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

2. 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.

3. 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)

4. What if Halley hadnt encouraged Newton to publish?

5. 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?

6. Explication of the Gravitational Theory

7. 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

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

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

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

11. 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

12. 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

13. 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.

14. 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.

15. 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?

16. 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.

17. 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.

18. 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

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

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

21. 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.