Orbit Calculations Research Articles

Gauge freedom in theN-body problem of celestial mechanics

The goal of this paper is to demonstrate how the internal symmetry of the N-body celestial-mechanics problem can be exploited in orbit calculation. We start with summarising research reported in (Efroimsky [CITE], [CITE]; Newman & Efroimsky [CITE]; Efroimsky & Goldreich [CITE]) and develop its application to planetary equations in non-inertial frames. This class of problems is treated by the variation-of-constants method. As explained in the previous publications, whenever a standard system of six planetary equations (in the Lagrange, Delaunay, or other form) is employed for N objects, the trajectory resides on a 9(N-1)-dimensional submanifold of the 12(N-1)-dimensional space spanned by the orbital elements and their time derivatives. The freedom in choosing this submanifold reveals an internal symmetry inherent in the description of the trajectory by orbital elements. This freedom is analogous to the gauge invariance of electrodynamics. In traditional derivations of the planetary equations this freedom is removed by hand through the introduction of the Lagrange constraint, either explicitly (in the variation-of-constants method) or implicitly (in the Hamilton-Jacobi approach). This constraint imposes the condition (called “osculation condition”) that both the instantaneous position and velocity be fit by a Keplerian ellipse (or hyperbola), i.e., that the instantaneous Keplerian ellipse (or hyperbola) be tangential to the trajectory. Imposition of any supplementary constraint different from that of Lagrange (but compatible with the equations of motion) would alter the mathematical form of the planetary equations without affecting the physical trajectory. However, for coordinate-dependent perturbations, any gauge different from that of Lagrange makes the Delaunay system non-canonical. Still, it turns out that in a more general case of disturbances dependent also upon velocities, there exists a “generalised Lagrange gauge”, i.e., a constraint under which the Delaunay system is canonical (and the orbital elements are osculating in the phase space). This gauge reduces to the regular Lagrange gauge for perturbations that are velocity-independent. Finally, we provide a practical example illustrating how the gauge formalism considerably simplifies the calculation of satellite motion about an oblate precessing planet.

Electron acceleration in solar flares

Abstract Observations suggest that electron acceleration in impulsive solar flares occurs in magnetic reconnection regions in the corona above the soft X-ray flare loops. Acceleration by a super-Dreicer electric field in a reconnecting current sheet appears to be the most direct way of producing electrons in the energy range between tens of keV and tens of MeV. Theoretical models for collisionless particle acceleration in large-scale current sheets formed in quadrupolar magnetic geometries are reviewed. Recent calculations of particle orbits and energy gains are described, stressing the use of global balance relations and exact MHD solutions for the magnetic fields and plasma flows in the current sheet. The results support the viewpoint that electrons that generate the continuum gamma-ray and hard X-ray emissions in impulsive solar flares are accelerated in a turbulent reconnecting current sheet.

Particle Acceleration by a Time-Varying Electric Field in Merging Magnetic Fields

Traditional models for particle acceleration by magnetic reconnection in solar flares assumed a constant electric field in a steady reconnecting magnetic field. Although this assumption may be justified during the gradual phase of flares, the situation is different during the impulsive phase. Observed rapid variations in flare emissions imply that reconnection is non-steady and a time-varying electric field is present in a reconnecting current sheet. This paper describes exploratory calculations of charged particle orbits in an oscillating electric field present either at a neutral plane or a neutral line of two-dimensional magnetic field. A simple analytical model makes it possible to explain the effects of particle trapping and resonant acceleration previously noted by Petkaki and MacKinnon in a numerical simulation. As an application, electron acceleration to X-ray generating energies in impulsive solar flares is discussed within the context of the model.

Stellar orbits near Sagittarius A

The SHARP/NTT stellar proper motion data now cover an interval from 1992 to 2000 and allow us to determine orbital accelerations for some of the most central stars of the Galaxy. We confirm the stellar acceleration measurements obtained by Ghez et al. with NIRC at the Keck telescope. Our analysis differs in three main points from that of Ghez et al.: (1) we combine the high-precision but shorter time-scale NIRC/Keck data with the lower precision but longer time-scale SHARP/NTT data set; (2) we statistically correct the observed accelerations for geometrical projection effects; (3) we exclude star S8 from the analysis of the amount and position of the central mass. From the combined SHARP/NTT and NIRC/Keck data sets we show that the stars S2, and most likely S1 and S8 as well, are on bound, fairly inclined (60°<i<80°), and eccentric (0.4<e<0.95) orbits around a central dark mass. The combination of both data sets results in a position of this central mass of and of the nominal radio position of Sgr A*. The mean statistically corrected enclosed mass derived from accelerations is Macc=(5±3)×106 M⊙ with current radial separations of S1 and S2 from Sgr A* of about 8–10 mpc. This enclosed mass estimate is derived from individual stellar orbits as close to the massive black hole at the centre of the Milky Way as currently possible. Although the uncertainties are large, this estimate is fully consistent with the enclosed mass range of (2.6–3.3)×106 M⊙ derived by Genzel et al. from radial and/or proper motion velocities of a homogenized sample of sources. Star S8 was excluded from the analysis, since for the current proper motion velocity and radial separation from the centre we find that the measured acceleration requires orbital motion around a compact object with a mass in excess of 3×106 M⊙. The data suggest either that this star was or is subject to a close interaction with a different object or that its position measurements are influenced by the emission of a different cluster star. Therefore we base the analysis of the enclosed mass solely on the available data for stars S1 and S2. We also discuss two late-type stars with projected separations from Sgr A* of about 0.5 and 1 arcsec. In addition to proper motions, these stars have known radial velocities. Orbit calculations indicate that such stars are very likely at larger physical distances from the centre and part of the larger scale central stellar cluster with a core radius of approximately 0.3 pc.

2524 統合 CAE 実現による人工衛星設計支援システムの構築

In order to develop and design a satellite considering a global competitiveness, it is indispensable to clear off the wall (the barrier to design) between the design areas in a satellite design, and to improve a new design environment in which designers can manage and organize the satellite information. In this research, to free the barrier to design between designers, the authors propose the smart master model of a satellite that can integrate with a few analysis systems in a satellite design. These analysis systems are the orbit calculation, thermal analysis, and structural analysis, etc. The authors have developed the integrated design environment for satellite in which designers can trial-and-error designing and evaluating instantaneously.

Design of heavy-ion APF-IH type linac for atomic physics and medical use

We have studied a compact heavy-ion linac for atomic physics and medical use. The design of the linac was based on using alternating-phase-focus (APF) and interdigital-H (IH) structures which give sufficient electric power efficiency. Thereby, it will be possible to design a small and high efficiency linac. The APF-IH linac was designed to accelerate ions from C 2+ to U 40+, from 30 to 300 keV/u and an operating frequency of 100 MHz. We made a half-scale cold model of this linac using orbit calculation and measured its RF characteristics. Then, we designed a APF-IH type linac using the results of the measurement.

On the optimal accuracy and double solution in the calculation of initial orbits

It is shown, by simulated calculation, that the reference vector algorithm we proposed of calculating initial orbits is “quasi-optimal”, because its accuracy approaches the Cramér-Rao lower bound in the statistical theory of estimation and is proportional to the observing error. Double solution exists in the orbit calculation: the smaller the eccentricity and the closer the mean anomaly M 0 is to ±90°, the greater is the probability of getting the false solution. We propose an algorithm which gives two solutions, one of which must be the true one and it has a high accuracy.

Diagnostic for fast charged particles at TEXTOR-94

A diagnostic for measuring the energy spectrum of fast charged particles has been developed at TEXTOR-94. It consists of a pair of solid state silicon passivated implanted planar silicon detectors which are actively water cooled. The detectors are mounted on a manipulator and are inserted into the vacuum vessel during plasma operation. The preamplifiers are located just behind the detectors. The noise level is strongly minimized by careful grounding and rf shielding. Collimators placed in front of the detectors allow to obtain radial and pitch angle-resolved measurements. Fast particles coming from the center of the plasma are detected by one detector. The second detector can be used as a background monitor or can provide an additional measurement at another position. Orbit calculations in a realistic magnetic field predict the detection efficiency. The calculated detection efficiency shows good agreement with our experiments. The stable temperature and excellent noise immunity of our system allow to measure the energy spectrum of the 3 MeV protons and 1 MeV tritons produced by the DD fusion reactions in discharges with different heating scenarios. High resolution energy spectra are even obtained in discharges heated with injection of deuterium in a deuterium plasma.

Effective Nuclear Charges for the First- through Third-Row Transition Metal Elements in Spin−Orbit Calculations

The effective nuclear charges (Zeff), which are empirical parameters in an approximate spin−orbit Hamiltonian, are determined for the first- through third-row transition metal elements by using experimental results for the fine structure splittings in atomic terms. All calculations use multiconfiguration self-consistent-field (MCSCF) wave functions, whose active space includes nd and (n + 1)sp orbitals (n is the principal quantum number), with the effective core potential (ECP) basis sets proposed by Stevens et al., augmented by one set of polarization f functions. First-order or second-order configuration interaction (FOCI or SOCI) calculations were also performed in order to understand disagreements between the MCSCF results and the experimental ones.

Detecting near collisions for satellites

A highly efficient algorithm is presented for detecting near collisions involving satellites. Rather than examine all possible pairings of a satellite with another orbiting object, the new approach examines trajectories at a sequence of coarse time steps. Objects which are spatially isolated cannot be involved in a collision, and are discarded. The time steps, orbit calculations, and discarding are repeatedly refined until the only remaining objects experience near collisions.

Galactic Orbits of Different Galactic Population Objects

It is evident that the knowledge of not only positions and velocities of objects belonging to different populations but also their osculating galactic orbits can clarify the structure and history of our Galaxy. Action variables being adiabatic invariants are especially useful for these purposes (Binney, May 1986). One of them is a usual area integral (and it can be found without any orbit calculation). The second action variable is connected with an energy integral but for 3–D orbits and arbitrary potentials it cannot be found analitically. Eccentricities resulting from orbit calculations can be used here (Lynden-Bell 1963). Comparison of eccentricities defined with different ways shown that differences between them are practically negligible (Kutuzov 1985, 1987). As for the third action variable and the corresponding third isolating integral orbit calculations can confirm its existence and control the validity of various approximations. Numerical technique allowing to find it and working at any potential is now in progress (Binney, Kumar 1993).

The temporal and spatial characteristics of TOPEX/POSEIDON radial orbit error

Satellite orbit error has long been the bane of oceanographers who analyze altimetry data. However, radial orbit error on TOPEX/POSEIDON (T/P) has been reduced to the 3 to 4‐cm root‐mean‐square (rms) level over a 10‐day repeat cycle, which represents an order of magnitude improvement over earlier altimetry missions such as Geosat. Consequently, oceanographers are now able to directly evaluate the absolute ocean topography to unprecedented accuracy levels. While significantly reduced, the T/P orbit error still requires quantification. This study examines the spatial and temporal characteristics of the T/P radial orbit error, as assessed through the analysis of laser tracking residuals and orbit comparisons with independently generated trajectories. Spectral analyses of the orbit differences between the orbits determined from satellite laser ranging and Doppler Orbitography and Radiopositioning Integrated by Satellite data and the independently determined reduced dynamic Global Positioning System (GPS) ephemerides indicate that the predominant power is at the once‐per‐orbital revolution frequency with 2‐ to 3‐cm peaks. When the orbit differences are colinearly aligned to a fixed geographic grid and spectral analysis is performed at each geographic grid point, a nearly 60‐day period is found with maximum amplitudes in the 2‐ to 4‐cm range. The contribution of both conservative and nonconservative force and measurement mismodeling to this error signal are assessed. We demonstrate that the ∼60‐day error period seen at fixed geographic locations arises from weaknesses in the dynamic ocean tidal models used in the orbit calculations. New tidal models have been developed which significantly reduce this error. Second‐generation orbits incorporating many model improvements have been computed and demonstrate a significant reduction in the radial orbit error signals. Some orbit error still exists, and methods for further model improvements and the possibility of achieving 1‐cm radial rms orbit accuracy in T/P are discussed.

Direct Energy Conversion for D-3He Reactor

Results of particle simulation indicate that ExB drift is available for the purpose of ion energy selection, which is necessary for direct energy conversion. High energy conversion rate of the traveling wave direct energy converter up to 0.8 is obtained both from orbit calculation and from computer simulation as a result of improvement of proton beam modulation. Computer simulation using a particle-circuit code demonstrates stabilization of the excited wave by the external electric load and stable response of the wave to variation of the load. A very preliminary design of electric circuits of the traveling wave direct energy converter is also presented. 8 refs., 7 figs.

A comparison of the bonding in organoiron clusters

The Mossbauer effect hyperfine parameters and the results of the Fenske-Hall molecular orbit (mo) calculations have been used to study the electronic properties of trinuclear iron, tetranuclear iron butterfly, Fe-Co, and Fe-Cu carbonyl clusters. The more negative Fe charge and the larger Fe 4s population in an Fe(CO)4 fragment as compared with that in an Fe(CO)3 or an Fe(CO)2 fragment is a result of the CO ligands rather than the near-neighbor metals. The clusters which contain heterometals have more negative isomer shifts. The isomer shift correlated well with the sum of the Fe 4s orbital population and the Zeff these electrons experience. The mo wave functions and the atomic charges generally give a larger calculated ΔE Q than is observed, indicating the need to include Sternheimer factors in the calculation. The valence contribution dominates the EFG.

Searches for millisecond pulsations in low-mass X-ray binaries, 2

view Abstract Citations (161) References (34) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Searches for Millisecond Pulsations in Low-Mass X-Ray Binaries. II. Vaughan, B. A. ; van der Klis, M. ; Wood, K. S. ; Norris, J. P. ; Hertz, P. ; Michelson, P. F. ; van Paradijs, J. ; Lewin, W. H. G. ; Mitsuda, K. ; Penninx, W. Abstract Coherent millisecond X-ray pulsations are expected from low-mass X-ray binaries (LMXBs), but remain undetected. Using the single-parameter Quadratic Coherence Recovery Technique (QCRT) to correct for unknown binary orbit motion, we have performed Fourier transform searches for coherent oscillations in all long, continuous segments of data obtained at 1 ms time resolution during Ginga observations of LMXB. We have searched the six known Z sources (GX 5-1, Cyg X-2, Sco X-1, GX 17+2, GX 340+0, and GX 349+2), seven of the 14 known atoll sources (GX 3+1. GX 9+1, GX 9+9, 1728-33. 1820-30, 1636-53 and 1608-52), the 'peculiar' source Cir X-1, and the high-mass binary Cyg X-3. We find no evidence for coherent pulsations in any of these sources, with 99% confidence limits on the pulsed fraction between 0.3% and 5.0% at frequencies below the Nyquist frequency of 512 Hz. A key assumption made in determining upper limits in previous searches is shown to be incorrect. We provide a recipe for correctly setting upper limits and detection thresholds. Finally we discuss and apply two strategies to improve sensitivity by utilizing multiple, independent, continuous segments of data with comparable count rates. Publication: The Astrophysical Journal Pub Date: November 1994 DOI: 10.1086/174818 Bibcode: 1994ApJ...435..362V Keywords: Neutron Stars; Orbit Calculation; Pulsed Radiation; Stellar Models; Stellar Oscillations; X Ray Astronomy; X Ray Binaries; Ginga Satellite; Mathematical Models; Nyquist Frequencies; Stellar Magnetic Fields; Stellar Mass; Stellar Rotation; Astronomy; METHODS: NUMERICAL; STARS: BINARIES: CLOSE; STARS: NEUTRON; STARS: OSCILLATIONS; X-RAYS: STARS full text sources ADS | data products SIMBAD (15)

The dynamical survival of small-scale substructure in relaxed galaxy clusters

view Abstract Citations (44) References (28) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS The Dynamical Survival of Small-Scale Substructure in Relaxed Galaxy Clusters Gonzalez-Casado, Guillermo ; Mamon, Gary A. ; Salvador-Sole, Eduard Abstract We consider the dynamical evolution of small-scale substructure in clusters within two extreme alternate scenarios for their possible origin: (1) the accretion of groups (or small clusters) on quasi-radial orbits and 2) the merger of clusters of similar masses, followed by the decoupling of their dense cores. Using simple analytical arguments and checking with numerical computations, we show that objects are destroyed by the tidal field of the global cluster potential if their mean density is small compared to the mean cluster density within the radius of closest approach of the group or detached core. Accreted groups and small clusters are thus tidally disrupted in one cluster crossing. Since the cores of clusters are much denser than groups, they are considerably more robust to tides, but the least massive are destroyed or severely stripped by tides, while the others are brought to the cluster center by dynamical friction (and subsequently merge) in less than one orbit. The longest lived substructures are detached cores, roughly 10 times less massive than the cluster, starting in near-circular orbits beyond 1 h^-1^ Mpc from the cluster center. Publication: The Astrophysical Journal Pub Date: October 1994 DOI: 10.1086/187548 arXiv: arXiv:astro-ph/9406066 Bibcode: 1994ApJ...433L..61G Keywords: Astronomical Models; Cosmology; Galactic Clusters; Galactic Evolution; Galactic Structure; Mathematical Models; Tides; Dynamical Systems; Equations Of Motion; Kinematics; Orbit Calculation; Orbital Mechanics; Astrophysics; GALAXIES: CLUSTERING; GALAXIES: KINEMATICS AND DYNAMICS; COSMOLOGY: THEORY; Astrophysics E-Print: accepted in ApJ Letters, 4 pages uuencoded compressed postscript (4 figures included), IAP preprint 465 full text sources arXiv | ADS |

Developments of the TEUFEL injector racetrack microtron

In this paper we report on developments of the 25 MeV racetrack microtron (RTM) that will be the electron source for the second phase of the TEUFEL project, to generate radiation of 10 μm in a 2.5 cm period hybrid undulator. The theoretical understanding of this unconventional, azimuthally varying field type of RTM has been extended. A comparison of analytically calculated orbit stability with that based on measured data will be presented; orbit calculations using measured field data show the designed performance. Construction and tuning of the 1300 MHz, 2.2 MV microwave cavity have been completed, and signal level measurements have been performed. The overall assembly of the microtron is nearing completion. At present a vacuum pressure better than 5 × 10 −7 Torr is achieved.

New osculating, original, and future orbits for ten one-apparition comets

view Abstract Citations References (8) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS New Osculating, Original, and Future Orbits for Ten One-Apparition Comets Todorovic-Juchniewicz, B. Abstract New values of orbital elements for ten hyperbolic comets discovered during the past few years were determined on a basis of all their observations selected and weighted according to the objective mathematical criteria. For four comets the best representation of the complete observational material is given by the nongravitational model of their motion. The original and future orbits of the comets were computed by numerical integration of equations of motion. The Oort effect (a tendency for original 1/a values to range from 0 to + 100 x 10 exp -6 AU) is clearly seen for six comets. Modifications in original (1/a) values due to the nongravitational effects are discussed. Publication: The Astronomical Journal Pub Date: July 1992 DOI: 10.1086/116246 Bibcode: 1992AJ....104..394T Keywords: Astronomical Catalogs; Astronomical Models; Comets; Orbit Calculation; Orbital Elements; Equations Of Motion; Oort Cloud; Solar System; Astronomy; COMETS; CELESTIAL MECHANICS full text sources ADS |

Determination of the visual orbit of the spectroscopic binary Alpha Andromedae with submilliarcsecond precision

view Abstract Citations (44) References (30) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Determination of the Visual Orbit of the Spectroscopic Binary alpha Andromedae with Submilliarcsecond Precison Pan, Xiaopei ; Shao, Michael ; Colavita, M. M. ; Armstrong, J. T. ; Mozurkewich, David ; Vivekanand, Maddali ; Denison, Craig S. ; Simon, Richard S. ; Johnston, Kenneth J. Abstract The visual orbit of the spectroscopic binary Alpha And is determined independently of spectroscopic data using the Mark III Stellar Interferometer. Observations of Alpha And in 1988 and 1989 clearly demonstrate submilliarcsecond measurement precision at optical wavelengths. All of the orbital elements of Alpha And are calculated utilizing observations from the stellar interferometer only and are in excellent agreement with the spectroscopic results. However, three of these elements can only be obtained from interferometric data. Using both interferometric and spectroscopic observations, the definitive orbital elements are determined including angular semimajor axis, inclination, position angle of ascending node, longitude of periastron, period eccentricity, and epoch of periastron passage. In addition, the magnitude difference between the two components is measured, yielding delta-m = 1.82 +/- 0.04 mag at 800 nm and delta-m = 1.99 +/- 0.04 mag at 550 nm. Incorporating photometric observations, the color indices between 550 nm and 800 nm for the primary and the companion are determined as -0.11 +/- 0.03 mag +0.07 +/- 0.05 mag, respectively. Publication: The Astrophysical Journal Pub Date: January 1992 DOI: 10.1086/170904 Bibcode: 1992ApJ...384..624P Keywords: Astronomical Spectroscopy; Binary Stars; Orbital Elements; Stellar Motions; Stellar Orbits; Angular Resolution; Orbit Calculation; Stellar Magnitude; Visual Observation; Astrophysics full text sources ADS | data products SIMBAD (1)

On relation between Hamada and Boozer Magnetic Coordinate Systems.

The relation between the Hamada and the Boozer magnetic coordinate systems is clarified by deriving them from a general magnetic fied coordinate system. The coordinate transformation from the Hamada to the Boozer coordinate system is performed using a transformation function, which is easily calculated with the knowledge of the magnetic field strength only.In non-axisymmetric systems, the Fourier spectrum of the magnetic field strength |B| in the Hamada coordinate system is broader than that in the Boozer coordinate system and the leading modes of IBI in the Hamada coordinate system significantly deviate from a simple model field in comparison with the Boozer coordinate system.The Boozer coordinate system is suitable for numerical calculations, especially, for neoclassical and orbit calculations in non-axisymmetric systems.