Circular orbit

A circular orbit is an orbit with a fixed distance around the barycenter; that is, in the shape of a circle. In this case, not only the distance, but also the speed, angular speed, potential and kinetic energy are constant. There is no periapsis or apoapsis. This orbit has no radial version. Listed below is a circular orbit in astrodynamics or celestial mechanics under standard assumptions. Here the centripetal force is the gravitational force, and the axis mentioned above is the line through the center of the central mass perpendicular to the orbital plane. Circular acceleration Transverse acceleration (perpendicular to velocity) causes change in direction. If it is constant in magnitude and changing in direction with the velocity, circular motion ensues. Taking two derivatives of the particle's coordinates with respect to time gives the centripetal acceleration : a, = \frac {v^2} {r} , = {\omega^2} {r} where: *v, is orbital velocity of

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A simple theoretical model for estimating the frequency characteristics of black hole mergers

Roberto Guarino

Gravitational waves, despite predicted within the Theory of General Relativity about a century ago, were observed experi-mentally only in the last few years, thanks to the recent advances of the LIGO and Virgo detectors. In this work, we introduce a simple theoretical model to study the gravitational irradiation of binary systems and derive the characteristics of the emitted gravitational waves (e.g., in terms of frequency). The simplicity of the model relies first on the consideration of the two-body problem and circular orbits. Second, we follow an energetic approach and make use of only one result of the Theory of General Relativity, to make the procedure clear and suitable for undergraduate education. The numerical solution is finally compared with the experimental data available for a few black hole mergers.

CANADIAN SCIENCE PUBLISHING2022

Properties and nature of Be stars 30. Reliable physical properties of a semi-detached B9.5e+G8III binary BR CMi = HD 61273 compared to those of other well studied semi-detached emission-line binaries

Pierre North, Matthias Wolf

Reliable determination of the basic physical properties of hot emission-line binaries with Roche-lobe filling secondaries is important for developing the theory of mass exchange in binaries. It is a very hard task, however, which is complicated by the presence of circumstellar matter in these systems. So far, only a small number of systems with accurate values of component masses, radii, and other properties are known. Here, we report the first detailed study of a new representative of this class of binaries, BR CMi, based on the analysis of radial velocities and multichannel photometry from several observatories, and compare its physical properties with those for other well-studied systems. BR CMi is an ellipsoidal variable seen under an intermediate orbital inclination of similar to 51 degrees, and it has an orbital period of 12.(d)919059(15) and a circular orbit. We used the disentangled component spectra to estimate the effective temperatures 9500(200) K and 4655(50) K by comparing them with model spectra. They correspond to spectral types B9.5e and G8III. We also used the disentangled spectra of both binary components as templates for the 2D cross-correlation to obtain accurate radial velocities and a reliable orbital solution. Some evidence of a secular period increase at a rate of (1.1 +/- 0.5) s per year was found. This, together with a very low mass ratio of 0.06 and a normal mass and radius of the mass gaining component, indicates that BR CMi is in a slow phase of the mass exchange after the mass-ratio reversal. It thus belongs to a still poorly populated subgroup of Be stars for which the origin of Balmer emission lines is safely explained as a consequence of mass transfer between the binary components.

EDP Sciences2015