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36:
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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.
1304:
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
1296:
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
1250:
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
867:
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
727:
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.
1300:
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.
723:
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.
1142:
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
875:
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.
821:
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
1283:
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.
731:
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.
1601:
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 -
572:
1129:
720:(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.
929:) 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
1281:
1239:. 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 (
964:(TEI). These are generally larger than small trajectory correction maneuvers. Insertion, injection and sometimes initiation are used to describe entry into a
1505:
914:
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
1316:, and others. These types of engines have very high specific impulse (fuel efficiency) but currently are only available with fairly low absolute thrust.
1247:(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).
952:
maneuvers leave a spacecraft in a destination orbit. In contrast, orbit injection maneuvers occur when a spacecraft enters a transfer orbit, e.g.
762:, high fidelity models of the trajectories are required to meet the mission goals. Calculating a "finite" burn requires a detailed model of the
894:
The trajectories that enabled NASA's twin
Voyager spacecraft to tour the four gas giant planets and achieve velocity to escape our solar system
1404:
1305:
been suggested that some forms of nuclear (fission or fusion based) or antimatter powered rockets would be capable of this trajectory.
745:
1293:
431:
2410:
1687:
1192:. The drawback of such trajectories is that they take much longer to complete than higher energy (more fuel) transfers such as
1139:
at the radius of the final desired orbit, where a third delta-v is performed, injecting the spacecraft into the desired orbit.
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1670:
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639:
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203:
1618:
Capture
Dynamics and Chaotic Motions in Celestial Mechanics: With Applications to the Construction of Low Energy Transfers
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852:
where the application of an impulse, typically from the use of a rocket engine, close to a gravitational body (where the
581:. With a good approximation of the delta-v budget designers can estimate the propellant required for planned maneuvers.
272:
817:
when travelling at high speed generates much more useful energy than one at low speed. Oberth effect occurs because the
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1586:
686:
616:
514:
The
Tsiolkovsky rocket equation, or ideal rocket equation, can be useful for analysis of maneuvers by vehicles using
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and approach to a very close distance (e.g. within visual contact). Rendezvous requires a precise match of the
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93:
468:. For spacecraft far from Earth (for example those in orbits around the Sun) an orbital maneuver is called a
1100:. From the initial orbit, a delta-v is applied boosting the spacecraft into the first transfer orbit with an
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1920:
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1135:. At this point, a second delta-v is applied sending the spacecraft into the second elliptical orbit with
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755:, where the word "finite" is used to mean "non-zero", or practically, again: over a longer period.
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352:
267:
522:) by expelling part of its mass at high speed. The rocket itself moves due to the conservation of
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1816:
1400:
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609:
223:
1210:. Following these pathways allows for long distances to be traversed for little expenditure of
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2370:
1972:
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989:
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140:
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1407:, procedures which bring the spacecraft into physical contact and create a link between them.
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The orbital maneuver to perform the
Hohmann transfer uses two engine impulses which move a
957:
577:
The delta-v for all the expected maneuvers are estimated for a mission are summarized in a
198:
155:
145:
73:
1308:
More practically, this type of maneuver is used in low thrust maneuvers, for example with
8:
2380:
2175:
1915:
1453:
1443:
1265:
1163:
240:
78:
708:
Figure 1: Approximation of a finite thrust maneuver with an impulsive change in velocity
2053:
1942:
1840:
1713:
1424:
716:
is the mathematical model of a maneuver as an instantaneous change in the spacecraft's
313:
188:
1364:
906:
maneuver, gravitational slingshot or swing-by is the use of the relative movement and
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2003:
1957:
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Low energy transfers follow special pathways in space, sometimes referred to as the
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2058:
1932:
1902:
1855:
1516:
1359:
1007:
926:
779:
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864:) than the same impulse applied further from the body for the same initial orbit.
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2033:
1937:
1927:
1826:
1750:
1646:
1612:
1576:
1144:
949:
937:
861:
827:
744:. 'Non-impulsive' refers to the momentum changing slowly over a long time, as in
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291:
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133:
127:
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1616:
1539:"Section I. The Environment of Space - Chapter 4. Interplanetary Trajectories"
1399:
of the two spacecraft, allowing them to remain at a constant distance through
502:
2551:
2390:
2385:
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1947:
1865:
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1336:
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170:
1714:
Trajectories with
Constant Tangential Thrust in Central Gravitational Fields
1520:
2455:
2365:
2239:
2222:
2080:
1977:
1845:
1347:
1147:
is 11.94 or greater, depending on the intermediate semi-major axis chosen.
1132:
1066:
919:
869:
806:
98:
88:
83:
1251:
any inclination change required over the duration of the spacecraft life.
2460:
2295:
2065:
2045:
1962:
1653:
Fly Me to the Moon: An
Insider's Guide to the New Science of Space Travel
1524:
1309:
1232:
1150:
The idea of the bi-elliptical transfer trajectory was first published by
1039:
980:
445:
262:
2028:
1742:
1384:
1173:
1078:
1051:
1033:). Hohmann was influenced in part by the German science fiction author
1014:
931:
915:
818:
763:
740:
Applying a low thrust over a longer period of time is referred to as a
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465:
342:
298:
257:
35:
2445:
1797:
1136:
834:
704:
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1368:
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1101:
783:
717:
523:
544:
The applied change in velocity of each maneuver is referred to as
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1240:
1211:
1086:
1022:
907:
831:
545:
535:
1188:
system and also in other systems, such as traveling between the
475:
When a spacecraft is not conducting a maneuver, especially in a
1342:
is the adjustment of the time-position of spacecraft along its
1259:
1017:
onto and off the transfer orbit. This maneuver was named after
911:
890:
838:
519:
515:
1025:
scientist who published a description of it in his 1925 book
2155:
1774:
1392:
1343:
1236:
1181:
1177:
1082:
461:
63:
856:
is low, and the speed is high) can give much more change in
1720:, NASA Lewis Research Center, 1960 (accessed 26 March 2014)
1346:, usually described as adjusting the orbiting spacecraft's
1185:
767:
766:
and its thrusters. The most important of details include:
510:
versus final velocity calculated from the rocket equation
1254:
Maximum efficiency of inclination change is achieved at
1176:, is a route in space which allows spacecraft to change
1085:
to another and may, in certain situations, require less
1734:
Handbook
Automated Rendezvous and Docking of Spacecraft
1503:
518:
propulsion. A rocket applies acceleration to itself (a
1268:
1110:
778:, thruster positions, thrust vectors, thrust curves,
554:
1565:(Washington: NASA Technical Translation F-44, 1960).
1414:
1383:
is a sequence of orbital maneuvers during which two
1055:
Bi-elliptic transfer from blue to red circular orbit
1002:
is an elliptical orbit used to transfer between two
758:
For a few space missions, such as those including a
1650:
1275:
1123:
566:
1203:trajectories, or ballistic capture trajectories.
1180:using very little fuel. These routes work in the
2549:
1545:. NASA Jet Propulsion Laboratory. Archived from
925:The "assist" is provided by the motion (orbital
1353:
941:probes' notable fly-bys of Jupiter and Saturn.
1578:Fundamentals of Astrodynamics and Applications
1504:Oberth, Herman; Oldenbourg Verlag, R. (1970).
1096:The bi-elliptic transfer consists of two half
1758:
1287:
1231:is an orbital maneuver aimed at changing the
1217:
841:, who apparently first described the effect.
425:
1688:"Basics of Space Flight: Orbital Mechanics"
922:and/or re-direct the path of a spacecraft.
623:. Unsourced material may be challenged and
2532:
1765:
1751:
746:electrically powered spacecraft propulsion
432:
418:
1319:
1272:
972:maneuver used for Apollo lunar landings.
687:Learn how and when to remove this message
563:
1772:
1679:
1645:
1611:
1363:
1050:
979:
889:
735:
703:
501:
1574:
1046:
2550:
2411:Transposition, docking, and extraction
1605:
1499:
1497:
1199:Low energy transfer are also known as
1157:
699:
1746:
1403:. Rendezvous is commonly followed by
1031:The Accessibility of Celestial Bodies
567:{\displaystyle \Delta \mathbf {v} \,}
1685:
1639:
1562:The Attainability of Heavenly Bodies
1077:is an orbital maneuver that moves a
1027:Die Erreichbarkeit der Himmelskörper
1006:of different altitudes, in the same
621:adding citations to reliable sources
588:
1494:
975:
13:
944:
748:, rather than by a short impulse.
555:
491:
14:
2574:
2471:Kepler's laws of planetary motion
1727:
879:
204:Kepler's laws of planetary motion
2531:
2466:Interplanetary Transport Network
2346:Collision avoidance (spacecraft)
1439:Collision avoidance (spacecraft)
1417:
1324:
1208:Interplanetary Transport Network
794:
593:
559:
34:
2431:Astronomical coordinate systems
2185:Longitude of the ascending node
1706:
1575:Vallado, David Anthony (2001).
1523:. NASA-TT-F-622. Archived from
844:The Oberth effect is used in a
786:offsets, and fuel consumption.
2504:Retrograde and prograde motion
1595:
1568:
1553:
1531:
1480:
1466:
1:
1513:NASA Technical Reports Server
1459:
860:and final speed (i.e. higher
584:
16:A movement during spaceflight
2451:Equatorial coordinate system
1433:Clohessy-Wiltshire equations
1354:Space rendezvous and docking
7:
1410:
935:onwards, including the two
498:Tsiolkovsky rocket equation
358:Tsiolkovsky rocket equation
10:
2579:
2203:Longitude of the periapsis
1659:Princeton University Press
1623:Princeton University Press
1387:, one of which is often a
1357:
1328:
1288:Constant-thrust trajectory
1262:), where orbital velocity
1229:Orbital inclination change
1224:orbital inclination change
1221:
1218:Orbital inclination change
1161:
1058:
987:
970:Powered Descent Initiation
883:
798:
789:
533:
529:
495:
486:
327:Engineering and efficiency
146:Bi-elliptic transfer orbit
2527:
2514:Specific angular momentum
2419:
2331:
2275:
2211:
2164:
2104:
2095:
1991:
1901:
1790:
1781:
1581:. Springer. p. 317.
470:deep-space maneuver (DSM)
837:and a founder of modern
353:Propellant mass fraction
252:Gravitational influences
2509:Specific orbital energy
1401:orbital station-keeping
1201:weak stability boundary
1194:Hohmann transfer orbits
224:Specific orbital energy
1921:Geostationary transfer
1543:Basics of Space Flight
1376:
1320:Rendezvous and docking
1277:
1235:of an orbiting body's
1125:
1056:
1000:Hohmann transfer orbit
990:Hohmann transfer orbit
985:
984:Hohmann Transfer Orbit
895:
813:is where the use of a
742:non-impulsive maneuver
709:
568:
511:
460:systems to change the
452:(otherwise known as a
141:Hohmann transfer orbit
2494:Orbital state vectors
2436:Characteristic energy
2406:Trans-lunar injection
2194:Argument of periapsis
1871:Prograde / Retrograde
1832:Hyperbolic trajectory
1718:Technical Report R-63
1506:"Ways to spaceflight"
1488:"The Rocket Equation"
1449:Spacecraft propulsion
1435:for co-orbit analysis
1391:, arrive at the same
1367:
1314:Hall-effect thrusters
1294:constant-acceleration
1278:
1190:satellites of Jupiter
1126:
1124:{\displaystyle r_{b}}
1071:aerospace engineering
1054:
983:
962:trans-Earth injection
954:trans-lunar injection
893:
736:Low thrust propulsion
707:
617:improve this section
569:
505:
337:Preflight engineering
69:Argument of periapsis
2341:Bi-elliptic transfer
1861:Parabolic trajectory
1686:Braeunig, Robert A.
1292:Constant-thrust and
1266:
1108:
1075:bi-elliptic transfer
1061:Bi-elliptic transfer
1047:Bi-elliptic transfer
958:trans-Mars injection
552:
479:, it is said to be
393:Propulsive maneuvers
2381:Low-energy transfer
1694:on February 4, 2012
1454:Orbital spaceflight
1444:Flyby (spaceflight)
1405:docking or berthing
1276:{\displaystyle v\,}
1170:low energy transfer
1164:low energy transfer
1158:Low energy transfer
700:Impulsive maneuvers
370:Efficiency measures
273:Sphere of influence
242:Celestial mechanics
24:Part of a series on
2376:Inclination change
2024:Distant retrograde
1425:Spaceflight portal
1397:orbital velocities
1377:
1371:photographed from
1273:
1121:
1057:
1037:and his 1897 book
986:
896:
714:impulsive maneuver
710:
636:"Orbital maneuver"
564:
512:
189:Dynamical friction
2563:Orbital maneuvers
2545:
2544:
2519:Two-line elements
2327:
2326:
2249:Eccentric anomaly
2091:
2090:
1958:Orbit of the Moon
1817:Highly elliptical
1672:978-0-691-12822-1
1632:978-0-691-09480-9
1549:on April 3, 2023.
996:orbital mechanics
854:gravity potential
776:moment of inertia
697:
696:
689:
671:
442:
441:
292:Lagrangian points
229:Vis-viva equation
199:Kepler's equation
46:Orbital mechanics
2570:
2535:
2534:
2476:Lagrangian point
2371:Hohmann transfer
2316:
2302:
2293:
2284:
2264:
2255:
2246:
2237:
2233:
2229:
2220:
2200:
2191:
2182:
2173:
2153:
2149:
2140:
2131:
2122:
2102:
2101:
2071:Heliosynchronous
2020:Lagrange points
1973:Transatmospheric
1788:
1787:
1767:
1760:
1753:
1744:
1743:
1721:
1710:
1704:
1703:
1701:
1699:
1690:. Archived from
1683:
1677:
1676:
1656:
1647:Belbruno, Edward
1643:
1637:
1636:
1613:Belbruno, Edward
1609:
1603:
1599:
1593:
1592:
1572:
1566:
1559:Walter Hohmann,
1557:
1551:
1550:
1535:
1529:
1528:
1521:2060/19720008133
1510:
1501:
1492:
1491:
1484:
1478:
1477:
1470:
1427:
1422:
1421:
1420:
1381:space rendezvous
1375:in December 1965
1360:Space rendezvous
1282:
1280:
1279:
1274:
1172:, or low energy
1130:
1128:
1127:
1122:
1120:
1119:
1091:Hohmann transfer
976:Hohmann transfer
927:angular momentum
828:Austro-Hungarian
780:specific impulse
760:space rendezvous
751:Another term is
692:
685:
681:
678:
672:
670:
629:
597:
589:
573:
571:
570:
565:
562:
456:) is the use of
450:orbital maneuver
434:
427:
420:
399:Orbital maneuver
348:Payload fraction
328:
309:Lissajous orbits
243:
214:Orbital velocity
161:Hyperbolic orbit
57:Orbital elements
47:
38:
21:
20:
2578:
2577:
2573:
2572:
2571:
2569:
2568:
2567:
2548:
2547:
2546:
2541:
2523:
2441:Escape velocity
2422:
2415:
2396:Rocket equation
2323:
2315:
2309:
2300:
2291:
2282:
2271:
2262:
2253:
2244:
2235:
2231:
2227:
2218:
2207:
2198:
2189:
2180:
2171:
2160:
2151:
2147:
2143:Semi-minor axis
2138:
2134:Semi-major axis
2129:
2120:
2114:
2087:
2009:Areosynchronous
1993:
1987:
1968:Sun-synchronous
1953:Near-equatorial
1897:
1777:
1771:
1730:
1725:
1724:
1712:W. E. Moeckel,
1711:
1707:
1697:
1695:
1684:
1680:
1673:
1644:
1640:
1633:
1625:. p. 224.
1610:
1606:
1600:
1596:
1589:
1573:
1569:
1558:
1554:
1537:
1536:
1532:
1527:on May 9, 2010.
1515:. p. 200.
1508:
1502:
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1472:
1471:
1467:
1462:
1423:
1418:
1416:
1413:
1362:
1356:
1333:
1327:
1322:
1290:
1267:
1264:
1263:
1226:
1220:
1166:
1160:
1145:semi-major axis
1115:
1111:
1109:
1106:
1105:
1098:elliptic orbits
1063:
1049:
1004:circular orbits
992:
978:
950:Orbit insertion
947:
945:Transfer orbits
888:
882:
862:specific energy
850:Oberth maneuver
803:
797:
792:
738:
702:
693:
682:
676:
673:
630:
628:
614:
598:
587:
558:
553:
550:
549:
542:
534:Main articles:
532:
500:
494:
492:Rocket equation
489:
438:
409:
408:
404:Orbit insertion
394:
386:
385:
371:
363:
362:
338:
330:
326:
319:
318:
314:Lyapunov orbits
305:
304:
288:
278:
277:
253:
245:
241:
234:
233:
219:Surface gravity
194:Escape velocity
184:
176:
175:
156:Parabolic orbit
152:
151:
118:
116:
113:two-body orbits
104:
103:
94:Semi-major axis
59:
49:
45:
17:
12:
11:
5:
2576:
2566:
2565:
2560:
2543:
2542:
2540:
2539:
2537:List of orbits
2528:
2525:
2524:
2522:
2521:
2516:
2511:
2506:
2501:
2496:
2491:
2489:Orbit equation
2486:
2478:
2473:
2468:
2463:
2458:
2453:
2448:
2443:
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2373:
2368:
2363:
2361:Gravity assist
2358:
2356:Delta-v budget
2353:
2348:
2343:
2337:
2335:
2329:
2328:
2325:
2324:
2322:
2321:
2313:
2307:
2298:
2289:
2287:Orbital period
2279:
2277:
2273:
2272:
2270:
2269:
2267:True longitude
2260:
2258:Mean longitude
2251:
2242:
2225:
2215:
2213:
2209:
2208:
2206:
2205:
2196:
2187:
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2168:
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2161:
2159:
2158:
2145:
2136:
2127:
2117:
2115:
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2105:
2099:
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2048:
2043:
2042:
2041:
2036:
2031:
2026:
2018:
2017:
2016:
2014:Areostationary
2011:
2006:
1997:
1995:
1989:
1988:
1986:
1985:
1983:Very low Earth
1980:
1975:
1970:
1965:
1960:
1955:
1950:
1945:
1940:
1935:
1930:
1925:
1924:
1923:
1918:
1911:Geosynchronous
1907:
1905:
1899:
1898:
1896:
1895:
1893:Transfer orbit
1890:
1889:
1888:
1883:
1873:
1868:
1863:
1858:
1853:
1851:Lagrange point
1848:
1843:
1834:
1829:
1824:
1819:
1810:
1805:
1800:
1794:
1792:
1785:
1779:
1778:
1773:Gravitational
1770:
1769:
1762:
1755:
1747:
1741:
1740:
1729:
1728:External links
1726:
1723:
1722:
1705:
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1671:
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1436:
1429:
1428:
1412:
1409:
1358:Main article:
1355:
1352:
1329:Main article:
1326:
1323:
1321:
1318:
1289:
1286:
1271:
1222:Main article:
1219:
1216:
1162:Main article:
1159:
1156:
1131:away from the
1118:
1114:
1104:at some point
1059:Main article:
1048:
1045:
1019:Walter Hohmann
988:Main article:
977:
974:
946:
943:
904:gravity assist
886:Gravity assist
884:Main article:
881:
880:Gravity assist
878:
858:kinetic energy
824:Hermann Oberth
799:Main article:
796:
793:
791:
788:
772:center of mass
737:
734:
701:
698:
695:
694:
602:This section
601:
599:
592:
586:
583:
579:delta-v budget
561:
557:
540:delta-v budget
531:
528:
496:Main article:
493:
490:
488:
485:
477:transfer orbit
440:
439:
437:
436:
429:
422:
414:
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376:Gravity assist
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221:
216:
211:
209:Orbital period
206:
201:
196:
191:
185:
182:
181:
178:
177:
174:
173:
171:Decaying orbit
168:
163:
158:
150:
149:
143:
136:
134:Transfer orbit
132:
131:
130:
128:Elliptic orbit
125:
123:Circular orbit
119:
110:
109:
106:
105:
102:
101:
96:
91:
86:
81:
76:
71:
66:
60:
55:
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51:
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43:
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39:
31:
30:
26:
25:
15:
9:
6:
4:
3:
2:
2575:
2564:
2561:
2559:
2558:Astrodynamics
2556:
2555:
2553:
2538:
2530:
2529:
2526:
2520:
2517:
2515:
2512:
2510:
2507:
2505:
2502:
2500:
2497:
2495:
2492:
2490:
2487:
2485:
2484:-body problem
2483:
2479:
2477:
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2399:
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2392:
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2387:
2386:Oberth effect
2384:
2382:
2379:
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2308:
2306:
2305:Orbital speed
2299:
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2290:
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2281:
2280:
2278:
2274:
2268:
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2250:
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2210:
2204:
2197:
2195:
2188:
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2170:
2169:
2167:
2163:
2157:
2146:
2144:
2137:
2135:
2128:
2126:
2119:
2118:
2116:
2110:
2107:
2106:
2103:
2100:
2098:
2094:
2082:
2079:
2078:
2076:
2072:
2069:
2067:
2064:
2060:
2059:Earth's orbit
2057:
2056:
2055:
2052:
2051:
2049:
2047:
2044:
2040:
2037:
2035:
2032:
2030:
2027:
2025:
2022:
2021:
2019:
2015:
2012:
2010:
2007:
2005:
2002:
2001:
1999:
1998:
1996:
1990:
1984:
1981:
1979:
1976:
1974:
1971:
1969:
1966:
1964:
1961:
1959:
1956:
1954:
1951:
1949:
1946:
1944:
1941:
1939:
1936:
1934:
1931:
1929:
1926:
1922:
1919:
1917:
1916:Geostationary
1914:
1913:
1912:
1909:
1908:
1906:
1904:
1900:
1894:
1891:
1887:
1884:
1882:
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1878:
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1874:
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1857:
1854:
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1828:
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1823:
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1814:
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1804:
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1784:
1780:
1776:
1768:
1763:
1761:
1756:
1754:
1749:
1748:
1745:
1739:
1738:Wigbert Fehse
1735:
1732:
1731:
1719:
1715:
1709:
1693:
1689:
1682:
1674:
1668:
1664:
1660:
1655:
1654:
1648:
1642:
1634:
1628:
1624:
1620:
1619:
1614:
1608:
1598:
1590:
1588:0-7923-6903-3
1584:
1580:
1579:
1571:
1564:
1563:
1556:
1548:
1544:
1540:
1534:
1526:
1522:
1518:
1514:
1507:
1500:
1498:
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1465:
1455:
1452:
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1447:
1445:
1442:
1440:
1437:
1434:
1431:
1430:
1426:
1415:
1408:
1406:
1402:
1398:
1394:
1390:
1389:space station
1386:
1382:
1374:
1370:
1366:
1361:
1351:
1349:
1345:
1341:
1340:orbit phasing
1338:
1337:astrodynamics
1332:
1331:Orbit phasing
1325:Orbit phasing
1317:
1315:
1311:
1306:
1302:
1298:
1295:
1285:
1269:
1261:
1257:
1252:
1248:
1246:
1245:orbital nodes
1242:
1238:
1234:
1230:
1225:
1215:
1213:
1209:
1204:
1202:
1197:
1195:
1191:
1187:
1183:
1179:
1175:
1171:
1165:
1155:
1153:
1152:Ary Sternfeld
1148:
1146:
1140:
1138:
1134:
1116:
1112:
1103:
1099:
1094:
1092:
1088:
1084:
1080:
1076:
1072:
1068:
1062:
1053:
1044:
1042:
1041:
1036:
1032:
1028:
1024:
1020:
1016:
1011:
1009:
1005:
1001:
997:
991:
982:
973:
971:
967:
966:descent orbit
963:
959:
955:
951:
942:
940:
939:
934:
933:
928:
923:
921:
917:
913:
909:
905:
901:
900:astrodynamics
892:
887:
877:
873:
871:
870:ion thrusters
865:
863:
859:
855:
851:
847:
846:powered flyby
842:
840:
836:
833:
829:
825:
820:
816:
815:rocket engine
812:
811:Oberth effect
808:
802:
801:Oberth effect
795:Oberth effect
787:
785:
781:
777:
773:
769:
765:
761:
756:
754:
749:
747:
743:
733:
729:
725:
721:
719:
715:
706:
691:
688:
680:
677:February 2024
669:
666:
662:
659:
655:
652:
648:
645:
641:
638: –
637:
633:
632:Find sources:
626:
622:
618:
612:
611:
607:
600:
596:
591:
590:
582:
580:
575:
547:
541:
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527:
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484:
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478:
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428:
423:
421:
416:
415:
413:
412:
405:
402:
400:
397:
396:
390:
389:
382:
381:Oberth effect
379:
377:
374:
373:
367:
366:
359:
356:
354:
351:
349:
346:
344:
341:
340:
334:
333:
329:
323:
322:
315:
312:
310:
307:
306:
300:
296:
295:
293:
287:
286:N-body orbits
282:
281:
274:
271:
269:
268:Perturbations
266:
264:
261:
259:
256:
255:
249:
248:
244:
238:
237:
230:
227:
225:
222:
220:
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207:
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137:
135:
129:
126:
124:
121:
120:
114:
108:
107:
100:
97:
95:
92:
90:
89:Orbital nodes
87:
85:
82:
80:
77:
75:
72:
70:
67:
65:
62:
61:
58:
53:
52:
48:
42:
41:
37:
33:
32:
29:Astrodynamics
28:
27:
23:
22:
19:
2499:Perturbation
2481:
2456:Ground track
2366:Gravity turn
2332:
2317:
2310:
2303:
2294:
2285:
2265:
2256:
2247:
2240:True anomaly
2238:
2223:Mean anomaly
2221:
2201:
2192:
2183:
2174:
2154:
2141:
2132:
2125:Eccentricity
2123:
2081:Lunar cycler
2054:Heliocentric
1994:other points
1943:Medium Earth
1841:Non-inclined
1717:
1708:
1696:. Retrieved
1692:the original
1681:
1652:
1641:
1617:
1607:
1597:
1577:
1570:
1560:
1555:
1547:the original
1542:
1533:
1525:the original
1512:
1482:
1474:"Navigation"
1468:
1380:
1378:
1348:true anomaly
1339:
1334:
1307:
1303:
1299:
1291:
1253:
1249:
1228:
1227:
1205:
1198:
1169:
1167:
1149:
1141:
1133:central body
1095:
1074:
1067:astronautics
1064:
1038:
1035:Kurd Laßwitz
1030:
1026:
1012:
999:
993:
965:
948:
936:
930:
924:
897:
874:
866:
849:
845:
843:
810:
807:astronautics
804:
757:
752:
750:
741:
739:
730:
726:
722:
713:
711:
683:
674:
664:
657:
650:
643:
631:
615:Please help
603:
576:
543:
513:
480:
474:
469:
453:
449:
443:
398:
166:Radial orbit
117:eccentricity
99:True anomaly
84:Mean anomaly
74:Eccentricity
18:
2461:Hill sphere
2296:Mean motion
2176:Inclination
2165:Orientation
2066:Mars cycler
2004:Areocentric
1876:Synchronous
1661:. pp.
1310:ion engines
1233:inclination
1040:Two Planets
968:, e.g. the
753:finite burn
508:mass ratios
446:spaceflight
299:Halo orbits
263:Hill sphere
79:Inclination
2552:Categories
2401:Rendezvous
2097:Parameters
1933:High Earth
1903:Geocentric
1856:Osculating
1813:Elliptical
1460:References
1385:spacecraft
1174:trajectory
1093:maneuver.
1079:spacecraft
1015:spacecraft
960:(TMI) and
932:Mariner 10
920:decelerate
916:accelerate
819:propellant
764:spacecraft
647:newspapers
585:Propulsion
466:spacecraft
458:propulsion
343:Mass ratio
258:Barycenter
2446:Ephemeris
2423:mechanics
2333:Maneuvers
2276:Variation
2039:Libration
2034:Lissajous
1938:Low Earth
1928:Graveyard
1827:Horseshoe
1698:March 22,
1243:) at the
1154:in 1934.
1137:periapsis
1081:from one
835:physicist
782:, thrust
604:does not
556:Δ
183:Equations
111:Types of
2212:Position
1837:Inclined
1808:Circular
1649:(2007).
1615:(2004).
1411:See also
1373:Gemini 6
1369:Gemini 7
1256:apoapsis
1102:apoapsis
839:rocketry
784:centroid
718:velocity
524:momentum
481:coasting
2421:Orbital
2391:Phasing
2351:Delta-v
2156:Apsides
2150:,
1948:Molniya
1866:Parking
1803:Capture
1791:General
1476:. NASA.
1241:delta v
1212:delta-v
1089:than a
1087:delta-v
956:(TLI),
938:Voyager
908:gravity
830:-born,
790:Assists
661:scholar
625:removed
610:sources
546:delta-v
536:Delta-v
530:Delta-v
506:Rocket
487:General
2077:Other
1978:Tundra
1846:Kepler
1822:Escape
1775:orbits
1669:
1629:
1585:
1490:. MIT.
1260:apogee
1258:, (or
1178:orbits
1073:, the
1023:German
1021:, the
998:, the
912:planet
832:German
826:, the
809:, the
663:
656:
649:
642:
634:
520:thrust
516:rocket
2319:Epoch
2108:Shape
2046:Lunar
2000:Mars
1992:About
1963:Polar
1783:Types
1509:(PDF)
1393:orbit
1344:orbit
1237:orbit
1182:Earth
1083:orbit
1008:plane
910:of a
668:JSTOR
654:books
464:of a
462:orbit
448:, an
64:Apsis
2111:Size
2050:Sun
2029:Halo
1881:semi
1700:2012
1667:ISBN
1627:ISBN
1602:713.
1583:ISBN
1186:Moon
1069:and
768:mass
640:news
608:any
606:cite
538:and
454:burn
1886:sub
1798:Box
1736:by
1663:176
1517:hdl
1335:In
1065:In
994:In
902:a
898:In
848:or
805:In
712:An
619:by
574:).
444:In
115:by
2554::
2234:,
2230:,
1839:/
1815:/
1716:,
1665:.
1657:.
1621:.
1541:.
1511:.
1496:^
1379:A
1350:.
1312:,
1214:.
1196:.
1168:A
1043:.
1010:.
918:,
872:.
774:,
770:,
526:.
483:.
472:.
2482:n
2314:0
2311:t
2301:v
2292:n
2283:T
2263:l
2254:L
2245:E
2236:f
2232:θ
2228:ν
2219:M
2199:ϖ
2190:ω
2181:Ω
2172:i
2152:q
2148:Q
2139:b
2130:a
2121:e
1766:e
1759:t
1752:v
1702:.
1675:.
1635:.
1591:.
1519::
1270:v
1184:-
1117:b
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1029:(
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684:(
679:)
675:(
665:·
658:·
651:·
644:·
627:.
613:.
560:v
548:(
433:e
426:t
419:v
301:)
297:(
148:)
139:(
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