Zel’dovich Λ and Weinberg’s relation: an explanation for the cosmological coincidences

In 1937 Dirac proposed the large number hypothesis (LNH). The idea was to explain that these numbers were large because the Universe is old. A time variation of certain “constants” was assumed. So far, no experimental evidence has significantly supported this time variation. Here we present a simplified cosmological model. We propose a new cosmological system of units, including a cosmological Planck’s constant that “absorbs” the well known large number 10¹²⁰. With this new Planck’s constant no large numbers appear at the cosmological level. They appear at lower levels, e.g. at the quantum world. We note here that Zel’dovich formula, for the cosmological constant Λ, is equivalent to the Weinberg’s relation. The immediate conclusion is that the speed of light c must be proportional to the Hubble parameter H, and therefore decrease with time. We find that the gravitational radius of the Universe and its size are one and the same constant (Mach’s principle). The usual cosmological Ω’s parameters for mass, lambda and curvature turn out to be all constants of order one. The anthropic principle is not necessary in this theory. It is shown that a factor of 10⁶¹ converts in this theory a Planck fluctuation (a quantum black hole) into a cosmological quantum black hole: the Universe today. General relativity and quantum mechanics give the same local solution of an expanding Universe with the law a(t)≈const?t. This constant is just the speed of light today. Then the Hubble parameter is exactly H=a(t)′/a(t)=1/t.     

Bicentennial decrease of the solar constant leads to the Earth’s unbalanced heat budget and deep climate cooling

Long-wave energy emitted by the Earth-atmosphere into space is characterized by changes in power over time that always lag behind the changes in power of the absorbed solar radiation due to slow variation in enthalpy of the Earth-atmosphere system. Long-term variation of the solar energy radiation absorbed by the Earth remains uncompensated by the energy radiated into space over the interval of time that is determined by the thermal inertia. The basic state of the climate system is when the debit and credit sides in the Earth’s global annual mean energy budget (including the air and water envelopes) are almost always unbalanced. The annual mean balance of the heat budget of the Earth-atmosphere over a long time period will reliably define the behavior and magnitude of the energy excess accumulated by the Earth or energy deficit to allow us to determine adequately and to predict beforehand the trend and amplitude of the forthcoming climate change using the prognosis of variations in the total solar irradiance (solar constant). The decrease in solar constant has been observed since the early 1990s. The Earth as a planet will have a negative balance in the energy budget in the future as well, because the Sun is entering the decline phase of the bicentennial luminosity changes. This will lead to a drop in temperature in approximately 2014. The increase in albedo and decrease in greenhouse gas concentration in the atmosphere will result in the additional decrease in absorbed portion of the solar energy and reduced greenhouse effect. The additional drop in temperature exceeding the effect of decreased solar constant can occur as a result of successive feedback effects. A deep bicentennial minimum in solar constant is to be anticipated in 2042 ± 11 and the 19th Little Ice Age (for the last 7500 years) may occur in 2055 ± 11.     

Zahn’s theory of dynamical tides and its application to stars

Zahn’s theory of dynamical tides is analyzed critically. We compare the results of this theory with our numerical calculations for stars with a convective core and a radiative envelope and with masses of one and a half and two solar masses. We show that for a binary system consisting of stars of one and a half or two solar masses and a point object with a mass equal to the solar mass and with an orbital period of one day under the assumption of a dense spectrum and moderately rapid dissipation, the evolution time scales of the semimajor axis will be shorter than those in Zahn’s theory by several orders of magnitude.     

Mach’s principle and Yukawa-like corrections to the Newtonian potential as a bound for the mean energy density of the universe

The (Newton + Yukawa)-type gravitational potential V(r)=?(γ M/r)[1+Aexp?(?r/B)](γ= the gravitational constant as measured at infinity, M= the mass of the source, A, B are constants) is considered in the framework of the Sciama linear approach to Mach’s principle. The coupling constant A of the Yukawa component is found to be related to the mass density and size of the observable (causally connected) universe.     

Polarization of GRB prompt emission and its application to POLAR’s data

Synchrotron emission polarization is very sensitive to the magnetic field configuration.Recently,polarization of synchrotron emission with a mixed(SM)magnetic field in the gamma-ray burst(GRB)afterglow phase has been developed.Here,we apply these SM models to the GRB prompt phase and compare their polarization properties with that of synchrotron emission in purely ordered(SO)magnetic field.We find that the polarization properties in an SM model are very similar to these in a corresponding SO model(e.g.,synchrotron emission in a mixed magnetic field with an aligned ordered part(SMA)and synchrotron emission with a purely ordered aligned magnetic field(SOA)),only with a lower polarization degree(PD).We also discuss the statistical properties of the models.We find PDs of the simulated bursts are concentrated around 25%for both SOA and synchrotron emission in a purely ordered toroidal magnetic field(SOT),while they can range from 0%to 25%for SMA and synchrotron emission in a mixed magnetic field with a toroidal ordered part(SMT),depending onξ_B value,i.e.,the ratio of magnetic reduction of the ordered magnetic field over that of random magnetic field.From statistics,if PDs of majority GRBs are non-zero,then it favors SO and SM models.Further,if there are some bright GRBs with prominently lower PDs than that of the majority GRBs,it favors SOT(SMT)models;if all the bright GRBs have comparable PDs with the majority ones,it favors SOA(SMA)models.Finally,we apply our results to POLAR’s data and find that~10%time-integrated PDs of the observed bursts favor SMA and SMT models,and theξ_B parameter of these bursts is constrained to be around 1.135.     

Changes in the Sun’s mass and gravitational constant estimated using modern observations of planets and spacecraft

More than 635 thousand positional observations of planets and spacecraft of various types (mostly radiotechnical ones, 1961–2010) were used to estimate possible changes in the gravitational constant, Sun’s mass, and semi-major axes of planetary orbits, as well as the associated value of the astronomical unit. The observations were analyzed based on the EPM2010 ephemerides constructed at the Institute of Applied Astronomy (Russian Academy of Sciences) in a post-Newtonian approximation as a result of simultanious numerical integration of the equations of motion of nine major planets, the Sun, the Moon, asteroids, and trans-Neptunian objects. The heliocentric gravitational constant GM _⊙ was found to vary with a rate of (GṀ _⊙/GM _⊙ = (−5.0 ± 4.1)) × 10⁻¹⁴ per year (at the 3σ level). The positive secular changes in the semimajor axes ȧ _i /a _i were found for Mercury, Venus, Mars, Jupiter, and Saturn provided by high-precision observations. These changes also correspond to the decrease in the heliocentric gravitational constant. The changing of GM _⊙, itself is probably caused by the loss of the mass M _⊙ of the Sun due to its radiation and solar wind; these effects are partly compensated by the material falling onto the Sun. Allowing for the maximum bounds on the possible change in the Sun’s mass M _⊙, it has been found from the change obtained in GM _⊙ that the annual change Ġ/G of the gravitational constant G falls within the interval −4.2 × 10⁻¹⁴ < ȧ/G < +7.5 × 10⁻¹⁴ with a 95% probability. The astronomical unit (AU) is connected by its definition only with the heliocentric gravitational constant. The decrease of GM _⊙ obtained in this paper should correspond to a secular decrease in the AU. It is shown, however, that the modern level of accuracy does not allow us to determine a change in the AU. The attained posibility of determining changes in GM _⊙ using high-accuracy observations encourages us to have a relation between GM _⊙ and the AU fixed for a certain moment in time, since it is inconvenient to have a time-dependent length for the AU.     

Dynamics of the Earth’s core from VLBI observations

The Earth’s rotation is accompanied by free circadian oscillations of its liquid core in the inner cavity of the lower mantle, which perturb the angular momentum of the entire Earth and produce an additional free nutation of the celestial pole called free core nutation (FCN). Since this nutation causes resonances in the diurnal tides and in the expansions of luni—solar nutation, its study, especially an improvement of the FCN period, is of fundamental importance for the theory of the Earth’s rotation. We have determined the FCN parameters from a joint analysis of equidistant series of coordinates of the celestial pole obtained from the combined processing of VLBI observations on global networks of stations for the interval 1984.0–2008.4 by IERS (International Earth Rotation and Reference System Service, Paris, France) and NEOS (National Earth Orientation Service, Washington, USA). Applying a moving least-squares filter (MLSF) to these data has shown that the FCN period averaged over this time interval differs significantly from the theoretical one and its phase varies over a wide range. Using the mean quadratic collocation (MQC) method, we have obtained a new, more accurate stochastic FCN model. Its analysis by the envelope method has revealed long-term linear phase trends, calling into question not only the adopted FCN period but also its stability and, hence, the stability of the resonant effects in the Earth’s luni—solar nutation.     

Optimizing expansions of the Earth’s gravity potential and its derivatives over ellipsoidal harmonics

A set of spherical harmonics is the most widely used representation of the Earth’s gravity potential. This series converges outside and on the surface of a reference sphere enveloping the Earth. However, the Earth’s surface is better approximated by the reference ellipsoid—a compressed ellipsoid of revolution that covers the entire Earth. The gravity potential can be expanded in a series over ellipsoidal harmonics on the surface of the reference ellipsoid and on the surface of other external confocal ellipsoids of revolution. In contrast to spherical harmonics, depending on the associated Legendre functions of the first kind, ellipsoidal harmonics depend also on the associated Legendre functions of the second kind. The latter contain the very slowly converging hypergeometric Gauss series. The number of series increases with increasing the order of their derivatives. In this work, we derived new series for the gravitational potential of the Earth and its derivatives over ellipsoidal harmonics. Starting from the first order derivative, all the series corresponding to higher order derivatives depend on the same two hypergeometric Gauss series. The latter converges considerably faster than that for the hypergeometric series previously used when computing the gravity potential and its derivatives.     

The seasonal variation of the newtonian constant of gravitation and its relationship with the “classical tests” of general relativity

The ratio between the Earth's perihelion advance (Δθ) _E and the solar gravitational red shift (GRS) (Δø _s e)a ₀/c ² has been rewritten using the assumption that the Newtonian constant of gravitationG varies seasonally and is given by the relationship, first found by Gasanalizade (1992b) for an aphelion-perihelion difference of (ΔG)_a?p . It is concluded that $$\begin{gathered} (\Delta \theta )_E = \frac{{3\pi }}{e}\frac{{(\Delta \phi _{sE} )_{A_0 } }}{{c^2 }}\frac{{(\Delta G)_{a - p} }}{{G_0 }} = 0.038388 \sec {\text{onds}} {\text{of}} {\text{arc}} {\text{per}} {\text{revolution,}} \hfill \\ \frac{{(\Delta G)_{a - p} }}{{G_0 }} = \frac{e}{{3\pi }}\frac{{(\Delta \theta )_E }}{{(\Delta \phi _{sE} )_{A_0 } /c^2 }} = 1.56116 \times 10^{ - 4} . \hfill \\ \end{gathered} $$ The results obtained here can be readily understood by using the Parametrized Post-Newtonian (PPN) formalism, which predicts an anisotropy in the “locally measured” value ofG, and without conflicting with the general relativity.     

Results of astrometric observations of Jupiter’s Galilean satellites at the Pulkovo Observatory from 1986 to 2005

The results of photographic observations of Jupiter’s Galilean satellites made with the 26-inch refractor at the Pulkovo Observatory from 1986 to 2005 are given. Satellite coordinates with respect to Jupiter and the mutual distances between the satellites have been determined. A scale-trale technique that does not require reference stars for the astrometric reduction of measurements has been used. The effect of the Jupiter phase has been taken into account in the jovicentric coordinates. The observation results have been compared with a modern theory of the Galilean satellites’ motions. Systematic observation errors depending on the observation technique have been studied. The intrinsic observation accuracy in the random quotient is characterized by the values 0.041″ over X and Y. The external accuracy of the relative Galilean satellite coordinates determined by comparing the observations with modern ephemerides turned out to be equal to 0.165″, 0.213″ for the Jovicentric coordinates and 0.134″, 0.170″ for the “satellite-satellite” coordinates. The highest accuracy of the relative satellite coordinates is reached at small distances between the satellites which are less than 100″: the corresponding mean-square errors of one observation are equal in to the external convergence to 0.050″, 0.070″. The results of photographic observations have been compared with the first CCD observations of the Jupiter satellites made in 2004 with the 26-inch refractor.     

Variable cosmological “constant” and motion of a test particle in a cloud of dust

We find that Einstein’s like field equations with coordinate-dependent cosmological “constant” Λ(x ⁱ ) imply a non geodesic law of motion for test particles moving in a continuous distribution of incoherent matter (“dust”). The deviation from the geodesic law depends on the derivatives ?Λ/? x ⁱ and, in the weak field approximation, causes an anomalous acceleration A～(Vc ²/γ ρ)?Λ/? t+(c ⁴/γ ρ)?Λ/? r where V=dr/dt, c=the speed of light, γ=8π G with G=the gravitational coupling, ρ=the mass density of the cloud, r and t are the radial and time coordinate respectively. Reasonable assumptions on Λ=Λ(t) give A<10^?8 cm/s² when ρ>10^?29 g/cm³ i.e. in all known astrophysical systems. A possible connection with the anomalous Pioneer acceleration is shortly discussed in the case of a cosmological “constant” coupled to matter.     

Solar Cycle Effects on the Dynamics of Jupiter’s and Saturn’s Magnetospheres

The giant planetary magnetospheres surrounding Jupiter and Saturn respond in quite different ways, compared to Earth, to changes in upstream solar wind conditions. Spacecraft have visited Jupiter and Saturn during both solar cycle minima and maxima. In this paper we explore the large-scale structure of the interplanetary magnetic field (IMF) upstream of Saturn and Jupiter as a function of solar cycle, deduced from solar wind observations by spacecraft and from models. We show the distributions of solar wind dynamic pressure and IMF azimuthal and meridional angles over the changing solar cycle conditions, detailing how they compare to Parker predictions and to our general understanding of expected heliospheric structure at 5 and 9 AU. We explore how Jupiter’s and Saturn’s magnetospheric dynamics respond to varying solar wind driving over a solar cycle under varying Mach number regimes, and consider how changing dayside coupling can have a direct effect on the nightside magnetospheric response. We also address how solar UV flux variability over a solar cycle influences the plasma and neutral tori in the inner magnetospheres of Jupiter and Saturn, and estimate the solar cycle effects on internally driven magnetospheric dynamics. We conclude by commenting on the effects of the solar cycle in the release of heavy ion plasma into the heliosphere, ultimately derived from the moons of Jupiter and Saturn.     

Possible experimental verification of Bellert’s cosmological red shift law using the Cosmic Microwave Background Radiation

The author presents a loose proposal of an experiment of measurements of the spectrum of the local black body thermal radiation of the quantum vacuum. The experiment may verify the Bellert’s and other theories about the nature of the cosmological red shift of electromagnetic waves and give a new interpretation of measurements of Cosmic Blackbody Radiation delivered by the satellite missions COBE and WMAP. Differently to the Big Bang theory, it is assumed that the quantum vacuum continuously generates thermal noise with the spectrum given by Planck’s law.     

Trials and tribulations of playing the devil’s advocate

Beginning with his student days at school and college, the author describes his training at Cambridge with special emphasis on his mentor Fred Hoyle. His early experience of participating in a controversy at Cambridge played a major role in giving him the confidence to defend his scientific ideas. All through his later life he chose areas that were not part of mainstream research. These included the steady state theory and later the quasi steady state cosmology, action at a distance, noncosmological redshifts, quantum conformal cosmology, etc. After being a founding member of the Institute of Theoretical Astronomy(IOTA) at Cambridge, the author joined the Tata Institute of Fundamental Research(TIFR) in Mumbai and later moved to Pune to set up the Inter-University Centre for Astronomy and Astrophysics(IUCAA). He briefly reviews his own work and ends by pointing out the difficulties a non-conformist scientist faces in his professional life. In the conclusion, he mentions his interests in science popularization and science fiction for which he has won awards and appreciation, including UNESCO’s Kalinga Prize.     

Optimization of the Return Trajectories from the Moon for Delivering Soil to a Specified Region on the Earth’s Surface

Solar System Research - The construction of the trajectories for spacecraft return from the Moon to the Earth for delivering lunar soil to the polygon specified by the corresponding geographical...     

Ambartsumian’s paradigm for the activity of galactic nuclei and the evolution of galaxies

Ambartsumian’s paradigm for the creation of galaxies owing to the decay of denser matter is examined. The roots of this concept can be found in the very earliest papers of Ambartsumian on quantum fields and the structure of atomic nuclei. In the early 1930’s his papers contained new ideas regarding the ejection by one physical object of another which had not originally existed inside the first. The basic observational data which served as the basis for the final formulation of the new concept are described. Special attention is devoted to those objects and phenomena, which, upon further study, have confirmed the validity of Ambartsumian’s reasoning and arguments. It is noted that the discovery of Hubble expansion’s acceleration of the universe opened up new possibilities for the interpretation of activity phenomena in terms of Ambartsumian’s concept. The further extension of this concept is discussed and it is suggested that the major result of this approach should be the proof of the existence of galaxies of all ages within a finite volume of space.     

Reversals of the Sun’s Polar Magnetic Fields in Relation to Activity Complexes and Coronal Holes

A spatiotemporal analysis of long-term measurements of the Sun’s magnetic field was carried out to study changes in its zonal structure and reversals of the polar fields in Cycles 21?–?24. A causal relationship between activity complexes, their remnant magnetic fields, and high-latitude magnetic fields has been demonstrated in the current cycle. The appearance of unipolar magnetic regions near the poles is largely determined by the decay of long-lived activity complexes. The nonuniform distribution of sunspot activity and its north–south asymmetry result in the asymmetry of remnant fields that are transported poleward due to meridional circulation. The asymmetry of high-latitude magnetic fields leads to an asynchrony of polar-field reversals in both hemispheres. The interaction of high-latitude unipolar magnetic regions with the polar fields affects the embedded coronal holes. The evolution of large-scale magnetic fields was also studied in a time–latitude aspect. It is shown that regular reversals of the Sun’s polar fields resulted from cyclic changes in high-latitude magnetic fields. A triple polarity reversal of the polar fields in Cycle 21 and short-term polarity alternations at the poles were interpreted taking into account the interaction of the remnant fields with the Sun’s polar fields.     

Ambartsumian’s invariance principle and some nonlinear relations in radiative transfer theory

This paper is devoted to one of the methods proposed by Ambartsumian in radiative transfer theory— the invariance principle. The possible connection of several well known nonlinear relations in the theory to a variational principle involving a translational transformation of the optical depth is discussed.     

The Recovery of CME-Related Dimmings and the ICME’s Enduring Magnetic Connection to the Sun

It is generally accepted that transient coronal holes (TCHs, dimmings) correspond to the magnetic footpoints of CMEs that remain rooted in the Sun as the CME expands out into the interplanetary space. However, the observation that the average intensity of the 12 May 1997 dimmings recover to their pre-eruption intensity in SOHO/EIT data within 48 hours, whilst suprathermal unidirectional electron heat fluxes are observed at 1 AU in the related ICME more than 70 hours after the eruption, leads us to question why and how the dimmings disappear whilst the magnetic connectivity is maintained. We also examine two other CME-related dimming events: 13 May 2005 and 6 July 2006. We study the morphology of the dimmings and how they recover. We find that, far from exhibiting a uniform intensity, dimmings observed in SOHO/EIT data have a deep central core and a more shallow extended dimming area. The dimmings recover not only by shrinking of their outer boundaries but also by internal brightenings. We quantitatively demonstrate that the model developed by Fisk and Schwadron (Astrophys. J. 560, 425, 2001) of interchange reconnections between “open” magnetic field and small coronal loops is a strong candidate for the mechanism facilitating the recovery of the dimmings. This process disperses the concentration of  “open” magnetic field (forming the dimming) out into the surrounding quiet Sun, thus recovering the intensity of the dimmings whilst still maintaining the magnetic connectivity to the Sun. Electronic Supplementary Material  The online version of this article () contains supplementary material, which is available to authorized users.     

High-Resolution Vector Magnetograms of the Sun’s Poles from Hinode: Flux Distributions and Global Coronal Modeling

The Sun’s polar fields play a leading role in structuring the large-scale solar atmosphere and in determining the interplanetary magnetic field. They are also believed to supply the seed field for the subsequent solar activity cycle. However, present-day synoptic observations do not have sufficient spatial resolution or sensitivity to diagnose accurately the high-latitude magnetic vector field. The high spatial resolution and sensitivity of the full-Stokes observations from the Hinode Solar Optical Telescope Spectro-Polarimeter, observing the poles long-term, allows us to build up a detailed picture of the Cycle 24 polar field reversal, including the changing latitude distribution of the high-latitude flux, and to study the effect on global coronal field models. The Hinode observations provide detailed information on the dominant facular-scale magnetic structure of the polar fields, and their field inclination and flux distribution. Hybrid synoptic magnetograms are constructed from Hinode polar measurements and full-disk magnetograms from the Synoptic Optical Long-term Investigations of the Sun (SOLIS) Vector Spectro-Magnetograph (VSM), and coronal potential field models are calculated. Loss of effective spatial resolution at the highest latitudes presents complications. Possible improvements to synoptic polar data are discussed.