The Vega project: A space mission to Venus and Halley’s comet

The launch of the Soviet space probes Vega 1 and Vega 2 to explore Venus, including its atmosphere, and flyby Halley??s comet, a rare guest in the inner Solar System, added a vivid page to the history of space exploration. This paper is dedicated to Designer General Vyacheslav M. Kovtunenko.     

The Dark UNiverse Explorer (DUNE): proposal to ESA’s cosmic vision

The Dark UNiverse Explorer (DUNE) is a wide-field space imager whose primary goal is the study of dark energy and dark matter with unprecedented precision. For this purpose, DUNE is optimised for the measurement of weak gravitational lensing but will also provide complementary measurements of baryonic accoustic oscillations, cluster counts and the Integrated Sachs Wolfe effect. Immediate auxiliary goals concern the evolution of galaxies, to be studied with unequalled statistical power, the detailed structure of the Milky Way and nearby galaxies, and the demographics of Earth-mass planets. DUNE is an Medium-class mission which makes use of readily available components, heritage from other missions, and synergy with ground based facilities to minimise cost and risks. The payload consists of a 1.2 m telescope with a combined visible/NIR field-of-view of 1 deg². DUNE will carry out an all-sky survey, ranging from 550 to 1600 nm, in one visible and three NIR bands which will form a unique legacy for astronomy. DUNE will yield major advances in a broad range of fields in astrophysics including fundamental cosmology, galaxy evolution, and extrasolar planet search. DUNE was recently selected by ESA as one of the mission concepts to be studied in its Cosmic Vision programme.

The past,present and future supernova threat to Earth’s biosphere

A brief review of the threat posed to Earth’s biosphere via near-by supernova detonations is presented. The expected radiation dosage, cosmic ray flux and expanding blast wave collision effects are considered, and it is argued that a typical supernova must be closer than ∼10-pc before any appreciable and potentially harmful atmosphere/biosphere effects are likely to occur. In contrast, the critical distance for Gamma-ray bursts is of order 1-kpc. In spite of the high energy effects potentially involved, the geological record provides no clear-cut evidence for any historic supernova induced mass extinctions and/or strong climate change episodes. This, however, is mostly a reflection of their being numerous possible (terrestrial and astronomical) forcing mechanisms acting upon the biosphere and the difficulty of distinguishing between competing scenarios. Key to resolving this situation, it is suggested, is the development of supernova specific extinction and climate change linked ecological models. Moving to the future, we estimate that over the remaining lifetime of the biosphere (∼2 Gyr) the Earth might experience 1 GRB and 20 supernova detonations within their respective harmful threat ranges. There are currently at least 12 potential pre-supernova systems within 1-kpc of the Sun. Of these systems IK Pegasi is the closest Type Ia pre-supernova candidate and Betelgeuse is the closest potential Type II supernova candidate. We review in some detail the past, present and future behavior of these two systems. Developing a detailed evolutionary model we find that IK Pegasi will likely not detonate until some 1.9 billion years hence, and that it affords absolutely no threat to Earth’s biosphere. Betelgeuse is the closest, reasonably well understood, pre-supernova candidate to the Sun at the present epoch, and may undergo detonation any time within the next several million years. The stand-off distance of Betelgeuse at the time of its detonation is estimated to fall between 150 and 300-pc—again, affording no possible threat to Earth’s biosphere. Temporally, the next most likely, close, potential Type Ic supernova to the Sun is the Wolf-Rayet star within the γ ² Velorum binary system located at least 260-pc away. It is suggested that evidence relating to large-scale astroengineering projects might fruitfully be looked for in those regions located within 10 to 30-pc of any pre-supernova candidate system.     

The Milky Way’s stellar disk

A suite of vast stellar surveys mapping the Milky Way, culminating in the Gaia mission, is revolutionizing the empirical information about the distribution and properties of stars in the Galactic stellar disk. We review and lay out what analysis and modeling machinery needs to be in place to test mechanism of disk galaxy evolution and to stringently constrain the Galactic gravitational potential, using such Galactic star-by-star measurements. We stress the crucial role of stellar survey selection functions in any such modeling; and we advocate the utility of viewing the Galactic stellar disk as made up of ‘mono-abundance populations’ (MAPs), both for dynamical modeling and for constraining the Milky Way’s evolutionary processes. We review recent work on the spatial and kinematical distribution of MAPs, and point out how further study of MAPs in the Gaia era should lead to a decisively clearer picture of the Milky Way’s dark-matter distribution and formation history.     

Sequential solution to Kepler’s equation

Seven sequential starter values for solving Kepler’s equation are proposed for fast orbit propagation. The proposed methods have constant complexity (not iterative), do not require pre-computed data, and can be implemented in just a few lines of code. The resulting sequential orbit propagation techniques can be done at different levels of accuracy and speed, depending essentially on the value of orbit eccentricity. Accuracy and algorithmic complexity are evaluated for all the proposed approaches and compared with several existing single-point techniques to solve Kepler’s equation. The new methods obtain improved accuracy at lower computational cost as compared to the best existing methods.     

Hubble’s Law Implies Benford’s Law for Distances to Galaxies

A recent article by Alexopoulos and Leontsinis presented empirical evidence that the first digits of the distances from the Earth to galaxies are a reasonably good fit to the probabilities predicted by Benford’s law, the well known logarithmic statistical distribution of significant digits. The purpose of the present article is to give a theoretical explanation, based on Hubble’s law and mathematical properties of Benford’s law, why galaxy distances might be expected to follow Benford’s law. The new galaxy-distance law derived here, which is robust with respect to change of scale and base, to additive and multiplicative computational or observational errors, and to variability of the Hubble constant in both time and space, predicts that conformity to Benford’s law will improve as more data on distances to galaxies becomes available. Conversely, with the logical derivation of this law presented here, the recent empirical observations may be viewed as independent evidence of the validity of Hubble’s law.     

Dynamic expansion points: an extension to Hadjidemetriou’s mapping method

Series expansions are widely used objects in perturbation theory in Celestial Mechanics and Physics in general. Their application nevertheless is limited due to the fact of convergence problems of the series on the one hand and constricted to regions in phase space, where small (expansion) parameters remain small on the other hand. In the mapping case, to overcome the latter problem, e.g., different expansion points are used to cover the whole phase space, resulting in a set of dynamical mappings for one dynamical system. In addition, the accuracy of such expansions depend not only on the order of truncation but also on the definition of the grid of the expansion points in phase space. A simple modification of the usual approach allows to increase the accuracy of the expanded mappings and to cover the whole phase space, where the series converge. Convergence problems due to the nonintegrability of the system can never be ruled out of the system, but the convergence of the series expansions in mapping models, which are convergent can be improved. The underlying idea is based on dynamic expansion points, which are the main subject of this article. As I will show it is possible to derive unique linear mappings, based on dynamically expanded generating functions, for the 3:1 resonance and the coupled standard map, which are valid in their whole phase spaces.     

Robe’s problem: its extension to 2+2 bodies

In the problem of 2+2 bodies in the Robe’s setup, one of the primaries of mass m^*₁m^{*}_{1} is a rigid spherical shell filled with a homogeneous incompressible fluid of density ρ ₁. The second primary is a mass point m ₂ outside the shell. The third and the fourth bodies (of mass m ₃ and m ₄ respectively) are small solid spheres of density ρ ₃ and ρ ₄ respectively inside the shell, with the assumption that the mass and the radius of third and fourth body are infinitesimal. We assume m ₂ is describing a circle around m^*₁m^{*}_{1}. The masses m ₃ and m ₄ mutually attract each other, do not influence the motion of m^*₁m^{*}_{1} and m ₂ but are influenced by them. We also assume masses m ₃ and m ₄ are moving in the plane of motion of mass m ₂. In the paper, the equations of motion, equilibrium solutions, linear stability of m ₃ and m ₄ are analyzed. There are four collinear equilibrium solutions for the given system. The collinear equilibrium solutions are unstable for all values of the mass parameters μ,μ ₃,μ ₄. There exist an infinite number of non collinear equilibrium solutions each for m ₃ and m ₄, lying on circles of radii λ,λ′ respectively (if the densities of m ₃ and m ₄ are different) and the centre at the second primary. These solutions are also unstable for all values of the parameters μ,μ ₃,μ ₄, φ, φ′. Such a model may be useful to study the motion of submarines due to the attraction of earth and moon.     

The brightening of Saturn’s F ring

Image photometry reveals that the F ring is approximately twice as bright during the Cassini tour as it was during the Voyager flybys of 1980 and 1981. It is also three times as wide and has a higher integrated optical depth. We have performed photometric measurements of more than 4800 images of Saturn’s F ring taken over a 5-year period with Cassini’s Narrow Angle Camera. We show that the ring is not optically thin in many observing geometries and apply a photometric model based on single-scattering in the presence of shadowing and obscuration, deriving a mean effective optical depth τ ≈ 0.033. Stellar occultation data from Voyager PPS and Cassini VIMS validate both the optical depth and the width measurements. In contrast to this decades-scale change, the baseline properties of the F ring have not changed significantly from 2004 to 2009. However, we have investigated one major, bright feature that appeared in the ring in late 2006. This transient feature increased the ring’s overall mean brightness by 84% and decayed with a half-life of 91 days.     

The Sun’s Strange Behavior: Maunder Minimum or Gleissberg Cycle?

During the last few years the Sun and solar wind have shown a behavior that was so unexpected that the phenomena was described as “the strange solar minimum”. It has been speculated that the 23/24 solar cycle minimum may have indicated the onset of a Maunder-Minimum-type Grand Minimum. Here we review what is known from 1500 years of proxy data about Maunder-type Grand Minima and the minima of the cyclic Centennial Gleissberg variations. We generate criteria that distinguish between the two types of event. Applying these criteria to the observed solar terrestrial data we conclude that the unexpected behavior began well before the solar cycle 23/24 minimum. The data do not support the Maunder Minimum conjecture. However, the behavior can be understood as a minimum of the Centennial Gleissberg Cycle that previously minimized in the beginning of the 20th century. We conclude that the Centennial Gleissberg Cycle is a persistent variation that has been present 80% of the time during the last 1500 years and should be explained by solar dynamo theory.     

The three-dimensional structure of Saturn’s E ring

Saturn’s diffuse E ring consists of many tiny (micron and sub-micron) grains of water ice distributed between the orbits of Mimas and Titan. Various gravitational and non-gravitational forces perturb these particles’ orbits, causing the ring’s local particle density to vary noticeably with distance from the planet, height above the ring-plane, hour angle and time. Using remote-sensing data obtained by the Cassini spacecraft in 2005 and 2006, we investigate the E-ring’s three-dimensional structure during a time when the Sun illuminated the rings from the south at high elevation angles (>15°). These observations show that the ring’s vertical thickness grows with distance from Enceladus’ orbit and its peak brightness density shifts from south to north of Saturn’s equator plane with increasing distance from the planet. These data also reveal a localized depletion in particle density near Saturn’s equatorial plane around Enceladus’ semi-major axis. Finally, variations are detected in the radial brightness profile and the vertical thickness of the ring as a function of longitude relative to the Sun. Possible physical mechanisms and processes that may be responsible for some of these structures include solar radiation pressure, variations in the ambient plasma, and electromagnetic perturbations associated with Saturn’s shadow.     

The effect of the Earth’s oblateness on the Moon’s physical libration in latitude

The Moon’s physical libration in latitude generated by gravitational forces caused by the Earth’s oblateness has been examined by a vector analytical method. Libration oscillations are described by a close set of five linear inhomogeneous differential equations, the dispersion equation has five roots, one of which is zero. A complete solution is obtained. It is revealed that the Earth’s oblateness: a) has little effect on the instantaneous axis of Moon’s rotation, but causes an oscillatory rotation of the body of the Moon with an amplitude of 0.072″ and pulsation period of 16.88 Julian years; b) causes small nutations of poles of the orbit and of the ecliptic along tight spirals, which occupy a disk with a cut in a center and with radius of 0.072″. Perturbations caused by the spherical Earth generate: a) physical librations in latitude with an amplitude of 34.275″; b) nutational motion for centers of small spiral nutations of orbit (ecliptic) pole over ellipses with semi-major axes of 113.850″ (85.158″) and the first pole rotates round the second one along a circle with radius of 28.691″; c) nutation of the Moon’s celestial pole over an ellipse with a semi-major axis of 45.04″ and with an axes ratio of about 0.004 with a period of T = 27.212 days. The principal ellipse’s axis is directed tangentially with respect to the precession circumference, along which the celestial pole moves nonuniformly nearly in one dimension. In contrast to the accepted concept, the latitude does not change while the Moon’s poles of rotation move. The dynamical reason for the inclination of the Moon’s mean equator with respect to the ecliptic is oblateness of the body of the Moon.     

The cyclical reversible transitions of the universe’s evolution

In this work we propose cyclical reversible transitions as the scenario in which the universe evolves, through a series consisting of reversible expansion, temporary stability, and contraction. Our model is based on the comparison between local and global time-dependent densities {ρ ₀(τ ₀),ρ(τ)} instead of the critical density ρ _c, local and global time-dependent Hubble parameters {H ₀(τ ₀),H(τ)}, and the variations {Δρ(τ),ΔH(τ)} due to cosmological chaotic fluctuations, which are generally ignored in certain oscillating models. By taking into account all these factors, a rate equation in the form of (H ₀/H)² ∝(ρ ₀/ρ) has been established, and from it we derive some others, to provide a mechanism that is responsible for the cyclical reversible transitions. Also, the problems of singularities, black hole overproduction, and the second law of thermodynamics arising in oscillating universe models are conceptually resolved.     

The growth of wind-waves in Titan’s hydrocarbon seas

Ocean wave growth on Titan is considered. The classic Sverdrup–Munk theory for terrestrial wave growth is applied to Titan, and is compared with a simple energy balance model that exposes the effect of Titan’s environmental parameters (air density, gravity, and fluid density). These approaches are compared with the only previously-published (semi-empirical) model (Ghafoor, N.A.-L., Zarnecki, J.C., Challenor, P., Srokosz, M.A. [2000] J. Geophys. Res. 105, 12,077–12,091, hereafter G2k), and allow the impact of various parameters such as atmospheric density to be transparently explored.Our model, like G2k, suggests fully-developed significant wave heights on Titan H_s = 0.2 U², where U is the windspeed (SI units): in dimensionless terms this is rather close to H_s = 0.2 U²/g, a rule of thumb previously noted for terrestrial waves (we find various datasets where the prefactor varies by ～2). It is noted that liquid and air densities affect the growth rate of waves, but not their fully-developed height: for 1 m/s winds wave amplitude reaches 0.15 m (75% of fully-developed) with a fetch of only 1 km, rather faster than predicted by G2k. Liquid viscosity has no major effect on gravity wave growth, but does influence the threshold windspeed at which gravity–capillary waves form in the first place.The model is used to develop predicted ranges for wave height to guide the design of the Titan Mare Explorer (TiME), a proposed Discovery-class mission to float a capsule on Ligeia Mare in 2023. For the expected maximum 1 m/s winds, a significant wave height of 0.2 m and wavelength of ～4 m can be expected. Assuming that wave heights follow Rayleigh statistics as they do on Earth, then given the wave period of ～4 s, individual waves of ～0.6 m might be encountered over a 3 month period.For predicted Titan winds at Kraken Mare, significant wave heights may reach ～0.6 m in the peak of summer but do not exceed the tidal amplitude at its northern end, consistent with the area around Mayda Insula being a tidal flat, while elsewhere on Kraken and Ligeia and at Ontario Lacus, shorelines may be wave- or tidally-dominated, depending on the specific location.