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as they would be if there were no externally generated field acting unequally at the given point and at the center of the reference body. The externally generated field is usually that produced by a perturbing third body, often the Sun or the Moon in the frequent example-cases of points on or above the Earth's surface in a geocentric reference frame.)
31:
1699:(and everything on its surface) is in free fall. When the force on the far particle is subtracted from the force on the near particle, this first term cancels, as do all other even-order terms. The remaining (residual) terms represent the difference mentioned above and are tidal force (acceleration) terms. When ∆
178:
The relationship of an astronomical body's size, to its distance from another body, strongly influences the magnitude of tidal force. The tidal force acting on an astronomical body, such as the Earth, is directly proportional to the diameter of the Earth and inversely proportional to the cube of the
734:
is used to describe the forces due to tidal acceleration. Note that for these purposes the only gravitational field considered is the external one; the gravitational field of the body (as shown in the graphic) is not relevant. (In other words, the comparison is with the conditions at the given point
216:
The tidal force corresponds to the difference in Y between two points on the graph, with one point on the near side of the body, and the other point on the far side. The tidal force becomes larger, when the two points are either farther apart, or when they are more to the left on the graph, meaning
101:
can refer to a situation in which a body or material (for example, tidal water) is mainly under the gravitational influence of a second body (for example, the Earth), but is also perturbed by the gravitational effects of a third body (for example, the Moon). The perturbing force is sometimes in such
716:
Figure 8: Graphic of tidal forces. The top picture shows the gravity field of a body to the right (not shown); the lower shows their residual gravity once the field at the centre of the sphere is subtracted; this is the tidal force. For visualization purposes, the top arrows may be assumed as equal
153:
When a body (body 1) is acted on by the gravity of another body (body 2), the field can vary significantly on body 1 between the side of the body facing body 2 and the side facing away from body 2. Figure 2 shows the differential force of gravity on a spherical body (body 1) exerted by another body
572:
When a body rotates while subject to tidal forces, internal friction results in the gradual dissipation of its rotational kinetic energy as heat. In the case for the Earth, and Earth's Moon, the loss of rotational kinetic energy results in a gain of about 2 milliseconds per century. If the body is
220:
For example, even though the Sun has a stronger overall gravitational pull on Earth, the Moon creates a larger tidal bulge because the Moon is closer. This difference is due to the way gravity weakens with distance: the Moon's closer proximity creates a steeper decline in its gravitational pull as
165:
is the distance from a planet at which tidal effects would cause an object to disintegrate because the differential force of gravity from the planet overcomes the attraction of the parts of the object for one another. These strains would not occur if the gravitational field were uniform, because a
89:
of objects. It arises because the gravitational field exerted on one body by another is not constant across its parts: the nearer side is attracted more strongly than the farther side. The difference is positive in the near side and negative in the far side, which causes a body to get stretched.
136:
Earth's rotation accounts further for the occurrence of two high tides per day on the same location. In this figure, the Earth is the central black circle while the Moon is far off to the right. It shows both the tidal field (thick red arrows) and the gravity field (thin blue arrows) exerted on
569:, and are slightly compressed, which is what happens to the Earth's oceans under the action of the Moon. All parts of the Earth are subject to the Moon's gravitational forces, causing the water in the oceans to redistribute, forming bulges on the sides near the Moon and far from the Moon.
596:
Tidal forces contribute to ocean currents, which moderate global temperatures by transporting heat energy toward the poles. It has been suggested that variations in tidal forces correlate with cool periods in the global temperature record at 6- to 10-year intervals, and that
1635:
675:
224:
Gravitational attraction is inversely proportional to the square of the distance from the source. The attraction will be stronger on the side of a body facing the source, and weaker on the side away from the source. The tidal force is proportional to the difference.
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The Earth is 81 times more massive than the Moon, the Earth has roughly 4 times the Moon's radius. As a result, at the same distance, the tidal force of the Earth at the surface of the Moon is about 20 times stronger than that of the Moon at the Earth's surface.
221:
you move across Earth (compared to the Sun's very gradual decline from its vast distance). This steeper gradient in the Moon's pull results in a larger difference in force between the near and far sides of Earth, which is what creates the bigger tidal bulge.
676:
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2004:
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of the gravitational acceleration at the center of the body (due to the given externally generated field) from the gravitational acceleration (due to the same field) at the given point. Correspondingly, the term
883:
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at the Earth's surface. Hence the tide-raising force (acceleration) due to the Sun is about 45% of that due to the Moon. The solar tidal acceleration at the Earth's surface was first given by Newton in the
1005:
717:
to 1 N, 2 N, and 3 N (from left to right); the resulting bottom arrows would equal, respectively, -1 N (negative, thus 180-degree rotated), 0 N (invisible), and 1 N. See Figure 2 for a more detailed version
1490:
2009:
The tidal accelerations at the surfaces of planets in the Solar System are generally very small. For example, the lunar tidal acceleration at the Earth's surface along the Moon–Earth axis is about
179:
distance from another body producing a gravitational attraction, such as the Moon or the Sun. Tidal action on bath tubs, swimming pools, lakes, and other small bodies of water is negligible.
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In the case of an infinitesimally small elastic sphere, the effect of a tidal force is to distort the shape of the body without any change in volume. The sphere becomes an
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Figure 3 is a graph showing how gravitational force declines with distance. In this graph, the attractive force decreases in proportion to the square of the distance (
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557:'s rings are inside the orbits of its principal moons. Tidal forces oppose gravitational coalescence of the material in the rings to form moons.
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2657:), and wrote that the force to raise the sea along the Sun-Earth axis is "twice as great" (i.e., 2 to 38604600) which comes to about 0.52 × 10
601:
variations in tidal forcing may contribute to millennial climate changes. No strong link to millennial climate changes has been found to date.
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106:): it is the difference between the force exerted by the third body on the second and the force exerted by the third body on the first.
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1630:{\displaystyle {\vec {a}}_{g}=-{\hat {r}}~G~{\frac {M}{R^{2}}}\pm {\hat {r}}~G~{\frac {2M}{R^{2}}}~{\frac {\Delta r}{R}}+\cdots }
3993:
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in a straight line under the influence of a gravitational field while still being influenced by (changing) tidal acceleration.
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90:
Thus, the tidal force is also known as the differential force, residual force, or secondary effect of the gravitational field.
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1940:
calculation. In the plane perpendicular to that axis, the tidal acceleration is directed inwards (towards the center where ∆
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1707:, the terms after the first residual term are very small and can be neglected, giving the approximate tidal acceleration
1372:{\displaystyle {\vec {a}}_{g}=-{\hat {r}}~G~{\frac {M}{R^{2}}}~{\frac {1}{\left(1\pm {\frac {\Delta r}{R}}\right)^{2}}}}
1090:. For simplicity, distances are first considered only in the direction pointing towards or away from the sphere of mass
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field at the surface of the Earth is known (along with another and weaker differential effect due to the Sun) as the
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Newton put the force to depress the sea at places 90 degrees distant from the Sun at "1 to 38604600" (in terms of
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cause strains on both bodies and may distort them or even, in extreme cases, break one or the other apart. The
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Figure 3: Graph showing how gravitational attraction drops off with increasing distance from a body
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1859:{\displaystyle {\vec {a}}_{t,{\text{axial}}}\approx \pm {\hat {r}}~2\Delta r~G~{\frac {M}{R^{3}}}}
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1126:. Leaving aside whatever gravitational acceleration may be experienced by the particle towards
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By generating conducting fluids within the interior of the Earth, tidal forces also affect the
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with two bulges, pointing towards and away from the other body. Larger objects distort into an
170:
only causes the entire body to accelerate together in the same direction and at the same rate.
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direction of the arrows on the right and left of the Earth indicates that where the Moon is at
133:. This is the primary mechanism driving tidal action, explaining two simultaneous tidal bulges.
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2020:, while the solar tidal acceleration at the Earth's surface along the Sun–Earth axis is about
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Tidal acceleration does not require rotation or orbiting bodies; for example, the body may be
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is zero. This term does not affect the observed acceleration of particles on the surface of
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s own mass, we have the acceleration on the particle due to gravitational force towards
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be the (relatively small) distance of the particle from the center of the body of mass
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Tidal effects become particularly pronounced near small bodies of high mass, such as
578:
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35:
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1928:
Tidal accelerations can also be calculated away from the axis connecting the bodies
27:
A gravitational effect also known as the differential force and the perturbing force
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2337:
Gravity from the Ground Up: An
Introductory Guide to Gravity and General Relativity
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621:
103:
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182:
17:
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1102:, then the new particle considered may be located on its surface, at a distance (
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1234:{\displaystyle {\vec {a}}_{g}=-{\hat {r}}~G~{\frac {M}{(R\pm \Delta r)^{2}}}}
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3285:
3280:
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2400:
2183:
The
Emperor's New Mind: Concerning Computers, Minds, and the Laws of Physics
590:
582:
562:
2732:
by
Mikolaj Sawicki of John A. Logan College and the University of Colorado.
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712:
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3657:
3516:
3408:
3398:
3343:
2819:
739:
705:
2747:
2717:"Stellar collisions: Tidal disruption of a star by a massive black hole"
2131:, I. N. Avsiuk, in "Soviet Astronomy Letters", vol. 3 (1977), pp. 96–99.
3804:
3794:
2964:
2934:
613:
38:
2156:"Tidal forces carry the mathematical signature of gravitational waves"
57:
effect that stretches a body along the line towards and away from the
3511:
2924:
2312:
1999:{\textstyle {\frac {1}{2}}\left|{\vec {a}}_{t,{\text{axial}}}\right|}
554:
142:
704:
Figure 7: Tidal force is responsible for the merge of galactic pair
573:
close enough to its primary, this can result in a rotation which is
30:
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711:
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120:
29:
2500:
Munk, Walter; Dzieciuch, Matthew; Jayne, Steven (February 2002).
137:
Earth's surface and center (label O) by the Moon (label S). The
109:
Tidal forces have also been shown to be fundamentally related to
3305:
2340:(illustrated ed.). Cambridge University Press. p. 45.
878:{\displaystyle {\vec {F}}_{g}=-{\hat {r}}~G~{\frac {Mm}{R^{2}}}}
684:
641:
633:
66:
2751:
1000:{\displaystyle {\vec {a}}_{g}=-{\hat {r}}~G~{\frac {M}{R^{2}}}}
589:
caused by tidal forces also cause a regular monthly pattern of
2502:"Millennial Climate Variability: Is There a Tidal Connection?"
2430:. Vol. 26. Encyclopedia Americana Corp. pp. 611–617.
1066:
experienced by a particle in the vicinity of the body of mass
645:
2443:"Possible forcing of global temperature by the oceanic tides"
2427:
The
Encyclopedia Americana: A Library of Universal Knowledge
1118:
may be taken as positive where the particle's distance from
721:
For a given (externally generated) gravitational field, the
2527:
10.1175/1520-0442(2002)015<0370:MCVITA>2.0.CO;2
577:
to the orbital motion, as in the case of the Earth's moon.
2279:
Sawicki, Mikolaj (1999). "Myths about gravity and tides".
213:) is inversely proportional to the cube of the distance.
61:
of another body due to spatial variations in strength in
1640:
The first term is the gravitational acceleration due to
1062:
Consider now the acceleration due to the sphere of mass
2369:
The NIST Reference on
Constants, Units, and Uncertainty
632:" of infalling matter. Tidal forces create the oceanic
2365:"2022 CODATA Value: Newtonian constant of gravitation"
1950:
77:, breaking apart of celestial bodies and formation of
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1016:
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produces dramatic volcanic effects on
Jupiter's moon
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260:
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is a distance along the axis joining the centers of
3813:
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3749:
3701:
3640:
3535:
3407:
3304:
3099:
2785:
687:getting torn apart by the gravitational tides of a
2396:Hamiltonian Dynamical Systems: A Reprint Selection
2180:
2154:arXiv, Emerging Technology from the (2019-12-14).
1998:
1909:
1858:
1755:considered, along the axis joining the centers of
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1371:
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877:
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315:
292:
266:
3721:North West Shelf Operational Oceanographic System
2634:The mathematical principles of natural philosophy
725:at a point with respect to a body is obtained by
612:in 1994 after breaking up under the influence of
1869:When calculated in this way for the case where ∆
3711:Deep-ocean Assessment and Reporting of Tsunamis
2447:Proceedings of the National Academy of Sciences
640:'s oceans, where the attracting bodies are the
616:'s tidal forces during a previous pass in 1992.
65:from the other body. It is responsible for the
2441:Keeling, C. D.; Whorf, T. P. (5 August 1997).
2763:
2274:
2272:
1744:{\displaystyle {\vec {a}}_{t,{\text{axial}}}}
102:cases called a tidal force (for example, the
8:
1917:is directed outwards from to the center of
125:Figure 2: Shown in red, the Moon's gravity
2770:
2756:
2748:
2674:Analysis and Prediction of Tides: GeoTide
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1477:{\displaystyle 1\mp 2x+3x^{2}\mp \cdots }
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2006:in linear approximation as in Figure 2.
1110:) from the centre of the sphere of mass
648:. Tidal forces are also responsible for
236:
34:Figure 1: Tidal interaction between the
2253:"The Tidal Force | Neil deGrasse Tyson"
2247:
2245:
2096:
3042:one-dimensional Saint-Venant equations
628:, where they are responsible for the "
366:{\displaystyle Gm~{\frac {2r}{d^{3}}}}
240:Gravitational body causing tidal force
747:Newton's law of universal gravitation
7:
3989:
1644:at the center of the reference body
757:from the center of a sphere of mass
2694:Gray, Meghan; Merrifield, Michael.
2142:"Astronomy: a physical perspective"
2105:"Hubble Views a Cosmic Interaction"
1484:which gives a series expansion of:
1074:as the distance from the center of
749:and laws of motion, a body of mass
3869:National Oceanographic Data Center
3296:World Ocean Circulation Experiment
3184:Global Ocean Data Analysis Project
2393:R. S. MacKay; J. D. Meiss (1987).
1824:
1671:
1609:
1344:
1212:
683:Figure 6: This simulation shows a
25:
3716:Global Sea Level Observing System
1248:term from the denominator gives:
69:and related phenomena, including
3999:
3988:
3979:
3978:
3174:Geochemical Ocean Sections Study
3090:
3079:
2688:Audio: Cain/Gay – Astronomy Cast
2651:Book 3, Proposition 36, Page 307
2222:; J -P Bibring; M Blanc (2003).
658:Tides may also induce seismicity
3904:Ocean thermal energy conversion
3627:Vine–Matthews–Morley hypothesis
2683:Case Western Reserve University
1944:is zero), and its magnitude is
217:closer to the attracting body.
2599:Admiralty manual of navigation
2576:ESA/Hubble Picture of the Week
1972:
1910:{\displaystyle {\vec {a}}_{t}}
1895:
1812:
1780:
1721:
1566:
1525:
1501:
1426:{\displaystyle 1/(1\pm x)^{2}}
1414:
1401:
1289:
1265:
1219:
1203:
1182:
1158:
1098:is itself a sphere of radius ∆
1023:
965:
941:
917:{\displaystyle {\vec {a}}_{g}}
902:
888:equivalent to an acceleration
838:
814:
790:{\displaystyle {\vec {F}}_{g}}
775:
1:
2730:Myths about Gravity and Tides
644:and, to a lesser extent, the
243:Body subjected to tidal force
3164:El Niño–Southern Oscillation
3134:Craik–Leibovich vortex force
2890:Luke's variational principle
2637:. Vol. 2. p. 307.
2572:"Inseparable galactic twins"
104:perturbing force on the Moon
2742:Tides and centrifugal force
2681:by J. Christopher Mihos of
2542:"Hungry for Power in Space"
1664:, i.e., at the point where
4068:
3229:Ocean dynamical thermostat
3077:
2037:gravitational acceleration
1032:{\displaystyle {\hat {r}}}
3974:
3764:Ocean acoustic tomography
3577:Mohorovičić discontinuity
3169:General circulation model
2805:Benjamin–Feir instability
2690:Tidal Forces – July 2007.
2661:as expressed in the text.
2257:www.haydenplanetarium.org
2111:. NASA. February 11, 2022
1051:(here, acceleration from
520:
242:
239:
3894:Ocean surface topography
3269:Thermohaline circulation
3259:Subsurface ocean current
3199:Hydrothermal circulation
3032:Wave–current interaction
2810:Boussinesq approximation
2708:University of Nottingham
2424:Rollin A Harris (1920).
2334:Schutz, Bernard (2003).
2228:. Springer. p. 16.
1691:because with respect to
1680:{\displaystyle \Delta r}
85:, and in extreme cases,
3931:Sea surface temperature
3914:Outline of oceanography
3109:Atmospheric circulation
3047:shallow water equations
3037:Waves and shallow water
2930:Significant wave height
2552:: 52. 23 September 1989
2468:10.1073/pnas.94.16.8321
2189:Oxford University Press
1043:pointing from the body
689:supermassive black hole
41:and a smaller companion
3926:Sea surface microlayer
3291:Wind generated current
2631:Newton, Isaac (1729).
2596:The Admiralty (1987).
2144:, M. L. Kutner (2003).
2000:
1911:
1860:
1745:
1681:
1658:
1631:
1478:
1427:
1373:
1235:
1094:. If the body of mass
1033:
1001:
918:
879:
791:
718:
709:
692:
665:Earth's magnetic field
617:
610:Comet Shoemaker-Levy 9
558:
526:gravitational constant
367:
317:
294:
268:
187:
150:
42:
4052:Concepts in astronomy
3759:Deep scattering layer
3741:World Geodetic System
3249:Princeton Ocean Model
3129:Coriolis–Stokes force
2779:Physical oceanography
2604:The Stationery Office
2160:MIT Technology Review
2001:
1912:
1861:
1746:
1703:is small compared to
1682:
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1632:
1479:
1428:
1374:
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1002:
919:
880:
792:
715:
703:
682:
656:, and tidal heating.
607:
552:
368:
318:
295:
269:
185:
131:tide generating force
124:
51:tide-generating force
33:
3779:Underwater acoustics
3339:Perigean spring tide
3204:Langmuir circulation
2915:Rossby-gravity waves
2738:by Donald E. Simanek
2736:Tidal Misconceptions
2129:"On the tidal force"
1948:
1885:
1770:
1711:
1668:
1648:
1491:
1437:
1390:
1255:
1148:
1059:has negative sign).
1014:
931:
892:
804:
765:
329:
307:
284:
258:
229:Sun, Earth, and Moon
200:), while the slope (
3941:Science On a Sphere
3547:Convergent boundary
3219:Modular Ocean Model
3179:Geostrophic current
2895:Mild-slope equation
2679:Gravitational Tides
2518:2002JCli...15..370M
2459:1997PNAS...94.8321K
2295:1999PhTea..37..438S
2282:The Physics Teacher
2086:Spacetime curvature
1751:for the distances ∆
246:Tidal acceleration
111:gravitational waves
95:celestial mechanics
63:gravitational field
4047:Effects of gravity
3597:Seafloor spreading
3587:Outer trench swell
3552:Divergent boundary
3452:Continental margin
3437:Carbonate platform
3334:Lunitidal interval
2715:Pau Amaro Seoane.
2620:Chapter 11, p. 277
2506:Journal of Climate
2353:Extract of page 45
2179:R Penrose (1999).
1996:
1907:
1856:
1741:
1677:
1654:
1627:
1474:
1423:
1369:
1231:
1029:
997:
914:
875:
787:
727:vector subtraction
723:tidal acceleration
719:
710:
693:
654:tidal acceleration
618:
559:
363:
313:
290:
264:
188:
151:
43:
18:Tidal interactions
4014:
4013:
4006:Oceans portal
3966:World Ocean Atlas
3956:Underwater glider
3899:Ocean temperature
3562:Hydrothermal vent
3527:Submarine volcano
3462:Continental shelf
3442:Coastal geography
3432:Bathymetric chart
3314:Amphidromic point
3002:Wave nonlinearity
2860:Infragravity wave
2644:978-0-11-772880-6
2613:978-0-11-772880-6
2453:(16): 8321–8328.
2410:978-0-85274-205-1
2347:978-0-521-45506-0
2235:978-3-540-00241-3
2202:978-0-19-286198-6
2056:Amphidromic point
1988:
1975:
1959:
1898:
1854:
1838:
1832:
1820:
1815:
1796:
1783:
1737:
1724:
1657:{\displaystyle m}
1619:
1605:
1601:
1580:
1574:
1569:
1555:
1539:
1533:
1528:
1504:
1367:
1354:
1323:
1319:
1303:
1297:
1292:
1268:
1229:
1196:
1190:
1185:
1161:
1078:to the center of
1026:
995:
979:
973:
968:
944:
905:
873:
852:
846:
841:
817:
778:
680:
630:spaghettification
593:on Earth's Moon.
542:
541:
515:10 m⋅s
467:10 m⋅s
419:10 m⋅s
361:
340:
316:{\displaystyle d}
293:{\displaystyle r}
267:{\displaystyle m}
174:Size and distance
97:, the expression
87:spaghettification
71:solid-earth tides
16:(Redirected from
4059:
4004:
4003:
3992:
3991:
3982:
3981:
3921:Pelagic sediment
3859:Marine pollution
3653:Deep ocean water
3522:Submarine canyon
3457:Continental rise
3349:Rule of twelfths
3264:Sverdrup balance
3194:Humboldt Current
3119:Boundary current
3094:
3083:
2900:Radiation stress
2870:Iribarren number
2845:Equatorial waves
2800:Ballantine scale
2795:Airy wave theory
2772:
2765:
2758:
2749:
2744:by Paolo Sirtoli
2726:
2724:
2723:
2711:
2662:
2648:
2628:
2622:
2617:
2593:
2587:
2586:
2584:
2582:
2568:
2562:
2561:
2559:
2557:
2538:
2532:
2531:
2529:
2497:
2491:
2490:
2480:
2470:
2438:
2432:
2431:
2421:
2415:
2414:
2390:
2384:
2383:
2381:
2380:
2361:
2355:
2351:
2331:
2325:
2324:
2313:10.1119/1.880345
2306:
2276:
2267:
2266:
2264:
2263:
2249:
2240:
2239:
2225:The Solar System
2220:Thérèse Encrenaz
2216:
2210:
2209:
2186:
2176:
2170:
2169:
2167:
2166:
2151:
2145:
2138:
2132:
2126:
2120:
2119:
2117:
2116:
2101:
2061:Disrupted planet
2030:
2025:
2019:
2014:
2005:
2003:
2002:
1997:
1995:
1991:
1990:
1989:
1986:
1977:
1976:
1968:
1960:
1952:
1916:
1914:
1913:
1908:
1906:
1905:
1900:
1899:
1891:
1865:
1863:
1862:
1857:
1855:
1853:
1852:
1840:
1836:
1830:
1818:
1817:
1816:
1808:
1799:
1798:
1797:
1794:
1785:
1784:
1776:
1750:
1748:
1747:
1742:
1740:
1739:
1738:
1735:
1726:
1725:
1717:
1686:
1684:
1683:
1678:
1663:
1661:
1660:
1655:
1636:
1634:
1633:
1628:
1620:
1615:
1607:
1603:
1602:
1600:
1599:
1590:
1582:
1578:
1572:
1571:
1570:
1562:
1556:
1554:
1553:
1541:
1537:
1531:
1530:
1529:
1521:
1512:
1511:
1506:
1505:
1497:
1483:
1481:
1480:
1475:
1467:
1466:
1432:
1430:
1429:
1424:
1422:
1421:
1400:
1384:Maclaurin series
1378:
1376:
1375:
1370:
1368:
1366:
1365:
1360:
1356:
1355:
1350:
1342:
1325:
1321:
1320:
1318:
1317:
1305:
1301:
1295:
1294:
1293:
1285:
1276:
1275:
1270:
1269:
1261:
1244:Pulling out the
1240:
1238:
1237:
1232:
1230:
1228:
1227:
1226:
1198:
1194:
1188:
1187:
1186:
1178:
1169:
1168:
1163:
1162:
1154:
1136:
1122:is greater than
1038:
1036:
1035:
1030:
1028:
1027:
1019:
1006:
1004:
1003:
998:
996:
994:
993:
981:
977:
971:
970:
969:
961:
952:
951:
946:
945:
937:
923:
921:
920:
915:
913:
912:
907:
906:
898:
884:
882:
881:
876:
874:
872:
871:
862:
854:
850:
844:
843:
842:
834:
825:
824:
819:
818:
810:
796:
794:
793:
788:
786:
785:
780:
779:
771:
681:
538:
535:
533:
516:
514:
507:
505:
498:
496:
484:
482:
468:
466:
459:
457:
450:
448:
436:
434:
420:
418:
411:
409:
402:
400:
388:
386:
372:
370:
369:
364:
362:
360:
359:
350:
342:
338:
322:
320:
319:
314:
299:
297:
296:
291:
273:
271:
270:
265:
237:
212:
207:
199:
21:
4067:
4066:
4062:
4061:
4060:
4058:
4057:
4056:
4017:
4016:
4015:
4010:
3998:
3970:
3809:
3783:
3745:
3726:Sea-level curve
3697:
3636:
3622:Transform fault
3572:Mid-ocean ridge
3538:
3531:
3497:Oceanic plateau
3403:
3389:Tidal resonance
3359:Theory of tides
3300:
3209:Longshore drift
3159:Ekman transport
3095:
3089:
3088:
3087:
3086:
3085:
3084:
3075:
3027:Wave turbulence
2960:Trochoidal wave
2885:Longshore drift
2781:
2776:
2721:
2719:
2714:
2693:
2670:
2665:
2645:
2630:
2629:
2625:
2614:
2606:. p. 277.
2602:. Vol. 1.
2595:
2594:
2590:
2580:
2578:
2570:
2569:
2565:
2555:
2553:
2540:
2539:
2535:
2499:
2498:
2494:
2440:
2439:
2435:
2423:
2422:
2418:
2411:
2392:
2391:
2387:
2378:
2376:
2363:
2362:
2358:
2348:
2333:
2332:
2328:
2304:10.1.1.695.8981
2278:
2277:
2270:
2261:
2259:
2251:
2250:
2243:
2236:
2218:
2217:
2213:
2203:
2178:
2177:
2173:
2164:
2162:
2153:
2152:
2148:
2139:
2135:
2127:
2123:
2114:
2112:
2103:
2102:
2098:
2094:
2076:Tidal stripping
2071:Tidal resonance
2052:
2023:
2021:
2012:
2010:
1965:
1961:
1946:
1945:
1888:
1883:
1882:
1844:
1773:
1768:
1767:
1714:
1709:
1708:
1666:
1665:
1646:
1645:
1608:
1591:
1583:
1545:
1494:
1489:
1488:
1458:
1435:
1434:
1413:
1388:
1387:
1343:
1334:
1330:
1329:
1309:
1258:
1253:
1252:
1218:
1202:
1151:
1146:
1145:
1134:
1012:
1011:
985:
934:
929:
928:
895:
890:
889:
863:
855:
807:
802:
801:
768:
763:
762:
698:
670:
547:
536:
531:
529:
512:
510:
503:
501:
494:
492:
480:
478:
464:
462:
455:
453:
446:
444:
432:
430:
416:
414:
407:
405:
398:
396:
384:
382:
351:
343:
327:
326:
305:
304:
282:
281:
256:
255:
231:
205:
201:
191:
176:
135:
134:
119:
28:
23:
22:
15:
12:
11:
5:
4065:
4063:
4055:
4054:
4049:
4044:
4039:
4034:
4029:
4019:
4018:
4012:
4011:
4009:
4008:
3996:
3986:
3975:
3972:
3971:
3969:
3968:
3963:
3958:
3953:
3948:
3946:Stratification
3943:
3938:
3933:
3928:
3923:
3918:
3917:
3916:
3906:
3901:
3896:
3891:
3886:
3881:
3876:
3871:
3866:
3861:
3856:
3851:
3846:
3838:
3836:Color of water
3833:
3831:Benthic lander
3828:
3823:
3817:
3815:
3811:
3810:
3808:
3807:
3802:
3797:
3791:
3789:
3785:
3784:
3782:
3781:
3776:
3771:
3766:
3761:
3755:
3753:
3747:
3746:
3744:
3743:
3738:
3736:Sea level rise
3733:
3731:Sea level drop
3728:
3723:
3718:
3713:
3707:
3705:
3699:
3698:
3696:
3695:
3690:
3685:
3680:
3675:
3670:
3665:
3660:
3655:
3650:
3644:
3642:
3638:
3637:
3635:
3634:
3629:
3624:
3619:
3614:
3609:
3604:
3599:
3594:
3589:
3584:
3579:
3574:
3569:
3567:Marine geology
3564:
3559:
3554:
3549:
3543:
3541:
3533:
3532:
3530:
3529:
3524:
3519:
3514:
3509:
3507:Passive margin
3504:
3502:Oceanic trench
3499:
3494:
3489:
3484:
3479:
3474:
3469:
3464:
3459:
3454:
3449:
3444:
3439:
3434:
3429:
3424:
3419:
3413:
3411:
3405:
3404:
3402:
3401:
3396:
3391:
3386:
3381:
3376:
3371:
3366:
3361:
3356:
3351:
3346:
3341:
3336:
3331:
3326:
3321:
3316:
3310:
3308:
3302:
3301:
3299:
3298:
3293:
3288:
3283:
3278:
3277:
3276:
3266:
3261:
3256:
3251:
3246:
3241:
3236:
3234:Ocean dynamics
3231:
3226:
3221:
3216:
3211:
3206:
3201:
3196:
3191:
3186:
3181:
3176:
3171:
3166:
3161:
3156:
3151:
3146:
3141:
3136:
3131:
3126:
3124:Coriolis force
3121:
3116:
3111:
3105:
3103:
3097:
3096:
3078:
3076:
3074:
3073:
3072:
3071:
3061:
3056:
3051:
3050:
3049:
3044:
3034:
3029:
3024:
3019:
3014:
3009:
3004:
2999:
2994:
2989:
2984:
2979:
2974:
2973:
2972:
2962:
2957:
2952:
2947:
2945:Stokes problem
2942:
2937:
2932:
2927:
2922:
2917:
2912:
2907:
2902:
2897:
2892:
2887:
2882:
2880:Kinematic wave
2877:
2872:
2867:
2862:
2857:
2852:
2847:
2842:
2837:
2832:
2827:
2822:
2817:
2812:
2807:
2802:
2797:
2791:
2789:
2783:
2782:
2777:
2775:
2774:
2767:
2760:
2752:
2746:
2745:
2739:
2733:
2727:
2712:
2696:"Tidal Forces"
2691:
2685:
2676:
2669:
2668:External links
2666:
2664:
2663:
2643:
2623:
2612:
2588:
2563:
2533:
2512:(4): 370–385.
2492:
2433:
2416:
2409:
2403:. p. 36.
2385:
2356:
2346:
2326:
2289:(7): 438–441.
2268:
2241:
2234:
2211:
2201:
2171:
2146:
2140:See p. 509 in
2133:
2121:
2095:
2093:
2090:
2089:
2088:
2083:
2078:
2073:
2068:
2063:
2058:
2051:
2048:
1994:
1984:
1981:
1974:
1971:
1964:
1958:
1955:
1936:, requiring a
1904:
1897:
1894:
1867:
1866:
1851:
1847:
1843:
1835:
1829:
1826:
1823:
1814:
1811:
1805:
1802:
1792:
1789:
1782:
1779:
1733:
1730:
1723:
1720:
1676:
1673:
1653:
1638:
1637:
1626:
1623:
1618:
1614:
1611:
1598:
1594:
1589:
1586:
1577:
1568:
1565:
1559:
1552:
1548:
1544:
1536:
1527:
1524:
1518:
1515:
1510:
1503:
1500:
1473:
1470:
1465:
1461:
1457:
1454:
1451:
1448:
1445:
1442:
1420:
1416:
1412:
1409:
1406:
1403:
1399:
1395:
1380:
1379:
1364:
1359:
1353:
1349:
1346:
1340:
1337:
1333:
1328:
1316:
1312:
1308:
1300:
1291:
1288:
1282:
1279:
1274:
1267:
1264:
1242:
1241:
1225:
1221:
1217:
1214:
1211:
1208:
1205:
1201:
1193:
1184:
1181:
1175:
1172:
1167:
1160:
1157:
1130:on account of
1025:
1022:
1008:
1007:
992:
988:
984:
976:
967:
964:
958:
955:
950:
943:
940:
911:
904:
901:
886:
885:
870:
866:
861:
858:
849:
840:
837:
831:
828:
823:
816:
813:
784:
777:
774:
761:feels a force
697:
694:
575:tidally locked
546:
543:
540:
539:
534:10 m⋅kg⋅s
518:
517:
508:
499:
490:
485:
476:
470:
469:
460:
451:
442:
437:
428:
422:
421:
412:
403:
394:
389:
380:
374:
373:
358:
354:
349:
346:
337:
334:
324:
312:
301:
289:
278:
275:
263:
252:
248:
247:
244:
241:
230:
227:
175:
172:
118:
115:
59:center of mass
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
4064:
4053:
4050:
4048:
4045:
4043:
4040:
4038:
4035:
4033:
4030:
4028:
4025:
4024:
4022:
4007:
4002:
3997:
3995:
3987:
3985:
3977:
3976:
3973:
3967:
3964:
3962:
3959:
3957:
3954:
3952:
3949:
3947:
3944:
3942:
3939:
3937:
3934:
3932:
3929:
3927:
3924:
3922:
3919:
3915:
3912:
3911:
3910:
3907:
3905:
3902:
3900:
3897:
3895:
3892:
3890:
3887:
3885:
3882:
3880:
3877:
3875:
3872:
3870:
3867:
3865:
3862:
3860:
3857:
3855:
3854:Marine energy
3852:
3850:
3847:
3845:
3844:
3839:
3837:
3834:
3832:
3829:
3827:
3824:
3822:
3821:Acidification
3819:
3818:
3816:
3812:
3806:
3803:
3801:
3798:
3796:
3793:
3792:
3790:
3786:
3780:
3777:
3775:
3774:SOFAR channel
3772:
3770:
3767:
3765:
3762:
3760:
3757:
3756:
3754:
3752:
3748:
3742:
3739:
3737:
3734:
3732:
3729:
3727:
3724:
3722:
3719:
3717:
3714:
3712:
3709:
3708:
3706:
3704:
3700:
3694:
3691:
3689:
3686:
3684:
3681:
3679:
3676:
3674:
3671:
3669:
3666:
3664:
3661:
3659:
3656:
3654:
3651:
3649:
3646:
3645:
3643:
3639:
3633:
3630:
3628:
3625:
3623:
3620:
3618:
3615:
3613:
3610:
3608:
3605:
3603:
3600:
3598:
3595:
3593:
3590:
3588:
3585:
3583:
3582:Oceanic crust
3580:
3578:
3575:
3573:
3570:
3568:
3565:
3563:
3560:
3558:
3557:Fracture zone
3555:
3553:
3550:
3548:
3545:
3544:
3542:
3540:
3534:
3528:
3525:
3523:
3520:
3518:
3515:
3513:
3510:
3508:
3505:
3503:
3500:
3498:
3495:
3493:
3492:Oceanic basin
3490:
3488:
3485:
3483:
3480:
3478:
3475:
3473:
3470:
3468:
3465:
3463:
3460:
3458:
3455:
3453:
3450:
3448:
3445:
3443:
3440:
3438:
3435:
3433:
3430:
3428:
3425:
3423:
3422:Abyssal plain
3420:
3418:
3415:
3414:
3412:
3410:
3406:
3400:
3397:
3395:
3392:
3390:
3387:
3385:
3382:
3380:
3377:
3375:
3372:
3370:
3367:
3365:
3362:
3360:
3357:
3355:
3352:
3350:
3347:
3345:
3342:
3340:
3337:
3335:
3332:
3330:
3329:Internal tide
3327:
3325:
3322:
3320:
3317:
3315:
3312:
3311:
3309:
3307:
3303:
3297:
3294:
3292:
3289:
3287:
3284:
3282:
3279:
3275:
3272:
3271:
3270:
3267:
3265:
3262:
3260:
3257:
3255:
3252:
3250:
3247:
3245:
3242:
3240:
3237:
3235:
3232:
3230:
3227:
3225:
3224:Ocean current
3222:
3220:
3217:
3215:
3212:
3210:
3207:
3205:
3202:
3200:
3197:
3195:
3192:
3190:
3187:
3185:
3182:
3180:
3177:
3175:
3172:
3170:
3167:
3165:
3162:
3160:
3157:
3155:
3152:
3150:
3147:
3145:
3142:
3140:
3137:
3135:
3132:
3130:
3127:
3125:
3122:
3120:
3117:
3115:
3112:
3110:
3107:
3106:
3104:
3102:
3098:
3093:
3082:
3070:
3067:
3066:
3065:
3062:
3060:
3057:
3055:
3052:
3048:
3045:
3043:
3040:
3039:
3038:
3035:
3033:
3030:
3028:
3025:
3023:
3022:Wave shoaling
3020:
3018:
3015:
3013:
3010:
3008:
3005:
3003:
3000:
2998:
2995:
2993:
2990:
2988:
2985:
2983:
2982:Ursell number
2980:
2978:
2975:
2971:
2968:
2967:
2966:
2963:
2961:
2958:
2956:
2953:
2951:
2948:
2946:
2943:
2941:
2938:
2936:
2933:
2931:
2928:
2926:
2923:
2921:
2918:
2916:
2913:
2911:
2908:
2906:
2903:
2901:
2898:
2896:
2893:
2891:
2888:
2886:
2883:
2881:
2878:
2876:
2873:
2871:
2868:
2866:
2865:Internal wave
2863:
2861:
2858:
2856:
2853:
2851:
2848:
2846:
2843:
2841:
2838:
2836:
2833:
2831:
2828:
2826:
2823:
2821:
2818:
2816:
2815:Breaking wave
2813:
2811:
2808:
2806:
2803:
2801:
2798:
2796:
2793:
2792:
2790:
2788:
2784:
2780:
2773:
2768:
2766:
2761:
2759:
2754:
2753:
2750:
2743:
2740:
2737:
2734:
2731:
2728:
2718:
2713:
2709:
2705:
2701:
2700:Sixty Symbols
2697:
2692:
2689:
2686:
2684:
2680:
2677:
2675:
2672:
2671:
2667:
2660:
2656:
2652:
2646:
2640:
2636:
2635:
2627:
2624:
2621:
2615:
2609:
2605:
2601:
2600:
2592:
2589:
2577:
2573:
2567:
2564:
2551:
2547:
2546:New Scientist
2543:
2537:
2534:
2528:
2523:
2519:
2515:
2511:
2507:
2503:
2496:
2493:
2488:
2484:
2479:
2474:
2469:
2464:
2460:
2456:
2452:
2448:
2444:
2437:
2434:
2429:
2428:
2420:
2417:
2412:
2406:
2402:
2398:
2397:
2389:
2386:
2374:
2370:
2366:
2360:
2357:
2354:
2349:
2343:
2339:
2338:
2330:
2327:
2322:
2318:
2314:
2310:
2305:
2300:
2296:
2292:
2288:
2284:
2283:
2275:
2273:
2269:
2258:
2254:
2248:
2246:
2242:
2237:
2231:
2227:
2226:
2221:
2215:
2212:
2208:
2204:
2198:
2194:
2190:
2185:
2184:
2175:
2172:
2161:
2157:
2150:
2147:
2143:
2137:
2134:
2130:
2125:
2122:
2110:
2106:
2100:
2097:
2091:
2087:
2084:
2082:
2079:
2077:
2074:
2072:
2069:
2067:
2066:Galactic tide
2064:
2062:
2059:
2057:
2054:
2053:
2049:
2047:
2045:
2044:
2038:
2034:
2029:
2018:
2007:
1992:
1982:
1979:
1969:
1962:
1956:
1953:
1943:
1939:
1935:
1931:
1926:
1924:
1920:
1902:
1892:
1880:
1876:
1872:
1849:
1845:
1841:
1833:
1827:
1821:
1809:
1803:
1800:
1790:
1787:
1777:
1766:
1765:
1764:
1762:
1758:
1754:
1731:
1728:
1718:
1706:
1702:
1698:
1694:
1690:
1674:
1651:
1643:
1624:
1621:
1616:
1612:
1596:
1592:
1587:
1584:
1575:
1563:
1557:
1550:
1546:
1542:
1534:
1522:
1516:
1513:
1508:
1498:
1487:
1486:
1485:
1471:
1468:
1463:
1459:
1455:
1452:
1449:
1446:
1443:
1440:
1418:
1410:
1407:
1404:
1397:
1393:
1385:
1362:
1357:
1351:
1347:
1338:
1335:
1331:
1326:
1314:
1310:
1306:
1298:
1286:
1280:
1277:
1272:
1262:
1251:
1250:
1249:
1247:
1223:
1215:
1209:
1206:
1199:
1191:
1179:
1173:
1170:
1165:
1155:
1144:
1143:
1142:
1140:
1133:
1129:
1125:
1121:
1117:
1113:
1109:
1105:
1101:
1097:
1093:
1089:
1085:
1081:
1077:
1073:
1069:
1065:
1060:
1058:
1054:
1050:
1046:
1042:
1020:
990:
986:
982:
974:
962:
956:
953:
948:
938:
927:
926:
925:
909:
899:
868:
864:
859:
856:
847:
835:
829:
826:
821:
811:
800:
799:
798:
782:
772:
760:
756:
752:
748:
743:
741:
736:
733:
728:
724:
714:
707:
702:
695:
690:
686:
668:
666:
661:
659:
655:
651:
650:tidal locking
647:
643:
639:
635:
631:
627:
623:
622:neutron stars
615:
611:
606:
602:
600:
599:harmonic beat
594:
592:
588:
584:
580:
579:Tidal heating
576:
570:
568:
564:
556:
551:
544:
527:
523:
519:
509:
500:
491:
489:
486:
477:
475:
472:
471:
461:
452:
443:
441:
438:
429:
427:
424:
423:
413:
404:
395:
393:
390:
381:
379:
376:
375:
356:
352:
347:
344:
335:
332:
325:
310:
302:
287:
279:
276:
261:
253:
250:
249:
245:
238:
235:
228:
226:
222:
218:
214:
211:
204:
198:
194:
184:
180:
173:
171:
169:
164:
160:
155:
148:
144:
140:
132:
128:
123:
116:
114:
112:
107:
105:
100:
96:
91:
88:
84:
80:
76:
75:tidal locking
72:
68:
64:
60:
56:
55:gravitational
52:
48:
40:
37:
36:spiral galaxy
32:
19:
4027:Tidal forces
3961:Water column
3909:Oceanography
3884:Observations
3879:Explorations
3849:Marginal sea
3842:
3800:OSTM/Jason-2
3632:Volcanic arc
3607:Slab suction
3368:
3324:Head of tide
3214:Loop Current
3154:Ekman spiral
2940:Stokes drift
2850:Gravity wave
2825:Cnoidal wave
2720:. Retrieved
2699:
2658:
2654:
2633:
2626:
2598:
2591:
2579:. Retrieved
2575:
2566:
2554:. Retrieved
2549:
2545:
2536:
2509:
2505:
2495:
2450:
2446:
2436:
2426:
2419:
2395:
2388:
2377:. Retrieved
2368:
2359:
2336:
2329:
2286:
2280:
2260:. Retrieved
2256:
2224:
2214:
2207:tidal force.
2206:
2182:
2174:
2163:. Retrieved
2159:
2149:
2136:
2124:
2113:. Retrieved
2108:
2099:
2081:Tidal tensor
2041:
2032:
2027:
2016:
2008:
1941:
1933:
1929:
1927:
1922:
1918:
1878:
1874:
1870:
1868:
1760:
1756:
1752:
1704:
1700:
1696:
1692:
1688:
1641:
1639:
1381:
1245:
1243:
1138:
1131:
1127:
1123:
1119:
1115:
1111:
1107:
1103:
1099:
1095:
1091:
1087:
1083:
1079:
1075:
1071:
1067:
1063:
1061:
1056:
1052:
1048:
1047:to the body
1044:
1009:
887:
758:
754:
753:at distance
750:
744:
737:
731:
722:
720:
662:
619:
595:
571:
560:
521:
487:
473:
439:
425:
391:
377:
232:
223:
219:
215:
209:
202:
196:
192:
189:
177:
159:tidal forces
158:
156:
152:
138:
130:
126:
108:
98:
92:
79:ring systems
50:
46:
44:
3951:Thermocline
3668:Mesopelagic
3641:Ocean zones
3612:Slab window
3477:Hydrography
3417:Abyssal fan
3384:Tidal range
3374:Tidal power
3369:Tidal force
3254:Rip current
3189:Gulf Stream
3149:Ekman layer
3139:Downwelling
3114:Baroclinity
3101:Circulation
2997:Wave height
2987:Wave action
2970:megatsunami
2950:Stokes wave
2910:Rossby wave
2875:Kelvin wave
2855:Green's law
2704:Brady Haran
1041:unit vector
740:freefalling
732:tidal force
696:Formulation
626:black holes
163:Roche limit
154:(body 2).
117:Explanation
99:tidal force
83:Roche limit
81:within the
47:tidal force
4021:Categories
3889:Reanalysis
3788:Satellites
3769:Sofar bomb
3617:Subduction
3592:Ridge push
3487:Ocean bank
3467:Contourite
3394:Tide gauge
3379:Tidal race
3364:Tidal bore
3354:Slack tide
3319:Earth tide
3239:Ocean gyre
3059:Wind setup
3054:Wind fetch
3017:Wave setup
3012:Wave radar
3007:Wave power
2905:Rogue wave
2835:Dispersion
2722:2018-12-28
2379:2024-05-18
2375:. May 2024
2262:2016-10-10
2191:. p.
2165:2023-11-12
2115:2022-07-09
2092:References
1925:is zero).
608:Figure 5:
591:moonquakes
553:Figure 4:
483:10 kg
435:10 kg
387:10 kg
303:Distance (
3751:Acoustics
3703:Sea level
3602:Slab pull
3539:tectonics
3447:Cold seep
3409:Landforms
3286:Whirlpool
3281:Upwelling
3064:Wind wave
2992:Wave base
2920:Sea state
2840:Edge wave
2830:Cross sea
2401:CRC Press
2321:0031-921X
2299:CiteSeerX
2043:Principia
1973:→
1896:→
1825:Δ
1813:^
1804:±
1801:≈
1781:→
1722:→
1672:Δ
1625:⋯
1610:Δ
1567:^
1558:±
1526:^
1517:−
1502:→
1472:⋯
1469:∓
1444:∓
1408:±
1345:Δ
1339:±
1290:^
1281:−
1266:→
1213:Δ
1210:±
1183:^
1174:−
1159:→
1024:^
966:^
957:−
942:→
903:→
839:^
830:−
815:→
776:→
563:ellipsoid
506:10 m
497:10 m
458:10 m
449:10 m
410:10 m
401:10 m
3984:Category
3936:Seawater
3663:Littoral
3658:Deep sea
3517:Seamount
3399:Tideline
3344:Rip tide
3274:shutdown
3244:Overflow
2977:Undertow
2820:Clapotis
2706:for the
2556:14 March
2487:11607740
2109:nasa.gov
2050:See also
2031:, where
2026:10
2015:10
1921:(where ∆
1055:towards
706:MRK 1034
587:Stresses
280:Radius (
166:uniform
127:residual
4037:Gravity
3994:Commons
3864:Mooring
3814:Related
3805:Jason-3
3795:Jason-1
3678:Pelagic
3673:Oceanic
3648:Benthic
2965:Tsunami
2935:Soliton
2581:12 July
2514:Bibcode
2455:Bibcode
2291:Bibcode
2035:is the
1082:, let ∆
1070:. With
614:Jupiter
545:Effects
537:
524:is the
139:outward
39:NGC 169
3683:Photic
3512:Seabed
2925:Seiche
2641:
2610:
2485:
2475:
2407:
2344:
2319:
2301:
2232:
2199:
1938:vector
1837:
1831:
1819:
1604:
1579:
1573:
1538:
1532:
1322:
1302:
1296:
1195:
1189:
1114:, and
1010:where
978:
972:
851:
845:
555:Saturn
339:
254:Mass (
157:These
145:or at
143:zenith
4042:Force
4032:Tides
3874:Ocean
3843:Alvin
3693:Swash
3537:Plate
3482:Knoll
3472:Guyot
3427:Atoll
3306:Tides
3069:model
2955:Swell
2787:Waves
2478:33744
1987:axial
1795:axial
1736:axial
1135:'
1039:is a
638:Earth
567:ovoid
530:6.674
474:Earth
440:Earth
392:Earth
208:= −2/
168:field
147:nadir
67:tides
53:is a
3841:DSV
3826:Argo
3688:Surf
3144:Eddy
2639:ISBN
2608:ISBN
2583:2013
2558:2016
2483:PMID
2405:ISBN
2373:NIST
2342:ISBN
2317:ISSN
2230:ISBN
2197:ISBN
2022:0.52
1932:and
1877:and
1759:and
1382:The
1141:as:
685:star
642:Moon
634:tide
511:2.44
502:3.84
493:1.74
488:Moon
479:5.97
463:1.10
454:3.84
445:6.37
431:7.34
426:Moon
415:5.05
406:1.50
397:6.37
383:1.99
277:Body
251:Body
195:= 1/
45:The
2550:123
2522:doi
2473:PMC
2463:doi
2309:doi
2193:264
2011:1.1
1433:is
1386:of
745:By
646:Sun
636:of
624:or
378:Sun
93:In
49:or
4023::
2702:.
2698:.
2649:,
2618:,
2574:.
2548:.
2544:.
2520:.
2510:15
2508:.
2504:.
2481:.
2471:.
2461:.
2451:94
2449:.
2445:.
2399:.
2371:.
2367:.
2315:.
2307:.
2297:.
2287:37
2285:.
2271:^
2255:.
2244:^
2205:.
2195:.
2187:.
2158:.
2107:.
2046:.
1881:,
1763::
1695:,
1116:∆r
1108:∆r
1106:±
924:,
797:,
708:.
667:.
660:.
652:,
585:.
583:Io
528:=
113:.
73:,
2771:e
2764:t
2757:v
2725:.
2710:.
2659:g
2655:g
2647:.
2616:.
2585:.
2560:.
2530:.
2524::
2516::
2489:.
2465::
2457::
2413:.
2382:.
2350:.
2323:.
2311::
2293::
2265:.
2238:.
2168:.
2118:.
2033:g
2028:g
2024:×
2017:g
2013:×
1993:|
1983:,
1980:t
1970:a
1963:|
1957:2
1954:1
1942:r
1934:M
1930:m
1923:r
1919:m
1903:t
1893:a
1879:M
1875:m
1871:r
1850:3
1846:R
1842:M
1834:G
1828:r
1822:2
1810:r
1791:,
1788:t
1778:a
1761:M
1757:m
1753:r
1732:,
1729:t
1719:a
1705:R
1701:r
1697:m
1693:M
1689:m
1675:r
1652:m
1642:M
1622:+
1617:R
1613:r
1597:2
1593:R
1588:M
1585:2
1576:G
1564:r
1551:2
1547:R
1543:M
1535:G
1523:r
1514:=
1509:g
1499:a
1464:2
1460:x
1456:3
1453:+
1450:x
1447:2
1441:1
1419:2
1415:)
1411:x
1405:1
1402:(
1398:/
1394:1
1363:2
1358:)
1352:R
1348:r
1336:1
1332:(
1327:1
1315:2
1311:R
1307:M
1299:G
1287:r
1278:=
1273:g
1263:a
1246:R
1224:2
1220:)
1216:r
1207:R
1204:(
1200:M
1192:G
1180:r
1171:=
1166:g
1156:a
1139:M
1132:m
1128:m
1124:R
1120:M
1112:M
1104:R
1100:r
1096:m
1092:M
1088:m
1084:r
1080:m
1076:M
1072:R
1068:m
1064:M
1057:M
1053:m
1049:m
1045:M
1021:r
991:2
987:R
983:M
975:G
963:r
954:=
949:g
939:a
910:g
900:a
869:2
865:R
860:m
857:M
848:G
836:r
827:=
822:g
812:F
783:g
773:F
759:M
755:R
751:m
691:.
532:×
522:G
513:×
504:×
495:×
481:×
465:×
456:×
447:×
433:×
417:×
408:×
399:×
385:×
357:3
353:d
348:r
345:2
336:m
333:G
323:)
311:d
300:)
288:r
274:)
262:m
210:X
206:′
203:Y
197:X
193:Y
149:.
20:)
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