4059:
3860:
737:
1436:
1573:
3873:
750:
1806:
3688:
1009:, but the universality of the gravitational constant is intact and the law still continues to be used as an excellent approximation of the effects of gravity in most applications. Relativity is required only when there is a need for extreme accuracy, or when dealing with very strong gravitational fields, such as those found near extremely massive and dense objects, or at small distances (such as
3589:
2644:
1671:
4685:
1356:"That one body may act upon another at a distance through a vacuum without the mediation of anything else, by and through which their action and force may be conveyed from one another, is to me so great an absurdity that, I believe, no man who has in philosophic matters a competent faculty of thinking could ever fall into it."
3330:
2014:
1365:
in 1675 and 1717). Moreover, he refused to even offer a hypothesis as to the cause of this force on grounds that to do so was contrary to sound science. He lamented that "philosophers have hitherto attempted the search of nature in vain" for the source of the gravitational force, as he was convinced
3926:
instead of being due to a force propagated between bodies. In
Einstein's theory, energy and momentum distort spacetime in their vicinity, and other particles move in trajectories determined by the geometry of spacetime. This allowed a description of the motions of light and mass that was consistent
1686:
If the bodies in question have spatial extent (as opposed to being point masses), then the gravitational force between them is calculated by summing the contributions of the notional point masses that constitute the bodies. In the limit, as the component point masses become "infinitely small", this
1058:
developed the idea that Kepler's laws must also apply to the orbit of the Moon around the Earth and then to all objects on Earth. The analysis required assuming that the gravitation force acted as if all of the mass of the Earth were concentrated at its center, an unproven conjecture at that time.
1360:
He never, in his words, "assigned the cause of this power". In all other cases, he used the phenomenon of motion to explain the origin of various forces acting on bodies, but in the case of gravity, he was unable to experimentally identify the motion that produces the force of gravity (although he
1330:
means "is proportional to". To make this into an equal-sided formula or equation, there needed to be a multiplying factor or constant that would give the correct force of gravity no matter the value of the masses or distance between them (the gravitational constant). Newton would need an accurate
3170:
4607:
loads refers to the instantaneous inertial loads generated by instantaneous angular velocities and accelerations, as well as translational accelerations (9 variables). It is as though one took a photograph, which also recorded the instantaneous position and properties of motion. In contrast, a
1698:
In this way, it can be shown that an object with a spherically symmetric distribution of mass exerts the same gravitational attraction on external bodies as if all the object's mass were concentrated at a point at its center. (This is not generally true for non-spherically symmetrical bodies.)
1305:
1072:
with new mathematical analysis to explain Kepler's empirical results. His explanation was in the form of a law of universal gravitation: any two bodies are attracted by a force proportional to their mass and inversely proportional to their separation squared. Newton's original formula was:
2213:
2969:
1679:
3654:(treated as particles travelling at the expected speed) that is calculated by using Newton's theory is only one-half of the deflection that is observed by astronomers. Calculations using general relativity are in much closer agreement with the astronomical observations.
1366:"by many reasons" that there were "causes hitherto unknown" that were fundamental to all the "phenomena of nature". These fundamental phenomena are still under investigation and, though hypotheses abound, the definitive answer has yet to be found. And in Newton's 1713
3657:
In spiral galaxies, the orbiting of stars around their centers seems to strongly disobey both Newton's law of universal gravitation and general relativity. Astrophysicists, however, explain this marked phenomenon by assuming the presence of large amounts of
1825:
2397:
3584:{\displaystyle {\frac {\phi }{c^{2}}}={\frac {GM_{\mathrm {sun} }}{r_{\mathrm {orbit} }c^{2}}}\sim 10^{-8},\quad \left({\frac {v_{\mathrm {Earth} }}{c}}\right)^{2}=\left({\frac {2\pi r_{\mathrm {orbit} }}{(1\ \mathrm {yr} )c}}\right)^{2}\sim 10^{-8},}
2274:
It is a generalisation of the vector form, which becomes particularly useful if more than two objects are involved (such as a rocket between the Earth and the Moon). For two objects (e.g. object 2 is a rocket, object 1 the Earth), we simply write
1059:
His calculations of the Moon orbit time was within 16% of the known value. By 1680, new values for the diameter of the Earth improved his orbit time to within 1.6%, but more importantly Newton had found a proof of his earlier conjecture.
4627:
Each particle in a system of a finite number of particles is subjected to a
Newtonian gravitational attraction from all the other particles, and to no other forces. If the initial state of the system is given, how will the particles
3628:
must be used to describe the system. General relativity reduces to
Newtonian gravity in the limit of small potential and low velocities, so Newton's law of gravitation is often said to be the low-gravity limit of general relativity.
1353:
While Newton was able to formulate his law of gravity in his monumental work, he was deeply uncomfortable with the notion of "action at a distance" that his equations implied. In 1692, in his third letter to
Bentley, he wrote:
3020:
1079:
2738:
2461:
3646:
per century discrepancy between the
Newtonian calculation, which arises only from the gravitational attractions from the other planets, and the observed precession, made with advanced telescopes during the 19th
2545:
2084:
2843:
91:
115:
4870:
1510:
925:
2628:
2311:
4805:
1710:
can be used to find the gravitational force. The theorem tells us how different parts of the mass distribution affect the gravitational force measured at a point located a distance
1382:.... It is enough that gravity does really exist and acts according to the laws I have explained, and that it abundantly serves to account for all the motions of celestial bodies."
3761:
3180:
Newton's description of gravity is sufficiently accurate for many practical purposes and is therefore widely used. Deviations from it are small when the dimensionless quantities
3619:
2792:
3213:
2009:{\displaystyle \mathbf {F} _{21}=-G{m_{1}m_{2} \over {|\mathbf {r} _{21}|}^{2}}{\hat {\mathbf {r} }}_{21}=-G{m_{1}m_{2} \over {|\mathbf {r} _{21}|}^{3}}\mathbf {r} _{21}}
5497:
5435:
2765:
2668:
3254:
1654:. This experiment was also the first test of Newton's theory of gravitation between masses in the laboratory. It took place 111 years after the publication of Newton's
1328:
4486:(The 1962 Dover edition, page 348 lists a table documenting the observed and calculated values for the precession of the perihelion of Mercury, Venus, and the Earth.)
4689:
3274:
5799:
4773:
4370:
1064:
848:
2477:; that is, the work done by gravity from one position to another is path-independent. This has the consequence that there exists a gravitational potential field
4496:
Greene, Geoffrey L.; Gudkov, Vladimir (2007). "Neutron interferometric method to provide improved constraints on non-Newtonian gravity at the nanometer scale".
4331:
3318:
3298:
3012:
2992:
2835:
2815:
781:
998:, where force is inversely proportional to the square of the distance between the bodies. Coulomb's law has charge in place of mass and a different constant.
4209:
370:
5605:
4117:
3165:{\displaystyle |\mathbf {g(r)} |={\begin{cases}{\dfrac {GMr}{R^{3}}},&{\text{if }}r<R\\\\{\dfrac {GM}{r^{2}}},&{\text{if }}r\geq R\end{cases}}}
4862:
3816:
1435:
489:
1300:{\displaystyle {\rm {Force\,of\,gravity}}\propto {\frac {\rm {mass\,of\,object\,1\,\times \,mass\,of\,object\,2}}{\rm {distance\,from\,centers^{2}}}}}
5091:
6103:
5410:
5387:
2267:
that describes the gravitational force that would be applied on an object in any given point in space, per unit mass. It is actually equal to the
5776:
5143:
6031:
6082:
5590:
4995:
4733:
2673:
1362:
4058:
3859:
736:
6108:
5760:
5733:
5575:
5490:
4463:
4292:
4249:
4175:
4148:
2408:
5853:
4034:
of a group of celestial bodies, predict their interactive forces; and consequently, predict their true orbital motions for all future times
5784:
5121:
5022:
1044:
4191:
2491:
1820:
to account for the direction of the gravitational force as well as its magnitude. In this formula, quantities in bold represent vectors.
5907:
4832:
3905:
444:
5012:
2208:{\displaystyle {\hat {\mathbf {r} }}_{21}\ {\stackrel {\mathrm {def} }{=}}\ {\frac {\mathbf {r_{2}-r_{1}} }{|\mathbf {r_{2}-r_{1}} |}}}
6180:
6088:
5636:
5619:
5560:
5034:
4208:
Isaac Newton: "In philosophy particular propositions are inferred from the phenomena and afterwards rendered general by induction": "
3756:
2964:{\displaystyle |\mathbf {g(r)} |={\begin{cases}0,&{\text{if }}r<R\\\\{\dfrac {GM}{r^{2}}},&{\text{if }}r\geq R\end{cases}}}
5741:
5570:
4824:
4350:
4343:
3836:
1529:
1331:
measure of this constant to prove his inverse-square law. When Newton presented Book 1 of the unpublished text in April 1686 to the
994:
of electrical forces, which is used to calculate the magnitude of the electrical force arising between two charged bodies. Both are
774:
4612:
condition refers to a system's state being invariant to time; otherwise, the first derivatives and all higher derivatives are zero.
5483:
5420:
5245:
4643:
A general, classical solution in terms of first integrals is known to be impossible. An exact theoretical solution for arbitrary
3993:. Solving this problem â from the time of the Greeks and on â has been motivated by the desire to understand the motions of the
5542:
5440:
5342:
5240:
5061:
1022:
110:
47:
6170:
5848:
5770:
821:", as it marked the unification of the previously described phenomena of gravity on Earth with known astronomical behaviors.
105:
6041:
365:
5565:
5325:
3642:
of the orbits of the planets, especially that of
Mercury, which was detected long after the life of Newton. There is a 43
2231:
is now a vector quantity, and the right hand side is multiplied by the appropriate unit vector. Also, it can be seen that
1585:
1424:
1416:
810:
806:
360:
6155:
5235:
767:
754:
515:
438:
5826:
203:
5720:
5710:
5585:
5430:
5289:
5086:
1450:
434:
235:
5668:
5148:
5051:
865:
6175:
6026:
5532:
5230:
5225:
5017:
4980:
4839:
4726:
4701:
4105:
4084:
4078:
3936:
2634:
2268:
1069:
654:
543:
469:
329:
262:
5111:
4706:
5820:
5815:
5195:
4765:
408:
6036:
5746:
5066:
5007:
4920:
2575:
2392:{\displaystyle \mathbf {g} (\mathbf {r} )=-G{m_{1} \over {{\vert \mathbf {r} \vert }^{2}}}\,\mathbf {\hat {r}} }
6165:
5923:
5917:
4990:
4655:
must be truncated, giving at best only an approximate solution; and an approach now obsolete. In addition, the
3766:
684:
528:
5884:
4975:
5951:
5180:
5044:
4797:
3898:
3277:
674:
634:
398:
5752:
5662:
5868:
5415:
5405:
5170:
5133:
5106:
5000:
4552:-body problem, especially Ms. Kovalevskaya's ~1868â1888, twenty-year complex-variables approach, failure;
4451:
4099:
3964:
3932:
3731:
3324:
in vacuum. For example, Newtonian gravity provides an accurate description of the Earth/Sun system, since
2033:
1339:
made a claim that Newton had obtained the inverse square law from him, ultimately a frivolous accusation.
1035:
started over with a more fundamental view, developing ideas of matter and action independent of theology.
961:
679:
496:
6160:
6000:
5979:
5972:
5912:
5462:
5369:
5255:
5250:
5039:
4952:
4719:
4660:
3826:
3726:
2466:
This formulation is dependent on the objects causing the field. The field has units of acceleration; in
1420:
829:
818:
689:
664:
350:
168:
5537:
4927:
4212:", Book 3, General Scholium, at p.392 in Volume 2 of Andrew Motte's English translation published 1729.
3597:
6067:
5986:
5965:
5958:
5833:
5688:
5646:
5376:
5096:
4853:
4515:
4072:
1639:
1379:
1348:
968:
709:
704:
669:
577:
573:
565:
555:
345:
338:
94:
3963:
In recent years, quests for non-inverse square terms in the law of gravity have been carried out by
3056:
2879:
2770:
1378:"I have not yet been able to discover the cause of these properties of gravity from phenomena and I
5185:
5165:
5081:
5071:
4932:
4391:
3986:
2254:
2076:
1572:
843:
838:
484:
425:
403:
148:
143:
138:
38:
3985:-body problem is an ancient, classical problem of predicting the individual motions of a group of
6129:
5595:
5580:
5552:
5029:
4757:
4548:
Leimanis and
Minorsky: Our interest is with Leimanis, who first discusses some history about the
4531:
4505:
4044:
4018:
3919:
3891:
3877:
3841:
3703:
3698:
3651:
3639:
3625:
3183:
2474:
1412:
1006:
995:
813:
to the square of the distance between their centers. Separated objects attract and are attracted
614:
355:
230:
198:
158:
5400:
5116:
4087: â different conventions for the metric tensor, in a theory of a dilaton coupled to gravity
2747:
2650:
1682:
Gravity field near the surface of the Earth â an object is shown accelerating toward the surface
3218:
6113:
6021:
5765:
5693:
5359:
5331:
5213:
5190:
5138:
5056:
4942:
4663:, but these, too, are approximate solutions; and again obsolete. See Sverre J. Aarseth's book
4630:
Rosenberg failed to realize, like everyone else, that it is necessary to determine the forces
4459:
4443:
4346:
4339:
4288:
4245:
4171:
4144:
3821:
1814:
1313:
1032:
1028:
624:
581:
538:
533:
474:
250:
240:
133:
4138:
6095:
5789:
5683:
5319:
5295:
5271:
5101:
4847:
4523:
4431:
4165:
4040:
4006:
3928:
3923:
2557:
is a point mass or the mass of a sphere with homogeneous mass distribution, the force field
2224:
1428:
1368:
1010:
991:
719:
699:
644:
639:
585:
560:
415:
273:
218:
193:
3259:
1775:
from the center. That is, the individual gravitational forces exerted on a point at radius
1658:
and 71 years after Newton's death, so none of Newton's calculations could use the value of
5794:
5715:
5675:
5641:
5307:
5076:
4970:
4652:
3736:
1678:
1647:
1040:
1036:
1002:
976:
714:
659:
609:
604:
523:
4519:
4423:
1793:
As a consequence, for example, within a shell of uniform thickness and density there is
5994:
5350:
5175:
5158:
5128:
4915:
4427:
4111:
4064:
3976:
3918:
The first two conflicts with observations above were explained by
Einstein's theory of
3864:
3321:
3303:
3283:
2997:
2977:
2820:
2800:
1643:
1593:
972:
967:
The first test of Newton's law of gravitation between masses in the laboratory was the
953:
741:
649:
550:
267:
213:
6149:
5931:
5600:
5395:
5277:
5219:
4648:
4224:
3927:
with all available observations. In general relativity, the gravitational force is a
1707:
1692:
1332:
814:
629:
456:
17:
4535:
4322:
Proposition 75, Theorem 35: p. 956 â I.Bernard Cohen and Anne
Whitman, translators:
5889:
5698:
5283:
5153:
4962:
4937:
4900:
4742:
4323:
4093:
3831:
2264:
1336:
1055:
833:
825:
694:
619:
308:
188:
3687:
1805:
4192:"Physics: Fundamental Forces and the Synthesis of Theory | Encyclopedia.com"
5858:
5301:
4910:
4789:
4362:
4285:
A history of the theories of aether & electricity. 1: The classical theories
4242:
Forces and fields: the concept of action at a distance in the history of physics
4096: â Celestial orbit whose trajectory is a conic section in the orbital plane
3990:
3811:
3659:
2216:
1048:
4527:
6072:
5425:
5313:
4695:
4447:
4054:
3944:
1399:
479:
153:
6077:
6059:
5863:
5840:
4554:
Section 1: The
Dynamics of Rigid Bodies and Mathematical Exterior Ballistics
3952:
3940:
3721:
3679:
3643:
1650:
in 1798, although Cavendish did not himself calculate a numerical value for
501:
1670:
5475:
4684:
6134:
5944:
5937:
4947:
4888:
4479:
3948:
2733:{\displaystyle \mathbf {g(r)} \cdot d\mathbf {A} =-4\pi GM_{\text{enc}},}
1817:
1748:
was concentrated at the center of the mass distribution (as noted above).
1688:
1611:
798:
420:
303:
278:
5506:
4905:
4893:
4781:
4510:
3786:
2637:, field in a symmetric body can be found by the mathematical equation:
2456:{\displaystyle \mathbf {F} (\mathbf {r} )=m\mathbf {g} (\mathbf {r} ).}
2223:
It can be seen that the vector form of the equation is the same as the
987:
393:
246:
163:
2565:) outside the sphere is isotropic, i.e., depends only on the distance
1039:
wrote about experimental measurements of falling and rolling objects.
4167:
Symmetries of Nature: A Handbook for Philosophy of Nature and Science
3998:
1662:; instead he could only calculate a force relative to another force.
452:
298:
208:
4711:
2540:{\displaystyle \mathbf {g} (\mathbf {r} )=-\nabla V(\mathbf {r} ).}
979:
in 1798. It took place 111 years after the publication of Newton's
5726:
4220:
4218:
3624:
In situations where either dimensionless parameter is large, then
1691:
the force (in vector form, see below) over the extents of the two
1677:
1669:
1571:
1406:
802:
288:
283:
225:
4140:
From Paradox to Reality: Our Basic Concepts of the Physical World
4002:
1402:
293:
256:
5479:
4715:
1809:
Gravity field surrounding Earth from a macroscopic perspective.
3994:
1797:
gravitational acceleration anywhere within the hollow sphere.
4308:
The Construction of Modern Science: Mechanisms and Mechanics
4081: â Restatement of Newton's law of universal gravitation
4024:
The classical physical problem can be informally stated as:
1434:
859:
The equation for universal gravitation thus takes the form:
4707:
Newton's Law of Universal Gravitation Javascript calculator
3158:
2957:
2467:
4338:, by I.Bernard Cohen. University of California Press 1999
4310:, by Richard S. Westfall. Cambridge University Press. 1978
1813:
Newton's law of universal gravitation can be written as a
1741:
as if all of the mass enclosed within a sphere of radius
1706:
a spherically symmetric distribution of matter, Newton's
86:{\displaystyle {\textbf {F}}={\frac {d\mathbf {p} }{dt}}}
1638:
was first accurately determined from the results of the
4367:
The NIST Reference on Constants, Units, and Uncertainty
934:
is the gravitational force acting between two objects,
815:
as if all their mass were concentrated at their centers
4363:"2022 CODATA Value: Newtonian constant of gravitation"
4270:
An Introduction to the Physics of Mass Length and Time
4120: â Physical interaction in post-classical physics
817:. The publication of the law has become known as the "
4005:. In the 20th century, understanding the dynamics of
3600:
3333:
3306:
3286:
3262:
3221:
3186:
3113:
3060:
3023:
3000:
2980:
2912:
2846:
2823:
2803:
2773:
2750:
2676:
2653:
2578:
2494:
2411:
2314:
2087:
1828:
1453:
1316:
1082:
868:
801:
attracts every other particle in the universe with a
50:
4422:
points from object 1 to object 2. See Fig. 11â6. of
4244:(Dover ed.). Mineola, N.Y: Dover Publications.
4089:
Pages displaying wikidata descriptions as a fallback
6122:
6054:
6012:
5898:
5877:
5808:
5655:
5629:
5618:
5551:
5520:
5513:
5449:
5386:
5341:
5264:
5206:
4961:
4881:
4816:
4749:
3621:is the radius of the Earth's orbit around the Sun.
1342:
4043:has been completely solved, as has the restricted
3971:Solutions of Newton's law of universal gravitation
3613:
3583:
3312:
3300:is the velocity of the objects being studied, and
3292:
3268:
3248:
3207:
3164:
3006:
2986:
2963:
2829:
2809:
2786:
2759:
2732:
2662:
2622:
2539:
2455:
2391:
2207:
2008:
1564:is the distance between the centers of the masses.
1504:
1391:In modern language, the law states the following:
1322:
1299:
919:
85:
5436:Statal Institute of Higher Education Isaac Newton
3039:
3033:
2862:
2856:
2687:
2681:
2383:
2026:is the force applied on body 2 exerted by body 1,
1751:The portion of the mass that is located at radii
1721:The portion of the mass that is located at radii
1505:{\displaystyle F=G{\frac {m_{1}m_{2}}{r^{2}}}\ }
1782:by the elements of the mass outside the radius
920:{\displaystyle F=G{\frac {m_{1}m_{2}}{r^{2}}},}
5800:Degenerate Higher-Order Scalar-Tensor theories
4558:the motion of a rigid body about a fixed point
4108: â Laws in physics about force and motion
4075: â Cosmological paradox involving gravity
3633:Observations conflicting with Newton's formula
2052:are respectively the masses of bodies 1 and 2,
5491:
4727:
4332:Mathematical Principles of Natural Philosophy
3922:, in which gravitation is a manifestation of
3899:
1674:Gravitational field strength within the Earth
775:
8:
4587:(Restricted Three-body Problem); Chapter 2,
4585:The Uniformization of the Three-body Problem
4143:. Cambridge University Press. pp. 28â.
3970:
2569:from the center of the sphere. In that case
2363:
2355:
1439:Diagram of two masses attracting one another
1405:attracts every single other point mass by a
983:and approximately 71 years after his death.
4235:
4233:
4118:Static forces and virtual-particle exchange
3638:Newton's theory does not fully explain the
1576:Error plot showing experimental values for
849:PhilosophiĂŠ Naturalis Principia Mathematica
5626:
5517:
5498:
5484:
5476:
4734:
4720:
4712:
4625:-body problem similarly (see References):
4318:
4316:
3906:
3892:
3670:
2623:{\displaystyle V(r)=-G{\frac {m_{1}}{r}}.}
1717:from the center of the mass distribution:
1001:Newton's law has later been superseded by
782:
768:
29:
4509:
4432:Euclidean vector#Addition and subtraction
4428:The Feynman Lectures on Physics, Volume I
4424:The Feynman Lectures on Physics, Volume I
4263:
4261:
4030:instantaneous position, velocity and time
4026:given the quasi-steady orbital properties
4021:is considerably more difficult to solve.
3605:
3599:
3569:
3556:
3535:
3505:
3504:
3491:
3477:
3449:
3448:
3442:
3424:
3408:
3385:
3384:
3365:
3364:
3354:
3343:
3334:
3332:
3305:
3285:
3261:
3240:
3228:
3220:
3199:
3190:
3185:
3141:
3127:
3112:
3091:
3077:
3059:
3051:
3043:
3029:
3024:
3022:
2999:
2979:
2940:
2926:
2911:
2890:
2874:
2866:
2852:
2847:
2845:
2822:
2802:
2778:
2772:
2749:
2721:
2697:
2677:
2675:
2652:
2606:
2600:
2577:
2526:
2503:
2495:
2493:
2442:
2434:
2420:
2412:
2410:
2378:
2377:
2376:
2367:
2358:
2354:
2352:
2346:
2340:
2323:
2315:
2313:
2197:
2190:
2177:
2172:
2167:
2159:
2146:
2141:
2139:
2121:
2120:
2115:
2113:
2112:
2103:
2092:
2090:
2089:
2086:
2000:
1995:
1986:
1980:
1974:
1969:
1963:
1962:
1954:
1944:
1937:
1922:
1911:
1909:
1908:
1899:
1893:
1887:
1882:
1876:
1875:
1867:
1857:
1850:
1835:
1830:
1827:
1491:
1480:
1470:
1463:
1452:
1315:
1288:
1265:
1252:
1227:
1222:
1203:
1196:
1183:
1179:
1175:
1156:
1149:
1136:
1134:
1107:
1100:
1084:
1083:
1081:
906:
895:
885:
878:
867:
67:
61:
52:
51:
49:
4102: â Thought experiment about gravity
1804:
6104:Gravitational interaction of antimatter
4287:(Repr ed.). New York: Dover Publ.
4129:
3678:
1415:intersecting both points. The force is
101:
37:
27:Classical statement of gravity as force
4458:. New York: W. H.Freeman and Company.
6109:Physics in the medieval Islamic world
6032:(2+1)-dimensional topological gravity
5528:Newton's law of universal gravitation
4986:Newton's law of universal gravitation
4690:Newton's law of universal gravitation
4634:before the motions can be determined.
3792:Newton's law of universal gravitation
2974:For a uniform solid sphere of radius
2797:Hence, for a hollow sphere of radius
2794:is the mass enclosed by the surface.
856:"), first published on 5 July 1687.
795:Newton's law of universal gravitation
464:Newton's law of universal gravitation
7:
5854:Asymptotic safety in quantum gravity
5144:Newton's theorem of revolving orbits
4575:), good precursor background to the
1734:causes the same force at the radius
846:and was formulated in Newton's work
5092:LeibnizâNewton calculus controversy
4833:standing on the shoulders of giants
3652:deflection of light rays by gravity
3256:are both much less than one, where
2297:and define the gravitational field
809:to the product of their masses and
445:Mechanics of planar particle motion
53:
5606:GibbonsâHawkingâYork boundary term
5459:
4659:-body problem may be solved using
4170:. Walter de Gruyter. pp. 8â.
3757:Introduction to general relativity
3539:
3536:
3518:
3515:
3512:
3509:
3506:
3462:
3459:
3456:
3453:
3450:
3398:
3395:
3392:
3389:
3386:
3372:
3369:
3366:
2751:
2654:
2517:
2128:
2125:
2122:
1768:gravitational force at the radius
1343:Newton's "causes hitherto unknown"
1285:
1281:
1278:
1275:
1272:
1269:
1266:
1262:
1259:
1256:
1253:
1249:
1246:
1243:
1240:
1237:
1234:
1231:
1228:
1219:
1216:
1213:
1210:
1207:
1204:
1200:
1197:
1193:
1190:
1187:
1184:
1172:
1169:
1166:
1163:
1160:
1157:
1153:
1150:
1146:
1143:
1140:
1137:
1126:
1123:
1120:
1117:
1114:
1111:
1108:
1104:
1101:
1097:
1094:
1091:
1088:
1085:
25:
5721:Modified Newtonian dynamics, MOND
5637:Classical theories of gravitation
4589:Capture in the Three-Body Problem
4164:Klaus Mainzer (2 December 2013).
4137:Fritz Rohrlich (25 August 1989).
4009:star systems became an important
3837:Mathematics of general relativity
3762:Mathematics of general relativity
1530:Newtonian constant of gravitation
5421:Isaac Newton Group of Telescopes
4683:
4573:Mathematical Exterior Ballistics
4225:The MichellâCavendish Experiment
4057:
3872:
3871:
3858:
3686:
3614:{\displaystyle r_{\text{orbit}}}
3036:
3030:
2859:
2853:
2698:
2684:
2678:
2642:
2527:
2504:
2496:
2443:
2435:
2421:
2413:
2380:
2359:
2324:
2316:
2227:form given earlier, except that
2191:
2187:
2183:
2178:
2174:
2160:
2156:
2152:
2147:
2143:
2093:
1996:
1970:
1912:
1883:
1831:
1618:in meters (m), and the constant
1522:is the force between the masses;
749:
748:
735:
68:
5543:History of gravitational theory
5441:Newton International Fellowship
5122:generalized GaussâNewton method
5035:Newton's method in optimization
4697:Feather and Hammer Drop on Moon
4484:Einstein's Theory of Relativity
3436:
1023:History of gravitational theory
948:are the masses of the objects,
5849:Causal dynamical triangulation
5538:Poisson's equation for gravity
4581:Section 2: Celestial Mechanics
3543:
3526:
3237:
3222:
3044:
3025:
2867:
2848:
2787:{\displaystyle M_{\text{enc}}}
2588:
2582:
2531:
2523:
2508:
2500:
2473:Gravitational fields are also
2447:
2439:
2425:
2417:
2328:
2320:
2198:
2168:
2097:
1981:
1964:
1916:
1894:
1877:
1431:of the distance between them:
1051:'s astronomical observations.
1:
4336:A Guide to Newton's Principia
4283:Whittaker, Edmund T. (1989).
4272:. Edinburgh University Press.
1062:In 1687 Newton published his
371:Koopmanâvon Neumann mechanics
5062:Newton's theorem about ovals
3989:interacting with each other
3640:precession of the perihelion
1634:. The value of the constant
952:is the distance between the
439:Non-inertial reference frame
5711:Infinite derivative gravity
5431:Sir Isaac Newton Sixth Form
5087:Corpuscular theory of light
5013:SchrödingerâNewton equation
4621:R. M. Rosenberg states the
3787:Introduction to gravitation
3208:{\displaystyle \phi /c^{2}}
2079:between bodies 1 and 2, and
366:Appell's equation of motion
236:Inertial frame of reference
6197:
5899:Unified-field-theoric and
4840:Notes on the Jewish Temple
4651:, but in practice such an
4593:Generalized n-body Problem
4528:10.1103/PhysRevC.75.015501
4085:Jordan and Einstein frames
3974:
3937:gravitational acceleration
2760:{\displaystyle \partial V}
2663:{\displaystyle \partial V}
2269:gravitational acceleration
2252:
1666:Bodies with spatial extent
1346:
1020:
1013:'s orbit around the Sun).
6181:Eponymous laws of physics
6042:JackiwâTeitelboim gravity
5821:Canonical quantum gravity
5816:Euclidean quantum gravity
4671:listed in the References.
3817:Derivations of relativity
3249:{\displaystyle (v/c)^{2}}
1433:
1372:in the second edition of
5918:Superfluid vacuum theory
5742:Nonsymmetric gravitation
5591:Post-Newtonian formalism
4991:post-Newtonian expansion
4871:Corruptions of Scripture
4863:Ancient Kingdoms Amended
4647:can be approximated via
4268:Feather, Norman (1959).
3767:Einstein field equations
3666:
2767:is a closed surface and
1323:{\displaystyle \propto }
1045:laws of planetary motion
529:Rotating reference frame
361:HamiltonâJacobi equation
6083:Mechanical explanations
5952:Heterotic string theory
5908:Noncommutative geometry
5827:WheelerâDeWitt equation
5553:General relativity (GR)
5533:Gauss's law for gravity
5507:Theories of gravitation
5181:Absolute space and time
5045:truncated Newton method
5018:Newton's laws of motion
4981:Newton's law of cooling
4452:Wheeler, John Archibald
4392:"Rotational Flattening"
4240:Hesse, Mary B. (2005).
4106:Newton's laws of motion
4079:Gauss's law for gravity
4013:-body problem too. The
3732:Lorentz transformations
3632:
3278:gravitational potential
954:centers of their masses
819:first great unification
470:Newton's laws of motion
330:Newton's laws of motion
5924:Logarithmic BEC vacuum
5869:Rainbow gravity theory
5747:Scalarâtensor theories
5521:Newtonian gravity (NG)
5416:Isaac Newton Telescope
5406:Isaac Newton Institute
5176:NewtonâPuiseux theorem
5171:Parallelogram of force
5159:kissing number problem
5149:NewtonâEuler equations
5052:GaussâNewton algorithm
5001:gravitational constant
4408:The vector difference
3965:neutron interferometry
3933:curvature of spacetime
3650:The predicted angular
3615:
3585:
3314:
3294:
3270:
3250:
3209:
3166:
3008:
2988:
2965:
2831:
2811:
2788:
2761:
2734:
2664:
2624:
2541:
2457:
2402:so that we can write:
2393:
2219:from body 1 to body 2.
2209:
2034:gravitational constant
2010:
1810:
1683:
1675:
1581:
1506:
1440:
1425:inversely proportional
1423:of the two masses and
1324:
1301:
962:gravitational constant
921:
830:empirical observations
811:inversely proportional
497:Simple harmonic motion
410:Euler's laws of motion
204:D'Alembert's principle
87:
6171:Concepts in astronomy
6001:Twistor string theory
5980:Type II string theory
5973:Bosonic string theory
5913:Semiclassical gravity
5878:Unified-field-theoric
5663:Poincaré gauge theory
5370:Isaac Newton Gargoyle
5280: (nephew-in-law)
5256:Copernican Revolution
5251:Scientific Revolution
5112:NewtonâCotes formulas
4976:Newton's inequalities
4953:Structural coloration
4661:numerical integration
4426:, equation (9.19) of
4396:farside.ph.utexas.edu
4114: â Social theory
3827:Differential geometry
3727:Equivalence principle
3616:
3586:
3315:
3295:
3271:
3269:{\displaystyle \phi }
3251:
3210:
3167:
3009:
2989:
2966:
2832:
2812:
2789:
2762:
2735:
2665:
2625:
2542:
2458:
2394:
2210:
2011:
1808:
1681:
1673:
1575:
1507:
1438:
1363:mechanical hypotheses
1325:
1302:
922:
351:Hamiltonian mechanics
169:Statistical mechanics
88:
18:Universal gravitation
6068:Aristotelian physics
6037:GaussâBonnet gravity
5987:Little string theory
5966:Type 0 string theory
5959:Type I string theory
5834:Loop quantum gravity
5761:Scalarâtensorâvector
5734:Tensorâvectorâscalar
5689:Gauge theory gravity
5647:Theory of everything
5377:Astronomers Monument
5067:NewtonâPepys problem
5040:Apollonius's problem
5008:NewtonâCartan theory
4921:NewtonâOkounkov body
4854:hypotheses non fingo
4843: (c. 1680)
4692:at Wikimedia Commons
4196:www.encyclopedia.com
3805:Relevant mathematics
3598:
3331:
3304:
3284:
3260:
3219:
3184:
3021:
2998:
2978:
2844:
2821:
2801:
2771:
2748:
2674:
2651:
2576:
2492:
2409:
2312:
2085:
1826:
1640:Cavendish experiment
1451:
1349:Action at a distance
1314:
1080:
1068:which combined his
1031:began to take root.
969:Cavendish experiment
866:
574:Angular acceleration
566:Rotational frequency
346:Lagrangian mechanics
339:Analytical mechanics
95:Second law of motion
48:
6156:Theories of gravity
5885:KaluzaâKlein theory
5186:Luminiferous aether
5134:Newton's identities
5107:Newton's cannonball
5082:Classical mechanics
5072:Newtonian potential
4933:Newtonian telescope
4520:2007PhRvC..75a5501G
4100:Newton's cannonball
3931:resulting from the
3674:Part of a series on
3667:Einstein's solution
2261:gravitational field
2255:Gravitational field
2077:displacement vector
1558:is the second mass;
1380:feign no hypotheses
996:inverse-square laws
844:classical mechanics
839:inductive reasoning
426:Harmonic oscillator
404:Equations of motion
39:Classical mechanics
33:Part of a series on
6130:Gravitational wave
6013:Generalisations /
5901:quantum-mechanical
5809:Quantum-mechanical
5622:general relativity
5596:Linearized gravity
5411:Isaac Newton Medal
5216: (birthplace)
5030:Newtonian dynamics
4928:Newton's reflector
4444:Misner, Charles W.
4045:three-body problem
4019:general relativity
3920:general relativity
3865:Physics portal
3842:Spacetime topology
3822:Spacetime diagrams
3750:General relativity
3722:Spacetime manifold
3715:Spacetime concepts
3704:General relativity
3699:Special relativity
3626:general relativity
3611:
3581:
3310:
3290:
3266:
3246:
3205:
3162:
3157:
3134:
3084:
3004:
2984:
2961:
2956:
2933:
2827:
2807:
2784:
2757:
2730:
2660:
2620:
2537:
2453:
2389:
2205:
2006:
1811:
1789:cancel each other.
1684:
1676:
1582:
1549:is the first mass;
1502:
1441:
1320:
1297:
1007:general relativity
917:
842:. It is a part of
824:This is a general
742:Physics portal
356:Routhian mechanics
231:Frame of reference
83:
6176:Newtonian gravity
6143:
6142:
6114:Theory of impetus
6050:
6049:
6022:Liouville gravity
5766:Conformal gravity
5694:Composite gravity
5684:Bimetric theories
5614:
5613:
5473:
5472:
5365: (sculpture)
5332:Abraham de Moivre
5286: (professor)
5214:Woolsthorpe Manor
5166:Newton's quotient
5139:Newton polynomial
5097:Newton's notation
4828: (1661â1665)
4688:Media related to
4669:-body Simulations
4498:Physical Review C
4465:978-0-7167-0344-0
4294:978-0-486-26126-3
4251:978-0-486-44240-2
4177:978-3-11-088693-1
4150:978-0-521-37605-1
4073:Bentley's paradox
4017:-body problem in
3987:celestial objects
3916:
3915:
3780:Classical gravity
3608:
3550:
3534:
3471:
3415:
3349:
3313:{\displaystyle c}
3293:{\displaystyle v}
3144:
3133:
3094:
3083:
3007:{\displaystyle M}
2987:{\displaystyle R}
2943:
2932:
2893:
2830:{\displaystyle M}
2810:{\displaystyle R}
2781:
2724:
2615:
2386:
2374:
2203:
2138:
2133:
2111:
2100:
1992:
1919:
1905:
1642:conducted by the
1570:
1569:
1501:
1497:
1310:where the symbol
1295:
1029:scientific method
1027:Around 1600, the
971:conducted by the
912:
792:
791:
539:Centrifugal force
534:Centripetal force
490:Euler's equations
475:Relative velocity
251:Moment of inertia
81:
55:
16:(Redirected from
6188:
6098:
6096:Entropic gravity
6091:
6015:extensions of GR
6003:
5989:
5982:
5975:
5968:
5961:
5954:
5947:
5940:
5926:
5843:
5836:
5829:
5790:Geometrodynamics
5779:
5755:
5736:
5729:
5678:
5671:
5627:
5518:
5500:
5493:
5486:
5477:
5461:
5356: (monotype)
5320:William Stukeley
5316: (disciple)
5296:Benjamin Pulleyn
5272:Catherine Barton
5191:Newtonian series
5102:Rotating spheres
4848:General Scholium
4743:Sir Isaac Newton
4736:
4729:
4722:
4713:
4698:
4687:
4672:
4641:
4635:
4619:
4613:
4602:
4596:
4546:
4540:
4539:
4513:
4493:
4487:
4477:
4471:
4469:
4440:
4434:
4406:
4400:
4399:
4388:
4382:
4381:
4379:
4378:
4359:
4353:
4320:
4311:
4305:
4299:
4298:
4280:
4274:
4273:
4265:
4256:
4255:
4237:
4228:
4227:, Laurent Hodges
4222:
4213:
4206:
4200:
4199:
4188:
4182:
4181:
4161:
4155:
4154:
4134:
4090:
4067:
4062:
4061:
4041:two-body problem
4007:globular cluster
4001:and the visible
3929:fictitious force
3924:curved spacetime
3908:
3901:
3894:
3880:
3875:
3874:
3867:
3863:
3862:
3832:Curved spacetime
3690:
3671:
3620:
3618:
3617:
3612:
3610:
3609:
3606:
3590:
3588:
3587:
3582:
3577:
3576:
3561:
3560:
3555:
3551:
3549:
3542:
3532:
3524:
3523:
3522:
3521:
3492:
3482:
3481:
3476:
3472:
3467:
3466:
3465:
3443:
3432:
3431:
3416:
3414:
3413:
3412:
3403:
3402:
3401:
3378:
3377:
3376:
3375:
3355:
3350:
3348:
3347:
3335:
3319:
3317:
3316:
3311:
3299:
3297:
3296:
3291:
3275:
3273:
3272:
3267:
3255:
3253:
3252:
3247:
3245:
3244:
3232:
3214:
3212:
3211:
3206:
3204:
3203:
3194:
3171:
3169:
3168:
3163:
3161:
3160:
3145:
3142:
3135:
3132:
3131:
3122:
3114:
3108:
3095:
3092:
3085:
3082:
3081:
3072:
3061:
3047:
3042:
3028:
3013:
3011:
3010:
3005:
2993:
2991:
2990:
2985:
2970:
2968:
2967:
2962:
2960:
2959:
2944:
2941:
2934:
2931:
2930:
2921:
2913:
2907:
2894:
2891:
2870:
2865:
2851:
2836:
2834:
2833:
2828:
2816:
2814:
2813:
2808:
2793:
2791:
2790:
2785:
2783:
2782:
2779:
2766:
2764:
2763:
2758:
2740:
2739:
2737:
2736:
2731:
2726:
2725:
2722:
2701:
2690:
2670:
2669:
2667:
2666:
2661:
2646:
2645:
2629:
2627:
2626:
2621:
2616:
2611:
2610:
2601:
2546:
2544:
2543:
2538:
2530:
2507:
2499:
2462:
2460:
2459:
2454:
2446:
2438:
2424:
2416:
2398:
2396:
2395:
2390:
2388:
2387:
2379:
2375:
2373:
2372:
2371:
2366:
2362:
2351:
2350:
2341:
2327:
2319:
2214:
2212:
2211:
2206:
2204:
2202:
2201:
2196:
2195:
2194:
2182:
2181:
2171:
2165:
2164:
2163:
2151:
2150:
2140:
2136:
2135:
2134:
2132:
2131:
2119:
2114:
2109:
2108:
2107:
2102:
2101:
2096:
2091:
2015:
2013:
2012:
2007:
2005:
2004:
1999:
1993:
1991:
1990:
1985:
1984:
1979:
1978:
1973:
1967:
1960:
1959:
1958:
1949:
1948:
1938:
1927:
1926:
1921:
1920:
1915:
1910:
1906:
1904:
1903:
1898:
1897:
1892:
1891:
1886:
1880:
1873:
1872:
1871:
1862:
1861:
1851:
1840:
1839:
1834:
1763:
1733:
1633:
1631:
1627:
1539:
1537:
1511:
1509:
1508:
1503:
1499:
1498:
1496:
1495:
1486:
1485:
1484:
1475:
1474:
1464:
1410:
1394:
1393:
1369:General Scholium
1329:
1327:
1326:
1321:
1306:
1304:
1303:
1298:
1296:
1294:
1293:
1292:
1226:
1135:
1130:
1129:
986:Newton's law of
926:
924:
923:
918:
913:
911:
910:
901:
900:
899:
890:
889:
879:
797:says that every
784:
777:
770:
757:
752:
751:
744:
740:
739:
645:Johann Bernoulli
640:Daniel Bernoulli
561:Tangential speed
465:
441:
416:Fictitious force
411:
263:Mechanical power
253:
194:Angular momentum
92:
90:
89:
84:
82:
80:
72:
71:
62:
57:
56:
30:
21:
6196:
6195:
6191:
6190:
6189:
6187:
6186:
6185:
6166:Scientific laws
6146:
6145:
6144:
6139:
6118:
6094:
6087:
6058:
6056:
6046:
6027:Lovelock theory
6014:
6008:
5999:
5985:
5978:
5971:
5964:
5957:
5950:
5943:
5936:
5922:
5900:
5894:
5873:
5839:
5832:
5825:
5804:
5795:Induced gravity
5775:
5771:Scalar theories
5751:
5732:
5725:
5716:Massive gravity
5676:Teleparallelism
5674:
5669:EinsteinâCartan
5667:
5651:
5642:Quantum gravity
5621:
5620:Alternatives to
5610:
5576:Exact solutions
5547:
5509:
5504:
5474:
5469:
5468:
5467:
5466:
5465:
5458:
5445:
5401:Newton's cradle
5382:
5337:
5310: (student)
5308:William Whiston
5304: (student)
5260:
5241:Religious views
5202:
5117:Newton's method
5077:Newtonian fluid
4971:Bucket argument
4957:
4877:
4812:
4745:
4740:
4696:
4680:
4675:
4653:infinite series
4642:
4638:
4620:
4616:
4603:
4599:
4579:-body problem;
4547:
4543:
4495:
4494:
4490:
4478:
4474:
4466:
4442:
4441:
4437:
4421:
4414:
4407:
4403:
4390:
4389:
4385:
4376:
4374:
4361:
4360:
4356:
4321:
4314:
4306:
4302:
4295:
4282:
4281:
4277:
4267:
4266:
4259:
4252:
4239:
4238:
4231:
4223:
4216:
4207:
4203:
4190:
4189:
4185:
4178:
4163:
4162:
4158:
4151:
4136:
4135:
4131:
4127:
4088:
4063:
4056:
4053:
3991:gravitationally
3979:
3973:
3961:
3912:
3883:
3870:
3857:
3856:
3848:
3847:
3846:
3806:
3798:
3797:
3796:
3781:
3773:
3772:
3771:
3751:
3743:
3742:
3741:
3737:Minkowski space
3716:
3708:
3669:
3635:
3601:
3596:
3595:
3565:
3525:
3500:
3493:
3487:
3486:
3444:
3438:
3437:
3420:
3404:
3380:
3379:
3360:
3356:
3339:
3329:
3328:
3302:
3301:
3282:
3281:
3258:
3257:
3236:
3217:
3216:
3195:
3182:
3181:
3178:
3156:
3155:
3139:
3123:
3115:
3109:
3106:
3105:
3089:
3073:
3062:
3052:
3019:
3018:
2996:
2995:
2994:and total mass
2976:
2975:
2955:
2954:
2938:
2922:
2914:
2908:
2905:
2904:
2888:
2875:
2842:
2841:
2819:
2818:
2817:and total mass
2799:
2798:
2774:
2769:
2768:
2746:
2745:
2717:
2672:
2671:
2649:
2648:
2647:
2643:
2641:
2602:
2574:
2573:
2556:
2490:
2489:
2470:, this is m/s.
2407:
2406:
2353:
2342:
2310:
2309:
2296:
2285:
2271:at that point.
2257:
2251:
2244:
2237:
2186:
2173:
2166:
2155:
2142:
2088:
2083:
2082:
2074:
2067:
2060:
2051:
2044:
2025:
1994:
1968:
1961:
1950:
1940:
1939:
1907:
1881:
1874:
1863:
1853:
1852:
1829:
1824:
1823:
1803:
1788:
1781:
1774:
1762:
1752:
1747:
1740:
1732:
1722:
1716:
1668:
1648:Henry Cavendish
1629:
1625:
1623:
1609:
1602:
1592:is measured in
1557:
1548:
1535:
1533:
1487:
1476:
1466:
1465:
1449:
1448:
1397:
1389:
1351:
1345:
1312:
1311:
1284:
1078:
1077:
1041:Johannes Kepler
1037:Galileo Galilei
1025:
1019:
1003:Albert Einstein
977:Henry Cavendish
946:
939:
902:
891:
881:
880:
864:
863:
788:
747:
734:
733:
726:
725:
724:
599:
591:
590:
570:
524:Circular motion
518:
508:
507:
506:
463:
433:
430:
409:
388:
380:
379:
376:
375:
333:
323:
315:
314:
313:
272:
268:Mechanical work
261:
245:
183:
175:
174:
173:
128:
120:
97:
73:
63:
46:
45:
28:
23:
22:
15:
12:
11:
5:
6194:
6192:
6184:
6183:
6178:
6173:
6168:
6163:
6158:
6148:
6147:
6141:
6140:
6138:
6137:
6132:
6126:
6124:
6123:Related topics
6120:
6119:
6117:
6116:
6111:
6106:
6101:
6100:
6099:
6092:
6080:
6075:
6070:
6064:
6062:
6052:
6051:
6048:
6047:
6045:
6044:
6039:
6034:
6029:
6024:
6018:
6016:
6010:
6009:
6007:
6006:
6005:
6004:
5995:Twistor theory
5992:
5991:
5990:
5983:
5976:
5969:
5962:
5955:
5948:
5941:
5929:
5928:
5927:
5915:
5910:
5904:
5902:
5896:
5895:
5893:
5892:
5887:
5881:
5879:
5875:
5874:
5872:
5871:
5866:
5861:
5856:
5851:
5846:
5845:
5844:
5837:
5830:
5818:
5812:
5810:
5806:
5805:
5803:
5802:
5797:
5792:
5787:
5782:
5781:
5780:
5768:
5763:
5758:
5757:
5756:
5744:
5739:
5738:
5737:
5730:
5718:
5713:
5708:
5696:
5691:
5686:
5681:
5680:
5679:
5672:
5659:
5657:
5653:
5652:
5650:
5649:
5644:
5639:
5633:
5631:
5624:
5616:
5615:
5612:
5611:
5609:
5608:
5603:
5598:
5593:
5588:
5583:
5578:
5573:
5568:
5563:
5557:
5555:
5549:
5548:
5546:
5545:
5540:
5535:
5530:
5524:
5522:
5515:
5511:
5510:
5505:
5503:
5502:
5495:
5488:
5480:
5471:
5470:
5457:
5456:
5455:
5454:
5453:
5451:
5447:
5446:
5444:
5443:
5438:
5433:
5428:
5423:
5418:
5413:
5408:
5403:
5398:
5392:
5390:
5384:
5383:
5381:
5380:
5373:
5366:
5357:
5347:
5345:
5339:
5338:
5336:
5335:
5334: (friend)
5329:
5328: (friend)
5323:
5322: (friend)
5317:
5311:
5305:
5299:
5293:
5292: (mentor)
5290:William Clarke
5287:
5281:
5275:
5268:
5266:
5262:
5261:
5259:
5258:
5253:
5248:
5246:Occult studies
5243:
5238:
5233:
5228:
5223:
5217:
5210:
5208:
5204:
5203:
5201:
5200:
5199:
5198:
5188:
5183:
5178:
5173:
5168:
5163:
5162:
5161:
5151:
5146:
5141:
5136:
5131:
5129:Newton fractal
5126:
5125:
5124:
5114:
5109:
5104:
5099:
5094:
5089:
5084:
5079:
5074:
5069:
5064:
5059:
5057:Newton's rings
5054:
5049:
5048:
5047:
5042:
5032:
5027:
5026:
5025:
5015:
5010:
5005:
5004:
5003:
4998:
4993:
4983:
4978:
4973:
4967:
4965:
4959:
4958:
4956:
4955:
4950:
4945:
4943:Newton's metal
4940:
4935:
4930:
4925:
4924:
4923:
4916:Newton polygon
4913:
4908:
4903:
4898:
4897:
4896:
4885:
4883:
4879:
4878:
4876:
4875:
4867:
4859:
4850:" (1713;
4844:
4836:
4829:
4820:
4818:
4817:Other writings
4814:
4813:
4811:
4810:
4802:
4794:
4786:
4778:
4770:
4762:
4753:
4751:
4747:
4746:
4741:
4739:
4738:
4731:
4724:
4716:
4710:
4709:
4704:
4693:
4679:
4678:External links
4676:
4674:
4673:
4665:Gravitational
4636:
4614:
4597:
4571:); Chapter 2,
4541:
4511:hep-ph/0608346
4488:
4472:
4464:
4448:Thorne, Kip S.
4435:
4419:
4412:
4401:
4383:
4354:
4334:. Preceded by
4312:
4300:
4293:
4275:
4257:
4250:
4229:
4214:
4201:
4183:
4176:
4156:
4149:
4128:
4126:
4123:
4122:
4121:
4115:
4112:Social gravity
4109:
4103:
4097:
4091:
4082:
4076:
4069:
4068:
4065:Physics portal
4052:
4049:
3977:n-body problem
3975:Main article:
3972:
3969:
3960:
3957:
3943:is due to its
3935:, because the
3914:
3913:
3911:
3910:
3903:
3896:
3888:
3885:
3884:
3882:
3881:
3868:
3853:
3850:
3849:
3845:
3844:
3839:
3834:
3829:
3824:
3819:
3814:
3808:
3807:
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3803:
3800:
3799:
3795:
3794:
3789:
3783:
3782:
3779:
3778:
3775:
3774:
3770:
3769:
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3745:
3744:
3740:
3739:
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3724:
3718:
3717:
3714:
3713:
3710:
3709:
3707:
3706:
3701:
3695:
3692:
3691:
3683:
3682:
3676:
3675:
3668:
3665:
3664:
3663:
3655:
3648:
3634:
3631:
3604:
3592:
3591:
3580:
3575:
3572:
3568:
3564:
3559:
3554:
3548:
3545:
3541:
3538:
3531:
3528:
3520:
3517:
3514:
3511:
3508:
3503:
3499:
3496:
3490:
3485:
3480:
3475:
3470:
3464:
3461:
3458:
3455:
3452:
3447:
3441:
3435:
3430:
3427:
3423:
3419:
3411:
3407:
3400:
3397:
3394:
3391:
3388:
3383:
3374:
3371:
3368:
3363:
3359:
3353:
3346:
3342:
3338:
3322:speed of light
3309:
3289:
3265:
3243:
3239:
3235:
3231:
3227:
3224:
3202:
3198:
3193:
3189:
3177:
3174:
3173:
3172:
3159:
3154:
3151:
3148:
3140:
3138:
3130:
3126:
3121:
3118:
3111:
3110:
3107:
3104:
3101:
3098:
3090:
3088:
3080:
3076:
3071:
3068:
3065:
3058:
3057:
3055:
3050:
3046:
3041:
3038:
3035:
3032:
3027:
3003:
2983:
2972:
2971:
2958:
2953:
2950:
2947:
2939:
2937:
2929:
2925:
2920:
2917:
2910:
2909:
2906:
2903:
2900:
2897:
2889:
2887:
2884:
2881:
2880:
2878:
2873:
2869:
2864:
2861:
2858:
2855:
2850:
2826:
2806:
2777:
2756:
2753:
2742:
2741:
2729:
2720:
2716:
2713:
2710:
2707:
2704:
2700:
2696:
2693:
2689:
2686:
2683:
2680:
2659:
2656:
2631:
2630:
2619:
2614:
2609:
2605:
2599:
2596:
2593:
2590:
2587:
2584:
2581:
2554:
2548:
2547:
2536:
2533:
2529:
2525:
2522:
2519:
2516:
2513:
2510:
2506:
2502:
2498:
2464:
2463:
2452:
2449:
2445:
2441:
2437:
2433:
2430:
2427:
2423:
2419:
2415:
2400:
2399:
2385:
2382:
2370:
2365:
2361:
2357:
2349:
2345:
2339:
2336:
2333:
2330:
2326:
2322:
2318:
2294:
2283:
2253:Main article:
2250:
2247:
2242:
2235:
2221:
2220:
2200:
2193:
2189:
2185:
2180:
2176:
2170:
2162:
2158:
2154:
2149:
2145:
2130:
2127:
2124:
2118:
2106:
2099:
2095:
2080:
2072:
2065:
2058:
2053:
2049:
2042:
2037:
2027:
2023:
2003:
1998:
1989:
1983:
1977:
1972:
1966:
1957:
1953:
1947:
1943:
1936:
1933:
1930:
1925:
1918:
1914:
1902:
1896:
1890:
1885:
1879:
1870:
1866:
1860:
1856:
1849:
1846:
1843:
1838:
1833:
1802:
1799:
1791:
1790:
1786:
1779:
1772:
1760:
1749:
1745:
1738:
1730:
1714:
1667:
1664:
1632:10 mâ
kgâ
s
1607:
1600:
1568:
1567:
1566:
1565:
1559:
1555:
1550:
1546:
1541:
1538:10 mâ
kgâ
s
1523:
1513:
1512:
1494:
1490:
1483:
1479:
1473:
1469:
1462:
1459:
1456:
1443:
1442:
1432:
1388:
1385:
1347:Main article:
1344:
1341:
1319:
1308:
1307:
1291:
1287:
1283:
1280:
1277:
1274:
1271:
1268:
1264:
1261:
1258:
1255:
1251:
1248:
1245:
1242:
1239:
1236:
1233:
1230:
1225:
1221:
1218:
1215:
1212:
1209:
1206:
1202:
1199:
1195:
1192:
1189:
1186:
1182:
1178:
1174:
1171:
1168:
1165:
1162:
1159:
1155:
1152:
1148:
1145:
1142:
1139:
1133:
1128:
1125:
1122:
1119:
1116:
1113:
1110:
1106:
1103:
1099:
1096:
1093:
1090:
1087:
1070:laws of motion
1033:René Descartes
1021:Main article:
1018:
1015:
944:
937:
928:
927:
916:
909:
905:
898:
894:
888:
884:
877:
874:
871:
790:
789:
787:
786:
779:
772:
764:
761:
760:
759:
758:
745:
728:
727:
723:
722:
717:
712:
707:
702:
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692:
687:
682:
677:
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612:
607:
601:
600:
597:
596:
593:
592:
589:
588:
569:
568:
563:
558:
553:
551:Coriolis force
548:
547:
546:
536:
531:
526:
520:
519:
514:
513:
510:
509:
505:
504:
499:
494:
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487:
477:
472:
467:
460:
449:
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429:
428:
423:
418:
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401:
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60:
42:
41:
35:
34:
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
6193:
6182:
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6174:
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6159:
6157:
6154:
6153:
6151:
6136:
6133:
6131:
6128:
6127:
6125:
6121:
6115:
6112:
6110:
6107:
6105:
6102:
6097:
6093:
6090:
6089:FatioâLe Sage
6086:
6085:
6084:
6081:
6079:
6076:
6074:
6071:
6069:
6066:
6065:
6063:
6061:
6055:Pre-Newtonian
6053:
6043:
6040:
6038:
6035:
6033:
6030:
6028:
6025:
6023:
6020:
6019:
6017:
6011:
6002:
5998:
5997:
5996:
5993:
5988:
5984:
5981:
5977:
5974:
5970:
5967:
5963:
5960:
5956:
5953:
5949:
5946:
5942:
5939:
5935:
5934:
5933:
5932:String theory
5930:
5925:
5921:
5920:
5919:
5916:
5914:
5911:
5909:
5906:
5905:
5903:
5897:
5891:
5888:
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5882:
5880:
5876:
5870:
5867:
5865:
5862:
5860:
5857:
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5850:
5847:
5842:
5838:
5835:
5831:
5828:
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5823:
5822:
5819:
5817:
5814:
5813:
5811:
5807:
5801:
5798:
5796:
5793:
5791:
5788:
5786:
5783:
5778:
5774:
5773:
5772:
5769:
5767:
5764:
5762:
5759:
5754:
5750:
5749:
5748:
5745:
5743:
5740:
5735:
5731:
5728:
5724:
5723:
5722:
5719:
5717:
5714:
5712:
5709:
5707:
5705:
5701:
5697:
5695:
5692:
5690:
5687:
5685:
5682:
5677:
5673:
5670:
5666:
5665:
5664:
5661:
5660:
5658:
5654:
5648:
5645:
5643:
5640:
5638:
5635:
5634:
5632:
5628:
5625:
5623:
5617:
5607:
5604:
5602:
5601:ADM formalism
5599:
5597:
5594:
5592:
5589:
5587:
5584:
5582:
5579:
5577:
5574:
5572:
5569:
5567:
5564:
5562:
5559:
5558:
5556:
5554:
5550:
5544:
5541:
5539:
5536:
5534:
5531:
5529:
5526:
5525:
5523:
5519:
5516:
5512:
5508:
5501:
5496:
5494:
5489:
5487:
5482:
5481:
5478:
5464:
5460:
5452:
5448:
5442:
5439:
5437:
5434:
5432:
5429:
5427:
5424:
5422:
5419:
5417:
5414:
5412:
5409:
5407:
5404:
5402:
5399:
5397:
5396:Newton (unit)
5394:
5393:
5391:
5389:
5385:
5379:
5378:
5374:
5372:
5371:
5367:
5364:
5362:
5358:
5355:
5353:
5349:
5348:
5346:
5344:
5340:
5333:
5330:
5327:
5326:William Jones
5324:
5321:
5318:
5315:
5312:
5309:
5306:
5303:
5300:
5298: (tutor)
5297:
5294:
5291:
5288:
5285:
5282:
5279:
5278:John Conduitt
5276:
5274: (niece)
5273:
5270:
5269:
5267:
5263:
5257:
5254:
5252:
5249:
5247:
5244:
5242:
5239:
5237:
5234:
5232:
5229:
5227:
5224:
5221:
5220:Cranbury Park
5218:
5215:
5212:
5211:
5209:
5207:Personal life
5205:
5197:
5194:
5193:
5192:
5189:
5187:
5184:
5182:
5179:
5177:
5174:
5172:
5169:
5167:
5164:
5160:
5157:
5156:
5155:
5154:Newton number
5152:
5150:
5147:
5145:
5142:
5140:
5137:
5135:
5132:
5130:
5127:
5123:
5120:
5119:
5118:
5115:
5113:
5110:
5108:
5105:
5103:
5100:
5098:
5095:
5093:
5090:
5088:
5085:
5083:
5080:
5078:
5075:
5073:
5070:
5068:
5065:
5063:
5060:
5058:
5055:
5053:
5050:
5046:
5043:
5041:
5038:
5037:
5036:
5033:
5031:
5028:
5024:
5023:Kepler's laws
5021:
5020:
5019:
5016:
5014:
5011:
5009:
5006:
5002:
4999:
4997:
4996:parameterized
4994:
4992:
4989:
4988:
4987:
4984:
4982:
4979:
4977:
4974:
4972:
4969:
4968:
4966:
4964:
4960:
4954:
4951:
4949:
4946:
4944:
4941:
4939:
4936:
4934:
4931:
4929:
4926:
4922:
4919:
4918:
4917:
4914:
4912:
4909:
4907:
4904:
4902:
4899:
4895:
4892:
4891:
4890:
4887:
4886:
4884:
4882:Contributions
4880:
4873:
4872:
4868:
4865:
4864:
4860:
4857:
4855:
4849:
4845:
4842:
4841:
4837:
4835:" (1675)
4834:
4830:
4827:
4826:
4822:
4821:
4819:
4815:
4808:
4807:
4803:
4800:
4799:
4795:
4792:
4791:
4787:
4784:
4783:
4779:
4776:
4775:
4771:
4768:
4767:
4763:
4760:
4759:
4755:
4754:
4752:
4748:
4744:
4737:
4732:
4730:
4725:
4723:
4718:
4717:
4714:
4708:
4705:
4703:
4699:
4694:
4691:
4686:
4682:
4681:
4677:
4670:
4668:
4662:
4658:
4654:
4650:
4649:Taylor series
4646:
4640:
4637:
4633:
4629:
4624:
4618:
4615:
4611:
4606:
4601:
4598:
4594:
4591:; Chapter 3,
4590:
4586:
4582:
4578:
4574:
4570:
4567:
4563:
4559:
4555:
4551:
4545:
4542:
4537:
4533:
4529:
4525:
4521:
4517:
4512:
4507:
4504:(1): 015501.
4503:
4499:
4492:
4489:
4485:
4481:
4476:
4473:
4467:
4461:
4457:
4453:
4449:
4445:
4439:
4436:
4433:
4429:
4425:
4418:
4411:
4405:
4402:
4397:
4393:
4387:
4384:
4372:
4368:
4364:
4358:
4355:
4352:
4351:0-520-08817-4
4348:
4345:
4344:0-520-08816-6
4341:
4337:
4333:
4329:
4328:The Principia
4325:
4319:
4317:
4313:
4309:
4304:
4301:
4296:
4290:
4286:
4279:
4276:
4271:
4264:
4262:
4258:
4253:
4247:
4243:
4236:
4234:
4230:
4226:
4221:
4219:
4215:
4211:
4205:
4202:
4197:
4193:
4187:
4184:
4179:
4173:
4169:
4168:
4160:
4157:
4152:
4146:
4142:
4141:
4133:
4130:
4124:
4119:
4116:
4113:
4110:
4107:
4104:
4101:
4098:
4095:
4092:
4086:
4083:
4080:
4077:
4074:
4071:
4070:
4066:
4060:
4055:
4050:
4048:
4046:
4042:
4037:
4035:
4031:
4027:
4022:
4020:
4016:
4012:
4008:
4004:
4000:
3996:
3992:
3988:
3984:
3978:
3968:
3966:
3958:
3956:
3954:
3950:
3946:
3942:
3939:of a body in
3938:
3934:
3930:
3925:
3921:
3909:
3904:
3902:
3897:
3895:
3890:
3889:
3887:
3886:
3879:
3869:
3866:
3861:
3855:
3854:
3852:
3851:
3843:
3840:
3838:
3835:
3833:
3830:
3828:
3825:
3823:
3820:
3818:
3815:
3813:
3810:
3809:
3802:
3801:
3793:
3790:
3788:
3785:
3784:
3777:
3776:
3768:
3765:
3763:
3760:
3758:
3755:
3754:
3747:
3746:
3738:
3735:
3733:
3730:
3728:
3725:
3723:
3720:
3719:
3712:
3711:
3705:
3702:
3700:
3697:
3696:
3694:
3693:
3689:
3685:
3684:
3681:
3677:
3673:
3672:
3661:
3656:
3653:
3649:
3645:
3641:
3637:
3636:
3630:
3627:
3622:
3602:
3578:
3573:
3570:
3566:
3562:
3557:
3552:
3546:
3529:
3501:
3497:
3494:
3488:
3483:
3478:
3473:
3468:
3445:
3439:
3433:
3428:
3425:
3421:
3417:
3409:
3405:
3381:
3361:
3357:
3351:
3344:
3340:
3336:
3327:
3326:
3325:
3323:
3307:
3287:
3279:
3263:
3241:
3233:
3229:
3225:
3200:
3196:
3191:
3187:
3175:
3152:
3149:
3146:
3136:
3128:
3124:
3119:
3116:
3102:
3099:
3096:
3086:
3078:
3074:
3069:
3066:
3063:
3053:
3048:
3017:
3016:
3015:
3001:
2981:
2951:
2948:
2945:
2935:
2927:
2923:
2918:
2915:
2901:
2898:
2895:
2885:
2882:
2876:
2871:
2840:
2839:
2838:
2824:
2804:
2795:
2775:
2754:
2727:
2718:
2714:
2711:
2708:
2705:
2702:
2694:
2691:
2657:
2640:
2639:
2638:
2636:
2617:
2612:
2607:
2603:
2597:
2594:
2591:
2585:
2579:
2572:
2571:
2570:
2568:
2564:
2560:
2553:
2534:
2520:
2514:
2511:
2488:
2487:
2486:
2484:
2480:
2476:
2471:
2469:
2450:
2431:
2428:
2405:
2404:
2403:
2368:
2347:
2343:
2337:
2334:
2331:
2308:
2307:
2306:
2304:
2300:
2293:
2289:
2282:
2278:
2272:
2270:
2266:
2262:
2256:
2249:Gravity field
2248:
2246:
2241:
2234:
2230:
2226:
2218:
2116:
2104:
2081:
2078:
2071:
2064:
2057:
2054:
2048:
2041:
2038:
2035:
2031:
2028:
2022:
2019:
2018:
2017:
2001:
1987:
1975:
1955:
1951:
1945:
1941:
1934:
1931:
1928:
1923:
1900:
1888:
1868:
1864:
1858:
1854:
1847:
1844:
1841:
1836:
1821:
1819:
1816:
1807:
1800:
1798:
1796:
1785:
1778:
1771:
1767:
1759:
1755:
1750:
1744:
1737:
1729:
1725:
1720:
1719:
1718:
1713:
1709:
1708:shell theorem
1705:
1700:
1696:
1694:
1690:
1680:
1672:
1665:
1663:
1661:
1657:
1653:
1649:
1645:
1641:
1637:
1621:
1617:
1613:
1606:
1599:
1595:
1591:
1587:
1579:
1574:
1563:
1560:
1554:
1551:
1545:
1542:
1531:
1527:
1524:
1521:
1518:
1517:
1516:
1492:
1488:
1481:
1477:
1471:
1467:
1460:
1457:
1454:
1447:
1446:
1445:
1444:
1437:
1430:
1426:
1422:
1418:
1414:
1408:
1404:
1401:
1396:
1395:
1392:
1386:
1384:
1383:
1381:
1375:
1371:
1370:
1364:
1361:invented two
1358:
1357:
1350:
1340:
1338:
1334:
1333:Royal Society
1317:
1289:
1223:
1180:
1176:
1131:
1076:
1075:
1074:
1071:
1067:
1066:
1060:
1057:
1052:
1050:
1046:
1042:
1038:
1034:
1030:
1024:
1016:
1014:
1012:
1008:
1005:'s theory of
1004:
999:
997:
993:
992:Coulomb's law
989:
984:
982:
978:
974:
970:
965:
963:
959:
955:
951:
947:
940:
933:
914:
907:
903:
896:
892:
886:
882:
875:
872:
869:
862:
861:
860:
857:
855:
851:
850:
845:
841:
840:
835:
831:
828:derived from
827:
822:
820:
816:
812:
808:
804:
800:
796:
785:
780:
778:
773:
771:
766:
765:
763:
762:
756:
746:
743:
738:
732:
731:
730:
729:
721:
718:
716:
713:
711:
708:
706:
703:
701:
698:
696:
693:
691:
688:
686:
683:
681:
678:
676:
673:
671:
668:
666:
663:
661:
658:
656:
653:
651:
648:
646:
643:
641:
638:
636:
633:
631:
628:
626:
623:
621:
618:
616:
613:
611:
608:
606:
603:
602:
595:
594:
587:
583:
579:
575:
572:
571:
567:
564:
562:
559:
557:
554:
552:
549:
545:
542:
541:
540:
537:
535:
532:
530:
527:
525:
522:
521:
517:
512:
511:
503:
500:
498:
495:
491:
488:
486:
483:
482:
481:
478:
476:
473:
471:
468:
466:
461:
458:
454:
451:
450:
446:
443:
440:
436:
432:
431:
427:
424:
422:
419:
417:
414:
412:
407:
405:
402:
400:
397:
395:
392:
391:
384:
383:
372:
369:
367:
364:
362:
359:
357:
354:
352:
349:
347:
344:
343:
341:
340:
335:
332:
331:
326:
325:
319:
318:
310:
307:
305:
302:
300:
297:
295:
292:
290:
287:
285:
282:
280:
277:
275:
271:
269:
266:
264:
260:
258:
255:
252:
248:
244:
242:
239:
237:
234:
232:
229:
227:
224:
220:
217:
215:
212:
211:
210:
207:
205:
202:
200:
197:
195:
192:
190:
187:
186:
179:
178:
170:
167:
165:
162:
160:
157:
155:
152:
150:
147:
145:
142:
140:
137:
135:
132:
131:
124:
123:
117:
114:
112:
109:
107:
104:
103:
100:
96:
77:
74:
64:
58:
44:
43:
40:
36:
32:
31:
19:
6161:Isaac Newton
6057:theories and
5890:Supergravity
5703:
5699:
5561:Introduction
5527:
5463:Isaac Newton
5375:
5368:
5360:
5351:
5284:Isaac Barrow
5222: (home)
4985:
4963:Newtonianism
4938:Newton scale
4901:Impact depth
4874: (1754)
4869:
4866: (1728)
4861:
4851:
4838:
4823:
4809: (1711)
4804:
4801: (1707)
4796:
4793: (1704)
4788:
4785: (1704)
4780:
4777: (1687)
4772:
4769: (1684)
4764:
4761: (1671)
4756:
4750:Publications
4666:
4664:
4656:
4644:
4639:
4631:
4626:
4622:
4617:
4610:steady-state
4609:
4605:Quasi-steady
4604:
4600:
4592:
4588:
4584:
4583:(Chapter 1,
4580:
4576:
4572:
4568:
4565:
4561:
4557:
4556:(Chapter 1,
4553:
4549:
4544:
4501:
4497:
4491:
4483:
4475:
4455:
4438:
4416:
4409:
4404:
4395:
4386:
4375:. Retrieved
4366:
4357:
4335:
4327:
4324:Isaac Newton
4307:
4303:
4284:
4278:
4269:
4241:
4204:
4195:
4186:
4166:
4159:
4139:
4132:
4094:Kepler orbit
4038:
4033:
4029:
4025:
4023:
4014:
4010:
3982:
3980:
3962:
3917:
3791:
3623:
3593:
3179:
2973:
2796:
2743:
2632:
2566:
2562:
2558:
2551:
2549:
2485:) such that
2482:
2478:
2475:conservative
2472:
2465:
2401:
2302:
2298:
2291:
2287:
2280:
2276:
2273:
2265:vector field
2260:
2258:
2239:
2232:
2228:
2222:
2069:
2062:
2055:
2046:
2039:
2029:
2020:
1822:
1812:
1794:
1792:
1783:
1776:
1769:
1765:
1757:
1753:
1742:
1735:
1727:
1723:
1711:
1703:
1701:
1697:
1685:
1659:
1655:
1651:
1635:
1619:
1615:
1604:
1597:
1589:
1583:
1577:
1561:
1552:
1543:
1525:
1519:
1514:
1417:proportional
1409:acting along
1390:
1377:
1373:
1367:
1359:
1355:
1352:
1337:Robert Hooke
1309:
1063:
1061:
1056:Isaac Newton
1054:Around 1666
1053:
1026:
1000:
985:
980:
966:
957:
949:
942:
935:
931:
929:
858:
853:
847:
837:
834:Isaac Newton
826:physical law
823:
807:proportional
794:
793:
584: /
580: /
578:displacement
576: /
462:
437: /
399:Displacement
337:
328:
322:Formulations
309:Virtual work
249: /
189:Acceleration
182:Fundamentals
5859:Causal sets
5753:BransâDicke
5571:Mathematics
5363:by Paolozzi
5302:Roger Cotes
4911:Newton disc
4825:Quaestiones
4798:Arithmetica
4456:Gravitation
3812:Four-vector
3660:dark matter
3176:Limitations
2635:Gauss's law
2290:instead of
2279:instead of
2217:unit vector
1801:Vector form
1702:For points
1689:integrating
1387:Modern form
1049:Tycho Brahe
1047:summarized
988:gravitation
720:von Neumann
387:Core topics
6150:Categories
6073:CGHS model
6060:toy models
5450:Categories
5426:XMM-Newton
5343:Depictions
5314:John Keill
5236:Apple tree
5231:Later life
5226:Early life
4806:De Analysi
4470:Page 1049.
4377:2024-05-18
4373:. May 2024
4125:References
3959:Extensions
3945:world line
1646:scientist
990:resembles
975:scientist
655:d'Alembert
635:Maupertuis
598:Scientists
480:Rigid body
154:Kinematics
6078:RST model
5864:DGP model
5841:Spin foam
5785:Whitehead
5777:Nordström
5706:) gravity
5656:Classical
5630:Paradigms
5581:Resources
5265:Relations
4774:Principia
4569:equations
4210:Principia
3953:spacetime
3941:free fall
3680:Spacetime
3644:arcsecond
3571:−
3563:∼
3498:π
3426:−
3418:∼
3337:ϕ
3264:ϕ
3188:ϕ
3150:≥
2949:≥
2752:∂
2712:π
2706:−
2692:⋅
2655:∂
2595:−
2518:∇
2515:−
2384:^
2335:−
2184:−
2153:−
2098:^
1932:−
1917:^
1845:−
1656:Principia
1612:kilograms
1584:Assuming
1374:Principia
1318:∝
1181:×
1132:∝
1065:Principia
981:Principia
854:Principia
700:Liouville
582:frequency
502:Vibration
219:potential
144:Continuum
139:Celestial
116:Textbooks
6135:Graviton
5945:F-theory
5938:M-theory
5514:Standard
5388:Namesake
5354:by Blake
4948:Spectrum
4889:Calculus
4858: )
4758:Fluxions
4536:39665455
4482:(1924),
4480:Max Born
4454:(1973).
4051:See also
3949:geodesic
3947:being a
3878:Category
3647:century.
3143:if
3093:if
2942:if
2892:if
1818:equation
1687:entails
1586:SI units
832:by what
805:that is
799:particle
755:Category
680:Hamilton
665:Lagrange
660:Clairaut
625:Horrocks
586:velocity
556:Pendulum
544:reactive
516:Rotation
485:dynamics
435:Inertial
421:Friction
304:Velocity
279:Momentum
159:Kinetics
149:Dynamics
127:Branches
111:Timeline
5566:History
4906:Inertia
4894:fluxion
4790:Queries
4782:Opticks
4766:De Motu
4702:YouTube
4566:Poisson
4516:Bibcode
3999:planets
3320:is the
3276:is the
2633:As per
2215:is the
2075:is the
2032:is the
1764:exerts
1644:British
1594:newtons
1528:is the
1427:to the
1421:product
1419:to the
1017:History
1011:Mercury
973:British
960:is the
836:called
715:Koopman
675:Poisson
670:Laplace
615:Huygens
610:Galileo
455: (
394:Damping
247:Inertia
241:Impulse
214:kinetic
164:Statics
134:Applied
106:History
5361:Newton
5352:Newton
4534:
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4349:
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4291:
4248:
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3594:where
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2225:scalar
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2110:
2016:where
1815:vector
1795:no net
1766:no net
1704:inside
1693:bodies
1614:(kg),
1515:where
1500:
1429:square
1398:Every
956:, and
930:where
852:("the
753:
705:Appell
690:Cauchy
685:Jacobi
630:Halley
620:Newton
605:Kepler
457:linear
453:Motion
299:Torque
274:Moment
209:Energy
199:Couple
5727:AQUAL
5586:Tests
5196:table
4632:first
4628:move?
4562:Euler
4532:S2CID
4506:arXiv
4003:stars
3607:orbit
2263:is a
1756:>
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1624:6.674
1596:(N),
1534:6.674
1407:force
1400:point
803:force
710:Gibbs
695:Routh
650:Euler
289:Speed
284:Space
226:Force
4564:and
4460:ISBN
4430:and
4371:NIST
4347:ISBN
4340:ISBN
4289:ISBN
4246:ISBN
4172:ISBN
4145:ISBN
4039:The
3981:The
3215:and
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2899:<
2286:and
2259:The
2045:and
1628:(15)
1603:and
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1411:the
1403:mass
941:and
294:Time
257:Mass
4700:on
4524:doi
3995:Sun
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2780:enc
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2245:.
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