A Pedagogical Discussion Concerning the Gravitational Energy Radiated by Keplerian Systems

We first discuss the use of dimensional arguments (and of the quadrupolar emission hypothesis) in the derivation of the gravitational power radiated on a circular orbit. Then, we show how to simply obtain the instantaneous power radiated on a general Keplerian orbit by approximating it locally by a circle. This allows recovering with a good precision, in the case of an ellipse, the highly non trivial dependence on the eccentricity of the average power given by general relativity. The whole approach is understandable by undergraduate students.Comment: A simpler method has been used in the calculations, which requires now only standard knowledge (the radius of curvature is defined by the normal acceleration). Two figures have been added. Concerning the dimensional analysis, the comparison with electromagnetism has been detaile

Signatures of Classical Periodic Orbits on a Smooth Quantum System

Gutzwiller's trace formula and Bogomolny's formula are applied to a non--specific, non--scalable Hamiltonian system, a two--dimensional anharmonic oscillator. These semiclassical theories reproduce well the exact quantal results over a large spatial and energy range.Comment: 12 pages, uuencoded postscript file (1526 kb

How to adapt broad-band gravitational-wave searches for r-modes

Up to now there has been no search for gravitational waves from the r-modes of neutron stars in spite of the theoretical interest in the subject. Several oddities of r-modes must be addressed to obtain an observational result: The gravitational radiation field is dominated by the mass current (gravitomagnetic) quadrupole rather than the usual mass quadrupole, and the consequent difference in polarization affects detection statistics and parameter estimation. To astrophysically interpret a detection or upper limit it is necessary to convert the wave amplitude to an r-mode amplitude. Also, it is helpful to know indirect limits on gravitational-wave emission to gauge the interest of various searches. Here I address these issues, thereby providing the ingredients to adapt broad-band searches for continuous gravitational waves to obtain r-mode results. I also show that searches of existing data can already have interesting sensitivities to r-modes.Comment: 8 pages, no figure

On Objective Measures of Rule Surprisingness

Most of the literature argues that surprisingness is an inherently subjective aspect of the discovered knowledge, which cannot be measured in objective terms. This paper departs from this view, and it has a twofold goal: (1) showing that it is indeed possible to define objective (rather than subjective) measures of discovered rule surprisingness; (2) proposing new ideas and methods for defining objective rule surprisingness measures

Collective action problems in the contracting of public services: Evidence from the UK’s Ministry of Justice

In this paper, we examine collective action problems in the UK government in the process of contracting public services to the private sector. In particular, we examine the Ministry of Justice (MoJ) and its evolution in contract monitoring as part of a larger effort of the government to join up departments in contract management. By analyzing MoJ’s management of the electronic tagging contract with G4S and Serco, we show that a lack of coordination within the department and with other departments was a major reason for the overbilling by the two companies. Recent efforts to join up contract management efforts throughout government show promise in rectifying these contracting issues

R-Mode Oscillations and Spindown of Young Rotating Magnetic Neutron Stars

Recent work has shown that a young, rapidly rotating neutron star loses angular momentum to gravitational waves generated by unstable r-mode oscillations. We study the spin evolution of a young, magnetic neutron star including both the effects of gravitational radiation and magnetic braking (modeled as magnetic dipole radiation). Our phenomenological description of nonlinear r-modes is similar to, but distinct from, that of Owen et al. (1998) in that our treatment is consistent with the principle of adiabatic invariance in the limit when direct driving and damping of the mode are absent. We show that, while magnetic braking tends to increase the r-mode amplitude by spinning down the neutron star, it nevertheless reduces the efficiency of gravitational wave emission from the star. For B >= 10^14 (\nus/300 Hz)^2 G, where \nus is the spin frequency, the spindown rate and the gravitational waveforms are significantly modified by the effect of magnetic braking. We also estimate the growth rate of the r-mode due to electromagnetic (fast magnetosonic) wave emission and due to Alfven wave emission in the neutron star magnetosphere. The Alfven wave driving of the r-mode becomes more important than the gravitational radiation driving when B >= 10^13 (\nus/150 Hz)^3 G; the electromagnetic wave driving of the r-mode is much weaker. Finally, we study the properties of local Rossby-Alfven waves inside the neutron star and show that the fractional change of the r-mode frequency due to the magnetic field is of order 0.5 (B/10^16 G)^2 (\nus/100 Hz)^-2.Comment: 18 pages, 4 figures; ApJ, accepted (v544: Nov 20, 2000); added two footnotes and more discussion of mode driving by Alfven wave

A simple derivation of Kepler's laws without solving differential equations

Proceeding like Newton with a discrete time approach of motion and a geometrical representation of velocity and acceleration, we obtain Kepler's laws without solving differential equations. The difficult part of Newton's work, when it calls for non trivial properties of ellipses, is avoided by the introduction of polar coordinates. Then a simple reconsideration of Newton's figure naturally leads to en explicit expression of the velocity and to the equation of the trajectory. This derivation, which can be fully apprehended by beginners at university (or even before) can be considered as a first application of mechanical concepts to a physical problem of great historical and pedagogical interest

Had the planet mars not existed: Kepler's equant model and its physical consequences

We examine the equant model for the motion of planets, which has been the starting point of Kepler's investigations before he modified it because of Mars observations. We show that, up to first order in eccentricity, this model implies for each orbit a velocity which satisfies Kepler's second law and Hamilton's hodograph, and a centripetal acceleration with an inverse square dependence on the distance to the sun. If this dependence is assumed to be universal, Kepler's third law follows immediately. This elementary execice in kinematics for undergraduates emphasizes the proximity of the equant model coming from Ancient Greece with our present knowledge. It adds to its historical interest a didactical relevance concerning, in particular, the discussion of the Aristotelian or Newtonian conception of motion

A Model for Prediction of the Tidal Currents in the English Channel

A model for prediction of tidal currents in the English Channel is presented. It is based on the classical harmonic description of tides deduced from the spectral development of the luni-solar tidal potential. The spatial distribution of the characteristic parameters (intensity, phase, and direction of the maximum velocity vector, ellipticity of the hodograph) for the 26 harmonic constituents introduced in the prediction procedure are deduced from a numerical simulation of 1 month’s duration for the entire English Channel. Two kinds of documents can be produced from this model : instantaneous velocity fields over a given area, and time series of the intensity and the direction of the velocity vector at a given location, over a given period. Four examples of prediction are presented, corresponding to specific areas and over periods where tidal currents have actually been observed. The comparison between predictions and observations is very satisfactory