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Low cost transfers of a spacecraft in a multi-gravitational orbital environment, which are based on connections between unstable periodic orbits, present several trade-offs, such time-of-flight v.s transfer fuel cost.
We report the detection of a 115 day periodicity in SWIFT/XRT monitoring data from the ultraluminous X-ray source (ULX) NGC 5408 X-1. Our ongoing campaign samples its X-ray flux approximately twice weekly and has now achieved a temporal baseline of more than 500 days. Timing analysis reveals a significant periodicity with a period of 115.5 +- 4 days. The fractional modulation amplitude decreases with increasing energy, ranging from 0.13 above 1 keV to 0.24 below 1 keV. The shape of the profile evolves as well, becoming less sharply peaked at higher energies. Periodogram analysis is consistent with a periodic process, however, continued monitoring is required to confirm the coherent nature of the modulation. Spectral analysis indicates that NGC 5408 X-1 can reach 0.3 - 10 keV luminosities of 2 x 10e40 ergs/s. We suggest that, like the 62 day period of the ULX in M82 (X41.4+60), the periodicity detected in NGC 5408 X-1 represents the orbital period of the black hole binary containing the ULX. If this is true then the secondary can only be a giant or supergiant star.
We report the detection of a 115 day periodicity in SWIFT/XRT monitoring data from the ultraluminous X-ray source (ULX) NGC 5408 X-1. Our o ngoing campaign samples its X-ray flux approximately twice weekly and has now achieved a temporal baseline of ti 485 days. Periodogram ana lysis reveals a significant periodicity with a period of 115.5 +/- 4 days. The modulation is detected with a significance of 3.2 x 10(exp -4) . The fractional modulation amplitude decreases with increasing e nergy, ranging from 0.13 +/- 0.02 above 1 keV to 0.24 +/- 0.02 below 1 keV. The shape of the profile evolves as well, becoming less sharply peaked at higher energies. The periodogram analysis is consistent wi th a periodic process, however, continued monitoring is required to c onfirm the coherent nature of the modulation. Spectral analysis indic ates that NGC 5408 X-1 can reach 0.3 - 10 keV luminosities of approxi mately 2 x 10 40 ergs/s . We suggest that, like the 62 day period of the ULX in M82 (X41.4-1-60), the periodicity detected in NGC 5408 X-1 represents the orbital period of the black hole binary containing the ULX. If this is true then the secondary can only be a giant or super giant star.
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
Combining all available photometric data from various surveys and literature with our observations, we present 10 sets of light curves for the eclipsing binary V0599 Aur covering a timescale of 20 yr. During the last two decades, the O’Connell effect continuously varied and went through at least two flips between positive and negative effects. The photometric solutions from our two sets of multicolored light curves show that V0599 Aur is a W-type shallow contact binary with an active spot on the secondary. Its absolute parameters are determined by combining the Gaia distance with the photometric solutions. The period investigation reveals a secular decrease and a cyclic variation in its orbital period. The former mainly originates from the mass transfer from the more massive secondary to the less massive primary. The latter can be preferentially explained as a result of cyclic magnetic activity of the secondary, with three observational supports: (1) the existence and evolution of an active spot suggested by the long-term photometry, (2) periodic variation in both the O’Connell effect and relative luminosity, and (3) weak correlations between O’Connell effect/relative luminosity changes and cyclic period variation. Together with the cyclic period variation and its theoretical reasonability by Applegate’s mechanism, we suggest that the secondary of V0599 Aur is a solar-type magnetic-activity star with an approximately 11 yr active cycle. Furthermore, by combining the secular period decrease with the Roche-lobe model, we infer that V0599 Aur is evolving from the marginal contact state controlled by thermal relaxation oscillation theory to the overcontact state.
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.