A period study of V450 Herculis

A detailed period study of the eclipsing binary system V450 Her has been presented. A new period (P= _. ^d 12724) has been given. The period changes in different portions of the O-C diagram, based on new period, have been estimated. The total period change ranges from 3.28×10^–6 d to 7.06×10^–5 d, which is appreciable.     

Period study of AW UMa

A detailed period study of the eclipsing binary system AW UMa is presented. A new period (P=0^d.4387317) is given. Period changes in different portions of the O-C diagram, based on new period, have been estimated. The total change in period (P) ranges from 2.2×10^–7 to 2.8×10^–6 d, which is normal for AW UMa systems. Two distinct linear trends of period are visible in the O-C diagram. A third trend shows a new change in the period behaviour, which is yet to be confined.     

Period variations in SZ Arietis

A new period (P=1^d.7175405) of the eclipsing binary system SZ Arietis has been presented. Period changes in different portions of the O-C diagram, with new period, have been estimated. The total change in period (P) ranges from 3.64×10^–5 d to 4.24×10^–4 d, which is appreciably large. However, leaving the unusual value, the average period change comes out to be of the order of 6×10^–5 d. The period changes around the years 1903, 1943, and 1977 are apparent in the O-C diagrams. A sinusoidal variation is also visible in the O-C diagrams which indicates that SZ Ari may be a three-body system, having a period of nearly 66 years.     

Period study of GH Pegasi

The period study of the eclipsing binary system GH Pegasi has been presented for the first time. A new period (P=2^d.556135) of GH Peg, based on all available times of minima, has been given. O–C diagrams of the system have also been presented for the first time, and the period changes present in the system have been analysed. The period shows changes around the year 1972 and 1981. The total period change in different portions of the O–C diagram, based on the corrected period, ranges from 5.2×10^–6 d to 7.0×10^–5 d. The photoelectric minima show sufficiently large scatter in the system.     

Period study of XY Ceti

A first period study of the eclipsing binary XY Ceti is presented. A new period (P=2^d.7807135), based on all available times of minima, is given. Period changes in different portions of the O–C diagram, with a new period, have been estimated. The total change in period (P/P) ranges from 1.1×10^–5 d to 1.2×10^–4 d, thus, P ranges from 3.1×10^–5 d to 3.3×10^–4 d. The O–C diagram suggests that the trend of the period has changed around the year 1959. Two portions of increasing and decreasing trends also reveal that the period changes (P/P) of the order of 10^–5 d are present, which are appreciably large.     

RS CVn-binary RW com: A possible three-body system

A first detailed period study of the eclipsing RS CVn-binary system RW Com is presented. A new period (P=0^d.2373455) based on 223 minima is given. The O–C diagrams of RW Com have been presented for the first time. Types of ten minima have been corrected judging the period trend. Period changes in different portions of the O–C diagram (Figure 2) have been estimated. The total change in period (P/P) ranges from 5.5×10^–7 to 6.4×10^–6. Thus, P ranges from 1.3×10^–7 d to 1.5×10^–6 d. Numerous minima are available in the time interval 1967 to 1986. This part of the O–C diagram (Figure 2) shows a sinusoidal variation, thus, it is suspected that RW Com could be a three-body system. The period of variation due to third body appears to be nearly 16 years.     

Detailed period study of Delta Capricorni

Detailed period study of the eclipsing binary system Delta Cap is presented. Available times of minima have been classified, and two minima have been found off the instant period trend. A new period of 1.^d0227789 has been given. Period changes in different portions of the O?C diagram have been estimated, which range from 6.4×10^?6 d to 1.8×10^?3 d (?), the average being 3.5×10^?5 d. A sinusoidal variation is evident in the O?C diagrams, which is indicative of the possible presence of a third body, having a period of nearly 62 years, however, it is yet to be confirmed.     

ST Persei: A possible multi-body system

Detailed period study of the eclipsing binary ST Per is presented. A new period (P=2^d.648339) is given. Period changes in different portions of the O-C diagram with a new period have been estimated. The total changes in period (P) ranges from 2.17×10^–5d to 2.64×10^–4d which is appreciably large. Sufficient number of minima in the time interval 1934 to 1985 for this system are available. Distinct increasing and decreasing trends are evident, the change in the tendency appears to have occurred around 1947. Sinusoidal variation is seen between cycles 7000–10000, which indicates that ST Per is a three-body system, the period of the third body being about 22 years. However, the sinusoidal variation is not perfectly symmetric in shape, therefore, it is suspected that ST Per is a four-(or multi-) body system.     

The Duplicity of Large Amplitude SX Phoenicis Star CY Aquarii

New photoelectric times of maximum light of the large amplitude SX Phoenicis star CY Aquarii are analyzed together with times of maximum light in the literature. The general shape of the fitted curve of the observed minus calculated (O-C) times of maximum light suggest the duplicity of the variable star, which causes long-term period variations in the light-time. The period changes of CY Aqr are probably consequences of a continuously increasing period combined with the light-time effect in a binary system. The secondary companion is less massive. Some spectroscopic orbital elements are derived from the O-C diagram. This revised version was published online in July 2006 with corrections to the Cover Date.     

Possible connection between period change and magnetic activity of the very short‐period binary VZ Piscium

New times of light minimum of the short‐period (P = 0^d.26) close binary system, VZ Psc, are presented. A period investigation of the binary star, by combining the three new eclipse times with the others collected from the literatures, shows that the variation of the period might be in an alternate way. Under the hypothesis that the variation of the orbital period is cyclic, a period of 25 years and an amplitude of 0.^d0030 for the cyclic change are determined. If this periodic variation is caused by the presence of a third body, the mass of the third body (m₃) should be no less than 0.081M_⊙. Since both components of VZ Psc are strong chromospherically active and the level of activity of the secondary component is higher than that of the primary one, the period may be more plausibly explained by cyclic magnetic activity of the less massive component. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

New period and period variations of DX Aquarii

The new period (P=0 _. ^d 461700) of the eclipsing binary system DX Aqr has been presented, which is based on available times of minima. O–C diagram of DX Aqr has been presented for the first time, and the period variations present in the system have been analysed. In all five period increases and five period decreases are nothed, and four period increases and five period decreases have been discussed. The strongest period increase occurs between 1975 and 1976. The total period change in different portions of the O–C diagram ranges from 1.40×10^–4 d to 3.61×10^–6 d. Appreciable period fluctuations have been noted to have occurred in the time intervals, 1964–1965 and 1974–1975.     

A new period and period changes of GG Cassiopeiae

The O–C diagram of the eclipsing binary GG Cassiopeiae has been presented for the first time, and the period changes present in the system have been analysed. In all three period changes are noted. The strongest period change has been found to occur in the time-interval 1942 to 1966. The total period change in different portions of the O–C diagram ranges from 7.1×10^–7 d to 2.0×10^–5 d. The stronger period changes appear to have occurred after 1942; prior to it, the system has shown a negligible period change. The overall picture of the O–C diagram suggests that the O–C values of the system GG Cas are negative after 1942. The presence of a third body does not appear probable. The period fluctuations are also appreciable. A new period (P=3 _. ^d 758733) has been presented.     

Orbital Period Studies of RS CVn-type binaries III. BH Virginis

The changes in the orbital period of the short-period RS CVn-type binaryBH Vir are studied based on the analysis of the O-C curve formed by allphotoelectric times of light minimum. It was discovered that the orbitalperiod of BH Vir may show a periodic variation with a period of 9.12years. A weak evidence also indicating a small amplitude oscillation witha period of 52.7 years in the change of the orbital period. Two possiblemechanisms (light times effects due to two hypothetical additional bodiesand magnetic activity cycle) that could explained the period behavior arestudied. The periodic changes in the orbital period can be explained asdue either to magnetic activity cycles in the two components or to thelight-times effects of the additional bodies.     

Period study of AX draconis

A new period (P = 0 _. ^d 5681643) for AX Draconis, based on all available times of minima, has been given. O-C diagrams for the star, based on various periods, have been given. A sinusoidal variation is apparent in figures, which is suggestive of the possible presence of a third body, having a period of more than 80 years.     

Some effects of elasticity on lunar rotation

A general Hamiltonian for a rotating Moon in the field of the Earth is expanded in terms of parameters orienting the spin angular momentum relative to the pricipal axes of the Moon and relative to coordinate axes fixed in the orbital plane. The effects of elastic distortion are included as modifications of the moment of inertia tensor, where the magnitude of the distortion is parameterized by the Love numberk ₂. The principal periodic terms in the longitude of a point on the Moon due to variations of the tide caused by the Earth are shown to have amplitudes between 3.9 × 10^–3 and 1.6 × 10^–2 with a period of an anomalistic month, 3.0 × 10^–4 and 1.2 × 10^–3 with a period of one-half an anomalistic month and 2.4 × 10^–4 and 9.6 × 10^–4 with a period of one-half of a nodical month. The extremes in the amplitudes correspond to rigidities of 8 × 10¹¹ cgs and 2 × 10¹¹ cgs, respectively, the former rigidity being comparable to that of the Earth. Only the largest amplitude given above is comparable to that detectable by the projected precision of the laser ranging to the lunar retrorereflectors, and this amplitude corresponds to an improbably low rigidity for the Moon. A detailed derivation of the free wobble of the lunar spin axis about the axis of maximum moment of inertia is given, where it is shown that elasticity can alter the period of the free wobble of 75.3 yr by only 3 × 10^–4 to 10^–3 of this period. Also, the effect of elasticity on the period of free libration is completely negligible by many orders of magnitude. If the Moon's rigidity is close to that of the Earth there is no effect of elasticity on the rotation which can be measured with the laser ranging and, therefore, no elastic properties of the Moon can be determined from variations in the rotation.Currently on leave from the Dept. of Physics, University of California, Santa, Barbara, California.Communication presented at the conference on Lunar Dynamics and Observational Coordinate Systems held January 15–17, 1973 at the Lunar Science Institute, Houston, Tex., U.S.A.     

Spin states and climates of eccentric exoplanets

The known extrasolar planets exhibit a wide range of orbital eccentricities e. This has a profound influence on their rotations and climates. Because of tides in their interiors, mostly solid exoplanets are expected eventually to despin to a state of spin-orbit resonance, where the orbital period is some integer or half-integer times the rotation period. The most important of these resonances is the synchronous state, where the planet's spin period exactly equals its orbital period (like Earth's Moon, and indeed most of the regular satellites in the Solar System). Such planets seem doomed to roast on one side and freeze on the other. However, synchronous planets rock back and forth by an angle of ∼2Arcsine with respect to the sub-stellar point. For e=0.055 (as for the Moon), this optical libration amounts to only ∼6°; but for a synchronous planet with e=0.50, for example, it would rise to ∼59°. This greatly expands the temperate “twilight zone” near the terminator and considerably improves the planet's prospects for habitability. For e?0.72389, the optical libration exceeds 90°; for such planets, the sector of permanent night vanishes, while the sunniest region splits in two. Furthermore, the synchronous state is not the only possible spin resonance. For example, Mercury (with e≈0.206) has an orbital period exactly 1.5 times its rotation period. A terrestrial exoplanet with e=0.40, say, is liable to have an orbital period of 2.0, 2.5, or 3.0 times its spin period. The corresponding insolation patterns are generally complicated, and all different from the synchronous state. Yet these non-synchronous resonances also protect certain longitudes from the worst extremes of temperature and solar radiation, and improve the planet's habitability, compared to non-resonant rotation. These results also have implications for the direct detectability of extrasolar planets, and the interpretation of their thermal emissions.     

The generalized uncertainty principle and the thermodynamic quantities near a black hole

The continuous complex Morlet wavelet transform is used to investigate temporal rotation cycle length of daily sunspot areas from May 9, 1874 to February 28, 2010, from a global point of view. The rotation cycle length of the Sun is found to have a secular trend: it decreased from the year of 1874 to 1950s, and since then the Sun is rotating more and more speedily in the long run. The rotation period appears around the maximum times of the Schwabe cycles with statistical significance, but in the minimum times it is always statistically insignificant, although it is found to have no relation with the Schwabe cycle. The period length of the rotation cycle displays the significant periods of 2.61 and 5.77 years.     

Period variations in BZ Eridani

The O-C diagram of BZ Eri has been presented for the first time, and the period variations present in the system have been analysed. In all, eight period decreases and eight period increases are noticed. Of these, four period decreases and seven period increases are appreciable. The strongest period changes are noticed in the interval 1960 to 1962. The total period change in different portions of the O-C diagram ranges from 1.17×10^–3 d to 3.96×10^–6 d. The trend of the period variation appears to have reversed around the year 1980.     

A new period and period trend of IZ Persei

A new period (P=3^d.687664) of the eclipsing binary system IZ Persei is given, based on 16 observed times of the minima. O–C diagrams of IZ Per have been presented for the first time, and the period variations have been estimated in different portions of the O–C diagram. Significant period changes do not appear to have occurred in IZ Per. The O–C diagrams suggest that the period of the system is continuously increasing at a rate of 25^s yr^–1. Period variations of the order of 10^–5 d appear to have occurred around the years 1969, 1972, and 1978. The period increases are stronger than the period decreases; but these are yet to be confirmed. The overall picture of IZ Per suggests that strong period changes are not present in the system; however, slow increase of period is apparent in IZ Per. The total period change (3×10^–6 d) till the last epoch is in agreement with the newly derived period of IZ Per.     

Period changes in EI Cephei

A new period (P=8^d.439422) of the eclipsing binary system EI Cephei has been given, which is based on all available times of minima. Periods using Strohmeier's (1958) epoch have also been presented for the observations given by other investigators. Period based on only photoelectric minima comes out to be 8^d.439336, which is lesser than the earlier periods given in the literature. O-C diagrams of EI Cephei have been presented for the first time, and period variations have been estimated in different portions of the O-C diagram (Figure 2) of EI Cephei. Strong period changes have occurred around the years 1959 and 1965. The total change in period (P/P) ranges from 6.7×10^–5 to 4.3×10^–4. Thus, P of the order of 10^–3 d are present, which fact suggests that strong period variations are present in EI Cephei. However, periods given by various investigators show no systematic trend of period variations. The existence of a third body in the system could not be confirmed.