Planar Circular Orbits Research Articles

Highly relativistic circular orbits of spinning particle in the Kerr field

The Mathisson-Papapetrou equations in Kerr's background are considered. The region of existence of highly relativistic planar circular orbits of a spinning particle in this background and dependence of the particle's Lorentz $\gamma$-factor on its spin and radial coordinate are investigated. It is shown that in contrast to the highly relativistic circular orbits of a spinless particle the corresponding orbits of a spinning particle are allowed in much wider space region. Some of these orbits show the significant attractive action of the spin-gravity coupling on a particle and others are caused by the significant repulsive action. Numerical estimates for electrons, protons and neutrinos in the gravitational field of black holes are presented.

Modification from the spin to the synchrotron radiation from a relativistic electron

An explicit expression for the spectral distribution of the radiation energy from a relativistic electron with a magnetic moment is derived. Consequentially for an extreme relativistic electron moving along a planar circular orbit, the spectral distributions of synchrotron radiation in σ- and π- polarization are calculated including the modification from electron's magnetic moment. It is shown that for the synchrotron radiation with high critical frequency ωc with ħωc≥ 10 keV, the modification may be considerable. The relationship between the polarization of synchronous electrons and radiation fields is obtained, and thus the information about spin polarization of electron beam from measuring the polarization of radiation fields is provided.

Robust outdoor stereo vision SLAM for heavy machine rotation sensing

The paper presents a robust outdoor stereo vision simultaneous localization and mapping (SLAM) algorithm. It estimates camera pose reliably in outdoor environments with directional sunlight illumination causing shadows and non-uniform scene lighting. The algorithm has been developed to measure a mining rope shovel’s rotation angle about its vertical axis (“swing” axis). A stereo camera is mounted externally to the shovel house (upper revolvable portion of the shovel), with a clear view of the shovel’s lower carbody. As the shovel house swings, the camera revolves with the shovel house in a planar circular orbit, seeing differing views of the carbody top. During the swing, the SLAM algorithm builds a map of observed 3D features on the carbody and simultaneously using these landmarks to estimate the camera position. This estimated camera position is then used to compute the shovel swing angle. Two novel techniques are employed to improve the SLAM algorithm’s robustness in outdoor environments. First, a “Locally Maximal” feature selection technique for Harris corners is used to select features more consistently in non-uniformly illuminated scenes. Another novel technique is the use of 3D “Feature Clusters” as SLAM landmarks rather than individual single features. The Feature Cluster landmarks improve the robustness of the landmark matching and allow significant reduction of the SLAM filter computational cost. This approach of estimating the shovel swing angle has a maximum error of ±1° upon SLAM map convergence. Results demonstrate the improvements of using the novel techniques compared to previous methods.

Guidance Trajectories for Spacecraft Rendezvous

In a previous paper of Miele et al. (J. Optim. Theory Appl. 132(1), 2007), we employed the single-subarc sequential gradient-restoration algorithm to optimize the three-dimensional rendezvous between a target spacecraft in a planar circular orbit and a chaser spacecraft with an initial separation distance and separation velocity. The achieved continuous solutions are characterized by two, three, or four subarcs depending on the performance index (time, fuel) and the constraints. In this paper, based on the solutions in Miele et al. (J. Optim. Theory Appl. 132(1), 2007), we employ the multiple-subarc sequential gradient-restoration algorithm to produce pieced guidance trajectories implementable in real time via constant control components. In other words, in this investigation, we force the controls to behave as parameters in each subarc. With the above understanding, we investigate four problems: (P1) minimum time, fuel free; (P2) minimum fuel, time free; (P3) minimum time, fuel given; (P4) minimum fuel, time given.

Weyl-conformally-invariant lightlikep-brane theories: New aspects in black hole physics and Kaluza-Klein dynamics

We introduce and study in some detail the properties of a novel class of Weyl-conformally invariant p-brane theories which describe intrinsically lightlike branes for any odd world-volume dimension. Their dynamics significantly differs from that of the ordinary (conformally non-invariant) Nambu-Goto p-branes. We present explicit solutions of the Weyl-invariant lightlike brane- (WILL-brane) equations of motion in various gravitational models of physical relevance exhibiting various new phenomena. In D=4 the WILL-membrane serves as a material and charged source for gravity and electromagnetism in the coupled Einstein-Maxwell-WILL-membrane system; it automatically positions itself on (``straddles'') the common event horizon of the corresponding matching black hole solutions, thus providing an explicit dynamical realization of the membrane paradigm in black hole physics. In product spaces of interest in Kaluza-Klein theories the WILL-brane wraps non-trivially around the compact (internal)dimensions and still describes massless mode dynamics in the non-compact (space-time) dimensions. Due to nontrivial variable size of the internal compact dimensions we find new types of physically interesting solutions describing massless brane modes trapped on bounded planar circular orbits with non-trivial angular momentum, and with linear dependence between energy and angular momentum.

The Influence of Velocity Dispersion on Dynamical Friction in Stellar Discs

We have investigated the force of dynamical friction on a softened point mass orbiting inside a disc galaxy on a planar circular orbit both analytically and by means of numerical simulations. Including a velocity dispersion large enough to stabilise the disc markedly changes the physical picture of the mechanisms producing friction, whereas the numerical value of the friction is almost unaffected. Self-gravity of the disc enhances the friction only by a moderate amount.

Rendezvous targeting and navigation for a translunar halo orbit

Two-spacecraft terminal-phase rendezvous targeting and navigation are examined for the circular restricted three-body problem. A targeting law and navigation filter are developed assuming the traditional passive targetactive chaser vehicle relationship. The targeting law is demonstrated using a small-radius translunar halo orbit and ideal navigation; the three-body terminal-phase rendezvous problem is then further characterized and contrasted with the two-body problem. Nonlinear simulation results validate the navigation filter design and provide data to assess the filter performance. To demonstrate the entire guidance and navigation system, two profiles for terminalphase rendezvous were considered in a planar circular orbit and two equivalent profiles in an % guided halo orbit.

The dynamics of weakly charged dust: Motion through Jupiter's gravitational and magnetic fields

We derive perturbation equations for the motion of weakly charged dust grains (q/M1→0, where q is the grain's electric charge and M1 its mass) in planetary rings, with emphasis on the Jovian ring system. Our analysis includes the effects of planetary oblateness and an arbitrarily complex magnetic field expressed in terms of spherical harmonics. The perturbation solutions are shown to agree with numerical integrations for most initial conditions, and to provide a simple means of understanding the nature of charged grain trajectories in terms of forced oscillator models. We identify “Lorentz resonances” where a frequency of the perturbing Lorentz force matches a natural orbital frequency of the grain. The resonances come in pairs, with one on either side of the synchronous orbit rs; as rs is approached, resonances are more closely spaced, and their zones become narrower. Large vertical and horizontal excursions from planar circular orbits are predicted at these locales, and this is confirmed in numerical simulations. The amplitudes of the vertical oscillations at resonance can be 1–2 orders of magnitude larger than those outside such zones. The enhanced vertical excursions mean that for shallow viewing angles the optical depth will decrease as lines of sight approach the Lorentz resonance radii. This then provides a mechanism for explaining some apparent boundaries in dusty rings, such as those of the Jovian halo and, less likely, the outer edges of the Jovian main ring and the gossamer ring. For future use, we list the low‐order resonances that lie at or near several features in the Voyager images. Theoretical ring cross sections and overall ring topology are obtained from averages of the analytical solutions over initial conditions. We find that because of the forced response to perturbations, short time solutions predict a warping of the halo out of the equatorial plane that is not seen in the available images. We then point out the significance of including a slow evolutionary process, such as plasma drag, in the dynamical model. Since the large vertical excursions produced as grains drift through Lorentz resonances apparently survive over the radial evolution time scale, the natural response will dominate the motion in the halo region, and the halo will not be appreciably warped.