1376:
514:
992:
1063:
47:
716:
606:
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902:
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constantly under high thrust until it reaches its target. In this high-thrust case, the trajectory approaches a straight line. If it is required that the spacecraft rendezvous with the target, rather than performing a flyby, then the spacecraft must flip its orientation halfway through the journey, and decelerate the rest of the way.
1315:
This trajectory requires that the spacecraft maintain a high acceleration for long durations. For interplanetary transfers, days, weeks or months of constant thrusting may be required. As a result, there are no currently available spacecraft propulsion systems capable of using this trajectory. It has
1307:
trajectories involve the spacecraft firing its engine in a prolonged constant burn. In the limiting case where the vehicle acceleration is high compared to the local gravitational acceleration, the spacecraft points straight toward the target (accounting for target motion), and remains accelerating
1261:
In general, inclination changes can require a great deal of delta-v to perform, and most mission planners try to avoid them whenever possible to conserve fuel. This is typically achieved by launching a spacecraft directly into the desired inclination, or as close to it as possible so as to minimize
878:
Since the Oberth maneuver happens in a very limited time (while still at low altitude), to generate a high impulse the engine necessarily needs to achieve high thrust (impulse is by definition the time multiplied by thrust). Thus the Oberth effect is far less useful for low-thrust engines, such as
738:
The off-set of the velocity vector after the end of real burn from the velocity vector at the same time resulting from the theoretical impulsive maneuver is only caused by the difference in gravitational force along the two paths (red and black in figure 1) which in general is small.
1311:
In the constant-thrust trajectory, the vehicle's acceleration increases during thrusting period, since the fuel use means the vehicle mass decreases. If, instead of constant thrust, the vehicle has constant acceleration, the engine thrust must decrease during the trajectory.
734:
In the physical world no truly instantaneous change in velocity is possible as this would require an "infinite force" applied during an "infinitely short time" but as a mathematical model it in most cases describes the effect of a maneuver on the orbit very well.
1153:
While they require one more engine burn than a
Hohmann transfer and generally requires a greater travel time, some bi-elliptic transfers require a lower amount of total delta-v than a Hohmann transfer when the ratio of final to initial
886:
Historically, a lack of understanding of this effect led investigators to conclude that interplanetary travel would require completely impractical amounts of propellant, as without it, enormous amounts of energy are needed.
832:
has more usable energy (due to its kinetic energy on top of its chemical potential energy) and it turns out that the vehicle is able to employ this kinetic energy to generate more mechanical power. It is named after
1294:
is the lowest. In some cases, it may require less total delta v to raise the spacecraft into a higher orbit, change the orbit plane at the higher apogee, and then lower the spacecraft to its original altitude.
742:
In the planning phase of space missions designers will first approximate their intended orbital changes using impulsive maneuvers that greatly reduces the complexity of finding the correct orbital transitions.
1612:
Sternfeld A., Sur les trajectoires permettant d'approcher d'un corps attractif central à partir d'une orbite keplérienne donnée. - Comptes rendus de l'Académie des sciences (Paris), vol. 198, pp. 711 -
583:
1140:
731:(magnitude and/or direction) as illustrated in figure 1. It is the limit case of a burn to generate a particular amount of delta-v, as the burn time tends to zero.
940:) of the gravitating body as it pulls on the spacecraft. The technique was first proposed as a mid-course maneuver in 1961, and used by interplanetary probes from
1292:
1250:. This maneuver is also known as an orbital plane change as the plane of the orbit is tipped. This maneuver requires a change in the orbital velocity vector (
975:(TEI). These are generally larger than small trajectory correction maneuvers. Insertion, injection and sometimes initiation are used to describe entry into a
1516:
925:
or other celestial body to alter the trajectory of a spacecraft, typically in order to save propellant, time, and expense. Gravity assistance can be used to
1327:, and others. These types of engines have very high specific impulse (fuel efficiency) but currently are only available with fairly low absolute thrust.
1258:(i.e. the point where the initial and desired orbits intersect, the line of orbital nodes is defined by the intersection of the two orbital planes).
963:
maneuvers leave a spacecraft in a destination orbit. In contrast, orbit injection maneuvers occur when a spacecraft enters a transfer orbit, e.g.
773:, high fidelity models of the trajectories are required to meet the mission goals. Calculating a "finite" burn requires a detailed model of the
905:
The trajectories that enabled NASA's twin
Voyager spacecraft to tour the four gas giant planets and achieve velocity to escape our solar system
1415:
1316:
been suggested that some forms of nuclear (fission or fusion based) or antimatter powered rockets would be capable of this trajectory.
756:
1304:
442:
2421:
1698:
1203:. The drawback of such trajectories is that they take much longer to complete than higher energy (more fuel) transfers such as
1150:
at the radius of the final desired orbit, where a third delta-v is performed, injecting the spacecraft into the desired orbit.
678:
1681:
1641:
650:
2481:
214:
1629:
Capture
Dynamics and Chaotic Motions in Celestial Mechanics: With Applications to the Construction of Low Energy Transfers
1549:
863:
where the application of an impulse, typically from the use of a rocket engine, close to a gravitational body (where the
592:. With a good approximation of the delta-v budget designers can estimate the propellant required for planned maneuvers.
283:
828:
when travelling at high speed generates much more useful energy than one at low speed. Oberth effect occurs because the
657:
1597:
697:
627:
525:
The
Tsiolkovsky rocket equation, or ideal rocket equation, can be useful for analysis of maneuvers by vehicles using
635:
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1218:
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2195:
17:
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and approach to a very close distance (e.g. within visual contact). Rendezvous requires a precise match of the
631:
104:
479:. For spacecraft far from Earth (for example those in orbits around the Sun) an orbital maneuver is called a
1111:. From the initial orbit, a delta-v is applied boosting the spacecraft into the first transfer orbit with an
646:
1572:
2461:
1931:
1443:
562:
1498:
1146:. At this point, a second delta-v is applied sending the spacecraft into the second elliptical orbit with
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508:
435:
368:
2573:
2386:
2213:
1669:
1633:
1234:
980:
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2524:
1484:
2509:
2034:
766:, where the word "finite" is used to mean "non-zero", or practically, again: over a longer period.
616:
363:
278:
533:) by expelling part of its mass at high speed. The rocket itself moves due to the conservation of
2519:
1827:
1411:
1211:
620:
234:
1221:. Following these pathways allows for long distances to be traversed for little expenditure of
2568:
2381:
1983:
1903:
1891:
1204:
1101:
1000:
428:
151:
1673:
1662:
1418:, procedures which bring the spacecraft into physical contact and create a link between them.
671:
2504:
2446:
2416:
2204:
2081:
2049:
2019:
1978:
1963:
1842:
1459:
1200:
1081:
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171:
79:
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1993:
1921:
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1813:
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1118:
1071:
1024:
The orbital maneuver to perform the
Hohmann transfer uses two engine impulses which move a
968:
588:
The delta-v for all the expected maneuvers are estimated for a mission are summarized in a
209:
166:
156:
84:
1319:
More practically, this type of maneuver is used in low thrust maneuvers, for example with
8:
2391:
2186:
1926:
1464:
1454:
1276:
1174:
251:
89:
719:
Figure 1: Approximation of a finite thrust maneuver with an impulsive change in velocity
2064:
1953:
1851:
1724:
1435:
727:
is the mathematical model of a maneuver as an instantaneous change in the spacecraft's
324:
199:
1375:
917:
maneuver, gravitational slingshot or swing-by is the use of the relative movement and
2431:
2329:
2259:
2014:
1968:
1886:
1677:
1637:
1593:
1006:
864:
786:
239:
176:
55:
1702:
1217:
Low energy transfers follow special pathways in space, sometimes referred to as the
2411:
2107:
2069:
1943:
1913:
1866:
1527:
1370:
1018:
937:
790:
770:
358:
123:
67:
875:) than the same impulse applied further from the body for the same initial orbit.
2451:
2044:
1948:
1938:
1837:
1761:
1657:
1623:
1587:
1155:
960:
948:
872:
838:
755:. 'Non-impulsive' refers to the momentum changing slowly over a long time, as in
414:
319:
229:
204:
1045:
2547:
2499:
2491:
2486:
2371:
2366:
2297:
2277:
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1861:
1847:
1823:
1818:
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1029:
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914:
896:
868:
834:
782:
589:
550:
487:
386:
302:
296:
219:
144:
138:
133:
1627:
1550:"Section I. The Environment of Space - Chapter 4. Interplanetary Trajectories"
1410:
of the two spacecraft, allowing them to remain at a constant distance through
513:
2562:
2401:
2396:
2315:
1958:
1876:
1748:
1557:
1407:
1399:
1347:
1341:
1255:
1162:
910:
825:
811:
391:
224:
181:
1725:
Trajectories with
Constant Tangential Thrust in Central Gravitational Fields
1531:
2466:
2376:
2250:
2233:
2091:
1988:
1856:
1358:
1158:
is 11.94 or greater, depending on the intermediate semi-major axis chosen.
1143:
1077:
930:
880:
817:
109:
99:
94:
1262:
any inclination change required over the duration of the spacecraft life.
2471:
2306:
2076:
2056:
1973:
1664:
Fly Me to the Moon: An
Insider's Guide to the New Science of Space Travel
1535:
1320:
1243:
1161:
The idea of the bi-elliptical transfer trajectory was first published by
1050:
991:
456:
273:
2039:
1753:
1395:
1184:
1089:
1062:
1044:). Hohmann was influenced in part by the German science fiction author
1025:
942:
926:
829:
774:
751:
Applying a low thrust over a longer period of time is referred to as a
518:
476:
353:
309:
268:
46:
2456:
1808:
1147:
845:
715:
605:
1383:
1379:
1266:
1112:
794:
728:
534:
555:
The applied change in velocity of each maneuver is referred to as
2361:
1251:
1222:
1097:
1033:
918:
842:
556:
546:
1199:
system and also in other systems, such as traveling between the
486:
When a spacecraft is not conducting a maneuver, especially in a
1353:
is the adjustment of the time-position of spacecraft along its
1270:
1028:
onto and off the transfer orbit. This maneuver was named after
922:
901:
849:
530:
526:
1036:
scientist who published a description of it in his 1925 book
2166:
1785:
1403:
1354:
1247:
1192:
1188:
1093:
472:
74:
867:
is low, and the speed is high) can give much more change in
1731:, NASA Lewis Research Center, 1960 (accessed 26 March 2014)
1357:, usually described as adjusting the orbiting spacecraft's
1196:
778:
777:
and its thrusters. The most important of details include:
521:
versus final velocity calculated from the rocket equation
1265:
Maximum efficiency of inclination change is achieved at
1187:, is a route in space which allows spacecraft to change
1096:
to another and may, in certain situations, require less
1745:
Handbook
Automated Rendezvous and Docking of Spacecraft
1514:
529:
propulsion. A rocket applies acceleration to itself (a
1279:
1121:
789:, thruster positions, thrust vectors, thrust curves,
565:
1576:(Washington: NASA Technical Translation F-44, 1960).
1425:
1394:
is a sequence of orbital maneuvers during which two
1066:
Bi-elliptic transfer from blue to red circular orbit
1013:
is an elliptical orbit used to transfer between two
769:
For a few space missions, such as those including a
1661:
1286:
1134:
577:
1214:trajectories, or ballistic capture trajectories.
1191:using very little fuel. These routes work in the
2560:
1556:. NASA Jet Propulsion Laboratory. Archived from
936:The "assist" is provided by the motion (orbital
1364:
952:probes' notable fly-bys of Jupiter and Saturn.
1589:Fundamentals of Astrodynamics and Applications
1515:Oberth, Herman; Oldenbourg Verlag, R. (1970).
1107:The bi-elliptic transfer consists of two half
1769:
1298:
1242:is an orbital maneuver aimed at changing the
1228:
852:, who apparently first described the effect.
436:
1699:"Basics of Space Flight: Orbital Mechanics"
933:and/or re-direct the path of a spacecraft.
634:. Unsourced material may be challenged and
2543:
1776:
1762:
757:electrically powered spacecraft propulsion
443:
429:
1330:
1283:
983:maneuver used for Apollo lunar landings.
698:Learn how and when to remove this message
574:
1783:
1690:
1656:
1622:
1374:
1061:
990:
900:
746:
714:
512:
1585:
1057:
14:
2561:
2422:Transposition, docking, and extraction
1616:
1510:
1508:
1210:Low energy transfer are also known as
1168:
710:
1757:
1414:. Rendezvous is commonly followed by
1042:The Accessibility of Celestial Bodies
578:{\displaystyle \Delta \mathbf {v} \,}
1696:
1650:
1573:The Attainability of Heavenly Bodies
1088:is an orbital maneuver that moves a
1038:Die Erreichbarkeit der Himmelskörper
1017:of different altitudes, in the same
632:adding citations to reliable sources
599:
1505:
986:
24:
955:
759:, rather than by a short impulse.
566:
502:
25:
2585:
2482:Kepler's laws of planetary motion
1738:
890:
215:Kepler's laws of planetary motion
2542:
2477:Interplanetary Transport Network
2357:Collision avoidance (spacecraft)
1450:Collision avoidance (spacecraft)
1428:
1335:
1219:Interplanetary Transport Network
805:
604:
570:
45:
2442:Astronomical coordinate systems
2196:Longitude of the ascending node
1717:
1586:Vallado, David Anthony (2001).
1534:. NASA-TT-F-622. Archived from
855:The Oberth effect is used in a
797:offsets, and fuel consumption.
2515:Retrograde and prograde motion
1606:
1579:
1564:
1542:
1491:
1477:
13:
1:
1524:NASA Technical Reports Server
1470:
871:and final speed (i.e. higher
595:
27:A movement during spaceflight
2462:Equatorial coordinate system
1444:Clohessy-Wiltshire equations
1365:Space rendezvous and docking
7:
1421:
946:onwards, including the two
509:Tsiolkovsky rocket equation
369:Tsiolkovsky rocket equation
10:
2590:
2214:Longitude of the periapsis
1670:Princeton University Press
1634:Princeton University Press
1398:, one of which is often a
1368:
1339:
1299:Constant-thrust trajectory
1273:), where orbital velocity
1240:Orbital inclination change
1235:orbital inclination change
1232:
1229:Orbital inclination change
1172:
1069:
998:
981:Powered Descent Initiation
894:
809:
800:
544:
540:
506:
497:
338:Engineering and efficiency
157:Bi-elliptic transfer orbit
2538:
2525:Specific angular momentum
2430:
2342:
2286:
2222:
2175:
2115:
2106:
2002:
1912:
1801:
1792:
1592:. Springer. p. 317.
481:deep-space maneuver (DSM)
848:and a founder of modern
364:Propellant mass fraction
263:Gravitational influences
2520:Specific orbital energy
1412:orbital station-keeping
1212:weak stability boundary
1205:Hohmann transfer orbits
235:Specific orbital energy
1932:Geostationary transfer
1554:Basics of Space Flight
1387:
1331:Rendezvous and docking
1288:
1246:of an orbiting body's
1136:
1067:
1011:Hohmann transfer orbit
1001:Hohmann transfer orbit
996:
995:Hohmann Transfer Orbit
906:
824:is where the use of a
753:non-impulsive maneuver
720:
579:
522:
471:systems to change the
463:(otherwise known as a
152:Hohmann transfer orbit
2505:Orbital state vectors
2447:Characteristic energy
2417:Trans-lunar injection
2205:Argument of periapsis
1882:Prograde / Retrograde
1843:Hyperbolic trajectory
1729:Technical Report R-63
1517:"Ways to spaceflight"
1499:"The Rocket Equation"
1460:Spacecraft propulsion
1446:for co-orbit analysis
1402:, arrive at the same
1378:
1325:Hall-effect thrusters
1305:constant-acceleration
1289:
1201:satellites of Jupiter
1137:
1135:{\displaystyle r_{b}}
1082:aerospace engineering
1065:
994:
973:trans-Earth injection
965:trans-lunar injection
904:
747:Low thrust propulsion
718:
628:improve this section
580:
516:
348:Preflight engineering
80:Argument of periapsis
2352:Bi-elliptic transfer
1872:Parabolic trajectory
1697:Braeunig, Robert A.
1303:Constant-thrust and
1277:
1119:
1086:bi-elliptic transfer
1072:Bi-elliptic transfer
1058:Bi-elliptic transfer
969:trans-Mars injection
563:
490:, it is said to be
404:Propulsive maneuvers
2392:Low-energy transfer
1705:on February 4, 2012
1465:Orbital spaceflight
1455:Flyby (spaceflight)
1416:docking or berthing
1287:{\displaystyle v\,}
1181:low energy transfer
1175:low energy transfer
1169:Low energy transfer
711:Impulsive maneuvers
381:Efficiency measures
284:Sphere of influence
253:Celestial mechanics
35:Part of a series on
2387:Inclination change
2035:Distant retrograde
1436:Spaceflight portal
1408:orbital velocities
1388:
1382:photographed from
1284:
1132:
1068:
1048:and his 1897 book
997:
907:
725:impulsive maneuver
721:
647:"Orbital maneuver"
575:
523:
200:Dynamical friction
2574:Orbital maneuvers
2556:
2555:
2530:Two-line elements
2338:
2337:
2260:Eccentric anomaly
2102:
2101:
1969:Orbit of the Moon
1828:Highly elliptical
1683:978-0-691-12822-1
1643:978-0-691-09480-9
1560:on April 3, 2023.
1007:orbital mechanics
865:gravity potential
787:moment of inertia
708:
707:
700:
682:
453:
452:
303:Lagrangian points
240:Vis-viva equation
210:Kepler's equation
57:Orbital mechanics
16:(Redirected from
2581:
2546:
2545:
2487:Lagrangian point
2382:Hohmann transfer
2327:
2313:
2304:
2295:
2275:
2266:
2257:
2248:
2244:
2240:
2231:
2211:
2202:
2193:
2184:
2164:
2160:
2151:
2142:
2133:
2113:
2112:
2082:Heliosynchronous
2031:Lagrange points
1984:Transatmospheric
1799:
1798:
1778:
1771:
1764:
1755:
1754:
1732:
1721:
1715:
1714:
1712:
1710:
1701:. Archived from
1694:
1688:
1687:
1667:
1658:Belbruno, Edward
1654:
1648:
1647:
1624:Belbruno, Edward
1620:
1614:
1610:
1604:
1603:
1583:
1577:
1570:Walter Hohmann,
1568:
1562:
1561:
1546:
1540:
1539:
1532:2060/19720008133
1521:
1512:
1503:
1502:
1495:
1489:
1488:
1481:
1438:
1433:
1432:
1431:
1392:space rendezvous
1386:in December 1965
1371:Space rendezvous
1293:
1291:
1290:
1285:
1183:, or low energy
1141:
1139:
1138:
1133:
1131:
1130:
1102:Hohmann transfer
987:Hohmann transfer
938:angular momentum
839:Austro-Hungarian
791:specific impulse
771:space rendezvous
762:Another term is
703:
696:
692:
689:
683:
681:
640:
608:
600:
584:
582:
581:
576:
573:
467:) is the use of
461:orbital maneuver
445:
438:
431:
410:Orbital maneuver
359:Payload fraction
339:
320:Lissajous orbits
254:
225:Orbital velocity
172:Hyperbolic orbit
68:Orbital elements
58:
49:
32:
31:
21:
2589:
2588:
2584:
2583:
2582:
2580:
2579:
2578:
2559:
2558:
2557:
2552:
2534:
2452:Escape velocity
2433:
2426:
2407:Rocket equation
2334:
2326:
2320:
2311:
2302:
2293:
2282:
2273:
2264:
2255:
2246:
2242:
2238:
2229:
2218:
2209:
2200:
2191:
2182:
2171:
2162:
2158:
2154:Semi-minor axis
2149:
2145:Semi-major axis
2140:
2131:
2125:
2098:
2020:Areosynchronous
2004:
1998:
1979:Sun-synchronous
1964:Near-equatorial
1908:
1788:
1782:
1741:
1736:
1735:
1723:W. E. Moeckel,
1722:
1718:
1708:
1706:
1695:
1691:
1684:
1655:
1651:
1644:
1636:. p. 224.
1621:
1617:
1611:
1607:
1600:
1584:
1580:
1569:
1565:
1548:
1547:
1543:
1538:on May 9, 2010.
1526:. p. 200.
1519:
1513:
1506:
1497:
1496:
1492:
1483:
1482:
1478:
1473:
1434:
1429:
1427:
1424:
1373:
1367:
1344:
1338:
1333:
1301:
1278:
1275:
1274:
1237:
1231:
1177:
1171:
1156:semi-major axis
1126:
1122:
1120:
1117:
1116:
1109:elliptic orbits
1074:
1060:
1015:circular orbits
1003:
989:
961:Orbit insertion
958:
956:Transfer orbits
899:
893:
873:specific energy
861:Oberth maneuver
814:
808:
803:
749:
713:
704:
693:
687:
684:
641:
639:
625:
609:
598:
569:
564:
561:
560:
553:
545:Main articles:
543:
511:
505:
503:Rocket equation
500:
449:
420:
419:
415:Orbit insertion
405:
397:
396:
382:
374:
373:
349:
341:
337:
330:
329:
325:Lyapunov orbits
316:
315:
299:
289:
288:
264:
256:
252:
245:
244:
230:Surface gravity
205:Escape velocity
195:
187:
186:
167:Parabolic orbit
163:
162:
129:
127:
124:two-body orbits
115:
114:
105:Semi-major axis
70:
60:
56:
28:
23:
22:
18:Orbit injection
15:
12:
11:
5:
2587:
2577:
2576:
2571:
2554:
2553:
2551:
2550:
2548:List of orbits
2539:
2536:
2535:
2533:
2532:
2527:
2522:
2517:
2512:
2507:
2502:
2500:Orbit equation
2497:
2489:
2484:
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2469:
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2459:
2454:
2449:
2444:
2438:
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2428:
2427:
2425:
2424:
2419:
2414:
2409:
2404:
2399:
2394:
2389:
2384:
2379:
2374:
2372:Gravity assist
2369:
2367:Delta-v budget
2364:
2359:
2354:
2348:
2346:
2340:
2339:
2336:
2335:
2333:
2332:
2324:
2318:
2309:
2300:
2298:Orbital period
2290:
2288:
2284:
2283:
2281:
2280:
2278:True longitude
2271:
2269:Mean longitude
2262:
2253:
2236:
2226:
2224:
2220:
2219:
2217:
2216:
2207:
2198:
2189:
2179:
2177:
2173:
2172:
2170:
2169:
2156:
2147:
2138:
2128:
2126:
2124:
2123:
2120:
2116:
2110:
2104:
2103:
2100:
2099:
2097:
2096:
2095:
2094:
2086:
2085:
2084:
2079:
2074:
2073:
2072:
2059:
2054:
2053:
2052:
2047:
2042:
2037:
2029:
2028:
2027:
2025:Areostationary
2022:
2017:
2008:
2006:
2000:
1999:
1997:
1996:
1994:Very low Earth
1991:
1986:
1981:
1976:
1971:
1966:
1961:
1956:
1951:
1946:
1941:
1936:
1935:
1934:
1929:
1922:Geosynchronous
1918:
1916:
1910:
1909:
1907:
1906:
1904:Transfer orbit
1901:
1900:
1899:
1894:
1884:
1879:
1874:
1869:
1864:
1862:Lagrange point
1859:
1854:
1845:
1840:
1835:
1830:
1821:
1816:
1811:
1805:
1803:
1796:
1790:
1789:
1784:Gravitational
1781:
1780:
1773:
1766:
1758:
1752:
1751:
1740:
1739:External links
1737:
1734:
1733:
1716:
1689:
1682:
1649:
1642:
1615:
1605:
1598:
1578:
1563:
1541:
1504:
1490:
1475:
1474:
1472:
1469:
1468:
1467:
1462:
1457:
1452:
1447:
1440:
1439:
1423:
1420:
1369:Main article:
1366:
1363:
1340:Main article:
1337:
1334:
1332:
1329:
1300:
1297:
1282:
1233:Main article:
1230:
1227:
1173:Main article:
1170:
1167:
1142:away from the
1129:
1125:
1115:at some point
1070:Main article:
1059:
1056:
1030:Walter Hohmann
999:Main article:
988:
985:
957:
954:
915:gravity assist
897:Gravity assist
895:Main article:
892:
891:Gravity assist
889:
869:kinetic energy
835:Hermann Oberth
810:Main article:
807:
804:
802:
799:
783:center of mass
748:
745:
712:
709:
706:
705:
613:This section
612:
610:
603:
597:
594:
590:delta-v budget
572:
568:
551:delta-v budget
542:
539:
507:Main article:
504:
501:
499:
496:
488:transfer orbit
451:
450:
448:
447:
440:
433:
425:
422:
421:
418:
417:
412:
406:
403:
402:
399:
398:
395:
394:
389:
387:Gravity assist
383:
380:
379:
376:
375:
372:
371:
366:
361:
356:
350:
347:
346:
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342:
335:
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265:
262:
261:
258:
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246:
243:
242:
237:
232:
227:
222:
220:Orbital period
217:
212:
207:
202:
196:
193:
192:
189:
188:
185:
184:
182:Decaying orbit
179:
174:
169:
161:
160:
154:
147:
145:Transfer orbit
143:
142:
141:
139:Elliptic orbit
136:
134:Circular orbit
130:
121:
120:
117:
116:
113:
112:
107:
102:
97:
92:
87:
82:
77:
71:
66:
65:
62:
61:
54:
51:
50:
42:
41:
37:
36:
26:
9:
6:
4:
3:
2:
2586:
2575:
2572:
2570:
2569:Astrodynamics
2567:
2566:
2564:
2549:
2541:
2540:
2537:
2531:
2528:
2526:
2523:
2521:
2518:
2516:
2513:
2511:
2508:
2506:
2503:
2501:
2498:
2496:
2495:-body problem
2494:
2490:
2488:
2485:
2483:
2480:
2478:
2475:
2473:
2470:
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2429:
2423:
2420:
2418:
2415:
2413:
2410:
2408:
2405:
2403:
2400:
2398:
2397:Oberth effect
2395:
2393:
2390:
2388:
2385:
2383:
2380:
2378:
2375:
2373:
2370:
2368:
2365:
2363:
2360:
2358:
2355:
2353:
2350:
2349:
2347:
2345:
2341:
2331:
2323:
2319:
2317:
2316:Orbital speed
2310:
2308:
2301:
2299:
2292:
2291:
2289:
2285:
2279:
2272:
2270:
2263:
2261:
2254:
2252:
2237:
2235:
2228:
2227:
2225:
2221:
2215:
2208:
2206:
2199:
2197:
2190:
2188:
2181:
2180:
2178:
2174:
2168:
2157:
2155:
2148:
2146:
2139:
2137:
2130:
2129:
2127:
2121:
2118:
2117:
2114:
2111:
2109:
2105:
2093:
2090:
2089:
2087:
2083:
2080:
2078:
2075:
2071:
2070:Earth's orbit
2068:
2067:
2066:
2063:
2062:
2060:
2058:
2055:
2051:
2048:
2046:
2043:
2041:
2038:
2036:
2033:
2032:
2030:
2026:
2023:
2021:
2018:
2016:
2013:
2012:
2010:
2009:
2007:
2001:
1995:
1992:
1990:
1987:
1985:
1982:
1980:
1977:
1975:
1972:
1970:
1967:
1965:
1962:
1960:
1957:
1955:
1952:
1950:
1947:
1945:
1942:
1940:
1937:
1933:
1930:
1928:
1927:Geostationary
1925:
1924:
1923:
1920:
1919:
1917:
1915:
1911:
1905:
1902:
1898:
1895:
1893:
1890:
1889:
1888:
1885:
1883:
1880:
1878:
1875:
1873:
1870:
1868:
1865:
1863:
1860:
1858:
1855:
1853:
1849:
1846:
1844:
1841:
1839:
1836:
1834:
1831:
1829:
1825:
1822:
1820:
1817:
1815:
1812:
1810:
1807:
1806:
1804:
1800:
1797:
1795:
1791:
1787:
1779:
1774:
1772:
1767:
1765:
1760:
1759:
1756:
1750:
1749:Wigbert Fehse
1746:
1743:
1742:
1730:
1726:
1720:
1704:
1700:
1693:
1685:
1679:
1675:
1671:
1666:
1665:
1659:
1653:
1645:
1639:
1635:
1631:
1630:
1625:
1619:
1609:
1601:
1599:0-7923-6903-3
1595:
1591:
1590:
1582:
1575:
1574:
1567:
1559:
1555:
1551:
1545:
1537:
1533:
1529:
1525:
1518:
1511:
1509:
1500:
1494:
1486:
1480:
1476:
1466:
1463:
1461:
1458:
1456:
1453:
1451:
1448:
1445:
1442:
1441:
1437:
1426:
1419:
1417:
1413:
1409:
1405:
1401:
1400:space station
1397:
1393:
1385:
1381:
1377:
1372:
1362:
1360:
1356:
1352:
1351:orbit phasing
1349:
1348:astrodynamics
1343:
1342:Orbit phasing
1336:Orbit phasing
1328:
1326:
1322:
1317:
1313:
1309:
1306:
1296:
1280:
1272:
1268:
1263:
1259:
1257:
1256:orbital nodes
1253:
1249:
1245:
1241:
1236:
1226:
1224:
1220:
1215:
1213:
1208:
1206:
1202:
1198:
1194:
1190:
1186:
1182:
1176:
1166:
1164:
1163:Ary Sternfeld
1159:
1157:
1151:
1149:
1145:
1127:
1123:
1114:
1110:
1105:
1103:
1099:
1095:
1091:
1087:
1083:
1079:
1073:
1064:
1055:
1053:
1052:
1047:
1043:
1039:
1035:
1031:
1027:
1022:
1020:
1016:
1012:
1008:
1002:
993:
984:
982:
978:
977:descent orbit
974:
970:
966:
962:
953:
951:
950:
945:
944:
939:
934:
932:
928:
924:
920:
916:
912:
911:astrodynamics
903:
898:
888:
884:
882:
881:ion thrusters
876:
874:
870:
866:
862:
858:
857:powered flyby
853:
851:
847:
844:
840:
836:
831:
827:
826:rocket engine
823:
822:Oberth effect
819:
813:
812:Oberth effect
806:Oberth effect
798:
796:
792:
788:
784:
780:
776:
772:
767:
765:
760:
758:
754:
744:
740:
736:
732:
730:
726:
717:
702:
699:
691:
688:February 2024
680:
677:
673:
670:
666:
663:
659:
656:
652:
649: –
648:
644:
643:Find sources:
637:
633:
629:
623:
622:
618:
611:
607:
602:
601:
593:
591:
586:
558:
552:
548:
538:
536:
532:
528:
520:
515:
510:
495:
493:
489:
484:
482:
478:
474:
470:
466:
462:
458:
446:
441:
439:
434:
432:
427:
426:
424:
423:
416:
413:
411:
408:
407:
401:
400:
393:
392:Oberth effect
390:
388:
385:
384:
378:
377:
370:
367:
365:
362:
360:
357:
355:
352:
351:
345:
344:
340:
334:
333:
326:
323:
321:
318:
317:
311:
307:
306:
304:
298:
297:N-body orbits
293:
292:
285:
282:
280:
279:Perturbations
277:
275:
272:
270:
267:
266:
260:
259:
255:
249:
248:
241:
238:
236:
233:
231:
228:
226:
223:
221:
218:
216:
213:
211:
208:
206:
203:
201:
198:
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191:
190:
183:
180:
178:
175:
173:
170:
168:
165:
164:
158:
155:
153:
149:
148:
146:
140:
137:
135:
132:
131:
125:
119:
118:
111:
108:
106:
103:
101:
100:Orbital nodes
98:
96:
93:
91:
88:
86:
83:
81:
78:
76:
73:
72:
69:
64:
63:
59:
53:
52:
48:
44:
43:
40:Astrodynamics
39:
38:
34:
33:
30:
19:
2510:Perturbation
2492:
2467:Ground track
2377:Gravity turn
2343:
2328:
2321:
2314:
2305:
2296:
2276:
2267:
2258:
2251:True anomaly
2249:
2234:Mean anomaly
2232:
2212:
2203:
2194:
2185:
2165:
2152:
2143:
2136:Eccentricity
2134:
2092:Lunar cycler
2065:Heliocentric
2005:other points
1954:Medium Earth
1852:Non-inclined
1728:
1719:
1707:. Retrieved
1703:the original
1692:
1663:
1652:
1628:
1618:
1608:
1588:
1581:
1571:
1566:
1558:the original
1553:
1544:
1536:the original
1523:
1493:
1485:"Navigation"
1479:
1391:
1389:
1359:true anomaly
1350:
1345:
1318:
1314:
1310:
1302:
1264:
1260:
1239:
1238:
1216:
1209:
1180:
1178:
1160:
1152:
1144:central body
1106:
1085:
1078:astronautics
1075:
1049:
1046:Kurd Laßwitz
1041:
1037:
1023:
1010:
1004:
976:
959:
947:
941:
935:
908:
885:
877:
860:
856:
854:
821:
818:astronautics
815:
768:
763:
761:
752:
750:
741:
737:
733:
724:
722:
694:
685:
675:
668:
661:
654:
642:
626:Please help
614:
587:
554:
524:
491:
485:
480:
464:
460:
454:
409:
177:Radial orbit
128:eccentricity
110:True anomaly
95:Mean anomaly
85:Eccentricity
29:
2472:Hill sphere
2307:Mean motion
2187:Inclination
2176:Orientation
2077:Mars cycler
2015:Areocentric
1887:Synchronous
1672:. pp.
1321:ion engines
1244:inclination
1051:Two Planets
979:, e.g. the
764:finite burn
519:mass ratios
457:spaceflight
310:Halo orbits
274:Hill sphere
90:Inclination
2563:Categories
2412:Rendezvous
2108:Parameters
1944:High Earth
1914:Geocentric
1867:Osculating
1824:Elliptical
1471:References
1396:spacecraft
1185:trajectory
1104:maneuver.
1090:spacecraft
1026:spacecraft
971:(TMI) and
943:Mariner 10
931:decelerate
927:accelerate
830:propellant
775:spacecraft
658:newspapers
596:Propulsion
477:spacecraft
469:propulsion
354:Mass ratio
269:Barycenter
2457:Ephemeris
2434:mechanics
2344:Maneuvers
2287:Variation
2050:Libration
2045:Lissajous
1949:Low Earth
1939:Graveyard
1838:Horseshoe
1709:March 22,
1254:) at the
1165:in 1934.
1148:periapsis
1092:from one
846:physicist
793:, thrust
615:does not
567:Δ
194:Equations
122:Types of
2223:Position
1848:Inclined
1819:Circular
1660:(2007).
1626:(2004).
1422:See also
1384:Gemini 6
1380:Gemini 7
1267:apoapsis
1113:apoapsis
850:rocketry
795:centroid
729:velocity
535:momentum
492:coasting
2432:Orbital
2402:Phasing
2362:Delta-v
2167:Apsides
2161:,
1959:Molniya
1877:Parking
1814:Capture
1802:General
1487:. NASA.
1252:delta v
1223:delta-v
1100:than a
1098:delta-v
967:(TLI),
949:Voyager
919:gravity
841:-born,
801:Assists
672:scholar
636:removed
621:sources
557:delta-v
547:Delta-v
541:Delta-v
517:Rocket
498:General
2088:Other
1989:Tundra
1857:Kepler
1833:Escape
1786:orbits
1680:
1640:
1596:
1501:. MIT.
1271:apogee
1269:, (or
1189:orbits
1084:, the
1034:German
1032:, the
1009:, the
923:planet
843:German
837:, the
820:, the
674:
667:
660:
653:
645:
531:thrust
527:rocket
2330:Epoch
2119:Shape
2057:Lunar
2011:Mars
2003:About
1974:Polar
1794:Types
1520:(PDF)
1404:orbit
1355:orbit
1248:orbit
1193:Earth
1094:orbit
1019:plane
921:of a
679:JSTOR
665:books
475:of a
473:orbit
459:, an
75:Apsis
2122:Size
2061:Sun
2040:Halo
1892:semi
1711:2012
1678:ISBN
1638:ISBN
1613:713.
1594:ISBN
1197:Moon
1080:and
779:mass
651:news
619:any
617:cite
549:and
465:burn
1897:sub
1809:Box
1747:by
1674:176
1528:hdl
1346:In
1076:In
1005:In
913:a
909:In
859:or
816:In
723:An
630:by
585:).
455:In
126:by
2565::
2245:,
2241:,
1850:/
1826:/
1727:,
1676:.
1668:.
1632:.
1552:.
1522:.
1507:^
1390:A
1361:.
1323:,
1225:.
1207:.
1179:A
1054:.
1021:.
929:,
883:.
785:,
781:,
537:.
494:.
483:.
2493:n
2325:0
2322:t
2312:v
2303:n
2294:T
2274:l
2265:L
2256:E
2247:f
2243:θ
2239:ν
2230:M
2210:ϖ
2201:ω
2192:Ω
2183:i
2163:q
2159:Q
2150:b
2141:a
2132:e
1777:e
1770:t
1763:v
1713:.
1686:.
1646:.
1602:.
1530::
1281:v
1195:-
1128:b
1124:r
1040:(
701:)
695:(
690:)
686:(
676:·
669:·
662:·
655:·
638:.
624:.
571:v
559:(
444:e
437:t
430:v
312:)
308:(
159:)
150:(
20:)
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