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Computer program uses an iterative method to construct precisely periodic orbits which dynamically approximate solutions that converge to precise dynamical solutions in the limit of the sequence. The method used is a modification of the generalized Newton-Raphson algorithm used in analyzing two point boundary problems.
This paper investigates the possible application of periodic orbit control maneuvers for so-called evolved-LISA (eLISA) missions, i.e., missions for which the constellation arm lengths and mean distance from the Earth are substantially reduced. We find that for missions with arm lengths of 106 km and Earth-trailing distance ranging from approx. 12deg to 20deg over the science lifetime, the occasional use of the spacecraft micro-Newton thrusters for constellation configuration maintenance should be able to essentially eliminate constellation distortion caused by Earth-induced tidal forces at a cost to science time of only a few percent. With interior angle variation kept to approx. +/-0:1deg, the required changes in the angles between the laser beam pointing directions for the two arms from any spacecraft could be kept quite small. This would considerably simplify the apparatus necessary for changing the transmitted beam directions.
BOKS 45906 was found to be a blue source in the Burrell-Optical-Kepler Survey which showed a 3 magnitude outburst lasting approximately 5 days. We present the Kepler light curve of this source which covers nearly 3 years. We find that it is in a faint optical state for approximately half the time and shows a series of outbursts separated by distinct dips in flux. Using data with 1 minute sampling, we find clear evidence that in its low state BOKS 45906 shows a flux variability on a period of 56.5574 plus or minus 0.0014 minutes and a semi-amplitude of approximately 3 percent. Since we can phase all the 1 minute cadence data on a common ephemeris using this period, it is probable that 56.56 minutes is the binary orbital period. Optical spectra of BOKS 45906 show the presence of Balmer lines in emission indicating it is not an AM CVn (pure Helium) binary. Swift data show that it is a weak X-ray source and is weakly detected in the bluest of the UVOT filters. We conclude that BOKS 45906 is a cataclysmic variable with a period shorter than the 'period-bounce' systems and therefore BOKS 45906 could be the first helium-rich cataclysmic variable detected in the Kepler field.
Periodic solution with nondegenerate orbit for functional differential equations taking into account small perturbation
Periodic earth-moon orbits in restricted three body problem
Classification scheme for symmetric periodic orbits in restricted three body problem with two dimensions and earth-moon mass ratio
A number of close binary stars show erratic changes in their orbital periods on time scales of order 5-10 yr. Recently it has been proposed that the period changes are the result of changes in the quadrupole moment of one star, caused in turn by an alteration of the internal structure of that star. Magnetic pressure, which either distorts the shape of the star or changes its tidally induced quadrupole moment, is suggested as the driving force behind the alteration. Here, the amount of energy required to distort one component of a binary and match the observed period changes is estimated. The rate at which energy is produced or lost is governed by the thermal time scale of the star, and the estimates indicate that the observed period changes would take at least 1000 yr for the tidal quadrupole mechanism, and of order 60 yr to match a period change in V471 Tau which took only 4 yr.
In this paper, we develop a method to solve for periodic orbits, i.e., Lyapunov and Halo orbits, using a functional interpolation scheme called the Theory of Func- tional Connections (TFC). Using this technique, a periodic constraint is analyti- cally embedded into the TFC constrained expression. By doing this, the system of differential equations governing the three-body problem is transformed into an unconstrained optimization problem where simple numerical schemes can be used to find a solution, e.g., nonlinear least-squares is used. This allows for a simpler numerical implementation with comparable accuracy and speed to the traditional differential corrector method.
Periodic orbits in restricted three body problem
We present the results of photometric observations of the black hole candidate GX339-4, obtained while the system was in an 'off' state. We show that a 14.8-h modulation was present, and provide evidence for a similar periodicity in the 'high' state from a reanalysis of previously published photometry and spectroscopy. The presence of the same period in both states implies that it is likely to be the orbital period of the system. The spectroscopy analysis provides evidence for an apparent change in the systemic velocity of the system. The amplitude of the observed radial velocity variations, however, permits only crude limits to be placed on the mass of the compact object. Only absorption-line spectroscopy of the secondary in the 'off' state will provide a convincing mass determination.
The determination of a set of equations is presented for equi-period orbits work. A set of figures for quick reference are provided as well.
Three body problem of two heavy mass particles oscillatory motion in periodic orbits on straight line under Newtonian attraction
An extension of Gutzwiller's (1967, 1969, 1970, 1971, 1990) semiclassical theory for chaotic systems that allows a determination of matrix elements in terms of classical periodic orbits. Associated zeta functions are derived. The semiclassical predictions are found to be in good agreement with Fourier transforms of quantum spectra of hydrogen in a magnetic field. Expressions for off-diagonal matrix elements are derived that are extensions of the Bohr correspondence relations for integrable systems.
From a pulse-timing analysis of Ginga observations of the binary X-ray pulsar Her X-1 obtained during the interval 1989 April-June local orbital parameters are determined for a short high state. An orbital epoch is also determined in the adjacent main high state. By comparing these orbital solutions with previously published results, a decrease is detected in the orbital period for Her X-1 over the interval 1971-1989. The value is substantially larger than the value predicted from current estimates of the mass-transfer rate, and motivates consideration of other mechanisms of mass transfer and/or mass loss. A second result from these observations is a close agreement between orbital parameters determined separately in main high and short high states. This agreement places strong constraints on the obliquity of the stellar companion, HZ Her, if undergoing forced precession with a 35-day period. As a consequence further doubt is placed on the slaved-disk model as the underlying cause of the 35-day cycle in Her X-1.
From a pulse-timing analysis of Ginga observations of the binary X-ray pulsar Her X-1 obtained during the interval 1989 April-June we have determined local orbital parameters for a Short High state. We have also determined an orbital epoch in the adjacent Main High state. By comparing these orbital solutions with previously published results, we have detected a decrease in the orbital period for Her X-1 at an average rate of dot-P/P = (- 1.32 +/- 0.16) x 10(exp -8) yr(exp -1) over the interval 1971-1989. This is substantially larger than the value predicted from current estimates of the mass transfer rate, and motivates consideration of other mechanisms of mass transfer and/or mass loss. A second result from these observations is a close agreement between orbital parameters determined separately in Main High and Short High states. This agreement places strong constraints on the obliquity of the stellar companion, HZ Her, if undergoing forced precession with a 35 day period. As a consequence further doubt is placed on the slaved-disk model as the underlying cause of the 35 day cycle in Her X-1.
CCD photometry of KO Vel obtained on five nights in April 1987 is reported. From this and the two previously published sets of CCD photometry, a new candidate orbital period of 0.422 d (10.12 h) is derived. The shape of the folded light curve is nonsinusoidal, which has made the Fourier transform method less effective than usual. It is shown that all three sets of light curves examined here are consistent with the proposed period. All three data sets for the presence of a shorter period are examined, and no conclusive evidence for a periodic variation on an approximately 1 hr time scale is found. The nature of KO Vel therefore still remains an open question.
Method is modification of generalized Newton-Ralphson algorithm for analyzing two-point boundary problems. It constructs sequence of solutions that converge to precise dynamic solution in the sequence limit. Program calculates periodic orbits in either circular or elliptical restricted three-body problems.
A method of analyzing long periodic variations of orbits from osculating elements is presented. A precision of 0.03 arc sec in inclination has been achieved with this technique for the GEOS 1 and 2 orbits. A combined numerical-analytical technique for computing mean elements is also described. This method has given mean elements with a precision of 0.1 arc sec in inclination and 10 cm in semimajor axis for the GEOS satellites. Application of these techniques to the determination of earth tidal parameters is also discussed.