An attempt is made to explain time non-dilation allegedly observed in quasar light curves. The explanation is based on the assumption that quasar black holes are, in some sense, foreign for our Friedmann-Robertson-Walker universe and do not participa
te in the Hubble flow. Although at first sight such a weird explanation requires unreasonably fine-tuned Big Bang initial conditions, we find a natural justification for it using the Milne cosmological model as an inspiration.
The purpose of this article is to present a simple solution of the classic dog-and-rabbit chase problem which emphasizes the use of concepts of elementary kinematics and, therefore, can be used in introductory mechanics course. The article is based o
n the teaching experience of introductory mechanics course at Novosibirsk State University for first year physics students which are just beginning to use advanced mathematical methods in physics problems. We hope it will be also useful for students and teachers at other universities too.
An elementary pedagogical derivation of the Lense-Thirring precession is given based on the use of Hamilton vector. The Hamilton vector is an extra constant of motion of the Kepler/Coulomb problem related simply to the more popular Runge-Lenz vector.
When a velocity-dependent Lorentz-like gravitomagnetic force is present, the Hamilton vector, as well as the canonical orbital momentum are no longer conserved and begin to precess. It is easy to calculate their precession rates, which are related to the Lense-Thirring precession of the orbit.
This is a comment on the recent paper by G. S. Adkins and J. McDonnell ``Orbital precession due to central-force perturbations published in Phys. Rev. D75 (2007), 082001 [arXiv:gr-qc/0702015]. We show that the main result of this paper, the formula f
or the precession of Keplerian orbits induced by central-force perturbations, can be obtained very simply by the use of Hamiltons vector.
