חוק הכבידה העולמי של ניוטון
הערות שוליים

↑  Fritz Rohrlich (25 באוגוסט 1989). From Paradox to Reality: Our Basic Concepts of the Physical World. Cambridge University Press. pp. 28–. ISBN 978-0-521-37605-1. {{cite book}}:  (עזרה)
↑  Klaus Mainzer (2 בדצמבר 2013). Symmetries of Nature: A Handbook for Philosophy of Nature and Science. Walter de Gruyter. pp. 8–. ISBN 978-3-11-088693-1. {{cite book}}:  (עזרה)
↑  "Physics: Fundamental Forces and the Synthesis of Theory | Encyclopedia.com". www.encyclopedia.com.
1 2 3  Proposition 75, Theorem 35: p. 956 – I.Bernard Cohen and Anne Whitman, translators: Isaac Newton, The Principia: Mathematical Principles of Natural Philosophy. Preceded by A Guide to Newton's Principia, by I.Bernard Cohen. University of California Press 1999 ISBN 0-520-08816-6 ISBN 0-520-08817-4
↑  Isaac Newton: "In [experimental] philosophy particular propositions are inferred from the phenomena and afterwards rendered general by induction": "Principia", Book 3, General Scholium, at p.392 in Volume 2 of Andrew Motte's English translation published 1729.
1 2  The Michell–Cavendish Experiment, Laurent Hodges
↑  Gillispie, Charles Coulston (1960). The Edge of Objectivity: An Essay in the History of Scientific Ideas. Princeton University Press. pp. 3–6. ISBN 0-691-02350-6.
↑  J.L. Heilbron, Electricity in the 17th and 18th Centuries: A Study of Early Modern Physics (Berkeley: University of California Press, 1979), 180.
1 2  Discussion points can be seen for example in the following papers:
1 2  Bullialdus (Ismael Bouillau) (1645), "Astronomia philolaica", Paris, 1645.
1 2  Borelli, G. A., "Theoricae Mediceorum Planetarum ex causis physicis deductae", Florence, 1666.
1 2  See especially p. 13 in Whiteside, D. T. (1970). "Before the Principia: The Maturing of Newton's Thoughts on Dynamical Astronomy, 1664–1684". Journal for the History of Astronomy. 1: 5–19. Bibcode:1970JHA.....1....5W. doi:10.1177/002182867000100103.
↑  H W Turnbull (ed.), Correspondence of Isaac Newton, Vol 2 (1676–1687), (Cambridge University Press, 1960), giving the Halley–Newton correspondence of May to July 1686 about Hooke's claims at pp. 431–448, see particularly page 431.
1 2  Hooke's 1674 statement in "An Attempt to Prove the Motion of the Earth from Observations" is available in online facsimile here.
↑  Purrington, Robert D. (2009). The First Professional Scientist: Robert Hooke and the Royal Society of London. Springer. p. 168. ISBN 978-3-0346-0036-1. Extract of page 168
↑  See page 239 in Curtis Wilson (1989), "The Newtonian achievement in astronomy", ch.13 (pages 233–274) in "Planetary astronomy from the Renaissance to the rise of astrophysics: 2A: Tycho Brahe to Newton", CUP 1989.
↑  en:Calendar (New Style) Act 1750
↑  Page 309 in H W Turnbull (ed.), Correspondence of Isaac Newton, Vol 2 (1676–1687), (Cambridge University Press, 1960), document #239.
↑  See Curtis Wilson (1989) at page 244.
↑  Page 297 in H W Turnbull (ed.), Correspondence of Isaac Newton, Vol 2 (1676–1687), (Cambridge University Press, 1960), document #235, 24 November 1679.
↑  Page 433 in H W Turnbull (ed.), Correspondence of Isaac Newton, Vol 2 (1676–1687), (Cambridge University Press, 1960), document #286, 27 May 1686.
1 2  Pages 435–440 in H W Turnbull (ed.), Correspondence of Isaac Newton, Vol 2 (1676–1687), (Cambridge University Press, 1960), document #288, 20 June 1686.
↑  Page 436, Correspondence, Vol.2, already cited.
↑  Propositions 70 to 75 in Book 1, for example in the 1729 English translation of the Principia, start at page 263.
↑  Propositions 43 to 45 in Book 1, in the 1729 English translation of the Principia, start at page 177.
↑  See especially pp. 13–20 in Whiteside, D. T. (1991). "The Prehistory of the 'Principia' from 1664 to 1686". Notes and Records of the Royal Society of London. 45 (1): 11–61. doi:10.1098/rsnr.1991.0002. JSTOR 531520free{{cite journal}}:  תחזוקה - ציטוט: postscript (link)
↑  See J. Bruce Brackenridge, "The key to Newton's dynamics: the Kepler problem and the Principia", (University of California Press, 1995), especially at pages 20–21.
↑  See for example the 1729 English translation of the Principia, at page 66.
↑  See especially p. 10 in Whiteside, D. T. (1970). "Before the Principia: The Maturing of Newton's Thoughts on Dynamical Astronomy, 1664–1684". Journal for the History of Astronomy. 1: 5–19. Bibcode:1970JHA.....1....5W. doi:10.1177/002182867000100103.
↑  See for example the results of Propositions 43–45 and 70–75 in Book 1, cited above.
↑  See also G E Smith, in Stanford Encyclopedia of Philosophy, "Newton's Philosophiae Naturalis Principia Mathematica".
↑  The second extract is quoted and translated in W.W. Rouse Ball, "An Essay on Newton's 'Principia'" (London and New York: Macmillan, 1893), at page 69.
↑  The original statements by Clairaut (in French) are found (with orthography here as in the original) in "Explication abregée du systême du monde, et explication des principaux phénomenes astronomiques tirée des Principes de M. Newton" (1759), at Introduction (section IX), page 6: "Il ne faut pas croire que cette idée ... de Hook diminue la gloire de M. Newton", and "L'exemple de Hook" [serve] "à faire voir quelle distance il y a entre une vérité entrevue & une vérité démontrée".
↑  The Construction of Modern Science: Mechanisms and Mechanics, by Richard S. Westfall. Cambridge University Press. 1978
↑  "Rotational Flattening". farside.ph.utexas.edu.
↑  The vector difference r2 − r1 points from object 1 to object 2. See Fig. 11–6. of The Feynman Lectures on Physics, Volume I, equation (9.19) of The Feynman Lectures on Physics, Volume I and Euclidean vector#Addition and subtraction
↑  Misner, Charles W.; Thorne, Kip S.; Wheeler, John Archibald (1973). Gravitation. New York: W. H.Freeman and Company. ISBN 978-0-7167-0344-0. Page 1049.
↑  Max Born (1924), Einstein's Theory of Relativity (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.)
↑  Leimanis and Minorsky: Our interest is with Leimanis, who first discusses some history about the n-body problem, especially Ms. Kovalevskaya's ~1868–1888, twenty-year complex-variables approach, failure; Section 1: The Dynamics of Rigid Bodies and Mathematical Exterior Ballistics (Chapter 1, the motion of a rigid body about a fixed point (Euler and Poisson equations); Chapter 2, Mathematical Exterior Ballistics), good precursor background to the n-body problem; Section 2: Celestial Mechanics (Chapter 1, The Uniformization of the Three-body Problem (Restricted Three-body Problem); Chapter 2, Capture in the Three-Body Problem; Chapter 3, Generalized n-body Problem).
↑  See References sited for Heggie and Hut. This Wikipedia page has made their approach obsolete.
↑  Quasi-steady 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 steady-state condition refers to a system's state being invariant to time; otherwise, the first derivatives and all higher derivatives are zero.
↑  R. M. Rosenberg states the n-body problem similarly (see References): 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 move? Rosenberg failed to realize, like everyone else, that it is necessary to determine the forces first before the motions can be determined.
↑  A general, classical solution in terms of first integrals is known to be impossible. An exact theoretical solution for arbitrary n can be approximated via Taylor series, but in practice such an infinite series must be truncated, giving at best only an approximate solution; and an approach now obsolete. In addition, the n-body problem may be solved using numerical integration, but these, too, are approximate solutions; and again obsolete. See Sverre J. Aarseth's book Gravitational N-body Simulations listed in the References.
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