3634:
1139:
3646:
549:
62:
3608:
3682:
3706:
3658:
3694:
1387:, making it not a merely different approach to the orbit of an object around its parent, but a period of orbital relations with other objects, normally Earth, and their orbits around the Sun. It applies to the elapsed time where planets return to the same kind of phenomenon or location, such as when any planet returns between its consecutive observed
2160:, the synodic period usually means the Sun-synodic period, namely, the time it takes the moon to complete its illumination phases, completing the solar phases for an astronomer on the planet's surface. The Earth's motion does not determine this value for other planets because an Earth observer is not orbited by the moons in question. For example,
3670:
1126:, the strength of universal gravity can be described using some reference material, such as water: the orbital period for an orbit just above the surface of a spherical body of water is 3 hours and 18 minutes. Conversely, this can be used as a kind of "universal"
1452:, is 29.5 mean solar days, since the Moon's phase and position relative to the Sun and Earth repeats after this period. This is longer than the sidereal period of its orbit around Earth, which is 27.3 mean solar days, owing to the motion of Earth around the Sun.
2172:
The concept of synodic period applies not just to the Earth, but also to other planets as well, and the formula for computation is the same as the one given above. Here is a table which lists the synodic periods of some planets relative to each other:
1270:
of the ellipses in which the centers of the bodies move, or equivalently, the semi-major axis of the ellipse in which one body moves, in the frame of reference with the other body at the origin (which is equal to their constant separation for circular
1439:
is also equal to the synodic period. For celestial bodies in the solar system, the synodic period (with respect to Earth and the Sun) differs from the tropical period owing to Earth's motion around the Sun. For example, the synodic period of the
1564:
Periods can be also defined under different specific astronomical definitions that are mostly caused by the small complex external gravitational influences of other celestial objects. Such variations also include the true placement of the
1477:
from the southern to the northern hemisphere. This period differs from the sidereal period because both the orbital plane of the object and the plane of the ecliptic precess with respect to the fixed stars, so their intersection, the
1757:
1430:
is the amount of time that it takes for an object to reappear at the same point in relation to two or more other objects. In common usage, these two objects are typically Earth and the Sun. The time between two successive
1254:
926:
738:
811:
631:
1072:
762:
In the special case of perfectly circular orbits, the semimajor axis a is equal to the radius of the orbit, and the orbital velocity is constant and equal to
1680:
1605:
One of the observable characteristics of two bodies which orbit a third body in different orbits, and thus have different orbital periods, is their
1482:, also precesses with respect to the fixed stars. Although the plane of the ecliptic is often held fixed at the position it occupied at a specific
457:
3485:
1176:
860:
3633:
2677:
2656:
Bradley W. Carroll, Dale A. Ostlie. An introduction to modern astrophysics. 2nd edition. Pearson 2007, p. 49 (equation 2.37 simplified).
3545:
565:
229:
298:
1080:
So, for the Earth as the central body (or any other spherically symmetric body with the same mean density, about 5,515 kg/m, e.g.
2728:
1616:
An example of this related period description is the repeated cycles for celestial bodies as observed from the Earth's surface, the
3540:
3420:
2839:
3505:
3259:
2557:
1525:
3578:
3217:
3208:
2945:
1520:) is the interval between two alignments of its rotational axis with the Sun, also viewed as two passages of the object at a
119:
676:
1301:
In a parabolic or hyperbolic trajectory, the motion is not periodic, and the duration of the full trajectory is infinite.
769:
3624:
3525:
2995:
583:
1032:
3470:
1505:), the point of its closest approach to the attracting body. It differs from the sidereal period because the object's
1138:
450:
383:
1486:, the orbital plane of the object still precesses, causing the draconitic period to differ from the sidereal period.
3726:
3450:
3277:
987:
When a very small body is in a circular orbit barely above the surface of a sphere of any radius and mean density
3588:
1150:(average of aphelion and perihelion) of some Solar System orbits (crosses denoting Kepler's values) showing that
3573:
3098:
2568:
1643:
has a synodic period of 398.8 days from Earth; thus, Jupiter's opposition occurs once roughly every 13 months.
1578:
378:
293:
1077:
Thus the orbital period in low orbit depends only on the density of the central body, regardless of its size.
670:
Inversely, for calculating the distance where a body has to orbit in order to have a given orbital period T:
3583:
2891:
2588:
1785:
1632:
1610:
1436:
1388:
249:
3445:
3047:
2967:
2955:
2583:
1636:
1556:), realigning with the Sun before the orbit completes. This cycle of axial precession for Earth, known as
1392:
1294:
667:
For all ellipses with a given semi-major axis the orbital period is the same, regardless of eccentricity.
654:
443:
166:
35:
3568:
3510:
3480:
3268:
3145:
3113:
3083:
3042:
3027:
2906:
351:
186:
94:
3645:
548:
3593:
3415:
3199:
3088:
3057:
2985:
2960:
2935:
2896:
2877:
2832:
2503:
2047:
1432:
224:
181:
171:
99:
2164:'s synodic period is 1.2648 days, 0.18% longer than Deimos's sidereal period of 1.2624 d.
3710:
3455:
3250:
2990:
2119:
2010:
1590:
1570:
1384:
1163:
479:
266:
104:
3736:
3698:
3686:
3650:
3128:
3017:
2915:
1586:
1355:
339:
214:
2693:
3495:
3393:
3323:
3078:
3032:
2950:
2724:
2673:
2157:
1582:
1545:
1483:
1419:
1407:
1316:
254:
191:
70:
2667:
3662:
3475:
3407:
3171:
3133:
3007:
2977:
2930:
2625:
2535:
1814:
1549:
1339:
1081:
424:
373:
138:
82:
525:
For celestial objects in general, the orbital period is determined by a 360° revolution of
3731:
3515:
3108:
3012:
3002:
2901:
2825:
2562:
1521:
1506:
1403:
of 398.8 days from Earth; thus, Jupiter's opposition occurs once roughly every 13 months.
1267:
839:
645:
429:
334:
244:
219:
28:
2641:
1410:
related to the orbits of objects, each of which are often used in the various fields of
3638:
3611:
3563:
3555:
3550:
3435:
3430:
3341:
3332:
2925:
2911:
2887:
2882:
2857:
2539:
2524:
1566:
1400:
756:
573:
401:
317:
311:
159:
153:
148:
1620:, applying to the elapsed time where planets return to the same kind of phenomenon or
1166:, when both orbiting bodies' masses have to be taken into account, the orbital period
3720:
3465:
3460:
3379:
3022:
2940:
2578:
2573:
2161:
2006:
1752:{\displaystyle {\frac {1}{T_{\mathrm {syn} }}}={\frac {1}{T_{1}}}-{\frac {1}{T_{2}}}}
1537:
1517:
1479:
1373:
1351:
1328:
1127:
1108:
1103: â 1,000 kg/m), or bodies with a similar density, e.g. Saturn's moons
526:
406:
239:
196:
1368:
is more particularly about the position of the parent star. It is the basis for the
540:
Periods in astronomy are expressed in units of time, usually hours, days, or years.
61:
3674:
3530:
3440:
3314:
3297:
3155:
3052:
2920:
2782:
2458:
2101:
1498:
1470:
1465:
1415:
1332:
530:
124:
114:
109:
1532:
is slightly shorter than the period for the Sun to complete one circuit along the
2718:
3535:
3370:
3140:
3120:
3037:
2751:
2493:
2344:
2137:
2083:
1553:
1336:
1310:
515:
288:
3103:
2513:
1594:
1574:
1541:
1502:
1369:
981:
969:
961:
854:, it is possible to rewrite the first equation without measuring the mass as:
368:
324:
283:
1589:, etc. Most are investigated by detailed complex astronomical theories using
44:
Time an astronomical object takes to complete one orbit around another object
17:
3520:
2872:
2593:
2065:
1863:
1494:
1411:
519:
507:
487:
2565:â time that it takes to complete one revolution around its axis of rotation
1469:), is the time that elapses between two passages of the object through its
1418:, particularly they must not be confused with other revolving periods like
1533:
1474:
1249:{\displaystyle T=2\pi {\sqrt {\frac {a^{3}}{G\left(M_{1}+M_{2}\right)}}}}
965:
921:{\displaystyle T={\sqrt {{\frac {a^{3}}{r^{3}}}{\frac {3\pi }{G\rho }}}}}
495:
3425:
2817:
2403:
2281:
2029:
1949:
1892:
1640:
1396:
1104:
851:
1631:
for example, when any planet returns between its consecutive observed
2374:
2313:
1930:
1911:
1646:
If the orbital periods of the two bodies around the third are called
1422:. Examples of some of the common orbital ones include the following:
973:
491:
1383:
refers not to the orbital relation to the parent star, but to other
3669:
3230:
2849:
2431:
1968:
1852:
1833:
1493:
is the time that elapses between two passages of an object at its
1445:
1343:
1085:
976:, completing an orbit every hour. If the same sphere were made of
752:
547:
503:
483:
89:
2694:"Precession of the Earth's Axis - Wolfram Demonstrations Project"
1767:
Table of synodic periods in the Solar System, relative to Earth:
2248:
1987:
1873:
1529:
1441:
977:
744:
511:
2821:
1593:
using precise positional observations of celestial objects via
2214:
1449:
1347:
499:
2804:
Bate, Roger B.; Mueller, Donald D.; White, Jerry E. (1971),
968:
half a metre in radius would travel at slightly more than 1
1354:. This is the orbital period in an inertial (non-rotating)
1122:
Thus, as an alternative for using a very small number like
748:
984:
above the surface for sustaining the same orbital period.
956:
is the density of the sphere in kilograms per cubic metre.
572:
of two point masses orbiting each other in a circular or
767:
751:, a small body has to orbit at a distance of 1.08
581:
3622:
2672:. Springer Science & Business Media. p. 50.
1683:
1179:
1035:
863:
772:
733:{\displaystyle a={\sqrt{\frac {GMT^{2}}{4\pi ^{2}}}}}
679:
586:
806:{\displaystyle v_{\text{o}}={\sqrt {\frac {GM}{r}}}}
743:
For instance, for completing an orbit every 24
3494:
3406:
3350:
3286:
3239:
3179:
3170:
3066:
2976:
2865:
2856:
2669:
991:(in kg/m), the above equation simplifies to (since
1751:
1248:
1066:
960:For instance, a small body in circular orbit 10.5
920:
805:
732:
626:{\displaystyle T=2\pi {\sqrt {\frac {a^{3}}{GM}}}}
625:
1067:{\displaystyle T={\sqrt {\frac {3\pi }{G\rho }}}}
522:orbiting a planet or moon to complete one orbit.
2612:
1473:, the point of its orbit where it crosses the
2833:
451:
8:
980:the small body would need to orbit just 6.7
2752:"Questions and Answers - Sten's Space Blog"
1287:is the sum of the masses of the two bodies,
518:. It may also refer to the time it takes a
3607:
3176:
2862:
2840:
2826:
2818:
2666:Oliver Montenbruck, Eberhard Gill (2000).
2175:
1769:
458:
444:
46:
2168:Synodic periods relative to other planets
1741:
1732:
1721:
1712:
1694:
1693:
1684:
1682:
1231:
1218:
1199:
1192:
1178:
1042:
1034:
944:is the orbit's semi-major axis in metres,
896:
888:
878:
872:
870:
862:
824:is the circular orbit's radius in meters,
786:
777:
771:
723:
715:
700:
686:
678:
606:
599:
585:
2489:
2486:Example of orbital periods: binary stars
1763:Examples of sidereal and synodic periods
1137:
3629:
2723:(6th ed.). Springer. p. 145.
2605:
349:
264:
68:
54:
3486:Transposition, docking, and extraction
2777:
2775:
2773:
2771:
2769:
2767:
2765:
34:For the album by Bump of Chicken, see
2717:Hannu Karttunen; et al. (2016).
1327:, determined by a 360° revolution of
663:is the mass of the more massive body.
7:
1674:, their synodic period is given by:
1560:, recurs roughly every 25,772 years.
1364:can be defined in several ways. The
1350:, this period is referred to as the
1497:(in the case of the planets in the
1701:
1698:
1695:
544:Small body orbiting a central body
25:
3546:Kepler's laws of planetary motion
964:above the surface of a sphere of
230:Kepler's laws of planetary motion
3704:
3692:
3680:
3668:
3656:
3644:
3632:
3606:
3541:Interplanetary Transport Network
3421:Collision avoidance (spacecraft)
2613:Bate, Mueller & White (1971)
850:For a perfect sphere of uniform
846:Effect of central body's density
478:) is the amount of time a given
60:
3506:Astronomical coordinate systems
3260:Longitude of the ascending node
2558:Geosynchronous orbit derivation
1158:² is constant (green line)
3579:Retrograde and prograde motion
1170:can be calculated as follows:
1134:Two bodies orbiting each other
1130:if we have a unit of density.
1099:and for a body made of water (
1088:with 5,243 kg/m) we get:
950:is the gravitational constant,
1:
2806:Fundamentals of Astrodynamics
3526:Equatorial coordinate system
1799:
1609:, which is the time between
1581:by other planets or bodies,
1806:
1792:
1558:precession of the equinoxes
1111:with 984 kg/m we get:
384:Tsiolkovsky rocket equation
3753:
3278:Longitude of the periapsis
2698:demonstrations.wolfram.com
2156:In the case of a planet's
1509:typically advances slowly.
1395:to the Sun. For example,
1308:
838:times (â 0.707 times) the
747:around a mass of 100
486:around another object. In
353:Engineering and efficiency
172:Bi-elliptic transfer orbit
33:
26:
3602:
3589:Specific angular momentum
1867:
1778:
1775:
1772:
1639:to the Sun. For example,
1107:with 1,088 kg/m and
1084:with 5,427 kg/m and
2569:Satellite revisit period
1552:(rotate with respect to
1323:typically refers to the
1311:Lunar month § Types
755:from the central body's
490:, it usually applies to
379:Propellant mass fraction
278:Gravitational influences
27:Not to be confused with
3584:Specific orbital energy
2589:List of periodic comets
2177:Orbital period (years)
1372:, and respectively the
1142:Log-log plot of period
845:
556:) and semi-minor axis (
537:Earth around the Sun.
250:Specific orbital energy
2996:Geostationary transfer
2783:"Planetary Fact Sheet"
2584:Opposition (astronomy)
2545:500,000 years or more
1753:
1444:'s orbit as seen from
1342:. For the case of the
1295:gravitational constant
1250:
1159:
1068:
938:is the sphere's radius
922:
807:
734:
655:gravitational constant
627:
561:
482:takes to complete one
167:Hohmann transfer orbit
3569:Orbital state vectors
3511:Characteristic energy
3481:Trans-lunar injection
3269:Argument of periapsis
2946:Prograde / Retrograde
2907:Hyperbolic trajectory
2756:www.astronomycafe.net
2720:Fundamental Astronomy
1754:
1251:
1141:
1069:
923:
808:
735:
628:
568:, the orbital period
552:The semi-major axis (
551:
363:Preflight engineering
95:Argument of periapsis
3416:Bi-elliptic transfer
2936:Parabolic trajectory
2627:Density of the Earth
2504:AM Canum Venaticorum
1681:
1346:orbiting around the
1340:projected in the sky
1177:
1033:
861:
828:This corresponds to
770:
677:
584:
419:Propulsive maneuvers
3456:Low-energy transfer
2787:nssdc.gsfc.nasa.gov
2178:
2011:near-Earth asteroid
1591:celestial mechanics
1571:astronomical bodies
1164:celestial mechanics
1146:vs semi-major axis
480:astronomical object
396:Efficiency measures
299:Sphere of influence
268:Celestial mechanics
50:Part of a series on
3451:Inclination change
3099:Distant retrograde
2646:, wolframalpha.com
2630:, wolframalpha.com
2176:
1749:
1587:general relativity
1491:anomalistic period
1448:, relative to the
1435:or two successive
1420:rotational periods
1356:frame of reference
1266:is the sum of the
1246:
1160:
1064:
918:
803:
730:
623:
566:Kepler's Third Law
562:
506:orbiting planets,
215:Dynamical friction
3727:Time in astronomy
3620:
3619:
3594:Two-line elements
3402:
3401:
3324:Eccentric anomaly
3166:
3165:
3033:Orbit of the Moon
2892:Highly elliptical
2679:978-3-540-67280-7
2549:
2548:
2483:
2482:
2154:
2153:
1747:
1727:
1707:
1583:orbital resonance
1567:centre of gravity
1457:draconitic period
1385:celestial objects
1317:celestial objects
1244:
1243:
1062:
1061:
916:
914:
894:
801:
800:
780:
728:
722:
621:
620:
476:revolution period
468:
467:
318:Lagrangian points
255:Vis-viva equation
225:Kepler's equation
72:Orbital mechanics
16:(Redirected from
3744:
3709:
3708:
3707:
3697:
3696:
3695:
3685:
3684:
3683:
3673:
3672:
3661:
3660:
3659:
3649:
3648:
3637:
3636:
3628:
3610:
3609:
3551:Lagrangian point
3446:Hohmann transfer
3391:
3377:
3368:
3359:
3339:
3330:
3321:
3312:
3308:
3304:
3295:
3275:
3266:
3257:
3248:
3228:
3224:
3215:
3206:
3197:
3177:
3146:Heliosynchronous
3095:Lagrange points
3048:Transatmospheric
2863:
2842:
2835:
2828:
2819:
2809:
2791:
2790:
2779:
2760:
2759:
2748:
2742:
2741:
2739:
2737:
2714:
2708:
2707:
2705:
2704:
2690:
2684:
2683:
2663:
2657:
2654:
2648:
2647:
2643:Density of water
2638:
2632:
2631:
2622:
2616:
2610:
2536:Proxima Centauri
2498:Orbital period.
2490:
2179:
1808:
1801:
1794:
1776:Sidereal period
1770:
1758:
1756:
1755:
1750:
1748:
1746:
1745:
1733:
1728:
1726:
1725:
1713:
1708:
1706:
1705:
1704:
1685:
1667: <
1630:
1629:
1625:
1546:equatorial plane
1335:relative to the
1319:in general, the
1255:
1253:
1252:
1247:
1245:
1242:
1241:
1237:
1236:
1235:
1223:
1222:
1204:
1203:
1194:
1193:
1073:
1071:
1070:
1065:
1063:
1060:
1052:
1044:
1043:
1025:
1018:
1015:
1013:
1012:
1009:
1006:
927:
925:
924:
919:
917:
915:
913:
905:
897:
895:
893:
892:
883:
882:
873:
871:
837:
836:
832:
813:
810:
809:
804:
802:
796:
788:
787:
782:
781:
778:
739:
737:
736:
731:
729:
727:
721:
720:
719:
706:
705:
704:
688:
687:
633:
630:
629:
624:
622:
619:
611:
610:
601:
600:
460:
453:
446:
425:Orbital maneuver
374:Payload fraction
354:
335:Lissajous orbits
269:
240:Orbital velocity
187:Hyperbolic orbit
83:Orbital elements
73:
64:
47:
21:
3752:
3751:
3747:
3746:
3745:
3743:
3742:
3741:
3717:
3716:
3715:
3705:
3703:
3693:
3691:
3681:
3679:
3667:
3657:
3655:
3643:
3631:
3623:
3621:
3616:
3598:
3516:Escape velocity
3497:
3490:
3471:Rocket equation
3398:
3390:
3384:
3375:
3366:
3357:
3346:
3337:
3328:
3319:
3310:
3306:
3302:
3293:
3282:
3273:
3264:
3255:
3246:
3235:
3226:
3222:
3218:Semi-minor axis
3213:
3209:Semi-major axis
3204:
3195:
3189:
3162:
3084:Areosynchronous
3068:
3062:
3043:Sun-synchronous
3028:Near-equatorial
2972:
2852:
2846:
2816:
2803:
2800:
2795:
2794:
2781:
2780:
2763:
2750:
2749:
2745:
2735:
2733:
2731:
2716:
2715:
2711:
2702:
2700:
2692:
2691:
2687:
2680:
2665:
2664:
2660:
2655:
2651:
2640:
2639:
2635:
2624:
2623:
2619:
2611:
2607:
2602:
2563:Rotation period
2554:
2508:17.146 minutes
2488:
2170:
1779:Synodic period
1765:
1737:
1717:
1689:
1679:
1678:
1673:
1666:
1659:
1652:
1627:
1623:
1621:
1603:
1554:reference stars
1522:right ascension
1514:tropical period
1507:semi-major axis
1461:draconic period
1406:There are many
1366:tropical period
1362:Orbital periods
1325:sidereal period
1313:
1307:
1305:Related periods
1286:
1279:
1268:semi-major axes
1227:
1214:
1213:
1209:
1205:
1195:
1175:
1174:
1136:
1053:
1045:
1031:
1030:
1016:
1010:
1007:
1004:
1003:
1001:
992:
906:
898:
884:
874:
859:
858:
848:
840:escape velocity
834:
830:
829:
789:
773:
768:
766:
711:
707:
696:
689:
675:
674:
646:semi-major axis
644:is the orbit's
612:
602:
582:
580:
560:) of an ellipse
546:
510:orbiting other
464:
435:
434:
430:Orbit insertion
420:
412:
411:
397:
389:
388:
364:
356:
352:
345:
344:
340:Lyapunov orbits
331:
330:
314:
304:
303:
279:
271:
267:
260:
259:
245:Surface gravity
220:Escape velocity
210:
202:
201:
182:Parabolic orbit
178:
177:
144:
142:
139:two-body orbits
130:
129:
120:Semi-major axis
85:
75:
71:
45:
42:
32:
29:Rotation period
23:
22:
15:
12:
11:
5:
3750:
3748:
3740:
3739:
3734:
3729:
3719:
3718:
3714:
3713:
3701:
3689:
3677:
3665:
3653:
3641:
3618:
3617:
3615:
3614:
3612:List of orbits
3603:
3600:
3599:
3597:
3596:
3591:
3586:
3581:
3576:
3571:
3566:
3564:Orbit equation
3561:
3553:
3548:
3543:
3538:
3533:
3528:
3523:
3518:
3513:
3508:
3502:
3500:
3492:
3491:
3489:
3488:
3483:
3478:
3473:
3468:
3463:
3458:
3453:
3448:
3443:
3438:
3436:Gravity assist
3433:
3431:Delta-v budget
3428:
3423:
3418:
3412:
3410:
3404:
3403:
3400:
3399:
3397:
3396:
3388:
3382:
3373:
3364:
3362:Orbital period
3354:
3352:
3348:
3347:
3345:
3344:
3342:True longitude
3335:
3333:Mean longitude
3326:
3317:
3300:
3290:
3288:
3284:
3283:
3281:
3280:
3271:
3262:
3253:
3243:
3241:
3237:
3236:
3234:
3233:
3220:
3211:
3202:
3192:
3190:
3188:
3187:
3184:
3180:
3174:
3168:
3167:
3164:
3163:
3161:
3160:
3159:
3158:
3150:
3149:
3148:
3143:
3138:
3137:
3136:
3123:
3118:
3117:
3116:
3111:
3106:
3101:
3093:
3092:
3091:
3089:Areostationary
3086:
3081:
3072:
3070:
3064:
3063:
3061:
3060:
3058:Very low Earth
3055:
3050:
3045:
3040:
3035:
3030:
3025:
3020:
3015:
3010:
3005:
3000:
2999:
2998:
2993:
2986:Geosynchronous
2982:
2980:
2974:
2973:
2971:
2970:
2968:Transfer orbit
2965:
2964:
2963:
2958:
2948:
2943:
2938:
2933:
2928:
2926:Lagrange point
2923:
2918:
2909:
2904:
2899:
2894:
2885:
2880:
2875:
2869:
2867:
2860:
2854:
2853:
2848:Gravitational
2847:
2845:
2844:
2837:
2830:
2822:
2815:
2814:External links
2812:
2811:
2810:
2799:
2796:
2793:
2792:
2761:
2743:
2729:
2709:
2685:
2678:
2658:
2649:
2633:
2617:
2604:
2603:
2601:
2598:
2597:
2596:
2591:
2586:
2581:
2576:
2571:
2566:
2560:
2553:
2550:
2547:
2546:
2543:
2540:Alpha Centauri
2532:
2531:
2528:
2525:Alpha Centauri
2521:
2520:
2517:
2510:
2509:
2506:
2500:
2499:
2496:
2487:
2484:
2481:
2480:
2477:
2475:
2473:
2471:
2469:
2467:
2465:
2463:
2461:
2455:
2454:
2451:
2448:
2446:
2444:
2442:
2440:
2438:
2436:
2434:
2428:
2427:
2424:
2421:
2418:
2416:
2414:
2412:
2410:
2408:
2406:
2400:
2399:
2396:
2393:
2390:
2387:
2385:
2383:
2381:
2379:
2377:
2371:
2370:
2367:
2364:
2361:
2358:
2355:
2353:
2351:
2349:
2347:
2341:
2340:
2337:
2334:
2331:
2328:
2325:
2322:
2320:
2318:
2316:
2310:
2309:
2306:
2303:
2300:
2297:
2294:
2291:
2288:
2286:
2284:
2278:
2277:
2274:
2271:
2268:
2265:
2262:
2259:
2256:
2253:
2251:
2245:
2244:
2241:
2238:
2235:
2232:
2229:
2226:
2223:
2220:
2217:
2211:
2210:
2207:
2204:
2201:
2198:
2195:
2192:
2189:
2186:
2183:
2169:
2166:
2152:
2151:
2148:
2145:
2143:
2140:
2134:
2133:
2130:
2127:
2125:
2122:
2116:
2115:
2112:
2109:
2107:
2104:
2098:
2097:
2094:
2091:
2089:
2086:
2080:
2079:
2076:
2073:
2071:
2068:
2062:
2061:
2058:
2055:
2053:
2050:
2044:
2043:
2040:
2037:
2035:
2032:
2026:
2025:
2022:
2019:
2017:
2014:
2003:
2002:
1999:
1996:
1993:
1990:
1984:
1983:
1980:
1977:
1974:
1971:
1965:
1964:
1961:
1958:
1955:
1952:
1946:
1945:
1942:
1939:
1936:
1933:
1927:
1926:
1923:
1920:
1917:
1914:
1908:
1907:
1904:
1901:
1898:
1895:
1889:
1888:
1885:
1882:
1879:
1876:
1870:
1869:
1866:
1860:
1855:
1849:
1848:
1845:
1842:
1839:
1836:
1830:
1829:
1826:
1823:
1820:
1817:
1811:
1810:
1803:
1796:
1789:
1781:
1780:
1777:
1774:
1764:
1761:
1760:
1759:
1744:
1740:
1736:
1731:
1724:
1720:
1716:
1711:
1703:
1700:
1697:
1692:
1688:
1671:
1664:
1657:
1650:
1618:synodic period
1607:synodic period
1602:
1601:Synodic period
1599:
1562:
1561:
1540:) because the
1510:
1487:
1471:ascending node
1453:
1428:synodic period
1401:synodic period
1381:synodic period
1321:orbital period
1306:
1303:
1299:
1298:
1288:
1284:
1277:
1272:
1257:
1256:
1240:
1234:
1230:
1226:
1221:
1217:
1212:
1208:
1202:
1198:
1191:
1188:
1185:
1182:
1135:
1132:
1120:
1119:
1097:
1096:
1075:
1074:
1059:
1056:
1051:
1048:
1041:
1038:
958:
957:
951:
945:
939:
929:
928:
912:
909:
904:
901:
891:
887:
881:
877:
869:
866:
847:
844:
826:
825:
815:
814:
799:
795:
792:
785:
776:
757:center of mass
741:
740:
726:
718:
714:
710:
703:
699:
695:
692:
685:
682:
665:
664:
658:
648:
635:
634:
618:
615:
609:
605:
598:
595:
592:
589:
574:elliptic orbit
545:
542:
472:orbital period
466:
465:
463:
462:
455:
448:
440:
437:
436:
433:
432:
427:
421:
418:
417:
414:
413:
410:
409:
404:
402:Gravity assist
398:
395:
394:
391:
390:
387:
386:
381:
376:
371:
365:
362:
361:
358:
357:
350:
347:
346:
343:
342:
337:
329:
328:
320:
316:
315:
310:
309:
306:
305:
302:
301:
296:
291:
286:
280:
277:
276:
273:
272:
265:
262:
261:
258:
257:
252:
247:
242:
237:
235:Orbital period
232:
227:
222:
217:
211:
208:
207:
204:
203:
200:
199:
197:Decaying orbit
194:
189:
184:
176:
175:
169:
162:
160:Transfer orbit
158:
157:
156:
154:Elliptic orbit
151:
149:Circular orbit
145:
136:
135:
132:
131:
128:
127:
122:
117:
112:
107:
102:
97:
92:
86:
81:
80:
77:
76:
69:
66:
65:
57:
56:
52:
51:
43:
37:Orbital Period
24:
14:
13:
10:
9:
6:
4:
3:
2:
3749:
3738:
3735:
3733:
3730:
3728:
3725:
3724:
3722:
3712:
3702:
3700:
3690:
3688:
3678:
3676:
3671:
3666:
3664:
3654:
3652:
3647:
3642:
3640:
3635:
3630:
3626:
3613:
3605:
3604:
3601:
3595:
3592:
3590:
3587:
3585:
3582:
3580:
3577:
3575:
3572:
3570:
3567:
3565:
3562:
3560:
3559:-body problem
3558:
3554:
3552:
3549:
3547:
3544:
3542:
3539:
3537:
3534:
3532:
3529:
3527:
3524:
3522:
3519:
3517:
3514:
3512:
3509:
3507:
3504:
3503:
3501:
3499:
3493:
3487:
3484:
3482:
3479:
3477:
3474:
3472:
3469:
3467:
3464:
3462:
3461:Oberth effect
3459:
3457:
3454:
3452:
3449:
3447:
3444:
3442:
3439:
3437:
3434:
3432:
3429:
3427:
3424:
3422:
3419:
3417:
3414:
3413:
3411:
3409:
3405:
3395:
3387:
3383:
3381:
3380:Orbital speed
3374:
3372:
3365:
3363:
3356:
3355:
3353:
3349:
3343:
3336:
3334:
3327:
3325:
3318:
3316:
3301:
3299:
3292:
3291:
3289:
3285:
3279:
3272:
3270:
3263:
3261:
3254:
3252:
3245:
3244:
3242:
3238:
3232:
3221:
3219:
3212:
3210:
3203:
3201:
3194:
3193:
3191:
3185:
3182:
3181:
3178:
3175:
3173:
3169:
3157:
3154:
3153:
3151:
3147:
3144:
3142:
3139:
3135:
3134:Earth's orbit
3132:
3131:
3130:
3127:
3126:
3124:
3122:
3119:
3115:
3112:
3110:
3107:
3105:
3102:
3100:
3097:
3096:
3094:
3090:
3087:
3085:
3082:
3080:
3077:
3076:
3074:
3073:
3071:
3065:
3059:
3056:
3054:
3051:
3049:
3046:
3044:
3041:
3039:
3036:
3034:
3031:
3029:
3026:
3024:
3021:
3019:
3016:
3014:
3011:
3009:
3006:
3004:
3001:
2997:
2994:
2992:
2991:Geostationary
2989:
2988:
2987:
2984:
2983:
2981:
2979:
2975:
2969:
2966:
2962:
2959:
2957:
2954:
2953:
2952:
2949:
2947:
2944:
2942:
2939:
2937:
2934:
2932:
2929:
2927:
2924:
2922:
2919:
2917:
2913:
2910:
2908:
2905:
2903:
2900:
2898:
2895:
2893:
2889:
2886:
2884:
2881:
2879:
2876:
2874:
2871:
2870:
2868:
2864:
2861:
2859:
2855:
2851:
2843:
2838:
2836:
2831:
2829:
2824:
2823:
2820:
2813:
2807:
2802:
2801:
2797:
2788:
2784:
2778:
2776:
2774:
2772:
2770:
2768:
2766:
2762:
2757:
2753:
2747:
2744:
2732:
2730:9783662530450
2726:
2722:
2721:
2713:
2710:
2699:
2695:
2689:
2686:
2681:
2675:
2671:
2670:
2662:
2659:
2653:
2650:
2645:
2644:
2637:
2634:
2629:
2628:
2621:
2618:
2615:, p. 33.
2614:
2609:
2606:
2599:
2595:
2592:
2590:
2587:
2585:
2582:
2580:
2579:Sidereal year
2577:
2575:
2574:Sidereal time
2572:
2570:
2567:
2564:
2561:
2559:
2556:
2555:
2551:
2544:
2541:
2537:
2534:
2533:
2529:
2526:
2523:
2522:
2519:12.9075 days
2518:
2515:
2512:
2511:
2507:
2505:
2502:
2501:
2497:
2495:
2492:
2491:
2485:
2478:
2476:
2474:
2472:
2470:
2468:
2466:
2464:
2462:
2460:
2457:
2456:
2452:
2449:
2447:
2445:
2443:
2441:
2439:
2437:
2435:
2433:
2430:
2429:
2425:
2422:
2419:
2417:
2415:
2413:
2411:
2409:
2407:
2405:
2402:
2401:
2397:
2394:
2391:
2388:
2386:
2384:
2382:
2380:
2378:
2376:
2373:
2372:
2368:
2365:
2362:
2359:
2356:
2354:
2352:
2350:
2348:
2346:
2343:
2342:
2338:
2335:
2332:
2329:
2326:
2323:
2321:
2319:
2317:
2315:
2312:
2311:
2307:
2304:
2301:
2298:
2295:
2292:
2289:
2287:
2285:
2283:
2280:
2279:
2275:
2272:
2269:
2266:
2263:
2260:
2257:
2254:
2252:
2250:
2247:
2246:
2242:
2239:
2236:
2233:
2230:
2227:
2224:
2221:
2218:
2216:
2213:
2212:
2208:
2205:
2202:
2199:
2196:
2193:
2190:
2187:
2184:
2181:
2180:
2174:
2167:
2165:
2163:
2159:
2149:
2146:
2144:
2141:
2139:
2136:
2135:
2131:
2128:
2126:
2123:
2121:
2118:
2117:
2113:
2110:
2108:
2105:
2103:
2100:
2099:
2095:
2092:
2090:
2087:
2085:
2082:
2081:
2077:
2074:
2072:
2069:
2067:
2064:
2063:
2059:
2056:
2054:
2051:
2049:
2046:
2045:
2041:
2038:
2036:
2033:
2031:
2028:
2027:
2023:
2020:
2018:
2015:
2012:
2008:
2007:99942 Apophis
2005:
2004:
2000:
1997:
1994:
1991:
1989:
1986:
1985:
1981:
1978:
1975:
1972:
1970:
1967:
1966:
1962:
1959:
1956:
1953:
1951:
1948:
1947:
1943:
1940:
1937:
1934:
1932:
1929:
1928:
1924:
1921:
1918:
1915:
1913:
1910:
1909:
1905:
1902:
1899:
1896:
1894:
1891:
1890:
1886:
1883:
1880:
1877:
1875:
1872:
1871:
1865:
1861:
1859:
1856:
1854:
1851:
1850:
1846:
1843:
1840:
1837:
1835:
1832:
1831:
1827:
1824:
1822:87.9691 days
1821:
1818:
1816:
1813:
1812:
1804:
1797:
1790:
1787:
1783:
1782:
1771:
1768:
1762:
1742:
1738:
1734:
1729:
1722:
1718:
1714:
1709:
1690:
1686:
1677:
1676:
1675:
1670:
1663:
1656:
1649:
1644:
1642:
1638:
1634:
1619:
1614:
1612:
1608:
1600:
1598:
1596:
1592:
1588:
1584:
1580:
1579:perturbations
1576:
1572:
1568:
1559:
1555:
1551:
1547:
1543:
1542:inclined axis
1539:
1538:sidereal year
1535:
1531:
1527:
1523:
1519:
1518:tropical year
1515:
1511:
1508:
1504:
1501:, called the
1500:
1496:
1492:
1488:
1485:
1481:
1480:line of nodes
1476:
1472:
1468:
1467:
1462:
1458:
1454:
1451:
1447:
1443:
1438:
1434:
1429:
1425:
1424:
1423:
1421:
1417:
1413:
1409:
1404:
1402:
1398:
1394:
1390:
1386:
1382:
1377:
1375:
1374:calendar year
1371:
1367:
1363:
1359:
1357:
1353:
1352:sidereal year
1349:
1345:
1341:
1338:
1334:
1330:
1326:
1322:
1318:
1312:
1304:
1302:
1296:
1292:
1289:
1283:
1276:
1273:
1269:
1265:
1262:
1261:
1260:
1238:
1232:
1228:
1224:
1219:
1215:
1210:
1206:
1200:
1196:
1189:
1186:
1183:
1180:
1173:
1172:
1171:
1169:
1165:
1157:
1153:
1149:
1145:
1140:
1133:
1131:
1129:
1125:
1117:
1114:
1113:
1112:
1110:
1106:
1102:
1094:
1091:
1090:
1089:
1087:
1083:
1078:
1057:
1054:
1049:
1046:
1039:
1036:
1029:
1028:
1027:
1024:
1021:
999:
995:
990:
985:
983:
979:
975:
971:
967:
963:
955:
952:
949:
946:
943:
940:
937:
934:
933:
932:
910:
907:
902:
899:
889:
885:
879:
875:
867:
864:
857:
856:
855:
853:
843:
841:
823:
820:
819:
818:
812:
797:
793:
790:
783:
774:
765:
764:
763:
760:
758:
754:
750:
746:
724:
716:
712:
708:
701:
697:
693:
690:
683:
680:
673:
672:
671:
668:
662:
659:
656:
652:
649:
647:
643:
640:
639:
638:
632:
616:
613:
607:
603:
596:
593:
590:
587:
579:
578:
577:
575:
571:
567:
564:According to
559:
555:
550:
543:
541:
538:
536:
532:
528:
523:
521:
517:
513:
509:
505:
501:
498:orbiting the
497:
493:
489:
485:
481:
477:
473:
461:
456:
454:
449:
447:
442:
441:
439:
438:
431:
428:
426:
423:
422:
416:
415:
408:
407:Oberth effect
405:
403:
400:
399:
393:
392:
385:
382:
380:
377:
375:
372:
370:
367:
366:
360:
359:
355:
348:
341:
338:
336:
333:
332:
326:
322:
321:
319:
313:
312:N-body orbits
308:
307:
300:
297:
295:
294:Perturbations
292:
290:
287:
285:
282:
281:
275:
274:
270:
263:
256:
253:
251:
248:
246:
243:
241:
238:
236:
233:
231:
228:
226:
223:
221:
218:
216:
213:
212:
206:
205:
198:
195:
193:
190:
188:
185:
183:
180:
179:
173:
170:
168:
164:
163:
161:
155:
152:
150:
147:
146:
140:
134:
133:
126:
123:
121:
118:
116:
115:Orbital nodes
113:
111:
108:
106:
103:
101:
98:
96:
93:
91:
88:
87:
84:
79:
78:
74:
67:
63:
59:
58:
55:Astrodynamics
53:
49:
48:
40:
38:
30:
19:
18:Synodic cycle
3711:Solar System
3574:Perturbation
3556:
3531:Ground track
3441:Gravity turn
3392:
3385:
3378:
3369:
3361:
3360:
3340:
3331:
3322:
3315:True anomaly
3313:
3298:Mean anomaly
3296:
3276:
3267:
3258:
3249:
3229:
3216:
3207:
3200:Eccentricity
3198:
3156:Lunar cycler
3129:Heliocentric
3069:other points
3018:Medium Earth
2916:Non-inclined
2805:
2798:Bibliography
2786:
2755:
2746:
2734:. Retrieved
2719:
2712:
2701:. Retrieved
2697:
2688:
2668:
2661:
2652:
2642:
2636:
2626:
2620:
2608:
2530:79.91 years
2459:50000 Quaoar
2182:Relative to
2171:
2155:
2102:50000 Quaoar
1969:134340 Pluto
1857:
1766:
1668:
1661:
1654:
1647:
1645:
1633:conjunctions
1617:
1615:
1611:conjunctions
1606:
1604:
1569:between two
1563:
1557:
1528:. One Earth
1516:of Earth (a
1513:
1499:Solar System
1490:
1466:nodal period
1464:
1460:
1456:
1437:conjunctions
1427:
1416:astrophysics
1405:
1389:conjunctions
1380:
1378:
1365:
1361:
1360:
1324:
1320:
1314:
1300:
1290:
1281:
1274:
1263:
1258:
1167:
1161:
1155:
1151:
1147:
1143:
1128:unit of time
1123:
1121:
1118:= 3.30 hours
1115:
1100:
1098:
1095:= 1.41 hours
1092:
1079:
1076:
1022:
1019:
997:
993:
988:
986:
959:
953:
947:
941:
935:
930:
849:
827:
821:
816:
761:
742:
669:
666:
660:
650:
641:
636:
569:
563:
557:
553:
539:
534:
524:
516:binary stars
475:
471:
469:
234:
192:Radial orbit
143:eccentricity
125:True anomaly
110:Mean anomaly
100:Eccentricity
36:
3699:Outer space
3687:Spaceflight
3651:Mathematics
3536:Hill sphere
3371:Mean motion
3251:Inclination
3240:Orientation
3141:Mars cycler
3079:Areocentric
2951:Synchronous
2736:December 7,
2494:Binary star
2345:2060 Chiron
2138:90377 Sedna
2120:136199 Eris
2084:2060 Chiron
1995:27.32 days
1841:224.7 days
1637:oppositions
1433:oppositions
1393:oppositions
1337:fixed stars
1331:around its
529:around its
325:Halo orbits
289:Hill sphere
105:Inclination
3721:Categories
3476:Rendezvous
3172:Parameters
3008:High Earth
2978:Geocentric
2931:Osculating
2888:Elliptical
2703:2019-02-10
2514:Beta Lyrae
1864:solar days
1862:365.25636
1660:, so that
1595:astrometry
1575:barycenter
1512:Also, the
1503:perihelion
1370:solar year
1309:See also:
508:exoplanets
369:Mass ratio
284:Barycenter
3737:Durations
3663:Astronomy
3521:Ephemeris
3498:mechanics
3408:Maneuvers
3351:Variation
3114:Libration
3109:Lissajous
3013:Low Earth
3003:Graveyard
2902:Horseshoe
2594:Leap year
2066:10 Hygiea
1819:0.240846
1730:−
1495:periapsis
1412:astronomy
1190:π
1058:ρ
1050:π
911:ρ
903:π
713:π
597:π
520:satellite
496:asteroids
488:astronomy
209:Equations
137:Types of
3287:Position
2912:Inclined
2883:Circular
2552:See also
2200:Neptune
2188:Jupiter
2024:2,837.6
2001:29.5306
1635:with or
1622:location
1534:ecliptic
1475:ecliptic
1391:with or
1329:one body
1271:orbits),
1000: =
996: =
966:tungsten
527:one body
3639:Physics
3625:Portals
3496:Orbital
3466:Phasing
3426:Delta-v
3231:Apsides
3225:,
3023:Molniya
2941:Parking
2878:Capture
2866:General
2808:, Dover
2450:1810.4
2404:Neptune
2282:Jupiter
2206:Quaoar
2197:Uranus
2194:Chiron
2191:Saturn
2150:365.3
2147:1.0001
2048:1 Ceres
2030:4 Vesta
1998:0.0809
1992:0.0748
1976:90,560
1957:59,800
1950:Neptune
1938:30,589
1919:10,747
1893:Jupiter
1828:115.88
1815:Mercury
1773:Object
1641:Jupiter
1628:
1624:
1550:precess
1548:slowly
1408:periods
1397:Jupiter
1333:primary
1293:is the
1259:where:
1154:³/
1105:Iapetus
1082:Mercury
1014:
1002:
931:where:
852:density
833:⁄
817:where:
653:is the
637:where:
531:primary
492:planets
39:(album)
3732:Orbits
3152:Other
3053:Tundra
2921:Kepler
2897:Escape
2850:orbits
2727:
2676:
2479:594.2
2453:447.4
2426:234.0
2423:386.1
2420:490.8
2398:98.93
2395:118.7
2392:127.0
2389:171.4
2375:Uranus
2369:55.44
2366:61.14
2363:63.28
2360:72.65
2357:126.1
2339:31.11
2336:32.82
2333:33.43
2330:35.87
2327:45.37
2324:70.87
2314:Saturn
2308:12.12
2305:12.37
2302:12.46
2299:12.78
2296:13.81
2293:15.51
2290:19.85
2276:1.887
2273:1.893
2270:1.895
2267:1.903
2264:1.924
2261:1.954
2258:2.009
2255:2.236
2243:557.0
2240:287.5
2237:248.1
2234:164.8
2231:84.01
2228:50.42
2225:29.46
2222:11.86
2219:1.881
2203:Pluto
2162:Deimos
2142:12050
2132:365.9
2129:1.002
2114:366.5
2111:1.003
2106:287.5
2096:372.6
2093:1.020
2088:50.42
2078:445.4
2075:1.219
2070:5.557
2060:466.7
2057:1.278
2052:4.600
2042:504.0
2039:1.380
2034:3.629
2021:7.769
2016:0.886
1982:366.7
1979:1.004
1973:248.1
1963:367.5
1960:1.006
1954:164.8
1944:369.7
1941:1.012
1935:84.01
1931:Uranus
1925:378.1
1922:1.035
1916:29.46
1912:Saturn
1906:398.9
1903:1.092
1897:11.86
1887:779.9
1884:2.135
1881:687.0
1878:1.881
1847:583.9
1844:1.599
1838:0.615
1825:0.317
1459:(also
1399:has a
1109:Tethys
753:meters
474:(also
3675:Stars
3394:Epoch
3183:Shape
3121:Lunar
3075:Mars
3067:About
3038:Polar
2858:Types
2600:Notes
2432:Pluto
2209:Eris
2185:Mars
1900:4331
1853:Earth
1834:Venus
1484:epoch
1446:Earth
1344:Earth
1086:Venus
745:hours
514:, or
512:stars
504:moons
484:orbit
90:Apsis
3186:Size
3125:Sun
3104:Halo
2956:semi
2738:2018
2725:ISBN
2674:ISBN
2249:Mars
2158:moon
2124:557
1988:Moon
1874:Mars
1653:and
1544:and
1530:year
1526:0 hr
1489:The
1455:The
1442:Moon
1426:The
1414:and
1379:The
1315:For
978:lead
576:is:
535:e.g.
470:The
2961:sub
2873:Box
2542:AB
2527:AB
2516:AB
2215:Sun
1577:),
1536:(a
1524:of
1463:or
1450:Sun
1348:Sun
1162:In
500:Sun
494:or
141:by
3723::
3309:,
3305:,
2914:/
2890:/
2785:.
2764:^
2754:.
2696:.
2538:â
2013:)
1868:â
1809:)
1802:)
1800:yr
1795:)
1788:)
1786:yr
1613:.
1597:.
1585:,
1376:.
1358:.
1280:+
1026:)
998:VĪ
982:mm
970:mm
962:cm
842:.
835:â2
759:.
749:kg
533:,
502:,
3627::
3557:n
3389:0
3386:t
3376:v
3367:n
3358:T
3338:l
3329:L
3320:E
3311:f
3307:θ
3303:ÎŊ
3294:M
3274:Ī
3265:Ī
3256:Ί
3247:i
3227:q
3223:Q
3214:b
3205:a
3196:e
2841:e
2834:t
2827:v
2789:.
2758:.
2740:.
2706:.
2682:.
2009:(
1858:1
1807:d
1805:(
1798:(
1793:d
1791:(
1784:(
1743:2
1739:T
1735:1
1723:1
1719:T
1715:1
1710:=
1702:n
1699:y
1696:s
1691:T
1687:1
1672:2
1669:T
1665:1
1662:T
1658:2
1655:T
1651:1
1648:T
1626:â
1573:(
1297:.
1291:G
1285:2
1282:M
1278:1
1275:M
1264:a
1239:)
1233:2
1229:M
1225:+
1220:1
1216:M
1211:(
1207:G
1201:3
1197:a
1187:2
1184:=
1181:T
1168:T
1156:T
1152:a
1148:a
1144:T
1124:G
1116:T
1101:Ī
1093:T
1055:G
1047:3
1040:=
1037:T
1023:Ī
1020:a
1017:Ī
1011:3
1008:/
1005:4
994:M
989:Ī
974:s
972:/
954:Ī
948:G
942:a
936:r
908:G
900:3
890:3
886:r
880:3
876:a
868:=
865:T
831:1
822:r
798:r
794:M
791:G
784:=
779:o
775:v
725:3
717:2
709:4
702:2
698:T
694:M
691:G
684:=
681:a
661:M
657:,
651:G
642:a
617:M
614:G
608:3
604:a
594:2
591:=
588:T
570:T
558:b
554:a
459:e
452:t
445:v
327:)
323:(
174:)
165:(
41:.
31:.
20:)
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