38:
773:
572:
348:
985:
if it is held still with respect to the field. This is why a person will feel himself pulled down by the force of gravity while standing still on the Earth's surface. In general the gravitational fields predicted by general relativity differ in their effects only slightly from those predicted by
964:
These equations are dependent on the distribution of matter, stress and momentum in a region of space, unlike
Newtonian gravity, which is depends on only the distribution of matter. The fields themselves in general relativity represent the curvature of spacetime. General relativity states that
209:
pointing directly towards the particle. The magnitude of the field at every point is calculated by applying the universal law, and represents the force per unit mass on any object at that point in space. Because the force field is conservative, there is a scalar potential energy per unit mass,
463:(equivalent to the inertial acceleration, so same mathematical form, but also defined as gravitational force per unit mass). The negative signs are inserted since the force acts antiparallel to the displacement. The equivalent field equation in terms of mass
221:
376:
is the radial vector of the test particle relative to the mass (or for Newton's second law of motion which is a time dependent function, a set of positions of test particles each occupying a particular point in space for the start of testing),
768:{\displaystyle \mathbf {g} =\sum _{i}\mathbf {g} _{i}={\frac {1}{m}}\sum _{i}\mathbf {F} _{i}=-G\sum _{i}m_{i}{\frac {\mathbf {R} -\mathbf {R} _{i}}{\left|\mathbf {R} -\mathbf {R} _{i}\right|^{3}}}=-\sum _{i}\nabla \Phi _{i},}
535:
161:
via their mass, and this distortion is what is perceived and measured as a "force". In such a model one states that matter moves in certain ways in response to the curvature of spacetime, and that there is either
1005:
are three dimensional graphs commonly used to educationally illustrate gravitational potential by drawing gravitational potential fields as a gravitational topography, depicting the potentials as so-called
568:
of the fields around each individual particle. A test particle in such a field will experience a force that equals the vector sum of the forces that it would experience in these individual fields. This is
895:
41:
Representation of the gravitational field of Earth and Moon combined (not to scale). Vector field (blue) and its associated scalar potential field (red). Point P between earth and moon is the
561:
for a test particle in the presence of a gravitational field, i.e. setting up and solving these equations allows the motion of a test mass to be determined and described.
343:{\displaystyle \mathbf {g} ={\frac {\mathbf {F} }{m}}={\frac {d^{2}\mathbf {R} }{dt^{2}}}=-GM{\frac {\mathbf {R} }{\left|\mathbf {R} \right|^{3}}}=-\nabla \Phi ,}
475:
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186:
1377:
1352:
1323:
1297:
1261:
1233:
1203:
1176:
1149:
1118:
1011:
864:
852:
948:
924:
408:
This includes Newton's law of universal gravitation, and the relation between gravitational potential and field acceleration.
147:
68:
used to explain the influences that a body extends into the space around itself. A gravitational field is used to explain
1398:
1408:
1141:
1084:
1064:
978:
834:
547:
538:
455:
185:
In classical mechanics, a gravitational field is a physical quantity. A gravitational field can be defined using
904:
859:
1044:
838:
215:
394:
966:
555:
174:
142:
have usually been taught in terms of a field model, rather than a point attraction. It results from the
542:
1039:
127:
42:
1024:
848:
558:
357:
139:
88:
80:
74:
1049:
991:
987:
844:
154:
1240:
A 'field' is any physical quantity which takes on different values at different points in space.
1373:
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17:
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31:
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92:
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402:
202:
123:
84:
62:
1344:
1108:
1054:
1034:
37:
1168:
Einstein's
General Theory of Relativity: with Modern Applications in Cosmology
1289:
858:
In general relativity, the gravitational field is determined by solving the
367:
158:
131:
214:, at each point in space associated with the force fields; this is called
974:
157:, rather than two particles attracting each other, the particles distort
96:
530:{\displaystyle \nabla \cdot \mathbf {g} =-\nabla ^{2}\Phi =-4\pi G\rho }
464:
111:
69:
50:
104:
173:
Gravity is distinguished from other forces by its obedience to the
135:
115:
100:
36:
986:
classical mechanics, but there are a number of easily verifiable
384:
119:
784:
is the sum of all gravitational fields due to all other masses
30:"Gravity field" redirects here. For Earth's gravity field, see
545:. Newton's law implies Gauss's law, but not vice versa; see
1198:(3 ed.). Springer Science & Business. p. 55.
138:, and since the 19th century, explanations for gravity in
851:
play the role of the gravitational force field and the
867:
575:
478:
224:
835:
Gravitational acceleration § General relativity
813:is the position vector of the gravitating particle
1368:Wheeler, J. A.; Misner, C.; Thorne, K. S. (1973).
1281:
889:
767:
564:The field around multiple particles is simply the
529:
342:
189:. Determined in this way, the gravitational field
890:{\displaystyle \mathbf {G} =\kappa \mathbf {T} ,}
839:Gravitational potential § General relativity
855:plays the role of the gravitational potential.
1343:. European Physics Series (2nd ed.). UK:
8:
981:, this will cause an object to experience a
130:attempted to model gravity as some kind of
548:Relation between Gauss's and Newton's laws
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255:
248:
235:
233:
225:
223:
1228:. Vol. II. Addison Wesley Longman.
79:exerted on another massive body. It has
1372:. W. H. Freeman & Co. p. 404.
1314:Whelan, P. M.; Hodgeson, M. J. (1978).
1192:Foster, J.; Nightingale, J. D. (2006).
1165:Grøn, Øyvind; Hervik, Sigbjørn (2007).
1113:. Vol. I. Addison Wesley Longman.
1096:
990:, one of the most well known being the
218:. The gravitational field equation is
1252:Forshaw, J. R.; Smith, A. G. (2009).
1060:Newton's law of universal gravitation
965:being in a region of curved space is
775:i.e. the gravitational field on mass
187:Newton's law of universal gravitation
7:
1195:A Short Course in General Relativity
753:
749:
506:
497:
479:
334:
331:
25:
949:Newtonian constant of gravitation
195:around a single particle of mass
880:
869:
710:
701:
683:
674:
631:
596:
577:
486:
309:
299:
262:
236:
226:
59:gravitational acceleration field
1316:Essential Principles of Physics
1225:The Feynman Lectures on Physics
1171:. Springer Japan. p. 256.
1110:The Feynman Lectures on Physics
925:Einstein gravitational constant
205:consisting at every point of a
1137:General Relativity from A to B
825:is that of the test particle.
554:These classical equations are
543:Poisson's equation for gravity
1:
1318:(2nd ed.). John Murray.
1280:; Trigg, G. L., eds. (1991).
148:gravitational potential field
18:Newtonian gravitational field
927:. The latter is defined as
99:(N/kg) or, equivalently, in
87:(L/T) and it is measured in
1142:University of Chicago Press
1085:Tests of general relativity
472:of the attracting mass is:
1425:
832:
456:gravitational acceleration
29:
1339:Kibble, T. W. B. (1973).
110:In its original concept,
1284:Encyclopaedia of Physics
860:Einstein field equations
1254:Dynamics and Relativity
1134:Geroch, Robert (1981).
1065:Newton's laws of motion
1045:Gravitational potential
539:Gauss's law for gravity
216:gravitational potential
166:, or that gravity is a
72:phenomena, such as the
891:
769:
531:
454:are both equal to the
395:gravitational constant
344:
164:no gravitational force
46:
892:
770:
532:
345:
175:equivalence principle
40:
1040:Gravitational energy
905:stress–energy tensor
865:
573:
476:
222:
128:Pierre-Simon Laplace
43:point of equilibrium
1399:Theories of gravity
1341:Classical Mechanics
1025:Classical mechanics
1012:sphere of influence
1008:gravitational wells
992:deflection of light
979:Newton's second law
849:Christoffel symbols
559:equations of motion
366:is the mass of the
358:gravitational force
181:Classical mechanics
140:classical mechanics
75:gravitational force
55:gravitational field
1409:General relativity
1050:Gravitational wave
1003:Embedding diagrams
977:of the field. By
887:
845:general relativity
829:General relativity
793:, except the mass
765:
748:
659:
628:
593:
527:
340:
155:general relativity
47:
1379:978-0-7167-0344-0
1354:978-0-07-084018-8
1325:978-0-7195-3382-2
1299:978-0-89573-752-6
1263:978-0-470-01460-8
1235:978-0-201-02115-8
1205:978-0-387-26078-5
1178:978-0-387-69199-2
1151:978-0-226-28864-2
1120:978-0-201-02115-8
998:Embedding diagram
739:
731:
650:
619:
617:
584:
323:
282:
243:
16:(Redirected from
1416:
1384:
1383:
1365:
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1358:
1336:
1330:
1329:
1311:
1305:
1303:
1288:(2nd ed.).
1287:
1274:
1268:
1267:
1249:
1243:
1242:
1220:Feynman, Richard
1216:
1210:
1209:
1189:
1183:
1182:
1162:
1156:
1155:
1131:
1125:
1124:
1105:Feynman, Richard
1101:
1080:Speed of gravity
1070:Potential energy
1030:Entropic gravity
994:in such fields.
983:fictitious force
956:
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922:
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902:
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168:fictitious force
144:spatial gradient
32:Gravity of Earth
27:Model in physics
21:
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1144:. p. 181.
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1103:
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952:
942:
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915:Einstein tensor
908:
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781:
776:
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571:
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537:which contains
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107:squared (m/s).
35:
28:
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15:
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5:
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1075:Specific force
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959:speed of light
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1278:Lerner, R. G.
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853:metric tensor
850:
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828:
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457:
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386:
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368:test particle
364:
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328:
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70:gravitational
67:
64:
60:
56:
52:
44:
39:
33:
19:
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1194:
1187:
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1007:
1002:
1001:
971:accelerating
963:
953:
943:
937:
933:
929:
919:
909:
899:
857:
842:
821:
815:
808:
804:
795:
789:
785:
777:
563:
556:differential
553:
546:
468:
459:
446:
438:
424:
415:
407:
403:del operator
389:
379:
372:
362:
352:
203:vector field
197:
191:
184:
172:
163:
152:
124:Isaac Newton
122:. Following
109:
85:acceleration
73:
58:
54:
48:
1370:Gravitation
1345:McGraw Hill
1055:Gravity map
1035:Gravitation
988:differences
1393:Categories
1092:References
967:equivalent
833:See also:
566:vector sum
1290:Wiley-VCH
1256:. Wiley.
877:κ
754:Φ
750:∇
741:∑
737:−
706:−
679:−
652:∑
645:−
621:∑
586:∑
525:ρ
519:π
513:−
507:Φ
498:∇
494:−
483:⋅
480:∇
335:Φ
332:∇
329:−
288:−
159:spacetime
134:field or
132:radiation
81:dimension
1222:(1970).
1107:(1970).
1018:See also
975:gradient
941:, where
802:itself.
97:kilogram
1404:Geodesy
973:up the
957:is the
947:is the
923:is the
913:is the
903:is the
465:density
451:
435:
429:
411:
401:is the
393:is the
356:is the
146:of the
112:gravity
93:newtons
51:physics
1376:
1351:
1322:
1304:p. 451
1296:
1260:
1232:
1202:
1175:
1148:
1117:
917:, and
897:where
847:, the
837:, and
819:, and
541:, and
397:, and
350:where
207:vector
120:masses
114:was a
105:second
101:meters
63:vector
201:is a
136:fluid
116:force
89:units
77:field
66:field
61:is a
1374:ISBN
1349:ISBN
1320:ISBN
1294:ISBN
1258:ISBN
1230:ISBN
1200:ISBN
1173:ISBN
1146:ISBN
1115:ISBN
951:and
432:and
385:time
103:per
95:per
53:, a
969:to
932:= 8
843:In
383:is
153:In
91:of
83:of
57:or
49:In
1395::
1347:.
1292:.
1238:.
1140:.
1014:.
1010:,
961:.
934:πG
907:,
551:.
405:.
387:,
370:,
360:,
177:.
170:.
150:.
126:,
1382:.
1357:.
1328:.
1302:.
1266:.
1208:.
1181:.
1154:.
1123:.
954:c
944:G
938:c
936:/
930:κ
920:κ
910:G
900:T
885:,
881:T
874:=
870:G
822:R
816:i
809:i
805:R
798:j
796:m
790:i
786:m
780:j
778:m
763:,
758:i
745:i
734:=
727:3
722:|
716:i
711:R
702:R
697:|
689:i
684:R
675:R
666:i
662:m
656:i
648:G
642:=
637:i
632:F
625:i
615:m
612:1
607:=
602:i
597:g
590:i
582:=
578:g
522:G
516:4
510:=
502:2
491:=
487:g
469:ρ
460:g
447:m
443:/
439:F
425:t
423:d
420:/
416:R
414:d
399:∇
390:G
380:t
373:R
363:m
353:F
338:,
326:=
319:3
314:|
310:R
306:|
300:R
294:M
291:G
285:=
277:2
273:t
269:d
263:R
257:2
253:d
246:=
241:m
237:F
231:=
227:g
212:Φ
198:M
192:g
45:.
34:.
20:)
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