C. Bracco — Page 2 | Searcharxiv

arXiv2008

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.

physics.pop-ph↗

arXiv1998

Scintillation in scalar-tensor theories of gravity

We study the scintillation produced by time-varying gravitational fields within scalar-tensor theories of gravity. The problem is treated in the geometrical optics approximation for a very distant light source emitting quasi plane monochromatic electromagnetic waves. We obtain a general formula giving the time dependence of the photon flux received by a freely falling observer. In the weak-field approximation, we show that the contribution to the scintillation effect due to the focusing of the light beam by a gravitational wave is of first order in the amplitude of the scalar perturbation. Thus scalar-tensor theories contrast with general relativity, which predicts that the only first-order effect is due to the spectral shift. Moreover, we find that the scintillation effects caused by the scalar field have a local character: they depend only on the value of the perturbation at the observer. This effect provides in principle a mean to detect the presence of a long range scalar field in the Universe, but its smallness constitutes a tremendous challenge for detection.

gr-qc↗