Newtonian cosmology with a varying gravitational constant

Newtonian cosmology is developed with the assumption that the gravitational constantG diminishes with time. The functional form adopted forG(t), a modification of a suggestion of Dirac, isG=A(k+t) ^–1, wheret is the age of the Universe and a small constantk is inserted to avoid a singularity in the two-body problem. IfR is the scale factor, normalized to unity at an epoch time , the differential equation is then . Here ₀ is the mean density at the epoch time. With the above form forG(t), the solution is reducible to quadratures.The scale factorR either increases indefinitely or has one and only one maximum. LetH ₀ be the present value of Hubble's constant /R and _0c the minimum density for a maximum ofR, i.e., for closure of the Universe. The conditions for a maximum lead to a boundary curve of _0c versusH ₀ and the numbers indicate strongly that thisG-variable Newtonian model corresponds to an open universe. An upward estimate of the age of the Universe from 10¹⁰ yr to five times such a value would still lead to the same conclusion.The present Newtonian cosmology appears to refute the statement, sometimes made, that the Dirac model forG necessarily leads to the conclusion that the age of the Universe is one-third the Hubble time. Appendix B treats this point, explaining that this incorrect conclusion arises from using all the assumptions in Dirac (1938). The present paper uses only Dirac's final result, viz,G(k+t)^–1, superposing it on the differential equation .     

A relation in families of periodic solutions

We show the existence of a general relation between the parameters of periodic solutions in dynamical systems with ignorable coordinates. In particular, for time-independent systems with an axis of symmetry, the relation takes the form T/A=–/E, whereT is the period,A is the angular momentum, is the angle through which the system has rotated after one period, andE is the energy.     

The north-south distribution of major solar flare events,sunspot magnetic classes and sunspot areas (1955–1974)

The north-south incidence has been studied of 31 white-light flares observed since 1859 and of 1669 events meeting the criteria for major flares of Dodson and Hedeman (1971) for the period 1955–1974. The asymmetry in favor of the northern hemisphere increases strikingly with the importance of the events. Similarly, magnetically complex sunspot groups (Mt. Wilson classes, and) display a more pronounced asymmetry in favor of the north than non-complex groups for 1962–1970. Contrary to the flare asymmetry, the spottedness asymmetry is independent of the size of sunspots.     

On the difference in darkness between sunspots

The effects of the magnetic field as well as the velocity field on sunspot equilibrium are discussed. The gas pressure difference, P, between a spot and the environments in the same horizontal layer is primarily determined by the magnetic field. Using recent model atmospheres we find that P shows a maximum value, P _max, at a depth of 650 ± 150 km below the photosphere. The value of P _max suggests that the curvature of the field lines is important for the equilibrium.It appears that, at an optical depth of unity in the umbra, the density has a value close to that of the environment at the same geometric depth (see Figure 4). If such is the case the expression for the umbra temperature (Equation (15)) may be considerably simplified (Equations (17) and (18)) and compared with observations.     

On the evolution of low mas binary systems

The evolution of parameters of close binary systems containing a red dwarf (with mass loss) and a condensed star is investigated. The mass loss from the system and asynchronism of the red dwarf rotation are taken into consideration. The calculations show that if the initial mass ratioq ₀2 then during 10⁷ yr the instability of mass loss process arises, and a bright X-ray source forms with luminosity close to the Eddington one. Ifq ₀>2 then during the mass loss phase the bright X-ray source arises twice. The models explain the existence of the forbidden interval of orbital periods and the absence of systems with periods less than 80 min.     

Observations of Cassiopeia A at 20 and 25 MHz with the uran-1 interferometer

The variation in elemental depletions seen in diffuse clouds in the interstellar medium is shown to be consistent with the exposure of grains to weak shocks. Shocks remove a weakly bound layer of amorphous oxide material from refractory cores. Depletions are shown to be the result of the incorporation of elements in refractory cores formed during equilibrium condensation in high temperature sources together with accretion under low (T1000K) temperature conditions. Evidence is presented for the high temperature condensation of CaAlTi grains. In addition to refractory CaAlTi particels, a refractory condensate containing 20% of available Mg, 60% of Si and 90% of Fe is inferred from data on depletions. An amorphous layer with a composition (2MgO) (SiO) condenses on these cores.     

The structure of a type-II supernova remnant G 160.5+2.8 (HB-9) observed at λ=12m

A two-dimensional brightness distribution of the old supernova remnant G 160.5+2.8 (HB-9) has been measured at a frequency of 25 MHz with the T-Shaped UTR-2 radio telescope, with the resolution 29×27. The source has a distinctly pronounced, almost spherical envelope. At the same time, individual features located near the internal boundary of the source are observable.Certain considerations are put forward to validate a suggestion that the brightest feature in the decameter range (maximum at=4^h55^m.3 and =46°.37) might be of an extragalactic origin.From structure considerations, the velocity of the pulsar PSR 0459+47 projected on HB-9 is estimated. The estimate does not contradict the hypothesis of Damasheket al. (1978) concerning a possible genetic relation between HB-9 and PSR 0459+47.     

Bifurcation points in close binary evolution: Medium-mass binaries

The remaining core hydrogen burning lifetime after case B of mass transfer of the secondary (mass gaining) component in a medium mass close binary star is estimated, for mediummass binaries with primaries in the mass range 5M to 9M . From the comparison of this quantity with the helium burning time-scale of the remnant primary a critical mass ratioq _c is derived such that for larger values ofq, mass transfer from the secondary towards the primary starts before the latter has evolved into a white dwarf. Consequences for the advanced stages of medium mass binaries are discussed.