43:
919:
649:
811:
1267:
Rabinowitz, D. L.; Barkume, K.; Brown, M. E.; Roe, H.; Schwartz, M.; Tourtellotte, S.; Trujillo, C. (2006). "Photometric
Observations Constraining the Size, Shape, and Albedo of 2003 EL
823:
414:
288:
179:
can be uni-, bi- or tri-axial, depending on what kind of ellipsoid is used to model it. Given the dimensions of an irregularly shaped object, one can calculate its mean radius:
554:
722:
703:
676:
475:
501:
440:
929:
predicts that over as little as a hundred days, a body rotating as rapidly as Haumea will have been distorted into the equilibrium form of a tri-axial ellipsoid.
514:
will be close in shape to an ellipsoid, with the details depending on the rate of the rotation. At moderate rates, it will assume the form of either a bi-axial (
355:
335:
315:
228:
208:
132:
112:
88:
1111:
1337:
1059:"High precision model of precession and nutation of the asteroids (1) Ceres, (4) Vesta, (433) Eros, (2867) Steins, and (25143) Itokawa"
1103:
1192:
1161:
914:{\displaystyle D=\left(2100~{\text{km}}\cdot 1680~{\text{km}}\cdot 1074~{\text{km}}\right)^{1/3}=1559~{\text{km}}}
360:
233:
1032:
986:
979:"Distorted, nonspherical transiting planets: impact on the transit depth and on the radius determination"
644:{\displaystyle R=\left((6378.1~{\text{km}})^{2}\cdot 6356.8~{\text{km}}\right)^{1/3}=6371.0~{\text{km}}}
1153:
1033:"Isotropic position and inertia ellipsoids and zonoids of the unit ball and normed n-dimensional Space"
820:
has dimensions 2,100 × 1,680 × 1,074 km, resulting in a mean diameter of
35:
28:
522:) ellipsoid. At faster rotations, non-ellipsoidal shapes can be expected, but these are not stable.
170:
158:
806:{\displaystyle D=(360~{\text{km}}\cdot 294~{\text{km}}\cdot 254~{\text{km}})^{1/3}=300{\text{ km}}}
1147:
1184:
511:
510:
are nearly spherical if they are not rotating. A rotating object that is massive enough to be in
63:
1058:
978:
1273:
1077:
1009:
1292:
1231:
1120:
1073:
1005:
926:
681:
654:
448:
187:
8:
922:
480:
419:
294:
1296:
1235:
1124:
1308:
1282:
1249:
1221:
995:
515:
340:
320:
300:
213:
193:
150:
117:
97:
73:
1132:
90:), which is twice the mean radius, is also used. For a non-spherical object, the mean
1188:
1157:
1312:
1253:
1300:
1239:
1128:
1081:
1013:
954:
519:
1085:
1017:
1178:
1043:
939:
183:
142:
as the object. In the case of a sphere, the mean radius is equal to the radius.
1332:
1244:
1209:
949:
1326:
507:
176:
46:
A sphere (top), rotational ellipsoid (left) and tri-axial ellipsoid (right)
1287:
21:
712:
146:
55:
1304:
1226:
715:, which is close in shape to a tri-axial ellipsoid with dimensions
709:
416:. The formula for a rotational ellipsoid is the special case where
1000:
27:"Mean diameter (astronomy)" redirects here. For other uses, see
16:
A measure for the size of planets and other Solar System objects
1040:
Geometric
Aspects of Functional Analysis: Israel Seminar (GAFA)
817:
651:. The equatorial and polar radii of a planet are often denoted
139:
135:
91:
59:
1271:, a Rapidly Rotating, Pluto-Sized Object in the Kuiper Belt".
944:
535:, which can be approximated as an oblate spheroid with radii
532:
42:
34:"Dimensions (astronomy)" redirects here. For other uses, see
816:
Assuming it is in hydrostatic equilibrium, the dwarf planet
1104:"Mean radius, mass, and inertia for reference Earth models"
1266:
145:
For any irregularly shaped rigid body, there is a unique
1208:
Dunham, E. T.; Desch, S. J.; Probst, L. (April 2019).
1210:"Haumea's Shape, Composition, and Internal Structure"
826:
725:
684:
657:
557:
483:
451:
422:
363:
343:
323:
303:
236:
216:
196:
120:
100:
76:
1056:
976:
913:
805:
697:
670:
643:
495:
469:
434:
408:
349:
329:
309:
282:
222:
202:
126:
106:
82:
1207:
1324:
1101:
1030:
1260:
1112:Physics of the Earth and Planetary Interiors
1057:Petit, A.; Souchay, J.; Lhotka, C. (2014).
977:Leconte, J.; Lai, D.; Chabrier, G. (2011).
1286:
1243:
1225:
1201:
1170:
1145:
1097:
1095:
999:
972:
970:
409:{\displaystyle R=(a\cdot b\cdot c)^{1/3}}
41:
1176:
1149:The Stability of Rotating Liquid Masses
717:360 km × 294 km × 254 km
171:Moment of inertia § Principal axes
1325:
1092:
967:
283:{\displaystyle R=(a^{2}\cdot c)^{1/3}}
66:. Alternatively, the closely related
1031:Milman, V. D.; Pajor, A. (1987–88).
13:
445:For a sphere, which is uni-axial (
134:) is defined as the radius of the
14:
1349:
1338:Units of measurement in astronomy
1102:Chambat, F.; Valette, B. (2001).
157:of an object are defined as the
1139:
1050:
1024:
775:
732:
585:
570:
389:
370:
263:
243:
164:
1:
1133:10.1016/S0031-9201(01)00200-X
960:
58:is a measure for the size of
1066:Astronomy & Astrophysics
987:Astronomy & Astrophysics
138:that would enclose the same
7:
1086:10.1051/0004-6361/201322905
1018:10.1051/0004-6361/201015811
933:
525:
161:of that special ellipsoid.
10:
1354:
1154:Cambridge University Press
168:
36:Dimension (disambiguation)
18:
1214:The Astrophysical Journal
1180:A Dictionary of Astronomy
719:, has a mean diameter of
149:with the same volume and
64:small Solar System bodies
29:Diameter (disambiguation)
1245:10.3847/1538-4357/ab13b3
1185:Oxford University Press
1078:2014A&A...565A..79P
1010:2011A&A...528A..41L
512:hydrostatic equilibrium
1146:Lyttleton, R. (1953).
1042:. Berlin, Heidelberg:
915:
807:
699:
672:
645:
497:
477:), this simplifies to
471:
436:
410:
351:
331:
311:
284:
224:
204:
128:
108:
84:
47:
1274:Astrophysical Journal
916:
808:
700:
698:{\displaystyle r_{p}}
673:
671:{\displaystyle r_{e}}
646:
551:, the mean radius is
498:
472:
470:{\displaystyle a=b=c}
437:
411:
352:
332:
312:
285:
230:has a mean radius of
225:
205:
129:
109:
85:
45:
1177:Ridpath, I. (2012).
824:
723:
682:
655:
555:
481:
449:
420:
361:
341:
321:
301:
234:
214:
194:
188:rotational ellipsoid
175:The dimensions of a
153:. In astronomy, the
118:
98:
74:
20:For other uses, see
1297:2006ApJ...639.1238R
1236:2019ApJ...877...41D
1125:2001PEPI..124..237C
496:{\displaystyle R=a}
435:{\displaystyle a=b}
295:tri-axial ellipsoid
923:rotational physics
911:
803:
695:
668:
641:
493:
467:
432:
406:
347:
327:
307:
280:
220:
200:
151:moments of inertia
124:
104:
80:
48:
1194:978-0-19-960905-5
927:deformable bodies
909:
905:
876:
872:
862:
858:
848:
844:
801:
772:
768:
758:
754:
744:
740:
639:
635:
606:
602:
582:
578:
350:{\displaystyle c}
330:{\displaystyle b}
310:{\displaystyle a}
223:{\displaystyle c}
203:{\displaystyle a}
127:{\displaystyle r}
107:{\displaystyle R}
83:{\displaystyle D}
1345:
1317:
1316:
1290:
1288:astro-ph/0509401
1281:(2): 1238–1251.
1264:
1258:
1257:
1247:
1229:
1205:
1199:
1198:
1174:
1168:
1167:
1143:
1137:
1136:
1108:
1099:
1090:
1089:
1063:
1054:
1048:
1047:
1037:
1028:
1022:
1021:
1003:
983:
974:
955:Planetary radius
920:
918:
917:
912:
910:
907:
903:
896:
895:
891:
882:
878:
877:
874:
870:
863:
860:
856:
849:
846:
842:
812:
810:
809:
804:
802:
799:
791:
790:
786:
773:
770:
766:
759:
756:
752:
745:
742:
738:
718:
704:
702:
701:
696:
694:
693:
677:
675:
674:
669:
667:
666:
650:
648:
647:
642:
640:
637:
633:
626:
625:
621:
612:
608:
607:
604:
600:
593:
592:
583:
580:
576:
550:
548:
542:
540:
518:) or tri-axial (
502:
500:
499:
494:
476:
474:
473:
468:
441:
439:
438:
433:
415:
413:
412:
407:
405:
404:
400:
357:has mean radius
356:
354:
353:
348:
336:
334:
333:
328:
316:
314:
313:
308:
289:
287:
286:
281:
279:
278:
274:
255:
254:
229:
227:
226:
221:
209:
207:
206:
201:
133:
131:
130:
125:
113:
111:
110:
105:
89:
87:
86:
81:
39:
32:
25:
1353:
1352:
1348:
1347:
1346:
1344:
1343:
1342:
1323:
1322:
1321:
1320:
1270:
1265:
1261:
1206:
1202:
1195:
1187:. p. 115.
1175:
1171:
1164:
1144:
1140:
1106:
1100:
1093:
1061:
1055:
1051:
1035:
1029:
1025:
981:
975:
968:
963:
940:Earth ellipsoid
936:
906:
887:
883:
873:
859:
845:
838:
834:
833:
825:
822:
821:
798:
782:
778:
774:
769:
755:
741:
724:
721:
720:
716:
705:, respectively.
689:
685:
683:
680:
679:
662:
658:
656:
653:
652:
636:
617:
613:
603:
588:
584:
579:
569:
565:
564:
556:
553:
552:
546:
544:
538:
536:
528:
482:
479:
478:
450:
447:
446:
421:
418:
417:
396:
392:
388:
362:
359:
358:
342:
339:
338:
322:
319:
318:
302:
299:
298:
270:
266:
262:
250:
246:
235:
232:
231:
215:
212:
211:
195:
192:
191:
186:, bi-axial, or
184:oblate spheroid
173:
167:
119:
116:
115:
99:
96:
95:
75:
72:
71:
40:
33:
26:
19:
17:
12:
11:
5:
1351:
1341:
1340:
1335:
1319:
1318:
1305:10.1086/499575
1268:
1259:
1200:
1193:
1169:
1162:
1138:
1091:
1049:
1023:
965:
964:
962:
959:
958:
957:
952:
950:Geometric mean
947:
942:
935:
932:
931:
930:
902:
899:
894:
890:
886:
881:
869:
866:
855:
852:
841:
837:
832:
829:
814:
797:
794:
789:
785:
781:
777:
765:
762:
751:
748:
737:
734:
731:
728:
706:
692:
688:
665:
661:
632:
629:
624:
620:
616:
611:
599:
596:
591:
587:
575:
572:
568:
563:
560:
527:
524:
492:
489:
486:
466:
463:
460:
457:
454:
431:
428:
425:
403:
399:
395:
391:
387:
384:
381:
378:
375:
372:
369:
366:
346:
326:
306:
277:
273:
269:
265:
261:
258:
253:
249:
245:
242:
239:
219:
199:
169:Main article:
166:
163:
159:principal axes
123:
103:
79:
15:
9:
6:
4:
3:
2:
1350:
1339:
1336:
1334:
1331:
1330:
1328:
1314:
1310:
1306:
1302:
1298:
1294:
1289:
1284:
1280:
1276:
1275:
1263:
1255:
1251:
1246:
1241:
1237:
1233:
1228:
1223:
1219:
1215:
1211:
1204:
1196:
1190:
1186:
1182:
1181:
1173:
1165:
1163:9781107615588
1159:
1155:
1151:
1150:
1142:
1134:
1130:
1126:
1122:
1118:
1114:
1113:
1105:
1098:
1096:
1087:
1083:
1079:
1075:
1071:
1067:
1060:
1053:
1045:
1041:
1034:
1027:
1019:
1015:
1011:
1007:
1002:
997:
993:
989:
988:
980:
973:
971:
966:
956:
953:
951:
948:
946:
943:
941:
938:
937:
928:
924:
900:
897:
892:
888:
884:
879:
867:
864:
853:
850:
839:
835:
830:
827:
819:
815:
795:
792:
787:
783:
779:
763:
760:
749:
746:
735:
729:
726:
714:
711:
707:
690:
686:
663:
659:
630:
627:
622:
618:
614:
609:
597:
594:
589:
573:
566:
561:
558:
534:
530:
529:
523:
521:
517:
513:
509:
508:dwarf planets
504:
490:
487:
484:
464:
461:
458:
455:
452:
443:
429:
426:
423:
401:
397:
393:
385:
382:
379:
376:
373:
367:
364:
344:
324:
304:
296:
291:
275:
271:
267:
259:
256:
251:
247:
240:
237:
217:
197:
189:
185:
180:
178:
172:
162:
160:
156:
152:
148:
143:
141:
137:
121:
101:
93:
77:
69:
68:mean diameter
65:
61:
57:
53:
44:
37:
30:
23:
1278:
1272:
1262:
1217:
1213:
1203:
1179:
1172:
1148:
1141:
1116:
1110:
1069:
1065:
1052:
1039:
1026:
991:
985:
506:Planets and
505:
444:
292:
181:
177:minor planet
174:
154:
144:
67:
51:
49:
531:For planet
165:Calculation
52:mean radius
22:Mean radius
1327:Categories
1227:1904.00522
1119:(3–4): 4.
1072:(A79): 3.
994:(A41): 9.
961:References
713:511 Davida
549:.8 km
541:.1 km
297:with axes
190:with axes
155:dimensions
1220:(1): 11.
1001:1101.2813
865:⋅
851:⋅
761:⋅
747:⋅
595:⋅
516:Maclaurin
383:⋅
377:⋅
257:⋅
147:ellipsoid
94:(denoted
56:astronomy
1313:11484750
1254:90262114
1046:: 65–66.
1044:Springer
934:See also
800: km
710:asteroid
526:Examples
1293:Bibcode
1232:Bibcode
1121:Bibcode
1074:Bibcode
1006:Bibcode
60:planets
1311:
1252:
1191:
1160:
921:. The
904:
871:
857:
843:
818:Haumea
767:
753:
739:
634:
631:6371.0
601:
598:6356.8
577:
574:6378.1
520:Jacobi
140:volume
136:sphere
92:radius
1333:Radii
1309:S2CID
1283:arXiv
1250:S2CID
1222:arXiv
1107:(PDF)
1062:(PDF)
1036:(PDF)
996:arXiv
982:(PDF)
945:Geoid
533:Earth
1189:ISBN
1158:ISBN
901:1559
868:1074
854:1680
840:2100
708:The
678:and
543:and
337:and
210:and
62:and
50:The
1301:doi
1279:639
1240:doi
1218:877
1129:doi
1117:124
1082:doi
1070:565
1014:doi
992:528
925:of
796:300
764:254
750:294
736:360
547:356
539:378
182:An
114:or
54:in
1329::
1307:.
1299:.
1291:.
1277:.
1269:61
1248:.
1238:.
1230:.
1216:.
1212:.
1183:.
1156:.
1152:.
1127:.
1115:.
1109:.
1094:^
1080:.
1068:.
1064:.
1038:.
1012:.
1004:.
990:.
984:.
969:^
908:km
875:km
861:km
847:km
771:km
757:km
743:km
638:km
605:km
581:km
503:.
442:.
317:,
293:A
290:.
1315:.
1303::
1295::
1285::
1256:.
1242::
1234::
1224::
1197:.
1166:.
1135:.
1131::
1123::
1088:.
1084::
1076::
1020:.
1016::
1008::
998::
898:=
893:3
889:/
885:1
880:)
836:(
831:=
828:D
813:.
793:=
788:3
784:/
780:1
776:)
733:(
730:=
727:D
691:p
687:r
664:e
660:r
628:=
623:3
619:/
615:1
610:)
590:2
586:)
571:(
567:(
562:=
559:R
545:6
537:6
491:a
488:=
485:R
465:c
462:=
459:b
456:=
453:a
430:b
427:=
424:a
402:3
398:/
394:1
390:)
386:c
380:b
374:a
371:(
368:=
365:R
345:c
325:b
305:a
276:3
272:/
268:1
264:)
260:c
252:2
248:a
244:(
241:=
238:R
218:c
198:a
122:r
102:R
78:D
70:(
38:.
31:.
24:.
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