** Professor of Physics (emeritus) **

University of California, Santa Cruz

* *

* Address * :
Physics Department,
CA 95064

* Phone * : (831) 423-5139

* Fax * : (831) 459-3043

*e-mail * :
michael@physics.ucsc.edu

- A session on Hooke and Newton at the 1993 Santa Fe meeting of the History of Science Society (with E. Drake)
- The Forum for the history of Physics session
at the 1995 March meeting of the American Physical
Society

featuring a keynote talk on Newton by S. Chandrasekhar - A symposium on Newtonian scholarship, held at the Royal Society of London on March 1997 (with R. Dalitz and J.B. Brackenridge)
- A debate on science and science studies at UCSC on May 1997 (with T. Porter) featuring Alan Sokal and a cast of celebrities in the so called science-wars.
- The Forum of the History of Physics session of the April 2000
meeting of the American Physical Society.

The topic of this session was " New Perspectives on the History of Ancient Astronomy"

The speakers were Owen Gingerich (Harvard), George Saliba (Columbia) and James Evans (Washington Univ.).

See an animation of the orbit of Mars according to Ptolemy's model, Mars' orbit , compared with Kepler's drawing of this orbit in Astronomia Nova (1609))FHP session on New Perspective on the Development of Ancient Astronomy

Summary of talks on the History of Ancient Astronomy

History of Science and Technology Initiative

The Foundations of Newtonian Scholarship

# Animations of periodic orbits

- C. Moore of the Santa Fe Institute
and I found several new 3-d period orbits for n equal masses
which move symmetrically under the action of gravitational forces.
To see some video animations of these orbits, click below

3-D period orbits of n equal masses, n=3,4,6,12

2 intersecting Lagrange orbits with 3 masses each

3 intersecting Lagrange orbits with 2 masses each

28 masses orbiting under gravitational forces

Science News article: Strange Orbits

**[animation of figure 8 orbit with 3 equal masses]****[animation of figure 8 orbit with 21 equal masses]** **Figure 8 orbit rotating around the x-axis of symmetry. Blue, red and green are the segments of the orbit occupied by each of the 3 particles shown at discrete time intervals T/12. The dashed lines correspond to the orbit below the x-y plane.****[postcript]****[animation of 3 masses rotating with omega=0.]****[animation of 3 masses rotating with omega=.5]****[animation of 3 masses rotating with omega=.9]****Figure 8 orbit rotating around the y-axis of symmetry.****[postcript]****[animation of 3 masses rotating with omega=.5]****----------------------------------------------------------------------------****Publications in history of science****------------------------------------------------------------------------------**- - Newton's Early Computational Method for Dynamics

Archives for History of Exact Science, 46 (1994) 221-251**pdf** - - Hooke, Orbital motion, and Newton's Principia

American Journal of Physics., 62,(1994) 331-350**pdf** - - Newton's Principia and Inverse Square Orbits

The College Mathematics Journal, 25 (1994) 211-222**pdf** - - Huygens and Newton on Curvature and its applications to Dynamics

De Zeventiende eeuw, Cultuur in de Nederlanden in interdisciplinair

perspectief, 12 (1996) 215-234 - - On Hooke's 1685 Manuscript on Orbital Mechanics

Historia Mathematica 25 (1998) 89-93.**pdf** - - Newton's unpublished perturbation method for the lunar motion

Pergamon International Journal of Engineering Science 36 (1998), 1391-1405. - - Comment on "An analysis of Newtons Projectile diagram"

European Journal of Physics 21 (2000) L5-6

See also reply by D. Topper and D.E. Vincent in

European Journal of Physics 21 (2000) L7-8

- -"Newton's Curvature Measure of Force: New Findings"

"A New translation and Guide to Newton's Principia" by I.B. Cohen

(University of California Press (1999)

- - Newton's perturbation methods and it application to Lunar motion

"Isaac Newton's Natural Philosophy" edited by I.B. Cohen and J. Buchwald, (M.I.T Press, 2001)**Book**

- - Curvature in Newton's Dynamics ( with J.B. Brackenridge)

in the "Cambridge Companion to Newton" edited by I. B. Cohen and G. Smith ( Cambridge, 2002) - - "Robert Hooke's Seminal Contributions to Orbital Dynamics"
**[pdf]**

Physics in Perspective 7, (March 2005) 4-34

Reprinted in "Robert Hooke Tercentennial Studies,

edited by Michael Cooper and Michael Hunter (Ashgate, London 2006) pp. 3-32 - -" Hooke's memorandum on the development of orbital
dynamics"

Early Science and Medicine, v.4 n.4, Nov. (2005)**[pdf]** - -"How Einstein discovered the Photon"

History of Physics Newsletter IX, no. 6 (2006), 18-19 - -"Einstein and Bose"

Letter to the Editor, Physics Today, June 2007**[pdf]** - -"Edmund C. Stoner and the discovery of the maximum mass
of white dwarfs

Journal for the History of Astronomy 39, (2008) 297-312**pdf**

Synopsis in History of Physics Newsletter 10 (2008), 9 - -"Early application of the calculus to the inverse square
force problem"

Archive for History of Exact Sciences 64 (2010) 269-300**pdf** - -" Placing Chandra's work in historical context"

Letter to Editor, Physics Today 64 (2011), Issue 7, p. 8**pdf** - -"Proposition 10, Boo2, in the Principia, revisited"

Archive for the History of Exact Sciences (2011) (to be published)**pdf** - -"Barrow and Leibniz on the Fundamental Theorem of the Calculus"

Historia Mathematica (2011) (to be published)**pdf** - -" The reception of Newton's Principia"
**pdf**# Recent publications in Physics and in Astrophysics

- - Correlated Wave packet treatment of neutrino and neutral

meson oscillations

**[Abstract]****[Postscript]**

Physics Letters B 447 (1999) 23-30

- - "Wave packets: Past and Present". Inntroduction to Wave Packets
in Chemistry and Physics edited by T. Uzer and J. Yeazell
(Wiley, 2000)
**[Postscript]** - - Periodic orbits for three equal mass particles with finite
angular momentum

Phys. Lett A 292 (2001)93-99

**[Postscript]** - Determination of masses and other properties of extra-solar
planetary systems with more than one planet,

Astrophysical Journal 568, 369-376 (2002)

**[pdf]** - Fit to the most recent stellar oscillations of GJ 876

( Zero of time is the time of the first Keck data point published by Marcy et. al., ApJ. July 20, 2001)

**[Postscript]** - Stability and eccentricity for two
planets in a 1:1 resonance, and application to extrasolar
planetary systems.

Astronomical Journal 124,2332 (2002)**[Postscript]** **On the possible existence of quark stars (with George Chapline)**

Annals N.Y. Academy of Sciences 302,192-196 (1977)

[PDF]- "A critique of q-entropy for thermal statistics"

Physical Review E 67, 036114 (2003)

**[Postscript]** - Reply to C. Tsallis's "Comments on critique of
q-entropy for thermal statistics by M. Nauenberg"

**Physical Review E 69, 038102 (2004)** - - Kepler's Area Law in the Principia: Filling in some
details in Newton's proof of Proposition 1

**Historia Mathematica 30, 441-456 (2003)**

- "The evolution of radiation towards thermal
equilibrium:

A soluble model which illustrates the foundations of statistical mechanics"

**American Journal of Physics 72, 313 (2004)** - -"A stochastic treatment for radiation in equilibrium
with a thermal reservoir"

**preprint (2006)**

- -"Curvature in Orbital Dynamics"

**American Journal of Physics 73, 340 (2005)**

- " Period relation for the 2:1 resonance in the GJ876
planetary system "

astro-ph/0507217, 8 July 2005

**[PDF]**

- "Continuity and Stability of families of figure
eight orbits with finite angular momemtum"

arXiv: math.DS/0504283, 13 April 2005

**Celestial Mechanics and Dynamical Astronomy 97 (2007) 93-99**

**[PDF]** - "New periodic orbits for the N-body problem"

arXiv: math.DS/0511219, 8 Nov. 2005

**Journal of Computation and Nonlinear Dynamics 1, 307 ( 2006)**

Special Issue Honoring the 60th birthday of Phillip Holmes.

**[PDF]**

- "Solved: The mystery of Huygens' anomalous suspension"

[anomalous suspension] - "Orbites periodiques du probleme des trois corps:
les origins, les contributions de Hill et de Poincare,
et quelques developpements recents"

L`heritage scientifique de Poincare, eds. E. Charpertier, E. Ghys, et A. Lesne (Belin, Paris, 2006), 128-157 - Comment on "Hot gases:the transition from line
spectra to thermal radiation"

American Journal of Physics 75, (2007), 215-223 [PDF]# Book Reviews

- - Chandrasekhar, Newton' Principia for the Common Reader

[review]

Am. J. Phys. 64 (1996) - - The Mathematical principles underlying the Principia revisited

Essay Review of "The Key to Newton's Dynamics: The Kepler problem and the Principia", by Bruce Brackenridge,

and "Newton's Principia" by Dana Densmore

in Journal for History of Astronomy, 29 (1998) 286-300 - -Niccolo Guicciardini, "Reading the Principia"

Centaurus, March (2001)**[PDF]**

- -N. Kollerstrom, "Newton and the Lunar Motion, Essay Review of "Newton's
forgotten Lunar Theory",

Journal for History of Astronomy, 32 (2001)162-168**[PDF]**

- -Ofer Gal, "Meanest Foundations and Nobler Superstructures:

Hooke, Newton and the Compounding of the Celestiall Motions of the Planets"

Isis (Sept. 2005)**[PDF]**

- - B. Rosenblum and Fred Kuttner, "Quantum Enigma:
Physics encounters Consciousness"

Foundations of Physics 37, (2007) 215-223**[PDF]**

- Niccolo Guicciardini, " Isaac Newton on Mathematical Certainty
and Method", MIT Press 2009

Notre Dame Philosophical Reviews

[http://ndpr.nd.edu/news/24393-isaac-newton-on-mathematical-certainty-and-method/]# Letters to the Editor

- "Refereeing Reform Recommendations"

[Physics Today, April 1994]

- "How Santa Cruz faculty built itself up"

[Physics Today, May 1994]

- Ex-Cathedra

The Scientist 40 (2000) 3The Sun in the Church - "Theory, Phenomenology, and `Who ordered that'n"

[Physics Today, January 2001]

- "Did Newton need Hooke's program to Divine Planetary motion?"

**Physics Today, Sept. 2003**

- "Hooke, Newton, Divining Planetary Motion"

[Physics Today, February 2004]

- "Hooke, Newton, and the Trials of Historical Examination"

[Physics Today, August 2004]

- "Gap in Einstein's early argument for the existence
of photons"

**[Physics Today, October, 2005 17-18]** - " Articles on non-extensive
statistical mechanics in Europhysics News"

**[Europhysics news, n.2 v. 57 (2006)]**

- " Bose Statistics"

[Physics Today, June 2007) - "On D. Mermin's review of `Quantum Enigma:
Physics Encounters Consciousness

[American Journal of Physics 75 (2007) 1061]

- "What is bad about this habit?"

[Physics Today, Sept. 2009]

- "Fluid dynamics and Pollock's paint applicators"

[Physics Today, Nov. 2010]

- "Time symmetric quantum mechanics questioned"

[Physics Today, May. 2011]

- "Placing Chandra in historical contexts"

[Physics Today, July. 2011]

- "Nature's manifest absurdity: A cautionary tale"

[Physics Today, June. 2012]

# Books

- - The Foundations of Newtonian Scholarship

edited by R.Dalitz and M. Nauenberg (World Scientific, 2000) B# Invited Lectures

----------------------------------- - - "Robert Hooke's Seminal Contributions to Orbital Dynamics"
**[PDF]**

Lecture presented at the Hooke Tercentenary conference at the London Royal Society, July 7-8, 2003

Published in Physics in Perspective 7, (March 2005) 4-34 [Background]

[PDF]

- - "The Early history of the three-body problem and the legacy
of Poincare"

Lecture presented at the Colloque Henri Poincare

on the 150 anniversary of his birth, Paris Dec. 16-18 (2004)

- -"Einstein's quantum theory of radiation revisited"

APS meeting, March 23, and NCAAPT meeting , April 9,2005

**[abstract]**

- "Edmund C. Stoner pioneering work on white dwarfs"

Physics colloquium at the University of Leeds, England, Nov. 29 (2007) and in Paris, Dec. 5 (2007) [pdf]

- - Newton's Early Computational Method for Dynamics

I received my Ph.d in physics at Cornell under Hans Bethe in 1960.
After a year and a half as a fellow at the Princeton Institute for
Advanced Studies,
I taught and did research in particle physics at Columbia and Stanford before coming in 1966 to the University
of California at Santa Cruz. I was a founding member
of its Physics Dept. initiating its program of particle
and theoretical condensed matter physics. I retired from teaching in 1994
and now
I am a Reseach Professor of Physics.
My primary research interests have been in particle physics,
condensed matter physics, astrophysics,
and nonlinear dynamics.
I also have had a long standing interest in the history of
physics and mathematics, particularly during the 17-century,
and I published articles on the works of Hooke, Newton
and Huygens, and book reviews in this field. More recently
I have written about more contemporary scientist like Poincare, Chandrasekhar and Stoner.
I also have been in various activities which have brought
historians of science and physicists
together.

For a list of publications and other activities, see publications,
recent publications

Sometimes it takesa short while before the videos appear.
To watch these videos full screen, click on the four petal icon at the bottom
right hand corner of the screen.

Quantum mechanics, relativity, and the Mass limit of compact stars

Quantum mechanics, relativity, and the mass limit of compact stars from Michael Nauenberg on Vimeo.

Kitchen sink experiments in fluid flow

Kitchen sink experiment in fluid flow from Michael Nauenberg on Vimeo.

The Physics underlying how dogs and cats lap from Michael Nauenberg on Vimeo.

Solution of the mystery of Huygen's anomalous supension

[anomalous suspension]

The Science of Leonardo from Michael Nauenberg on Vimeo.