1273:
1271:
1268:
1264:
1261:
1259:
1256:
1254:
1251:
1249:
1246:
1245:
1243:
1239:
1236:
1234:
1231:
1229:
1226:
1225:
1223:
1222:
1220:
1214:
1208:
1205:
1203:
1200:
1198:
1195:
1193:
1190:
1188:
1185:
1183:
1180:
1178:
1175:
1173:
1170:
1168:
1165:
1163:
1160:
1158:
1155:
1153:
1150:
1146:
1143:
1141:
1140:Geostationary
1138:
1137:
1136:
1133:
1132:
1130:
1128:
1124:
1118:
1115:
1111:
1108:
1106:
1103:
1102:
1101:
1098:
1096:
1093:
1091:
1088:
1086:
1083:
1081:
1078:
1076:
1073:
1071:
1068:
1066:
1062:
1059:
1057:
1054:
1052:
1049:
1047:
1044:
1042:
1038:
1035:
1033:
1030:
1028:
1025:
1023:
1020:
1019:
1017:
1013:
1010:
1008:
1004:
1000:
992:
987:
985:
980:
978:
973:
972:
969:
965:
963:
959:
942:
936:
928:
924:
917:
915:
913:
909:
904:
898:
894:
890:
886:
885:
877:
875:
871:
865:
859:
856:
851:
847:
843:
837:
834:
829:
822:
816:
814:
812:
810:
808:
806:
804:
802:
798:
793:
789:
783:
780:
775:
771:
765:
762:
757:
753:
747:
744:
733:on 2020-09-05
732:
728:
724:
718:
715:
711:
707:
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1349:Eccentricity
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1305:Lunar cycler
1278:Heliocentric
1218:other points
1167:Medium Earth
1065:Non-inclined
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935:cite journal
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1685:Hill sphere
1520:Mean motion
1400:Inclination
1389:Orientation
1290:Mars cycler
1228:Areocentric
1100:Synchronous
638:"APOLLO 12"
620:"Apollo 10"
348: Earth
294: Earth
189:" studies.
114:Free return
62:, although
1776:Categories
1625:Rendezvous
1321:Parameters
1157:High Earth
1127:Geocentric
1080:Osculating
1037:Elliptical
891:. p.
788:"Ranger 4"
737:2019-06-10
559:References
467:Clementine
359: Moon
305: Moon
288:trajectory
238:trajectory
52:spacecraft
1670:Ephemeris
1647:mechanics
1557:Maneuvers
1500:Variation
1263:Libration
1258:Lissajous
1162:Low Earth
1152:Graveyard
1051:Horseshoe
723:"Luna 01"
512:from the
509:Beresheet
494:Chang'e 1
475:Asiasat-3
451:satellite
437:Australia
433:Cloncurry
1436:Position
1061:Inclined
1032:Circular
527:See also
473:In 1997
442:In 1990
421:Saturn V
398:Surveyor
394:Ranger 4
390:Ranger 3
152:Modeling
1645:Orbital
1615:Phasing
1575:Delta-v
1380:Apsides
1374:,
1172:Molniya
1090:Parking
1027:Capture
1015:General
573:"Hiten"
483:SMART-1
459:delta-v
246:GRAIL-A
226:History
216:gravity
81:around
54:to the
46:) is a
1301:Other
1202:Tundra
1070:Kepler
1046:Escape
999:orbits
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406:Apollo
375:Luna 2
370:Luna 1
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103:apogee
91:rocket
1543:Epoch
1332:Shape
1270:Lunar
1224:Mars
1216:About
1187:Polar
1007:Types
824:(PDF)
659:(PDF)
597:(PDF)
521:GRAIL
448:Hiten
444:Japan
417:S-IVB
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83:Earth
68:Hiten
1335:Size
1274:Sun
1253:Halo
1105:semi
941:link
897:ISBN
846:NASA
828:NASA
792:NASA
727:NASA
624:NASA
601:NASA
577:NASA
425:burn
383:Zond
379:Luna
260:Moon
138:loop
87:burn
56:Moon
1110:sub
1022:Box
893:372
413:J-2
368:'s
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