Quasi-circular Orbits Research Articles

Energy losses by gravitational radiation in inspiraling compact binaries to 5/2 post-Newtonian order.

This paper derives the total power or energy loss rate generated in the form of gravitational waves by an inspiraling compact binary system to the $\frac{5}{2}$ post-Newtonian (2.5PN) approximation of general relativity. Extending a recently developed gravitational-wave generation formalism valid for arbitrary (slowly moving) systems, we compute the mass multipole moments of the system and the relevant tails present in the wave zone to 2.5PN order. In the case of two point masses moving on a quasicircular orbit, we find that the 2.5PN contribution in the energy loss rate is entirely due to tails. Relying on an energy balance argument we derive the laws of variation of the instantaneous frequency and phase of the binary. The 2.5PN order in the accumulated phase is significantly large, being grossly of the same order of magnitude as the previous 2PN order, but opposite in sign. However, finite mass effects at 2.5PN order are small. The results of this paper should be useful when analyzing the data from inspiraling compact binaries in future gravitational-wave detectors such as VIRGO and LIGO.

Gravitational waves from inspiralling compact binaries: Energy loss and waveform to second-post-Newtonian order.

Gravitational waves generated by inspiralling compact binaries are investigated to the second-post-Newtonian (2PN) approximation of general relativity. Using a recently developed 2PN-accurate wave generation formalism, we compute the gravitational waveform and associated energy loss rate from a binary system of point masses moving on a quasicircular orbit. The crucial new input is our computation of the 2PN-accurate ``source'' quadrupole moment of the binary. Tails in both the waveform and energy loss rate at infinity are explicitly computed. Gravitational radiation reaction effects on the orbital frequency and phase of the binary are deduced from the energy loss. In the limiting case of a very small mass ratio between the two bodies we recover the results obtained by black hole perturbation methods. We find that finite mass ratio effects are very significant as they increase the 2PN contribution to the phase by up to 52%. The results of this paper should be of use when deciphering the signals observed by the future LIGO-VIRGO network of gravitational-wave detectors.

Three-dimensional initial data for the collision of two black holes. II. Quasicircular orbits for equal-mass black holes.

The construction of initial-data sets representing binary black-hole configurations in quasi-circular orbits is studied in the context of the conformal-imaging formalism. An effective-potential approach for locating quasi-circular orbits is outlined for the general case of two holes of arbitrary size and with arbitrary spins. Such orbits are explicitly determined for the case of two equal-sized nonrotating holes, and the innermost stable quasi-circular orbit is located. The characteristics of this innermost orbit are compared to previous estimates for it, and the entire sequence of quasi-circular orbits is compared to results from the post-Newtonian approximation. Some aspects of the numerical evolution of such data sets are explored.

Why we have not yet found a retrograde planet in the solar system?

In this paper we use the Jacobian integral of the circular restricted three-body problem to establish a testing function of a moving testing particle when it moves like a planet. This function determines whether or not the particle will stay in a definite region (which may be called “stable region”, SR). By means of checking with an electronic computer, we can find that the SR of quasicircular orbit of retrograde planet motion is much less than the SR of direct planet motion. It is the reason why the existence of a retrograde planet is very rare.

Optimal low-thrust transfer between neighbouring quasi-circular orbits around an oblate planet

The problem of optimal low-thrust, limited power transfer between quasi-circular orbits ( e ⋍ 0) around an oblate planet is analysed. It is assumed that the orbital changes due to thrust acceleration and Earth oblateness are of the same order. A first order solution to the problem is obtained by application of Pontryagin's Maximum Principle. Subsequently, by application of Hori's method for generalized canonical systems, a first order solution in a small parameter ϵ is derived. Finally, three particular cases of long-time transfer and the orbit maintenance manoeuvre are considered. The results obtained are in agreement and represent an extension of the work done by Marec.

Optimal low-thrust limited power transfer between neighbouring quasi-circular orbits of small inclinations around an oblate planet

A complete analytic study about the influence of Earth's oblateness on the optimal low-thrust limited power transfer of small amplitude (orbit correction) between quasi-circular orbits of small inclinations is carried out up to the first order in a small parameter defined by the nondimensional thrust acceleration. The coefficient for the second zonal harmonic J 20 and the nondimensional thrust acceleration are supposed to be the same order of magnitude. Hori's method for generalized canonical systems is applied in order to obtain the analytical solution for adjoint and state differential equations. Simple analytic solutions are obtained explicitly for long-time transfer.

Studies of low-energy HZE cosmic rays on cosmos satellites

Fluxes of ions with energies below 20 MeV/nucleon have been studied in a series of experiments performed in near-Earth space at an altitude of about 300 km. Use was made of polymeric dielectric track detectors. It was found that, after the solar maximum of 1981–1982, fluxes of ions of the anomalous oxygen component first appeared in near-Earth space in 1984 and reached their maximum in 1987. The values for the oxygen ion fluxes recorded in quasi-circular satellite orbits are in agreement with the data for fluxes of the same particles in interplanetary space, given the assumption that the oxygen ions are singly charged.

Three-dimensional periodic orbits in barred galaxies

We study the properties of the families of three-dimensional periodic orbits which bifurcate from the vertical critical orbits of the retrograde family of quasi-circular plane periodic orbits which extend from the galactic center up to infinity. We consider the case of a barred galaxy with a strong central bulge. The values of the parameters are chosen in such a way as to cover the cases of a strong or weak bar with a fast or slow rotation.

The Rippled-Field Magnetron (Cross-Field Free Electron Laser)

Millimeter-wave emission from the rippled-field magnetron (cross-field free electron laser (FEL)) is investigated experimentally and theoretically. In this device, electrons move in quasi-circular orbits under the combined action of a radial electric field, a uniform axial magnetic field, and a radial azimuthally periodic wiggler magnetic field. In excess of 300 kW of RF power is observed in two narrow spectral lines whose frequency can be tuned continuously from ~25 to ~50 GHz by variation of the axial magnetic field. The observations are interpreted as a FEL type of instability, associated with a resonance in the particle motion of a layer of electrons embedded in the dense spacecharge cloud. The resonance is shown to occur when 2kwυ0 ≈ (Ω>0/γ0) √1 -(ωp/γ0)2, where kw is the wiggler wavenumber, υ0 is the azimuthal electron velocity, Ω0 is the relativistic cyclotron frequency in the axial magnetic field, wp is the relativistic plasma frequency, and γ0 = [1 - (υ0/c)2]-1/2 of the resonant electron layer.

Generation of electromagnetic radiation from a rotating electron ring in a rippled magnetic field

Calculations show that modes resembling the free-electron laser (FEL) instability are excited when electrons move in quasicircular orbits under the combined action of a uniform axial magnetic field and an azimuthally periodic wiggler magnetic field. In the model, a thin annular ring of rotating electrons is confined in a hollow cylindrical waveguide, or between concentric cylinders comprising a coaxial waveguide, and the dispersion equations for the transverse magnetic (TMlm ) modes are derived and analyzed. Coherent radiation occurs near frequencies ω corresponding to the crossing points of the electromagnetic modes ω=ωc(l,m) and the beam modes ω=(l+N)Ω∥, where ωc and Ω∥ are the waveguide cutoff frequency and the electron cyclotron frequency, respectively, and N is the number of wiggler periods.

Millimeter wave emission from a rotating electron ring in a rippled magnetic field

We report measurements of millimeter wave emission from a rotating relativistic electron ring (2 MV, 1 kA) in which electrons move in quasi-circular orbits under the combined action of a uniform axial magnetic field and an azimuthally periodic wiggler magnetic field. We observe radiation at frequencies above 91 GHz, at power levels in excess of 200 kW.

Packing effect of fluffy particles

Packing forces, produced by an anisotropic sublimation of mantle material of grains located at the surface layer of loosely conglomerated fluffy particles, move the grains towards the center of the fluffy particles. This leads to a reduction of the empty space inside the fluffy particle and consequently to an increase of the mass density of the fluffy particle with time. As observed by the Helios dust experiment, fluffy particles of low density are ejected by comets with high eccentricity e and large semimajor axis a Since e and a of fluffy particles decrease with time due to the Poynting-Robertson effect, the accompanying increase of the density of fluffy particles seems to explain the existence of normal dense particles in quasi-circular orbits as detected during in situ measurements. It also explains that the majority of lunar craters have been produced by normal dense particles rather than by low density particles.

Propulsion Requirements for Controllable Satellites

Propulsion requirements are determined for several controllable satellite missions. High thrust propulsion syslems such as chemical rockets and low thrust propulsion systems such as ion rockets are considered. Rendezvous missions are treated by determining minimum fuel maneuvers for small, simultaneous changes in the elements of quasi-circular orbits. Orbit transfer missions are treated by determining minimum fuel maneuvers for large changes in the elements of circular orbits. Orbit maintenance missions are treated by determining the propulsion necessary to cancel perturbations due to the atmosphere, the Earth's bulge, and the sun and moon. A closed-form analytic solution is found for the optimum low thrust transfer between inclined circular orbits of different radii. (auth)