117:. The same mechanism has provided the energy to melt the lower layers of the ice surrounding the rocky mantle of Jupiter's next-closest large moon, Europa. However, the heating of the latter is weaker, because of reduced flexing—Europa has half Io's orbital frequency and a 14% smaller radius; also, while Europa's orbit is about twice as eccentric as Io's, tidal force falls off with the cube of distance and is only a quarter as strong at Europa. Jupiter maintains the moons' orbits via tides they raise on it and thus its rotational energy ultimately powers the system. Saturn's moon
142:, with 3.2 TW being due to tidal interactions with the Moon and 0.5 TW being due to tidal interactions with the Sun. Egbert & Ray (2001) confirmed that overall estimate, writing "The total amount of tidal energy dissipated in the Earth-Moon-Sun system is now well-determined. The methods of space geodesy—altimetry, satellite laser ranging, lunar laser ranging—have converged to 3.7 TW
74:). Sustained tidal heating occurs when the elliptical orbit is prevented from circularizing due to additional gravitational forces from other bodies that keep tugging the object back into an elliptical orbit. In this more complex system, orbital and rotational energy still is being converted to thermal energy; however, now the orbit's
149:
Heller et al. (2021) estimated that shortly after the Moon was formed, when the Moon orbited 10-15 times closer to Earth than it does now, tidal heating might have contributed ~10 W/m of heating over perhaps 100 million years, and that this could have accounted for a temperature increase of up to 5°C
543:
which measures the efficiency at which the satellite dissipates tidal energy into frictional heat. This imaginary portion is defined by interplay of the body's rheology and self-gravitation. It, therefore, is a function of the body's radius, density, and rheological parameters (the
383:
57:
than near apoapsis. Thus the deformation of the body due to tidal forces (i.e. the tidal bulge) varies over the course of its orbit, generating internal friction which heats its interior. This energy gained by the object comes from its
137:
Munk & Wunsch (1998) estimated that Earth experiences 3.7 TW (0.0073 W/m) of tidal heating, of which 95% (3.5 TW or 0.0069 W/m) is associated with ocean tides and 5% (0.2 TW or 0.0004 W/m) is associated with
257:
552:, and others – dependent upon the rheological model). The rheological parameters' values, in turn, depend upon the temperature and the concentration of partial melt in the body's interior.
537:
214:
498:
45:
processes: orbital and rotational energy is dissipated as heat in either (or both) the surface ocean or interior of a planet or satellite. When an object is in an
248:
463:
443:
423:
403:
669:
909:
Segatz, M.; Spohn, T.; Ross, M.N.; Schubert, G. (August 1988). "Tidal dissipation, surface heat flow, and figure of viscoelastic models of Io".
1142:
158:
Harada et al. (2014) proposed that tidal heating may have created a molten layer at the core-mantle boundary within Earth's Moon.
775:"Habitability of the early Earth: liquid water under a faint young Sun facilitated by strong tidal heating due to a closer Moon"
470:
121:
is similarly thought to have a liquid water ocean beneath its icy crust, due to tidal heating related to its resonance with
378:{\displaystyle {\dot {E}}_{\text{Tidal}}=-\operatorname {Im} (k_{2}){\frac {21}{2}}{\frac {GM_{h}^{2}R^{5}ne^{2}}{a^{6}}}}
1147:
993:"Increased Tidal Dissipation Using Advanced Rheological Models: Implications for Io and Tidally Active Exoplanets"
938:
584:
503:
183:
129:
which eject material from
Enceladus are thought to be powered by friction generated within its interior.
1152:
217:
67:
1108:
1014:
957:
883:
796:
745:
699:
618:
251:
79:
1044:"Tidal Dissipation Compared to Seismic Dissipation: In Small Bodies, in Earths, and in Superearths"
579:
221:
167:
90:
Tidal heating is responsible for the geologic activity of the most volcanically active body in the
831:
1098:
1055:
1004:
973:
947:
812:
786:
650:
634:
569:
555:
The tidally dissipated power in a nonsynchronised rotator is given by a more complex expression.
936:
Henning, Wade G. (2009). "Tidally Heated
Terrestrial Exoplanets: Viscoelastic Response Models".
684:
66:, so over time in a two-body system, the initial elliptical orbit decays into a circular orbit (
774:
642:
609:
103:
63:
1116:
1065:
1022:
965:
918:
891:
872:"Strong tidal heating in an ultralow-viscosity zone at the core–mantle boundary of the Moon"
843:
804:
753:
707:
626:
118:
46:
870:
Harada, Y; Goosens, S; Matsumoto, K; Yan, J; Ping, J; Noda, H; Harayama, J (27 July 2014).
476:
70:) and the rotational periods of the two bodies adjust towards matching the orbital period (
114:
227:
1112:
1018:
961:
887:
800:
749:
703:
622:
969:
448:
428:
408:
388:
107:
75:
59:
42:
1070:
1043:
711:
607:
Peale, S.J.; Cassen, P.; Reynolds, R.T. (1979). "Melting of Io by Tidal
Dissipation".
1136:
977:
922:
871:
816:
574:
545:
110:
71:
1121:
1086:
654:
122:
91:
630:
564:
540:
466:
139:
126:
50:
1027:
992:
808:
17:
549:
95:
646:
848:
758:
733:
734:"Estimatesof tidal energy dissipationfrom TOPEX/Poseidon altimeter data"
638:
99:
895:
27:
Orbital and friction heating on a planet or moon oceans, or interior
1009:
791:
1103:
1060:
952:
172:
Jupiter's closest moon Io experiences considerable tidal heating.
54:
1087:"Tidal Dissipation in a Homogeneous Spherical Body. I. Methods"
773:
Heller, R; Duda, JP; Winkler, M; Reitner, J; Gizon, L (2021).
685:"Abyssal recipes II: energetics of tidal and wind mixing"
692:
Deep Sea
Research Part I: Oceanographic Research Papers
732:
Egbert, Gary D.; Ray, Richard D. (October 15, 2001).
539:
represents the imaginary portion of the second-order
506:
479:
451:
431:
411:
391:
260:
230:
186:
531:
492:
457:
437:
417:
397:
377:
242:
208:
102:. Io's eccentricity persists as the result of its
667:Peale, S.J. (2003). "Tidally induced volcanism".
1085:Efroimsky, Michael; Makarov, Valeri V. (2014).
465:are respectively the satellite's mean radius,
8:
670:Celestial Mechanics and Dynamical Astronomy
602:
600:
532:{\displaystyle \operatorname {Im} (k_{2})}
1120:
1102:
1069:
1059:
1026:
1008:
991:Renaud, Joe P.; Henning, Wade G. (2018).
951:
847:
832:"How Much Did the Moon Heat Young Earth?"
790:
757:
520:
505:
500:is the host (or central) body's mass and
484:
478:
450:
430:
410:
390:
367:
356:
343:
333:
328:
318:
308:
299:
274:
263:
262:
259:
229:
209:{\displaystyle {\dot {E}}_{\text{Tidal}}}
200:
189:
188:
185:
596:
7:
683:Munk, Walter; Wunsch, Carl (1998).
25:
830:Jure Japelj (11 January 2022).
738:Journal of Geophysical Research
53:acting on it are stronger near
526:
513:
305:
292:
1:
712:10.1016/S0967-0637(98)00070-3
78:would shrink rather than its
970:10.1088/0004-637X/707/2/1000
923:10.1016/0019-1035(88)90001-2
631:10.1126/science.203.4383.892
1071:10.1088/0004-637X/746/2/150
1042:Efroimsky, Michael (2012).
1169:
809:10.1007/s12542-021-00582-7
165:
1122:10.1088/0004-637X/795/1/6
1091:The Astrophysical Journal
1048:The Astrophysical Journal
997:The Astrophysical Journal
939:The Astrophysical Journal
585:Planetary differentiation
216:, in a satellite that is
1143:Concepts in astrophysics
1028:10.3847/1538-4357/aab784
180:The tidal heating rate,
533:
494:
459:
439:
419:
399:
379:
244:
210:
534:
495:
493:{\displaystyle M_{h}}
460:
440:
420:
400:
380:
245:
211:
150:on the early Earth.
68:tidal circularization
41:) occurs through the
849:10.1029/2022EO220017
759:10.1029/2000JC000699
744:(C10): 22475–22502.
504:
477:
473:, and eccentricity.
449:
429:
409:
389:
258:
228:
184:
1113:2014ApJ...795....6E
1019:2018ApJ...857...98R
962:2009ApJ...707.1000H
888:2014NatGe...7..569H
801:2021PalZ...95..563H
750:2001JGR...10622475E
704:1998DSRI...45.1977M
623:1979Sci...203..892P
580:Io Volcano Observer
467:mean orbital motion
338:
243:{\displaystyle I=0}
168:Tidal heating of Io
127:water vapor geysers
86:Moons of Gas Giants
570:Tidal acceleration
529:
490:
455:
435:
415:
395:
375:
324:
240:
206:
104:orbital resonances
1148:Planetary science
876:Nature Geoscience
698:(12): 1977–2010.
617:(4383): 892–894.
458:{\displaystyle e}
438:{\displaystyle a}
418:{\displaystyle n}
398:{\displaystyle R}
373:
316:
277:
271:
203:
197:
64:rotational energy
16:(Redirected from
1160:
1127:
1126:
1124:
1106:
1082:
1076:
1075:
1073:
1063:
1039:
1033:
1032:
1030:
1012:
988:
982:
981:
955:
946:(2): 1000–1015.
933:
927:
926:
906:
900:
899:
896:10.1038/ngeo2211
867:
861:
860:
858:
856:
851:
827:
821:
820:
794:
770:
764:
763:
761:
729:
723:
722:
720:
718:
689:
680:
674:
665:
659:
658:
604:
538:
536:
535:
530:
525:
524:
499:
497:
496:
491:
489:
488:
471:orbital distance
464:
462:
461:
456:
444:
442:
441:
436:
424:
422:
421:
416:
404:
402:
401:
396:
384:
382:
381:
376:
374:
372:
371:
362:
361:
360:
348:
347:
337:
332:
319:
317:
309:
304:
303:
279:
278:
275:
273:
272:
264:
249:
247:
246:
241:
218:spin-synchronous
215:
213:
212:
207:
205:
204:
201:
199:
198:
190:
145:
47:elliptical orbit
21:
1168:
1167:
1163:
1162:
1161:
1159:
1158:
1157:
1133:
1132:
1131:
1130:
1084:
1083:
1079:
1041:
1040:
1036:
990:
989:
985:
935:
934:
930:
908:
907:
903:
869:
868:
864:
854:
852:
829:
828:
824:
772:
771:
767:
731:
730:
726:
716:
714:
687:
682:
681:
677:
666:
662:
606:
605:
598:
593:
561:
516:
502:
501:
480:
475:
474:
447:
446:
427:
426:
407:
406:
387:
386:
363:
352:
339:
320:
295:
261:
256:
255:
252:eccentric orbit
226:
225:
187:
182:
181:
178:
170:
164:
156:
143:
135:
88:
33:(also known as
28:
23:
22:
15:
12:
11:
5:
1166:
1164:
1156:
1155:
1150:
1145:
1135:
1134:
1129:
1128:
1077:
1034:
983:
928:
917:(2): 187–206.
901:
882:(8): 569–572.
862:
822:
785:(4): 563–575.
765:
724:
675:
660:
595:
594:
592:
589:
588:
587:
582:
577:
572:
567:
560:
557:
528:
523:
519:
515:
512:
509:
487:
483:
454:
434:
414:
394:
370:
366:
359:
355:
351:
346:
342:
336:
331:
327:
323:
315:
312:
307:
302:
298:
294:
291:
288:
285:
282:
270:
267:
250:), and has an
239:
236:
233:
196:
193:
177:
174:
166:Main article:
163:
160:
155:
152:
134:
131:
108:Galilean moons
87:
84:
76:semimajor axis
60:orbital energy
43:tidal friction
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
1165:
1154:
1151:
1149:
1146:
1144:
1141:
1140:
1138:
1123:
1118:
1114:
1110:
1105:
1100:
1096:
1092:
1088:
1081:
1078:
1072:
1067:
1062:
1057:
1053:
1049:
1045:
1038:
1035:
1029:
1024:
1020:
1016:
1011:
1006:
1002:
998:
994:
987:
984:
979:
975:
971:
967:
963:
959:
954:
949:
945:
941:
940:
932:
929:
924:
920:
916:
912:
905:
902:
897:
893:
889:
885:
881:
877:
873:
866:
863:
850:
845:
841:
837:
833:
826:
823:
818:
814:
810:
806:
802:
798:
793:
788:
784:
780:
776:
769:
766:
760:
755:
751:
747:
743:
739:
735:
728:
725:
713:
709:
705:
701:
697:
693:
686:
679:
676:
672:
671:
664:
661:
656:
652:
648:
644:
640:
636:
632:
628:
624:
620:
616:
612:
611:
603:
601:
597:
590:
586:
583:
581:
578:
576:
575:Tidal locking
573:
571:
568:
566:
563:
562:
558:
556:
553:
551:
547:
546:shear modulus
542:
521:
517:
510:
507:
485:
481:
472:
468:
452:
432:
412:
392:
368:
364:
357:
353:
349:
344:
340:
334:
329:
325:
321:
313:
310:
300:
296:
289:
286:
283:
280:
268:
265:
254:is given by:
253:
237:
234:
231:
223:
219:
194:
191:
175:
173:
169:
161:
159:
153:
151:
147:
141:
132:
130:
128:
124:
120:
116:
112:
109:
105:
101:
97:
93:
85:
83:
81:
77:
73:
72:tidal locking
69:
65:
61:
56:
52:
48:
44:
40:
39:tidal flexing
36:
35:tidal working
32:
31:Tidal heating
19:
18:Tidal Heating
1153:Tidal forces
1094:
1090:
1080:
1051:
1047:
1037:
1000:
996:
986:
943:
937:
931:
914:
910:
904:
879:
875:
865:
853:. Retrieved
839:
835:
825:
782:
778:
768:
741:
737:
727:
715:. Retrieved
695:
691:
678:
673:87, 129–155.
668:
663:
614:
608:
554:
179:
171:
157:
148:
136:
98:, a moon of
92:Solar System
89:
80:eccentricity
51:tidal forces
38:
34:
30:
29:
565:Cryovolcano
541:Love number
140:Earth tides
1137:Categories
1010:1707.06701
792:2007.03423
591:References
1104:1406.2376
1061:1105.3936
1003:(2): 98.
978:119286375
953:0912.1907
817:244532427
550:viscosity
511:
290:
284:−
269:˙
195:˙
119:Enceladus
106:with the
55:periapsis
1097:(1): 6.
855:26 March
717:26 March
655:21271617
647:17771724
559:See also
222:coplanar
115:Ganymede
1109:Bibcode
1054:: 150.
1015:Bibcode
958:Bibcode
884:Bibcode
797:Bibcode
746:Bibcode
700:Bibcode
639:1747884
619:Bibcode
610:Science
176:Formula
100:Jupiter
62:and/or
976:
911:Icarus
815:
653:
645:
637:
445:, and
385:where
144:
125:. The
111:Europa
49:, the
1099:arXiv
1056:arXiv
1005:arXiv
974:S2CID
948:arXiv
813:S2CID
787:arXiv
688:(PDF)
651:S2CID
635:JSTOR
276:Tidal
202:Tidal
146:..."
133:Earth
123:Dione
857:2023
779:PalZ
719:2023
643:PMID
154:Moon
113:and
1117:doi
1095:795
1066:doi
1052:746
1023:doi
1001:857
966:doi
944:707
919:doi
892:doi
844:doi
840:103
836:EOS
805:doi
754:doi
742:106
708:doi
627:doi
615:203
37:or
1139::
1115:.
1107:.
1093:.
1089:.
1064:.
1050:.
1046:.
1021:.
1013:.
999:.
995:.
972:.
964:.
956:.
942:.
915:75
913:.
890:.
878:.
874:.
842:.
838:.
834:.
811:.
803:.
795:.
783:95
781:.
777:.
752:.
740:.
736:.
706:.
696:45
694:.
690:.
649:.
641:.
633:.
625:.
613:.
599:^
548:,
508:Im
469:,
425:,
405:,
311:21
287:Im
220:,
162:Io
96:Io
94::
82:.
1125:.
1119::
1111::
1101::
1074:.
1068::
1058::
1031:.
1025::
1017::
1007::
980:.
968::
960::
950::
925:.
921::
898:.
894::
886::
880:7
859:.
846::
819:.
807::
799::
789::
762:.
756::
748::
721:.
710::
702::
657:.
629::
621::
527:)
522:2
518:k
514:(
486:h
482:M
453:e
433:a
413:n
393:R
369:6
365:a
358:2
354:e
350:n
345:5
341:R
335:2
330:h
326:M
322:G
314:2
306:)
301:2
297:k
293:(
281:=
266:E
238:0
235:=
232:I
224:(
192:E
20:)
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.