arXiv subjects

Michael Nauenberg

Publications and source records attributed to Michael Nauenberg.

22 records · Page 2Linked to original sources

arXiv2001

Kepler's Area Law in the Principia: Filling in some details in Newton's proof of Prop. 1

During the past 25 years there has been a controversy regarding the adequacy of Newton's proof of Prop. 1 in Book 1 of the {\it Principia}. This proposition is of central importance because its proof of Kepler's area law allowed Newton to introduce a geometric measure for time to solve problems in orbital dynamics in the {\it Principia}. It is shown here that the critics of Prop. 1 have misunderstood Newton's fundamental limit argument by neglecting to consider the justification for this limit which he gave in Lemma 3. We clarify the proof of Prop. 1 by filling in some details left out by Newton which show that his proof of this proposition was adequate and well grounded.

math.HO↗

arXiv2001

Determination of masses and other properties of extra-solar planetary systems with more than one planet

Recent analysis of the Doppler shift oscillations of the light from extra-solar planetary systems indicate that some of these systems have more than one large planet. In this case it has been shown that the masses of these planets can be determined without the familiar ambiguity due to the unknown inclination angle of the plane of the orbit of the central star provided, however, that its mass is known. A method is presented here which determines also a lower limit to the mass of this star from these observations. As an illustration, our method is applied to the Keck and Lick data for GJ876.

astro-ph↗

arXiv2001

Periodic orbits for three particles with finite angular momentum

We present a novel numerical method to calculate periodic orbits for dynamical systems by an iterative process which is based directly on the action integral in classical mechanics. New solutions are obtained for the planar motion of three equal mass particles on a common periodic orbit with finite total angular momentum, under the action of attractive pairwise forces of the form $1/r^{p+1}$. It is shown that for $-2 < p \le 0$, Lagrange's 1772 circular solution is the limiting case of a complex symmetric orbit. The evolution of this orbit and another recently discovered one in the shape of a figure eight is investigated for a range of angular momenta. Extensions to n equal mass particles and to three particles of different masses are also discussed briefly.

nlin.CD↗

arXiv1998

Correlated Wave Packet treatment of Neutrino and Neutral Meson Oscillations

A quantum wave packet treatment of neutrino and neutral K and B meson oscillations is presented which incorporates the recoil particle in the production process, and includes the effect of the localization and lifetime of the source assumed to be a resonance or unstable particle. This approach removes the ambiguities in the conventional single particle treatment of these oscillations with the recoil particle. A fundamental connection between the stochastic decay time of the source and the space-time coordinates of the correlated final state particles is derived.

hep-ph↗