2325:
133:
163:
2830:
36:
4814:
2890:
It is often said that the semi-major axis is the "average" distance between the primary focus of the ellipse and the orbiting body. This is not quite accurate, because it depends on what the average is taken over. The time- and angle-averaged distance of the orbiting body can vary by 50-100% from the
2815:
lunar orbit, on the other hand, has a semi-major axis of 379,730 km, the Earth's counter-orbit taking up the difference, 4,670 km. The Moon's average barycentric orbital speed is 1.010 km/s, whilst the Earth's is 0.012 km/s. The total of these speeds gives a geocentric lunar
813:
2033:
1780:
2796:); thus, the orbital parameters of the planets are given in heliocentric terms. The difference between the primocentric and "absolute" orbits may best be illustrated by looking at the Earth–Moon system. The mass ratio in this case is
3379:
Note that for a given amount of total mass, the specific energy and the semi-major axis are always the same, regardless of eccentricity or the ratio of the masses. Conversely, for a given total mass and semi-major axis, the total
3259:
2769:
and its path relative to its primary are both ellipses. The semi-major axis is sometimes used in astronomy as the primary-to-secondary distance when the mass ratio of the primary to the secondary is significantly large
3454:
The reason for the assumption of prominent elliptical orbits lies probably in the much larger difference between aphelion and perihelion. That difference (or ratio) is also based on the eccentricity and is computed as
988:
3523:
1350:
3396:). However, the minimal difference between the semi-major and semi-minor axes shows that they are virtually circular in appearance. That difference (or ratio) is based on the eccentricity and is computed as
2239:
1127:
3449:
1651:) to the edge of the ellipse. The semi-minor axis is half of the minor axis. The minor axis is the longest line segment perpendicular to the major axis that connects two points on the ellipse's edge.
1192:
2734:
2415:
1260:
3011:
1699:
690:
3138:
3184:
1895:
2522:
1636:
685:
1437:
2088:
2299:
2950:
3337:
with respect to which the elements of the orbit are to be calculated (e.g. geocentric equatorial for an orbit around Earth, or heliocentric ecliptic for an orbit around the Sun),
2632:
1067:
1040:
1531:
1485:
3373:
1557:
1382:
2155:
1583:
3299:
3075:
3045:
2794:
1932:
1806:
1788:
can be obtained as the limit of a sequence of ellipses where one focus is kept fixed as the other is allowed to move arbitrarily far away in one direction, keeping
1687:
850:
832:
can be obtained as the limit of a sequence of ellipses where one focus is kept fixed as the other is allowed to move arbitrarily far away in one direction, keeping
678:
2550:
2445:
2157:
of the minor axis lie at the height of the asymptotes over/under the hyperbola's vertices. Either half of the minor axis is called the semi-minor axis, of length
1694:
2247:, this is important in physics and astronomy, and measure the distance a particle will miss the focus by if its journey is unperturbed by the body at the focus.
2116:
3197:
821:
is, depending on the convention, plus or minus one half of the distance between the two branches. Thus it is the distance from the center to either
2851:
53:
2118:, corresponding to the minor axis of an ellipse, can be drawn perpendicular to the transverse axis or major axis, the latter connecting the two
3954:
3907:
888:
3458:
100:
72:
1269:
2170:
875:
for the curve: in an ellipse, the minor axis is the shorter one; in a hyperbola, it is the one that does not intersect the hyperbola.
79:
2816:
average orbital speed of 1.022 km/s; the same value may be obtained by considering just the geocentric semi-major axis value.
1647:
The semi-minor axis of an ellipse runs from the center of the ellipse (a point halfway between and on the line running between the
1074:
3399:
558:
86:
4691:
1147:
2657:
4751:
3526:
3393:
2582:
2369:
1205:
1001:
330:
68:
2962:
2454:
Note that for all ellipses with a given semi-major axis, the orbital period is the same, disregarding their eccentricity.
2165:, the semi-minor and semi-major axes' lengths appear in the equation of the hyperbola relative to these axes as follows:
399:
2762:
may be ignored. Making that assumption and using typical astronomy units results in the simpler form Kepler discovered.
2758:
is the mass of the orbiting body. Typically, the central body's mass is so much greater than the orbiting body's, that
2458:
3102:
3854:
3151:
2959:(the fraction of the orbital period that has elapsed since pericentre, expressed as an angle) gives the time-average
2877:
119:
2859:
808:{\displaystyle {\begin{aligned}b&=a{\sqrt {1-e^{2}}},\\\ell &=a(1-e^{2}),\\a\ell &=b^{2}.\end{aligned}}}
4746:
4626:
4045:
3304:
2448:
1832:
4711:
4465:
2469:
2336:(average of aphelion and perihelion) of some Solar System orbits (crosses denoting Kepler's values) showing that
1590:
2243:
The semi-minor axis is also the distance from one of focuses of the hyperbola to an asymptote. Often called the
2122:(turning points) of the hyperbola, with the two axes intersecting at the center of the hyperbola. The endpoints
4784:
4151:
2855:
1389:
57:
2042:
3330:
3315:
1923:
is, depending on the convention, plus or minus one half of the distance between the two branches; if this is
2811: = 0.0549, its semi-minor axis is 383,800 km. Thus the Moon's orbit is almost circular.) The
93:
4731:
4201:
2255:
2909:
4676:
3979:
Williams, Darren M. (November 2003). "Average distance between a star and planet in an eccentric orbit".
3327:
2594:
551:
484:
1069:
of the ellipse from a focus — that is, of the distances from a focus to the endpoints of the major axis
4656:
4483:
1197:
651:
17:
1644:
of the distance from the center to either focus and the distance from the center to either directrix.
4794:
1045:
1018:
4779:
4304:
3958:
3915:
2840:
1490:
1444:
479:
394:
3358:
1536:
1361:
4838:
4789:
4097:
3381:
3264:
2844:
1355:
350:
46:
2324:
4651:
4253:
4173:
4161:
3344:
2743:
2644:
is the semi-major axis. This form turns out to be a simplification of the general form for the
2125:
1562:
544:
267:
3272:
2250:
The semi-minor axis and the semi-major axis are related through the eccentricity, as follows:
2028:{\displaystyle {\frac {\left(x-h\right)^{2}}{a^{2}}}-{\frac {\left(y-k\right)^{2}}{b^{2}}}=1.}
4774:
4716:
4686:
4474:
4351:
4319:
4289:
4248:
4233:
4112:
3189:
3094:
452:
287:
195:
3050:
3020:
2773:
1775:{\displaystyle {\begin{aligned}b&=a{\sqrt {1-e^{2}}},\\a\ell &=b^{2}.\end{aligned}}}
4799:
4621:
4405:
4294:
4263:
4191:
4166:
4141:
4102:
4083:
4038:
3988:
3537:
1791:
1672:
835:
663:
325:
282:
272:
200:
2535:
2430:
8:
4661:
4456:
4196:
367:
205:
3992:
2098:
4334:
4223:
4121:
3334:
635:. For the special case of a circle, the lengths of the semi-axes are both equal to the
440:
315:
4701:
4599:
4529:
4284:
4238:
4156:
3850:
3581:
3571:
3558:
3547:
2896:
1667:
658:
355:
292:
171:
132:
4681:
4613:
4377:
4339:
4213:
4183:
4136:
3996:
3592:
3384:
is always the same. This statement will always be true under any given conditions.
3143:
2645:
2566:
2244:
1827:
The length of the semi-minor axis could also be found using the following formula:
1648:
872:
612:
592:
525:
474:
239:
183:
4017:
4843:
4721:
4314:
4218:
4208:
4107:
4031:
2161:. Denoting the semi-major axis length (distance from the center to a vertex) as
530:
435:
345:
320:
4817:
4769:
4761:
4756:
4641:
4636:
4567:
4547:
4538:
4131:
4117:
4093:
4088:
4063:
2906:(the true orbital angle, measured at the focus) results in the semi-minor axis
2766:
2574:
2358:
2119:
1641:
1139:
822:
502:
418:
412:
335:
260:
254:
249:
3869:
3254:{\displaystyle \varepsilon ={\frac {v^{2}}{2}}-{\frac {\mu }{|\mathbf {r} |}}}
2364:
of a small body orbiting a central body in a circular or elliptical orbit is:
4832:
4671:
4666:
4585:
4228:
4146:
3883:
3086:
2464:
of a small body orbiting a central body in a circular or elliptical orbit is
2354:
632:
507:
340:
297:
3080:
4736:
4646:
4520:
4503:
4361:
4258:
4126:
3936:
2956:
2903:
2649:
2578:
1015:
The semi-major axis is the mean value of the maximum and minimum distances
608:
588:
225:
215:
210:
4741:
4576:
4346:
4326:
4243:
628:
389:
3387:
983:{\displaystyle {\frac {(x-h)^{2}}{a^{2}}}+{\frac {(y-k)^{2}}{b^{2}}}=1,}
611:
or one half of the major axis, and thus runs from the centre, through a
4309:
4023:
3567:
3518:{\displaystyle {\frac {r_{\text{a}}}{r_{\text{p}}}}={\frac {1+e}{1-e}}}
2807:
lunar orbit, is 384,400 km. (Given the lunar orbit's eccentricity
469:
425:
384:
162:
4000:
2581:
objects, the semi-major axis is related to the period of the orbit by
4726:
4078:
3451:, which for typical planet eccentricities yields very small results.
2803:. The Earth–Moon characteristic distance, the semi-major axis of the
2586:
2562:
1920:
818:
624:
596:
3847:
Fundamental
Planetary Sciences: physics, chemistry, and habitability
2829:
35:
3577:
1785:
829:
584:
572:
2092:
The transverse axis of a hyperbola coincides with the major axis.
1345:{\displaystyle r_{\text{min}}=a(1-e),\quad r_{\text{max}}=a(1+e).}
27:
Term in geometry; longest and shortest semidiameters of an ellipse
4631:
3788:
3704:
580:
2234:{\displaystyle {\frac {x^{2}}{a^{2}}}-{\frac {y^{2}}{b^{2}}}=1.}
2037:
In terms of the semi-latus rectum and the eccentricity, we have
3760:
3732:
3525:. Due to the large difference between aphelion and perihelion,
1911:
are the distances from each focus to any point in the ellipse.
636:
3392:
Planet orbits are always cited as prime examples of ellipses (
631:
with the semi-major axis and has one end at the center of the
4436:
4055:
3937:"The Geometry of Orbits: Ellipses, Parabolas, and Hyperbolas"
3648:
3620:
2570:
1132:
1122:{\displaystyle a={\frac {r_{\text{max}}+r_{\text{min}}}{2}}.}
190:
3676:
3444:{\displaystyle {\frac {a}{b}}={\frac {1}{\sqrt {1-e^{2}}}}}
2751:
595:, with ends at the two most widely separated points of the
3081:
Energy; calculation of semi-major axis from state vectors
3017:
The time-averaged value of the reciprocal of the radius,
2095:
In a hyperbola, a conjugate axis or minor axis of length
1187:{\displaystyle b={\sqrt {r_{\text{max}}r_{\text{min}}}}.}
646:
of an ellipse is related to the semi-minor axis's length
3849:. New York: Cambridge University Press. pp. 24–31.
2891:
orbital semi-major axis, depending on the eccentricity.
2729:{\displaystyle T^{2}={\frac {4\pi ^{2}}{G(M+m)}}a^{3},}
3461:
3402:
3388:
Semi-major and semi-minor axes of the planets' orbits
3361:
3275:
3200:
3154:
3105:
3053:
3023:
2965:
2912:
2776:
2660:
2597:
2538:
2472:
2433:
2410:{\displaystyle T=2\pi {\sqrt {\frac {a^{3}}{\mu }}},}
2372:
2258:
2173:
2128:
2101:
2045:
1935:
1835:
1794:
1697:
1675:
1593:
1565:
1539:
1493:
1447:
1392:
1364:
1272:
1255:{\displaystyle e={\sqrt {1-{\frac {b^{2}}{a^{2}}}}},}
1208:
1150:
1077:
1048:
1021:
891:
838:
688:
666:
3006:{\displaystyle a\left(1+{\frac {e^{2}}{2}}\right)\,}
1358:, with one focus at the origin and the other on the
2565:, the semi-major axis is one of the most important
60:. Unsourced material may be challenged and removed.
3817:1 AU (astronomical unit) equals 149.6 million km.
3517:
3443:
3367:
3293:
3253:
3178:
3132:
3069:
3039:
3005:
2944:
2788:
2728:
2626:
2544:
2516:
2439:
2409:
2293:
2233:
2149:
2110:
2082:
2027:
1889:
1800:
1774:
1681:
1630:
1577:
1551:
1525:
1479:
1431:
1376:
1344:
1254:
1186:
1121:
1061:
1034:
982:
844:
807:
672:
4830:
3844:
3133:{\displaystyle a=-{\frac {\mu }{2\varepsilon }}}
3179:{\displaystyle a={\frac {\mu }{2\varepsilon }}}
3840:
3838:
3836:
3834:
3832:
3830:
3146:and, depending on the convention, the same or
4039:
2425:is the length of the orbit's semi-major axis,
1890:{\displaystyle 2b={\sqrt {(p+q)^{2}-f^{2}}},}
1131:In astronomy these extreme points are called
552:
4018:Semi-major and semi-minor axes of an ellipse
3375:is the specific energy of the orbiting body.
3827:
2858:. Unsourced material may be challenged and
2517:{\displaystyle h={\sqrt {a\mu (1-e^{2})}},}
1631:{\displaystyle a={\frac {\ell }{1-e^{2}}}.}
1004:, in which an arbitrary point is given by (
4813:
4046:
4032:
3845:Lissauer, Jack J.; de Pater, Imke (2019).
3333:of an orbiting object in coordinates of a
1640:In an ellipse, the semi-major axis is the
559:
545:
3002:
2878:Learn how and when to remove this message
1432:{\displaystyle r(1+e\cos \theta )=\ell .}
1138:The semi-minor axis of an ellipse is the
120:Learn how and when to remove this message
4053:
3978:
3353:is the mass of the gravitating body, and
2323:
2083:{\displaystyle a={\ell \over e^{2}-1}.}
131:
14:
4831:
4692:Transposition, docking, and extraction
2899:indeed results in the semi-major axis.
591:that runs through the center and both
4027:
3881:
2294:{\displaystyle b=a{\sqrt {e^{2}-1}}.}
2945:{\displaystyle b=a{\sqrt {1-e^{2}}}}
2856:adding citations to reliable sources
2823:
2765:The orbiting body's path around the
1927:in the x-direction the equation is:
58:adding citations to reliable sources
29:
3872:, Math Open Reference, 12 May 2013.
2819:
2627:{\displaystyle T^{2}\propto a^{3},}
24:
3955:"7.1 Alternative Characterization"
3908:"7.1 Alternative Characterization"
3870:"Major / Minor axis of an ellipse"
1903:is the distance between the foci,
1658:is related to the semi-major axis
1000:) is the center of the ellipse in
642:The length of the semi-major axis
25:
4855:
4752:Kepler's laws of planetary motion
4011:
2558:is the eccentricity of the orbit.
2319:
871:The major and minor axes are the
331:Kepler's laws of planetary motion
4812:
4747:Interplanetary Transport Network
4627:Collision avoidance (spacecraft)
3305:standard gravitational parameter
3239:
2895:averaging the distance over the
2828:
2449:standard gravitational parameter
161:
69:"Semi-major and semi-minor axes"
34:
4712:Astronomical coordinate systems
4466:Longitude of the ascending node
1307:
45:needs additional citations for
4785:Retrograde and prograde motion
3972:
3947:
3929:
3900:
3875:
3863:
3244:
3234:
2707:
2695:
2506:
2487:
2144:
2129:
1860:
1847:
1520:
1508:
1474:
1462:
1417:
1396:
1336:
1324:
1301:
1289:
1062:{\displaystyle r_{\text{min}}}
1035:{\displaystyle r_{\text{max}}}
949:
936:
908:
895:
883:The equation of an ellipse is
765:
746:
13:
1:
3820:
1526:{\displaystyle r=\ell /(1+e)}
1480:{\displaystyle r=\ell /(1-e)}
1354:Now consider the equation in
627:is a line segment that is at
4732:Equatorial coordinate system
3368:{\displaystyle \varepsilon }
2314:
1914:
1552:{\displaystyle \theta =\pi }
1377:{\displaystyle \theta =\pi }
1200:of an ellipse is defined as
615:, and to the perimeter. The
7:
3981:American Journal of Physics
485:Tsiolkovsky rocket equation
10:
4860:
4484:Longitude of the periapsis
4020:With interactive animation
878:
454:Engineering and efficiency
273:Bi-elliptic transfer orbit
4808:
4795:Specific angular momentum
4700:
4612:
4556:
4492:
4445:
4385:
4376:
4272:
4182:
4071:
4062:
3314:is orbital velocity from
2754:of the central body, and
2459:specific angular momentum
2303:Note that in a hyperbola
2150:{\displaystyle (0,\pm b)}
1919:The semi-major axis of a
1662:through the eccentricity
1578:{\displaystyle \theta =0}
817:The semi-major axis of a
3294:{\displaystyle \mu =GM,}
2349:is constant (green line)
480:Propellant mass fraction
379:Gravitational influences
4790:Specific orbital energy
3529:is easily visualized.
3382:specific orbital energy
3265:specific orbital energy
3093:can be calculated from
2328:Log-log plot of period
351:Specific orbital energy
140:) and semi-minor axis (
4202:Geostationary transfer
3519:
3445:
3369:
3345:gravitational constant
3318:of an orbiting object,
3295:
3255:
3180:
3134:
3089:, the semi-major axis
3071:
3070:{\displaystyle a^{-1}}
3041:
3040:{\displaystyle r^{-1}}
3007:
2946:
2790:
2789:{\displaystyle M\gg m}
2744:gravitational constant
2730:
2628:
2546:
2518:
2441:
2411:
2350:
2295:
2235:
2151:
2112:
2084:
2029:
1891:
1802:
1776:
1683:
1632:
1579:
1553:
1527:
1481:
1433:
1378:
1346:
1256:
1188:
1123:
1063:
1036:
984:
846:
809:
674:
268:Hohmann transfer orbit
145:
4775:Orbital state vectors
4717:Characteristic energy
4687:Trans-lunar injection
4475:Argument of periapsis
4152:Prograde / Retrograde
4113:Hyperbolic trajectory
3888:mathworld.wolfram.com
3520:
3446:
3370:
3296:
3256:
3190:hyperbolic trajectory
3181:
3135:
3095:orbital state vectors
3072:
3042:
3008:
2947:
2791:
2731:
2629:
2552:are as defined above,
2547:
2519:
2442:
2412:
2327:
2296:
2236:
2152:
2113:
2085:
2030:
1892:
1803:
1801:{\displaystyle \ell }
1777:
1684:
1682:{\displaystyle \ell }
1633:
1580:
1554:
1528:
1482:
1434:
1379:
1347:
1257:
1189:
1124:
1064:
1037:
1002:Cartesian coordinates
985:
847:
845:{\displaystyle \ell }
810:
675:
673:{\displaystyle \ell }
464:Preflight engineering
196:Argument of periapsis
135:
4622:Bi-elliptic transfer
4142:Parabolic trajectory
3459:
3400:
3359:
3273:
3198:
3152:
3103:
3051:
3021:
2963:
2910:
2852:improve this section
2774:
2658:
2595:
2545:{\displaystyle \mu }
2536:
2470:
2451:of the central body.
2440:{\displaystyle \mu }
2431:
2370:
2256:
2171:
2126:
2099:
2043:
1933:
1833:
1792:
1695:
1673:
1654:The semi-minor axis
1591:
1563:
1537:
1491:
1445:
1390:
1362:
1270:
1206:
1148:
1142:of these distances:
1075:
1046:
1019:
889:
836:
686:
664:
520:Propulsive maneuvers
54:improve this article
4662:Low-energy transfer
3993:2003AmJPh..71.1198W
3882:Weisstein, Eric W.
3527:Kepler's second law
2955:averaging over the
2902:averaging over the
2648:, as determined by
2640:is the period, and
2332:vs semi-major axis
2307:can be larger than
623:) of an ellipse or
497:Efficiency measures
400:Sphere of influence
369:Celestial mechanics
151:Part of a series on
4657:Inclination change
4305:Distant retrograde
3515:
3441:
3394:Kepler's first law
3365:
3291:
3251:
3176:
3130:
3067:
3037:
3003:
2942:
2786:
2726:
2624:
2583:Kepler's third law
2542:
2514:
2437:
2407:
2351:
2291:
2231:
2147:
2111:{\displaystyle 2b}
2108:
2080:
2025:
1887:
1816:tend to infinity,
1798:
1772:
1770:
1679:
1628:
1575:
1549:
1523:
1477:
1441:The mean value of
1429:
1374:
1342:
1252:
1184:
1119:
1059:
1032:
980:
860:tend to infinity,
842:
825:of the hyperbola.
805:
803:
670:
316:Dynamical friction
146:
4826:
4825:
4800:Two-line elements
4608:
4607:
4530:Eccentric anomaly
4372:
4371:
4239:Orbit of the Moon
4098:Highly elliptical
4001:10.1119/1.1578073
3987:(11): 1198–1200.
3912:www.geom.uiuc.edu
3815:
3814:
3513:
3484:
3481:
3471:
3439:
3438:
3411:
3249:
3222:
3174:
3128:
2995:
2940:
2897:eccentric anomaly
2888:
2887:
2880:
2711:
2573:, along with its
2509:
2402:
2401:
2286:
2223:
2196:
2075:
2017:
1974:
1882:
1733:
1668:semi-latus rectum
1623:
1356:polar coordinates
1315:
1280:
1247:
1245:
1179:
1176:
1166:
1114:
1107:
1094:
1056:
1029:
969:
928:
724:
659:semi-latus rectum
607:) is the longest
569:
568:
419:Lagrangian points
356:Vis-viva equation
326:Kepler's equation
173:Orbital mechanics
130:
129:
122:
104:
16:(Redirected from
4851:
4816:
4815:
4757:Lagrangian point
4652:Hohmann transfer
4597:
4583:
4574:
4565:
4545:
4536:
4527:
4518:
4514:
4510:
4501:
4481:
4472:
4463:
4454:
4434:
4430:
4421:
4412:
4403:
4383:
4382:
4352:Heliosynchronous
4301:Lagrange points
4254:Transatmospheric
4069:
4068:
4048:
4041:
4034:
4025:
4024:
4005:
4004:
3976:
3970:
3969:
3967:
3966:
3957:. Archived from
3951:
3945:
3944:
3933:
3927:
3926:
3924:
3923:
3914:. Archived from
3904:
3898:
3897:
3895:
3894:
3879:
3873:
3867:
3861:
3860:
3842:
3553:Semi-minor axis
3542:Semi-major axis
3532:
3531:
3524:
3522:
3521:
3516:
3514:
3512:
3501:
3490:
3485:
3483:
3482:
3479:
3473:
3472:
3469:
3463:
3450:
3448:
3447:
3442:
3440:
3437:
3436:
3421:
3417:
3412:
3404:
3374:
3372:
3371:
3366:
3352:
3342:
3325:
3313:
3300:
3298:
3297:
3292:
3260:
3258:
3257:
3252:
3250:
3248:
3247:
3242:
3237:
3228:
3223:
3218:
3217:
3208:
3185:
3183:
3182:
3177:
3175:
3173:
3162:
3144:elliptical orbit
3139:
3137:
3136:
3131:
3129:
3127:
3116:
3092:
3076:
3074:
3073:
3068:
3066:
3065:
3046:
3044:
3043:
3038:
3036:
3035:
3012:
3010:
3009:
3004:
3001:
2997:
2996:
2991:
2990:
2981:
2951:
2949:
2948:
2943:
2941:
2939:
2938:
2923:
2883:
2876:
2872:
2869:
2863:
2832:
2824:
2820:Average distance
2802:
2801:
2795:
2793:
2792:
2787:
2761:
2757:
2749:
2741:
2735:
2733:
2732:
2727:
2722:
2721:
2712:
2710:
2690:
2689:
2688:
2675:
2670:
2669:
2646:two-body problem
2643:
2639:
2633:
2631:
2630:
2625:
2620:
2619:
2607:
2606:
2567:orbital elements
2557:
2551:
2549:
2548:
2543:
2531:
2523:
2521:
2520:
2515:
2510:
2505:
2504:
2480:
2463:
2446:
2444:
2443:
2438:
2424:
2416:
2414:
2413:
2408:
2403:
2397:
2396:
2387:
2386:
2363:
2348:
2347:
2335:
2331:
2310:
2306:
2300:
2298:
2297:
2292:
2287:
2279:
2278:
2269:
2245:impact parameter
2240:
2238:
2237:
2232:
2224:
2222:
2221:
2212:
2211:
2202:
2197:
2195:
2194:
2185:
2184:
2175:
2164:
2160:
2156:
2154:
2153:
2148:
2117:
2115:
2114:
2109:
2089:
2087:
2086:
2081:
2076:
2074:
2067:
2066:
2053:
2034:
2032:
2031:
2026:
2018:
2016:
2015:
2006:
2005:
2000:
1996:
1980:
1975:
1973:
1972:
1963:
1962:
1957:
1953:
1937:
1926:
1910:
1906:
1902:
1896:
1894:
1893:
1888:
1883:
1881:
1880:
1868:
1867:
1846:
1823:
1819:
1815:
1811:
1807:
1805:
1804:
1799:
1781:
1779:
1778:
1773:
1771:
1764:
1763:
1734:
1732:
1731:
1716:
1688:
1686:
1685:
1680:
1665:
1661:
1657:
1637:
1635:
1634:
1629:
1624:
1622:
1621:
1620:
1601:
1584:
1582:
1581:
1576:
1558:
1556:
1555:
1550:
1532:
1530:
1529:
1524:
1507:
1486:
1484:
1483:
1478:
1461:
1438:
1436:
1435:
1430:
1383:
1381:
1380:
1375:
1351:
1349:
1348:
1343:
1317:
1316:
1313:
1282:
1281:
1278:
1261:
1259:
1258:
1253:
1248:
1246:
1244:
1243:
1234:
1233:
1224:
1216:
1193:
1191:
1190:
1185:
1180:
1178:
1177:
1174:
1168:
1167:
1164:
1158:
1128:
1126:
1125:
1120:
1115:
1110:
1109:
1108:
1105:
1096:
1095:
1092:
1085:
1068:
1066:
1065:
1060:
1058:
1057:
1054:
1041:
1039:
1038:
1033:
1031:
1030:
1027:
989:
987:
986:
981:
970:
968:
967:
958:
957:
956:
934:
929:
927:
926:
917:
916:
915:
893:
873:axes of symmetry
867:
863:
859:
855:
851:
849:
848:
843:
814:
812:
811:
806:
804:
797:
796:
764:
763:
725:
723:
722:
707:
679:
677:
676:
671:
656:
649:
645:
561:
554:
547:
526:Orbital maneuver
475:Payload fraction
455:
436:Lissajous orbits
370:
341:Orbital velocity
288:Hyperbolic orbit
184:Orbital elements
174:
165:
148:
147:
136:The semi-major (
125:
118:
114:
111:
105:
103:
62:
38:
30:
21:
4859:
4858:
4854:
4853:
4852:
4850:
4849:
4848:
4829:
4828:
4827:
4822:
4804:
4722:Escape velocity
4703:
4696:
4677:Rocket equation
4604:
4596:
4590:
4581:
4572:
4563:
4552:
4543:
4534:
4525:
4516:
4512:
4508:
4499:
4488:
4479:
4470:
4461:
4452:
4441:
4432:
4428:
4424:Semi-minor axis
4419:
4415:Semi-major axis
4410:
4401:
4395:
4368:
4290:Areosynchronous
4274:
4268:
4249:Sun-synchronous
4234:Near-equatorial
4178:
4058:
4052:
4014:
4009:
4008:
3977:
3973:
3964:
3962:
3953:
3952:
3948:
3935:
3934:
3930:
3921:
3919:
3906:
3905:
3901:
3892:
3890:
3880:
3876:
3868:
3864:
3857:
3843:
3828:
3823:
3587:Difference (%)
3564:Difference (%)
3502:
3491:
3489:
3478:
3474:
3468:
3464:
3462:
3460:
3457:
3456:
3432:
3428:
3416:
3403:
3401:
3398:
3397:
3390:
3360:
3357:
3356:
3350:
3340:
3335:reference frame
3331:position vector
3321:
3316:velocity vector
3311:
3301:
3274:
3271:
3270:
3261:
3243:
3238:
3233:
3232:
3227:
3213:
3209:
3207:
3199:
3196:
3195:
3186:
3166:
3161:
3153:
3150:
3149:
3140:
3120:
3115:
3104:
3101:
3100:
3090:
3083:
3058:
3054:
3052:
3049:
3048:
3028:
3024:
3022:
3019:
3018:
2986:
2982:
2980:
2973:
2969:
2964:
2961:
2960:
2934:
2930:
2922:
2911:
2908:
2907:
2884:
2873:
2867:
2864:
2849:
2833:
2822:
2799:
2797:
2775:
2772:
2771:
2759:
2755:
2747:
2739:
2736:
2717:
2713:
2691:
2684:
2680:
2676:
2674:
2665:
2661:
2659:
2656:
2655:
2641:
2637:
2634:
2615:
2611:
2602:
2598:
2596:
2593:
2592:
2559:
2555:
2553:
2537:
2534:
2533:
2529:
2524:
2500:
2496:
2479:
2471:
2468:
2467:
2461:
2452:
2432:
2429:
2428:
2426:
2422:
2417:
2392:
2388:
2385:
2371:
2368:
2367:
2361:
2345:
2341: /
2337:
2333:
2329:
2322:
2317:
2308:
2304:
2301:
2274:
2270:
2268:
2257:
2254:
2253:
2241:
2217:
2213:
2207:
2203:
2201:
2190:
2186:
2180:
2176:
2174:
2172:
2169:
2168:
2162:
2158:
2127:
2124:
2123:
2100:
2097:
2096:
2090:
2062:
2058:
2057:
2052:
2044:
2041:
2040:
2035:
2011:
2007:
2001:
1986:
1982:
1981:
1979:
1968:
1964:
1958:
1943:
1939:
1938:
1936:
1934:
1931:
1930:
1924:
1917:
1908:
1904:
1900:
1897:
1876:
1872:
1863:
1859:
1845:
1834:
1831:
1830:
1821:
1817:
1813:
1809:
1793:
1790:
1789:
1782:
1769:
1768:
1759:
1755:
1748:
1739:
1738:
1727:
1723:
1715:
1705:
1698:
1696:
1693:
1692:
1674:
1671:
1670:
1663:
1659:
1655:
1638:
1616:
1612:
1605:
1600:
1592:
1589:
1588:
1564:
1561:
1560:
1538:
1535:
1534:
1503:
1492:
1489:
1488:
1457:
1446:
1443:
1442:
1439:
1391:
1388:
1387:
1363:
1360:
1359:
1352:
1312:
1308:
1277:
1273:
1271:
1268:
1267:
1262:
1239:
1235:
1229:
1225:
1223:
1215:
1207:
1204:
1203:
1194:
1173:
1169:
1163:
1159:
1157:
1149:
1146:
1145:
1129:
1104:
1100:
1091:
1087:
1086:
1084:
1076:
1073:
1072:
1053:
1049:
1047:
1044:
1043:
1026:
1022:
1020:
1017:
1016:
990:
963:
959:
952:
948:
935:
933:
922:
918:
911:
907:
894:
892:
890:
887:
886:
881:
865:
861:
857:
853:
837:
834:
833:
815:
802:
801:
792:
788:
781:
772:
771:
759:
755:
736:
730:
729:
718:
714:
706:
696:
689:
687:
684:
683:
665:
662:
661:
654:
647:
643:
639:of the circle.
617:semi-minor axis
601:semi-major axis
583:is its longest
565:
536:
535:
531:Orbit insertion
521:
513:
512:
498:
490:
489:
465:
457:
453:
446:
445:
441:Lyapunov orbits
432:
431:
415:
405:
404:
380:
372:
368:
361:
360:
346:Surface gravity
321:Escape velocity
311:
303:
302:
283:Parabolic orbit
279:
278:
245:
243:
240:two-body orbits
231:
230:
221:Semi-major axis
186:
176:
172:
144:) of an ellipse
126:
115:
109:
106:
63:
61:
51:
39:
28:
23:
22:
15:
12:
11:
5:
4857:
4847:
4846:
4841:
4839:Conic sections
4824:
4823:
4821:
4820:
4818:List of orbits
4809:
4806:
4805:
4803:
4802:
4797:
4792:
4787:
4782:
4777:
4772:
4770:Orbit equation
4767:
4759:
4754:
4749:
4744:
4739:
4734:
4729:
4724:
4719:
4714:
4708:
4706:
4698:
4697:
4695:
4694:
4689:
4684:
4679:
4674:
4669:
4664:
4659:
4654:
4649:
4644:
4642:Gravity assist
4639:
4637:Delta-v budget
4634:
4629:
4624:
4618:
4616:
4610:
4609:
4606:
4605:
4603:
4602:
4594:
4588:
4579:
4570:
4568:Orbital period
4560:
4558:
4554:
4553:
4551:
4550:
4548:True longitude
4541:
4539:Mean longitude
4532:
4523:
4506:
4496:
4494:
4490:
4489:
4487:
4486:
4477:
4468:
4459:
4449:
4447:
4443:
4442:
4440:
4439:
4426:
4417:
4408:
4398:
4396:
4394:
4393:
4390:
4386:
4380:
4374:
4373:
4370:
4369:
4367:
4366:
4365:
4364:
4356:
4355:
4354:
4349:
4344:
4343:
4342:
4329:
4324:
4323:
4322:
4317:
4312:
4307:
4299:
4298:
4297:
4295:Areostationary
4292:
4287:
4278:
4276:
4270:
4269:
4267:
4266:
4264:Very low Earth
4261:
4256:
4251:
4246:
4241:
4236:
4231:
4226:
4221:
4216:
4211:
4206:
4205:
4204:
4199:
4192:Geosynchronous
4188:
4186:
4180:
4179:
4177:
4176:
4174:Transfer orbit
4171:
4170:
4169:
4164:
4154:
4149:
4144:
4139:
4134:
4132:Lagrange point
4129:
4124:
4115:
4110:
4105:
4100:
4091:
4086:
4081:
4075:
4073:
4066:
4060:
4059:
4054:Gravitational
4051:
4050:
4043:
4036:
4028:
4022:
4021:
4013:
4012:External links
4010:
4007:
4006:
3971:
3946:
3928:
3899:
3874:
3862:
3855:
3825:
3824:
3822:
3819:
3813:
3812:
3809:
3806:
3803:
3800:
3797:
3794:
3791:
3785:
3784:
3781:
3778:
3775:
3772:
3769:
3766:
3763:
3757:
3756:
3753:
3750:
3747:
3744:
3741:
3738:
3735:
3729:
3728:
3725:
3722:
3719:
3716:
3713:
3710:
3707:
3701:
3700:
3697:
3694:
3691:
3688:
3685:
3682:
3679:
3673:
3672:
3669:
3666:
3663:
3660:
3657:
3654:
3651:
3645:
3644:
3641:
3638:
3635:
3632:
3629:
3626:
3623:
3617:
3616:
3613:
3610:
3607:
3604:
3601:
3598:
3595:
3589:
3588:
3585:
3575:
3565:
3562:
3551:
3540:
3535:
3511:
3508:
3505:
3500:
3497:
3494:
3488:
3477:
3467:
3435:
3431:
3427:
3424:
3420:
3415:
3410:
3407:
3389:
3386:
3377:
3376:
3364:
3354:
3348:
3338:
3319:
3290:
3287:
3284:
3281:
3278:
3269:
3246:
3241:
3236:
3231:
3226:
3221:
3216:
3212:
3206:
3203:
3194:
3172:
3169:
3165:
3160:
3157:
3148:
3126:
3123:
3119:
3114:
3111:
3108:
3099:
3082:
3079:
3064:
3061:
3057:
3034:
3031:
3027:
3015:
3014:
3000:
2994:
2989:
2985:
2979:
2976:
2972:
2968:
2953:
2937:
2933:
2929:
2926:
2921:
2918:
2915:
2900:
2886:
2885:
2836:
2834:
2827:
2821:
2818:
2785:
2782:
2779:
2725:
2720:
2716:
2709:
2706:
2703:
2700:
2697:
2694:
2687:
2683:
2679:
2673:
2668:
2664:
2654:
2623:
2618:
2614:
2610:
2605:
2601:
2591:
2575:orbital period
2554:
2541:
2528:
2513:
2508:
2503:
2499:
2495:
2492:
2489:
2486:
2483:
2478:
2475:
2466:
2436:
2427:
2421:
2406:
2400:
2395:
2391:
2384:
2381:
2378:
2375:
2366:
2359:orbital period
2321:
2320:Orbital period
2318:
2316:
2313:
2290:
2285:
2282:
2277:
2273:
2267:
2264:
2261:
2252:
2230:
2227:
2220:
2216:
2210:
2206:
2200:
2193:
2189:
2183:
2179:
2167:
2146:
2143:
2140:
2137:
2134:
2131:
2107:
2104:
2079:
2073:
2070:
2065:
2061:
2056:
2051:
2048:
2039:
2024:
2021:
2014:
2010:
2004:
1999:
1995:
1992:
1989:
1985:
1978:
1971:
1967:
1961:
1956:
1952:
1949:
1946:
1942:
1929:
1916:
1913:
1886:
1879:
1875:
1871:
1866:
1862:
1858:
1855:
1852:
1849:
1844:
1841:
1838:
1829:
1797:
1767:
1762:
1758:
1754:
1751:
1749:
1747:
1744:
1741:
1740:
1737:
1730:
1726:
1722:
1719:
1714:
1711:
1708:
1706:
1704:
1701:
1700:
1691:
1689:, as follows:
1678:
1642:geometric mean
1627:
1619:
1615:
1611:
1608:
1604:
1599:
1596:
1587:
1574:
1571:
1568:
1548:
1545:
1542:
1522:
1519:
1516:
1513:
1510:
1506:
1502:
1499:
1496:
1476:
1473:
1470:
1467:
1464:
1460:
1456:
1453:
1450:
1428:
1425:
1422:
1419:
1416:
1413:
1410:
1407:
1404:
1401:
1398:
1395:
1386:
1373:
1370:
1367:
1341:
1338:
1335:
1332:
1329:
1326:
1323:
1320:
1311:
1306:
1303:
1300:
1297:
1294:
1291:
1288:
1285:
1276:
1266:
1251:
1242:
1238:
1232:
1228:
1222:
1219:
1214:
1211:
1202:
1183:
1172:
1162:
1156:
1153:
1144:
1140:geometric mean
1118:
1113:
1103:
1099:
1090:
1083:
1080:
1071:
1052:
1025:
979:
976:
973:
966:
962:
955:
951:
947:
944:
941:
938:
932:
925:
921:
914:
910:
906:
903:
900:
897:
885:
880:
877:
841:
800:
795:
791:
787:
784:
782:
780:
777:
774:
773:
770:
767:
762:
758:
754:
751:
748:
745:
742:
739:
737:
735:
732:
731:
728:
721:
717:
713:
710:
705:
702:
699:
697:
695:
692:
691:
682:
680:, as follows:
669:
621:minor semiaxis
605:major semiaxis
567:
566:
564:
563:
556:
549:
541:
538:
537:
534:
533:
528:
522:
519:
518:
515:
514:
511:
510:
505:
503:Gravity assist
499:
496:
495:
492:
491:
488:
487:
482:
477:
472:
466:
463:
462:
459:
458:
451:
448:
447:
444:
443:
438:
430:
429:
421:
417:
416:
411:
410:
407:
406:
403:
402:
397:
392:
387:
381:
378:
377:
374:
373:
366:
363:
362:
359:
358:
353:
348:
343:
338:
336:Orbital period
333:
328:
323:
318:
312:
309:
308:
305:
304:
301:
300:
298:Decaying orbit
295:
290:
285:
277:
276:
270:
263:
261:Transfer orbit
259:
258:
257:
255:Elliptic orbit
252:
250:Circular orbit
246:
237:
236:
233:
232:
229:
228:
223:
218:
213:
208:
203:
198:
193:
187:
182:
181:
178:
177:
170:
167:
166:
158:
157:
153:
152:
128:
127:
42:
40:
33:
26:
9:
6:
4:
3:
2:
4856:
4845:
4842:
4840:
4837:
4836:
4834:
4819:
4811:
4810:
4807:
4801:
4798:
4796:
4793:
4791:
4788:
4786:
4783:
4781:
4778:
4776:
4773:
4771:
4768:
4766:
4765:-body problem
4764:
4760:
4758:
4755:
4753:
4750:
4748:
4745:
4743:
4740:
4738:
4735:
4733:
4730:
4728:
4725:
4723:
4720:
4718:
4715:
4713:
4710:
4709:
4707:
4705:
4699:
4693:
4690:
4688:
4685:
4683:
4680:
4678:
4675:
4673:
4670:
4668:
4667:Oberth effect
4665:
4663:
4660:
4658:
4655:
4653:
4650:
4648:
4645:
4643:
4640:
4638:
4635:
4633:
4630:
4628:
4625:
4623:
4620:
4619:
4617:
4615:
4611:
4601:
4593:
4589:
4587:
4586:Orbital speed
4580:
4578:
4571:
4569:
4562:
4561:
4559:
4555:
4549:
4542:
4540:
4533:
4531:
4524:
4522:
4507:
4505:
4498:
4497:
4495:
4491:
4485:
4478:
4476:
4469:
4467:
4460:
4458:
4451:
4450:
4448:
4444:
4438:
4427:
4425:
4418:
4416:
4409:
4407:
4400:
4399:
4397:
4391:
4388:
4387:
4384:
4381:
4379:
4375:
4363:
4360:
4359:
4357:
4353:
4350:
4348:
4345:
4341:
4340:Earth's orbit
4338:
4337:
4336:
4333:
4332:
4330:
4328:
4325:
4321:
4318:
4316:
4313:
4311:
4308:
4306:
4303:
4302:
4300:
4296:
4293:
4291:
4288:
4286:
4283:
4282:
4280:
4279:
4277:
4271:
4265:
4262:
4260:
4257:
4255:
4252:
4250:
4247:
4245:
4242:
4240:
4237:
4235:
4232:
4230:
4227:
4225:
4222:
4220:
4217:
4215:
4212:
4210:
4207:
4203:
4200:
4198:
4197:Geostationary
4195:
4194:
4193:
4190:
4189:
4187:
4185:
4181:
4175:
4172:
4168:
4165:
4163:
4160:
4159:
4158:
4155:
4153:
4150:
4148:
4145:
4143:
4140:
4138:
4135:
4133:
4130:
4128:
4125:
4123:
4119:
4116:
4114:
4111:
4109:
4106:
4104:
4101:
4099:
4095:
4092:
4090:
4087:
4085:
4082:
4080:
4077:
4076:
4074:
4070:
4067:
4065:
4061:
4057:
4049:
4044:
4042:
4037:
4035:
4030:
4029:
4026:
4019:
4016:
4015:
4002:
3998:
3994:
3990:
3986:
3982:
3975:
3961:on 2018-10-24
3960:
3956:
3950:
3942:
3938:
3932:
3918:on 2018-10-24
3917:
3913:
3909:
3903:
3889:
3885:
3878:
3871:
3866:
3858:
3856:9781108411981
3852:
3848:
3841:
3839:
3837:
3835:
3833:
3831:
3826:
3818:
3810:
3807:
3804:
3801:
3798:
3795:
3792:
3790:
3787:
3786:
3782:
3779:
3776:
3773:
3770:
3767:
3764:
3762:
3759:
3758:
3754:
3751:
3748:
3745:
3742:
3739:
3736:
3734:
3731:
3730:
3726:
3723:
3720:
3717:
3714:
3711:
3708:
3706:
3703:
3702:
3698:
3695:
3692:
3689:
3686:
3683:
3680:
3678:
3675:
3674:
3670:
3667:
3664:
3661:
3658:
3655:
3652:
3650:
3647:
3646:
3642:
3639:
3636:
3633:
3630:
3627:
3624:
3622:
3619:
3618:
3614:
3611:
3608:
3605:
3602:
3599:
3596:
3594:
3591:
3590:
3586:
3583:
3579:
3576:
3573:
3569:
3566:
3563:
3560:
3556:
3552:
3549:
3545:
3541:
3539:
3536:
3534:
3533:
3530:
3528:
3509:
3506:
3503:
3498:
3495:
3492:
3486:
3475:
3465:
3452:
3433:
3429:
3425:
3422:
3418:
3413:
3408:
3405:
3395:
3385:
3383:
3362:
3355:
3349:
3346:
3339:
3336:
3332:
3329:
3324:
3320:
3317:
3310:
3309:
3308:
3306:
3288:
3285:
3282:
3279:
3276:
3268:
3266:
3229:
3224:
3219:
3214:
3210:
3204:
3201:
3193:
3191:
3170:
3167:
3163:
3158:
3155:
3147:
3145:
3124:
3121:
3117:
3112:
3109:
3106:
3098:
3096:
3088:
3087:astrodynamics
3078:
3062:
3059:
3055:
3032:
3029:
3025:
2998:
2992:
2987:
2983:
2977:
2974:
2970:
2966:
2958:
2954:
2935:
2931:
2927:
2924:
2919:
2916:
2913:
2905:
2901:
2898:
2894:
2893:
2892:
2882:
2879:
2871:
2861:
2857:
2853:
2847:
2846:
2842:
2837:This section
2835:
2831:
2826:
2825:
2817:
2814:
2810:
2806:
2783:
2780:
2777:
2768:
2763:
2753:
2745:
2723:
2718:
2714:
2704:
2701:
2698:
2692:
2685:
2681:
2677:
2671:
2666:
2662:
2653:
2651:
2647:
2621:
2616:
2612:
2608:
2603:
2599:
2590:
2588:
2584:
2580:
2576:
2572:
2568:
2564:
2539:
2527:
2511:
2501:
2497:
2493:
2490:
2484:
2481:
2476:
2473:
2465:
2460:
2455:
2450:
2434:
2420:
2404:
2398:
2393:
2389:
2382:
2379:
2376:
2373:
2365:
2360:
2356:
2355:astrodynamics
2344:
2340:
2326:
2312:
2288:
2283:
2280:
2275:
2271:
2265:
2262:
2259:
2251:
2248:
2246:
2228:
2225:
2218:
2214:
2208:
2204:
2198:
2191:
2187:
2181:
2177:
2166:
2141:
2138:
2135:
2132:
2121:
2105:
2102:
2093:
2077:
2071:
2068:
2063:
2059:
2054:
2049:
2046:
2038:
2022:
2019:
2012:
2008:
2002:
1997:
1993:
1990:
1987:
1983:
1976:
1969:
1965:
1959:
1954:
1950:
1947:
1944:
1940:
1928:
1922:
1912:
1884:
1877:
1873:
1869:
1864:
1856:
1853:
1850:
1842:
1839:
1836:
1828:
1825:
1795:
1787:
1765:
1760:
1756:
1752:
1750:
1745:
1742:
1735:
1728:
1724:
1720:
1717:
1712:
1709:
1707:
1702:
1690:
1676:
1669:
1652:
1650:
1645:
1643:
1625:
1617:
1613:
1609:
1606:
1602:
1597:
1594:
1586:
1572:
1569:
1566:
1546:
1543:
1540:
1517:
1514:
1511:
1504:
1500:
1497:
1494:
1471:
1468:
1465:
1458:
1454:
1451:
1448:
1426:
1423:
1420:
1414:
1411:
1408:
1405:
1402:
1399:
1393:
1385:
1371:
1368:
1365:
1357:
1339:
1333:
1330:
1327:
1321:
1318:
1309:
1304:
1298:
1295:
1292:
1286:
1283:
1274:
1265:
1249:
1240:
1236:
1230:
1226:
1220:
1217:
1212:
1209:
1201:
1199:
1181:
1170:
1160:
1154:
1151:
1143:
1141:
1136:
1134:
1116:
1111:
1101:
1097:
1088:
1081:
1078:
1070:
1050:
1023:
1013:
1011:
1007:
1003:
999:
995:
977:
974:
971:
964:
960:
953:
945:
942:
939:
930:
923:
919:
912:
904:
901:
898:
884:
876:
874:
869:
839:
831:
826:
824:
820:
798:
793:
789:
785:
783:
778:
775:
768:
760:
756:
752:
749:
743:
740:
738:
733:
726:
719:
715:
711:
708:
703:
700:
698:
693:
681:
667:
660:
653:
640:
638:
634:
633:conic section
630:
626:
622:
618:
614:
610:
606:
602:
598:
594:
590:
586:
582:
578:
574:
562:
557:
555:
550:
548:
543:
542:
540:
539:
532:
529:
527:
524:
523:
517:
516:
509:
508:Oberth effect
506:
504:
501:
500:
494:
493:
486:
483:
481:
478:
476:
473:
471:
468:
467:
461:
460:
456:
450:
449:
442:
439:
437:
434:
433:
427:
423:
422:
420:
414:
413:N-body orbits
409:
408:
401:
398:
396:
395:Perturbations
393:
391:
388:
386:
383:
382:
376:
375:
371:
365:
364:
357:
354:
352:
349:
347:
344:
342:
339:
337:
334:
332:
329:
327:
324:
322:
319:
317:
314:
313:
307:
306:
299:
296:
294:
291:
289:
286:
284:
281:
280:
274:
271:
269:
265:
264:
262:
256:
253:
251:
248:
247:
241:
235:
234:
227:
224:
222:
219:
217:
216:Orbital nodes
214:
212:
209:
207:
204:
202:
199:
197:
194:
192:
189:
188:
185:
180:
179:
175:
169:
168:
164:
160:
159:
156:Astrodynamics
155:
154:
150:
149:
143:
139:
134:
124:
121:
113:
102:
99:
95:
92:
88:
85:
81:
78:
74:
71: –
70:
66:
65:Find sources:
59:
55:
49:
48:
43:This article
41:
37:
32:
31:
19:
4780:Perturbation
4762:
4737:Ground track
4647:Gravity turn
4598:
4591:
4584:
4575:
4566:
4546:
4537:
4528:
4521:True anomaly
4519:
4504:Mean anomaly
4502:
4482:
4473:
4464:
4455:
4435:
4423:
4422:
4414:
4413:
4406:Eccentricity
4404:
4362:Lunar cycler
4335:Heliocentric
4275:other points
4224:Medium Earth
4122:Non-inclined
3984:
3980:
3974:
3963:. Retrieved
3959:the original
3949:
3941:www.bogan.ca
3940:
3931:
3920:. Retrieved
3916:the original
3911:
3902:
3891:. Retrieved
3887:
3877:
3865:
3846:
3816:
3554:
3543:
3538:Eccentricity
3453:
3391:
3378:
3322:
3302:
3262:
3187:
3141:
3084:
3016:
2957:mean anomaly
2904:true anomaly
2889:
2874:
2868:October 2023
2865:
2850:Please help
2838:
2812:
2808:
2804:
2764:
2737:
2635:
2585:(originally
2579:Solar System
2560:
2525:
2456:
2453:
2418:
2352:
2342:
2338:
2302:
2249:
2242:
2094:
2091:
2036:
1918:
1898:
1826:
1820:faster than
1808:fixed. Thus
1783:
1653:
1646:
1639:
1440:
1353:
1263:
1198:eccentricity
1195:
1137:
1130:
1014:
1009:
1005:
997:
993:
991:
882:
870:
864:faster than
852:fixed. Thus
827:
816:
652:eccentricity
650:through the
641:
629:right angles
620:
616:
609:semidiameter
604:
600:
589:line segment
576:
570:
293:Radial orbit
244:eccentricity
226:True anomaly
220:
211:Mean anomaly
201:Eccentricity
141:
137:
116:
107:
97:
90:
83:
76:
64:
52:Please help
47:verification
44:
4742:Hill sphere
4577:Mean motion
4457:Inclination
4446:Orientation
4347:Mars cycler
4285:Areocentric
4157:Synchronous
2813:barycentric
2587:empirically
1384:direction:
426:Halo orbits
390:Hill sphere
206:Inclination
4833:Categories
4682:Rendezvous
4378:Parameters
4214:High Earth
4184:Geocentric
4137:Osculating
4094:Elliptical
3965:2007-09-06
3922:2007-09-06
3893:2024-08-20
3821:References
3568:Perihelion
3307:), where:
2805:geocentric
2767:barycenter
2589:derived):
577:major axis
470:Mass ratio
385:Barycenter
110:March 2017
80:newspapers
18:Minor axis
4727:Ephemeris
4704:mechanics
4614:Maneuvers
4557:Variation
4320:Libration
4315:Lissajous
4219:Low Earth
4209:Graveyard
4108:Horseshoe
3884:"Ellipse"
3799:30.10870
3796:30.11000
3771:19.19770
3768:19.21840
3507:−
3426:−
3363:ε
3328:cartesian
3277:μ
3230:μ
3225:−
3202:ε
3171:ε
3164:μ
3125:ε
3118:μ
3113:−
3060:−
3030:−
2928:−
2839:does not
2781:≫
2682:π
2609:∝
2563:astronomy
2540:μ
2494:−
2485:μ
2435:μ
2399:μ
2383:π
2315:Astronomy
2281:−
2199:−
2139:±
2069:−
2055:ℓ
1991:−
1977:−
1948:−
1921:hyperbola
1915:Hyperbola
1870:−
1796:ℓ
1746:ℓ
1721:−
1677:ℓ
1610:−
1603:ℓ
1567:θ
1547:π
1541:θ
1501:ℓ
1469:−
1455:ℓ
1424:ℓ
1415:θ
1412:
1372:π
1366:θ
1296:−
1221:−
943:−
902:−
840:ℓ
819:hyperbola
779:ℓ
753:−
734:ℓ
712:−
668:ℓ
625:hyperbola
597:perimeter
310:Equations
238:Types of
4493:Position
4118:Inclined
4089:Circular
3743:9.56730
3740:9.58260
3715:5.19820
3712:5.20440
3687:1.51740
3684:1.52400
3659:0.99986
3656:1.00000
3631:0.72298
3628:0.72300
3603:0.37870
3600:0.38700
3578:Aphelion
2120:vertices
1786:parabola
1666:and the
830:parabola
657:and the
585:diameter
573:geometry
4702:Orbital
4672:Phasing
4632:Delta-v
4437:Apsides
4431:,
4229:Molniya
4147:Parking
4084:Capture
4072:General
3989:Bibcode
3808:30.400
3805:29.820
3789:Neptune
3780:20.110
3777:18.330
3752:10.124
3705:Jupiter
3593:Mercury
3343:is the
3142:for an
2860:removed
2845:sources
2750:is the
2742:is the
2526:where:
2447:is the
2419:where:
2346:
1133:apsides
1008:,
996:,
992:where (
879:Ellipse
581:ellipse
94:scholar
4844:Orbits
4358:Other
4259:Tundra
4127:Kepler
4103:Escape
4056:orbits
3853:
3802:0.004
3793:0.010
3765:0.046
3761:Uranus
3749:9.041
3737:0.057
3733:Saturn
3724:5.459
3721:4.950
3709:0.049
3696:1.666
3693:1.382
3681:0.093
3668:1.017
3665:0.983
3662:0.014
3653:0.017
3640:0.728
3637:0.718
3634:0.002
3625:0.007
3612:0.467
3609:0.307
3597:0.206
3267:) and
3192:, and
3188:for a
2798:81.300
2738:where
2650:Newton
2636:where
2577:. For
2569:of an
1899:where
1533:, for
823:vertex
637:radius
599:. The
579:of an
575:, the
96:
89:
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67:
4600:Epoch
4389:Shape
4327:Lunar
4281:Mars
4273:About
4244:Polar
4064:Types
3774:0.11
3746:0.16
3718:0.12
3690:0.44
3649:Earth
3621:Venus
3326:is a
3047:, is
2571:orbit
613:focus
191:Apsis
101:JSTOR
87:books
4392:Size
4331:Sun
4310:Halo
4162:semi
3851:ISBN
3811:1.9
3783:9.7
3677:Mars
3671:3.5
3643:1.4
3606:2.2
2843:any
2841:cite
2752:mass
2532:and
2457:The
2357:the
1907:and
1812:and
1649:foci
1559:and
1487:and
1196:The
1042:and
856:and
593:foci
587:: a
73:news
4167:sub
4079:Box
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2353:In
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2020:=
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