2,243 research outputs found
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
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
Analysis of Super-Kamiokande 5-day Measurements of the Solar Neutrino Flux
Data in 5-day bins, recently released by the Super-Kamiodande Consortium, has
been analyzed by a likelihood procedure that has certain advantages over the
Lomb-Scargle procedure used by the consortium. The two most prominent peaks in
the power spectrum of the 10-day data were at 9.42 y-1 and 26.57 y-1, and it
was clear that one was an alias of the other caused by the regularity of the
binning. There were reasons to believe that the 9.42 y-1 peak was an alias of
the 26.57 y-1 peak, but analysis of the 5-day data makes it clear that the
reverse is the case. In addition to a strong peak near 9.42 y-1, we find peaks
at 43.72 y-1and at 39.28 y-1. After comparing this analysis with a
power-spectrum analysis of magnetic-field data, we suggest that these three
peaks may be attributed to a harmonic of the solar rotation rate and to an
r-mode oscillation with spherical harmonic indices l = 2, m = 2.Comment: Accepted for publication in Astrophysical Journa
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
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