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Answering the Causal Question? Mark Sonnick Newtons Law of Gravitation Neil DeGrasse Tyson

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Chronology b. 1642, Woolsthorpe, Lincolnshire 1661: Matriculates at Trinity College, Cambridge 1665: Newton earns his B.A.; Plague 1665-1667: Returns to farm (? Disputed – did he revisit Cambridge?) Annus Mirabilis Optics, Chemistry, Calculus (Fluxions), Forces on Moon 1667: Cambridge Reopens; Newton elected Fellow of T.C.

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Chronology – Contd June 1669: De Analysi per Aequationes Numero Terminorum Infinitas (On Analysis of Equations Unlimited in Number of Terms) October: selected as Lucasian Professor…he was 26! 1670 – 1671: De Methodis Serierum et Fluxionum (On the Method of Series and Fluxions) complied… Not published until 1736! 1684: Edmund Halley visits Newton; planetary orbits. 1687: Philosophiae Naturalis Principia Mathematica (Mathematical Principles of Natural Philosophy)

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What if Halley hadnt encouraged Newton to publish?

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Post-Principia 1696: Career at Mint begins 1704: Optics incorporates Calculus (Fluxions) Investigations into light Corpuscular theory of light; but space permeated by aether 1713: Principia 2 nd ed. d. 1727 (age 85) Questions?

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Explication of the Gravitational Theory

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Gravitation – Principia Book III Planetary Orbits – Keplers 2 nd and 3 rd Laws 2 nd Law – R sweeps out equal areas equal times 3 rd Law – τ 2 ~ R 3 1. Circumjovial planets obey laws 2 + 3 2. Circumsaturnal planets obey laws 2 + 3 3. 5 Primary Planets: orbits encompass Sun (Merc., Venus, Mars, Jup., Sat.) (Note that the Earth is absent here) 4. 5 Planets + Earth: Law 3 5. 5 Planets: Law 2 (only for orbit about the Sun, not earth) 6. Moon: Law 2

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What kind of force generates this motion? Galileo: momentum, acceleration, inertia Newton modifies these concepts; introduces forces. Recall

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What kind of force generates this motion? Centripetal acceleration s A B C DE 45° s r m v

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An Inverse-Square Law Using Newtons 2 nd Law: R M m v F

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The Moon Newton calculated accel. of moon, using values for radius of earth and period of moons orbit. a = 2.74 x 10 -3 m/s 2 = g at moon Newton knew g at earth = 9.80 m/s 2 Thus: Accel. of moon in its orbit…solely due to gravity! Image from the public domain

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Generalizing Gravity Force of gravity varies with product of two masses, inverse square of distance. What causes gravity? Newton: gravity not innate A not material cause for gravity Does not mention aether in the Principia

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Generalizing Gravity Later, Optics: aether A medium that permeates the universe and permits for forces to act at a distance. Still, not a cause for gravity. Light interacts with aether Prelude to spacetime? Questions? Image from the public domain.

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Back to the Principia Gravitation for Extended Bodies… No net force within a homogeneous spherical shell. Solid angles Conceptual: spherical dist. of mass Outside the shell: there is a force! Same as point mass at center of sphere. Within a solid sphere Force proportional to distance from the center Newtons formulation does not hold for objects lacking spherical symmetry.

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Question Inertial Mass: Ability of a mass to resist motion. Gravitational Mass: Ability of a mass to exert/feel gravitational attraction. Do these have to be the same thing? What if they arent?

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Inertial and Gravitational Masses Not just a modern physics concept Newton wondered about this question. Identical pendulums made of different materials: Should have different m i to m g ratio.

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m i, m g, and Keplers 3 rd Law Principia Difference in grav. and inertial masses is inconsistent with Keplers 3 rd Law. New factor would have to be added.

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Eotvos Experiment Web page 1889 Experiment to investigate difference between inertial and gravitational masses Pre-Einstein Torsion balance http://mysite.verizon.net/retiche/Physics/cf81.gif

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Eotvos Experiment Quotes difference of 6 x 10 -9 Modern questions about accuracy of data analysis and appropriate propagation of errors.

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Conclusion Gravity: unification of heavens and earth. Did Newton answer the causal question? Any other questions?

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Works Cited Baird, Eric. "Newton's Aether Model." Arxiv. Cornell University, accessed 18 February, 2013, http://arxiv.org/pdf/physics/0011003.pdf.http://arxiv.org/pdf/physics/0011003.pdf Cushing, James. 1998. Philosophical Concepts in Physics. Cambridge: Cambridge University Press. Densmore, Dana. 1996. Newton's Principia: The Central Argument. Santa Fe, New Mexico: Green Lion Press. Feingold, Mordechai. 2004. The Newtonian Moment: Isaac Newton and the Making of Modern Culture. New York: Oxford University Press. Snow, A. J. 1975. Matter and Gravity in Newton's Physical Philosophy. History, Philosophy, and Sociology of Science. New York: Arno Press.

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