25:
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TOSHI SHIDA, On the Body Tides of the Earth, A Proposal for the
International Geodetic Association, Proceedings of the Tokyo Mathematico-Physical Society. 2nd Series, 1911-1912, Volume 6, Issue 16, Pages 242-258, ISSN 2185-2693,
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Hinderer, Tanja; Lackey, Benjamin D.; Lang, Ryan N.; Read, Jocelyn S. (23 June 2010). "Tidal deformability of neutron stars with realistic equations of state and their gravitational wave signatures in binary inspiral".
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represents the ratio of the horizontal (transverse) displacement of an element of mass of the planet's crust to that of the corresponding static ocean tide. In potential notation the transverse displacement is
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938:
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423:
is defined as the cubical dilation or the ratio of the additional potential (self-reactive force) produced by the deformation of the deforming potential. It can be represented as
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1161:"Tidal Deformation of the Solid Earth: A Finite Difference Discretization", S.K.Poulsen; Niels Bohr Institute, University of Copenhagen; p 24;
368:. However, the deformation of the sphere causes the potential field to change, and thereby deform the sphere even more. The theoretical maximum is
43:
167:; also defined as the vertical (radial) displacement or variation of the planet's elastic properties. In terms of the tide generating potential
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1201:
61:
508:
739:." The magnitudes of the Love numbers depend on the rigidity and mass distribution of the spheroid. Love numbers
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1107:
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Love
Augustus Edward Hough. The yielding of the earth to disturbing forces 82 Proc. R. Soc. Lond. A 1909
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or other gravitating object, and the susceptibility of its shape to change in response to an external
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145:, which was needed to obtain a complete overall description of the solid Earth's response to the
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According to
Cartwright, "An elastic solid spheroid will yield to an external tide potential
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8:
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39:
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Tides: A Scientific
History; David E. Cartwright; Cambridge University Press, 1999,
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1106:. Measuring the Love numbers of compact objects in binary mergers is a key goal of
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1162:
1486:
1214:
Yazadjiev, Stoytcho S.; Doneva, Daniela D.; Kokkotas, Kostas D. (October 2018).
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1514:
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1380:
1313:
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and the self-attraction of this tide will increase the external potential by
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are thought to have high rigidity in the crust, and thus a low Love number:
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1127:
109:
1322:
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is defined as the ratio of the body tide to the height of the static
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can also be calculated for higher orders of spherical harmonics.
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is acceleration due to gravity. For a hypothetical solid Earth
105:
1453:"Tidal deformation and dissipation of rotating black holes"
1184:
Earth Tides; D.C.Agnew, University of
California; 2007; 174
146:
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in vacuum have vanishing Love numbers for all multipoles
141:. Later, in 1912, Toshi Shida added a third Love number,
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943:
For Earth's tides one can calculate the tilt factor as
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1216:"Tidal Love numbers of neutron stars in f(R) gravity"
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For elastic Earth the Love numbers lie in the range:
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may be too technical for most readers to understand
1345:Damour, Thibault; Nagar, Alessandro (2009-10-23).
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1402:Binnington, Taylor; Poisson, Eric (2009-10-14).
1347:"Relativistic tidal properties of neutron stars"
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553:{\displaystyle l\nabla (V(\theta ,\phi ))/g}
1404:"Relativistic theory of tidal Love numbers"
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933:{\displaystyle 0.084\leq l_{2}\leq 0.088}
894:{\displaystyle 0.304\leq k_{2}\leq 0.312}
855:{\displaystyle 0.616\leq h_{2}\leq 0.624}
62:Learn how and when to remove this message
46:, without removing the technical details.
16:Parameters describing a planet's rigidity
1062:{\displaystyle 0.05\leq k_{2}\leq 0.17}
342:. For a liquid Earth, one would expect
1507:
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1128:http://doi.org/10.1098/rspa.1909.0008
44:make it understandable to non-experts
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18:
462:{\displaystyle kV(\theta ,\phi )/g}
249:{\displaystyle hV(\theta ,\phi )/g}
131:response of the Earth to the tides—
13:
1525:Dimensionless numbers of mechanics
1024:, where subscript two is assumed.
567:
515:
203:{\displaystyle V(\theta ,\phi )/g}
14:
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1451:Chia, Horng Sheng (2021-07-06).
23:
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1220:The European Physical Journal C
127:which characterize the overall
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100:parameters that measure the
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1099:{\displaystyle k_{\ell }=0}
657:degree 2 by a surface tide
10:
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1438:10.1103/PhysRevD.80.084018
1381:10.1103/PhysRevD.80.084035
1314:10.1103/PhysRevD.81.123016
1017:{\displaystyle 1+h-(3/2)k}
732:{\displaystyle k_{2}U_{2}}
117:Augustus Edward Hough Love
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573:{\displaystyle \nabla }
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394:. For the real Earth,
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119:introduced the values
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1306:2010PhRvD..81l3016H
1242:2018EPJC...78..818Y
611:{\displaystyle l=0}
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32:This article
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1323:1721.1/64461
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76:Love numbers
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1530:Geodynamics
1226:(10): 818.
1071:black holes
153:Definitions
134:Earth tides
1509:Categories
1470:2010.07300
1233:1803.09534
1114:References
139:body tides
1495:2470-0010
1421:0906.1366
1389:1550-7998
1364:0906.0096
1297:0911.3535
1086:ℓ
1054:≤
1041:≤
992:−
960:−
925:≤
912:≤
886:≤
873:≤
847:≤
834:≤
568:∇
534:ϕ
528:θ
516:∇
446:ϕ
440:θ
284:ϕ
264:θ
233:ϕ
227:θ
187:ϕ
181:θ
115:In 1909,
52:June 2024
1332:14819350
1268:30524193
1165:Archived
582:gradient
560:, where
469:, where
102:rigidity
1475:Bibcode
1426:Bibcode
1369:Bibcode
1302:Bibcode
1259:6244867
1238:Bibcode
129:elastic
38:Please
1493:
1387:
1330:
1266:
1256:
1200:
793:, and
622:Values
256:where
96:) are
90:, and
1515:Tides
1465:arXiv
1416:arXiv
1359:arXiv
1328:S2CID
1292:arXiv
1228:arXiv
928:0.088
909:0.084
889:0.312
870:0.304
850:0.624
831:0.616
147:tides
104:of a
1491:ISSN
1385:ISSN
1264:PMID
1198:ISBN
1057:0.17
1038:0.05
901:and
588:and
123:and
74:The
1483:doi
1461:104
1434:doi
1377:doi
1318:hdl
1310:doi
1254:PMC
1246:doi
1141:doi
653:of
382:2.5
137:or
42:to
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1094:0
1091:=
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989:h
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842:2
838:h
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670:2
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600:l
590:k
586:h
548:g
544:/
540:)
537:)
531:,
525:(
522:V
519:(
513:l
501:l
483:0
480:=
477:k
457:g
453:/
449:)
443:,
437:(
434:V
431:k
420:k
402:h
379:=
376:h
356:1
353:=
350:h
330:0
327:=
324:h
304:g
244:g
240:/
236:)
230:,
224:(
221:V
218:h
198:g
194:/
190:)
184:,
178:(
175:V
160:h
143:l
125:k
121:h
93:l
87:k
81:h
78:(
65:)
59:(
54:)
50:(
36:.
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