1 / 21

Newton’s Law of Gravitation

Newton’s Law of Gravitation . Answering the Causal Question? Mark Sonnick. Neil DeGrasse Tyson. Chronology. b . 1642, Woolsthorpe , Lincolnshire 1661: Matriculates at Trinity College, Cambridge 1665: Newton earns his B.A.; Plague

dorit
Download Presentation

Newton’s Law of Gravitation

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Newton’s Law of Gravitation Answering the Causal Question? Mark Sonnick 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 – Cont’d • June 1669: De Analysi per AequationesNumeroTerminorumInfinitas(On Analysis of Equations Unlimited in Number of Terms) • October: selected as Lucasian Professor…he was 26! • 1670 – 1671: De MethodisSerierum et Fluxionum(On the Method of Series and Fluxions) complied… • Not published until 1736! • 1684: Edmund Halley visits Newton; planetary orbits. • 1687: PhilosophiaeNaturalis Principia Mathematica (Mathematical Principles of Natural Philosophy)

  4. What if Halley hadn’t 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 2nd ed. • d. 1727 (age 85) • Questions?

  6. Explication of the Gravitational Theory

  7. Gravitation – Principia Book III • Planetary Orbits – Kepler’s 2nd and 3rd Laws • 2nd Law – R sweeps out equal areas equal times • 3rd Law – τ2 ~ R3 • “Circumjovial planets” obey laws 2 + 3 • “Circumsaturnal planets” obey laws 2 + 3 • 5 Primary Planets: orbits encompass Sun (Merc., Venus, Mars, Jup., Sat.) (Note that the Earth is absent here) • 5 Planets + Earth: Law 3 • 5 Planets: Law 2 (only for orbit about the Sun, not earth) • 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 B D E s s m v 45° A C r

  10. An Inverse-Square Law • Using Newton’s 2nd Law: v M R m F

  11. The Moon • Newton calculated accel. of moon, using values for radius of earth and period of moon’s orbit. • a = 2.74 x 10-3 m/s2 = gatmoon • Newton knew gatearth = 9.80 m/s2 • 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 • Newton’s 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 aren’t?

  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 mi to mg ratio.

  17. mi, mg, and Kepler’s 3rd Law • Principia • Difference in grav. and inertial masses is inconsistent with Kepler’s 3rd 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. • 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.

More Related