Evolution of motion of two viscoelastic planets in the field of forces of their mutual attraction

Translational-rotational motion of two viscoelastic planets in a gravitational force field is studied. The planets are modeled by homogeneous isotropic viscoelastic bodies. In their natural undeformed state each of the planets represents a sphere. We investigate a specific case when the planet’s centers of mass move in a fixed plane, the axis of rotation for each planet being directed along the normal to this plane. An equation describing the evolution of a slow angular variable (perihelion longitude) is derived. The observed displacement of the perihelion of Mercury is compared with the results obtained in the considered model problem about motion of two viscoelastic planets. Quite important is the fact that the planet of smaller mass (Mercury) moves not in a central Newtonian field of forces, but rather in the gravitational field of a rotating viscoelastic planet (Sun).     

On the Precession of Saturn

The precession of Saturn under the effect of the gravity of the Sun, Jupiter and planet’s satellites has been investigated. Saturn is considered to be an axisymmetric (A = B) solid body close to the dynamically spherical one. The orbits of Saturn and Jupiter are considered to be Keplerian ellipses in the inertial coordinate system. It has been shown that the entire set of small parameters of the problem can be reduced to two independent parameters. The averaged Hamiltonian function of the problem and the integrals of evolutionary equations are obtained disregarding the effect of satellites. Using the small parameter method, the expressions for the precession frequency and the nutation angle of the planet’s axis of rotation caused by the gravity of the Sun and Jupiter are obtained. Considering the planet with satellites as a whole preceding around the normal to the unmovable plane of Saturn’s orbit, the satellites effect on the Saturn rotation is taken into account via the corrections in the formula for the undisturbed precession frequency. The satellites are shown to have no effect on the nutation angle (in the framework of the accepted model), and the disturbances from Jupiter to make the main contribution to the nutation angle evolution. The effect of Jupiter on the nutation angle and the precession period is described with regard to the attraction of satellites.     

Habitable zone limits for dry planets

Most discussion of habitable planets has focused on Earth-like planets with globally abundant liquid water. For an "aqua planet" like Earth, the surface freezes if far from its sun, and the water vapor greenhouse effect runs away if too close. Here we show that "land planets" (desert worlds with limited surface water) have wider habitable zones than aqua planets. For planets at the inner edge of the habitable zone, a land planet has two advantages over an aqua planet: (i) the tropics can emit longwave radiation at rates above the traditional runaway limit because the air is unsaturated and (ii) the dry air creates a dry stratosphere that limits hydrogen escape. At the outer limits of the habitable zone, the land planet better resists global freezing because there is less water for clouds, snow, and ice. Here we describe a series of numerical experiments using a simple three-dimensional global climate model for Earth-sized planets. Other things (CO(2), rotation rate, surface pressure) unchanged, we found that liquid water remains stable at the poles of a low-obliquity land planet until net insolation exceeds 415 W/m(2) (170% that of modern Earth), compared to 330 W/m(2) (135%) for the aqua planet. At the outer limits, we found that a low-obliquity land planet freezes at 77%, while the aqua planet freezes at 90%. High-obliquity land and aqua planets freeze at 58% and 72%, respectively, with the poles offering the last refuge. We show that it is possible that, as the Sun brightens, an aqua planet like Earth can lose most of its hydrogen and become a land planet without first passing through a sterilizing runaway greenhouse. It is possible that Venus was a habitable land planet as recently as 1 billion years ago.     

An estimate of the prevalence of biocompatible and habitable planets

A Monte Carlo computer model of extra-solar planetary formation and evolution, which includes the planetary geochemical carbon cycle, is presented. The results of a run of one million galactic disc stars are shown where the aim was to assess the possible abundance of both biocompatible and habitable planets. (Biocompatible planets are defined as worlds where the long-term presence of surface liquid water provides environmental conditions suitable for the origin and evolution of life. Habitable planets are those worlds with more specifically Earthlike conditions). The model gives an estimate of 1 biocompatible planet per 39 stars, with the subset of habitable planets being much rarer at 1 such planet per 413 stars. The nearest biocompatible planet may thus lie approximately 14 LY distant and the nearest habitable planet approximately 31 LY away. If planets form in multiple star systems then the above planet/star ratios may be more than doubled. By applying the results to stars in the solar neighbourhood, it is possible to identify 28 stars at distances of < 22 LY with a non-zero probability of possessing a biocompatible planet.     

Cosmic ray impact on extrasolar earth-like planets in close-in habitable zones

Because of their different origins, cosmic rays can be subdivided into galactic cosmic rays and solar/stellar cosmic rays. The flux of cosmic rays to planetary surfaces is mainly determined by two planetary parameters: the atmospheric density and the strength of the internal magnetic moment. If a planet exhibits an extended magnetosphere, its surface will be protected from high-energy cosmic ray particles. We show that close-in extrasolar planets in the habitable zone of M stars are synchronously rotating with their host star because of the tidal interaction. For gravitationally locked planets the rotation period is equal to the orbital period, which is much longer than the rotation period expected for planets not subject to tidal locking. This results in a relatively small magnetic moment. We found that an Earth-like extrasolar planet, tidally locked in an orbit of 0.2 AU around an M star of 0.5 solar masses, has a rotation rate of 2% of that of the Earth. This results in a magnetic moment of less than 15% of the Earth's current magnetic moment. Therefore, close-in extrasolar planets seem not to be protected by extended Earth-like magnetospheres, and cosmic rays can reach almost the whole surface area of the upper atmosphere. Primary cosmic ray particles that interact with the atmosphere generate secondary energetic particles, a so-called cosmic ray shower. Some of the secondary particles can reach the surface of terrestrial planets when the surface pressure of the atmosphere is on the order of 1 bar or less. We propose that, depending on atmospheric pressure, biological systems on the surface of Earth-like extrasolar planets at close-in orbital distances can be strongly influenced by secondary cosmic rays.     

Pervasive orbital eccentricities dictate the habitability of extrasolar earths

The long-term habitability of Earth-like planets requires low orbital eccentricities. A secular perturbation from a distant stellar companion is a very important mechanism in exciting planetary eccentricities, as many of the extrasolar planetary systems are associated with stellar companions. Although the orbital evolution of an Earth-like planet in a stellar binary system is well understood, the effect of a binary perturbation on a more realistic system containing additional gas-giant planets has been very little studied. Here, we provide analytic criteria confirmed by a large ensemble of numerical integrations that identify the initial orbital parameters leading to eccentric orbits. We show that an extrasolar earth is likely to experience a broad range of orbital evolution dictated by the location of a gas-giant planet, which necessitates more focused studies on the effect of eccentricity on the potential for life.     

Tides and the evolution of planetary habitability

Tides raised on a planet by the gravity of its host star can reduce the planet's orbital semi-major axis and eccentricity. This effect is only relevant for planets orbiting very close to their host stars. The habitable zones of low-mass stars are also close in, and tides can alter the orbits of planets in these locations. We calculate the tidal evolution of hypothetical terrestrial planets around low-mass stars and show that tides can evolve planets past the inner edge of the habitable zone, sometimes in less than 1 billion years. This migration requires large eccentricities (>0.5) and low-mass stars ( less or similar to 0.35 M(circle)). Such migration may have important implications for the evolution of the atmosphere, internal heating, and the Gaia hypothesis. Similarly, a planet that is detected interior to the habitable zone could have been habitable in the past. We consider the past habitability of the recently discovered, approximately 5 M(circle) planet, Gliese 581 c. We find that it could have been habitable for reasonable choices of orbital and physical properties as recently as 2 Gyr ago. However, when constraints derived from the additional companions are included, most parameter choices that indicate past habitability require the two inner planets of the system to have crossed their mutual 3:1 mean motion resonance. As this crossing would likely have resulted in resonance capture, which is not observed, we conclude that Gl 581 c was probably never habitable.     

Taxonomy of the extrasolar planet

When a star is described as a spectral class G2V, we know that the star is similar to our Sun. We know its approximate mass, temperature, age, and size. When working with an extrasolar planet database, it is very useful to have a taxonomy scale (classification) such as, for example, the Harvard classification for stars. The taxonomy has to be easily interpreted and present the most relevant information about extrasolar planets. I propose an extrasolar planet taxonomy scale with four parameters. The first parameter concerns the mass of an extrasolar planet in the form of units of the mass of other known planets, where M represents the mass of Mercury, E that of Earth, N Neptune, and J Jupiter. The second parameter is the planet's distance from its parent star (semimajor axis) described in a logarithm with base 10. The third parameter is the mean Dyson temperature of the extrasolar planet, for which I established four main temperature classes: F represents the Freezing class, W the Water class, G the Gaseous class, and R the Roasters class. I devised one additional class, however: P, the Pulsar class, which concerns extrasolar planets orbiting pulsar stars. The fourth parameter is eccentricity. If the attributes of the surface of the extrasolar planet are known, we are able to establish this additional parameter where t represents a terrestrial planet, g a gaseous planet, and i an ice planet. According to this taxonomy scale, for example, Earth is 1E0W0t, Neptune is 1N1.5F0i, and extrasolar planet 55 Cnc e is 9E-1.8R1.     

Theory of longitude librations of mercury based on the ground radar observations

On the basis of the analytic theory of longitude libration of Mercury (in the elliptical orbit) and the data of determination of values of the angular velocity of Mercury rotation obtained using high-precision complex method of ground radar tracking, the amplitude, phase, and period of free libration and amplitudes of five fundamental harmonics (annual, semi-annual, third annual, …) of forced librations in longitude of the planet are determined.     

Anthropic selection for the Moon's mass

This paper investigates whether anthropic selection explains the unusually large size of our Moon. It is shown that obliquity stability of the Earth is possible across a wide range of different starting conditions for the Earth-Moon system. However, the lunar mass and angular momentum from the actual Earth-Moon system are remarkable in that they very nearly produce an unstable obliquity. This may be because the particular properties of our Earth-Moon system simultaneously allow a stable obliquity and a slow rotation rate. A slow rotation rate may have been anthropically selected because it minimizes the equator-pole temperature difference, thus minimizing climatic fluctuations. The great merit of this idea is that it can be tested using extrasolar planet search programs planned for the near future. If correct, such anthropic selection predicts that most extrasolar planetary systems will have significantly larger perturbation frequencies than our own Solar System.     

A Celestial Mechanics Model of Oscillations of the Poles of a Deformable Earth

The problem of Chandler motion of the Earth's poles is studied in the context of the model of a viscoelastic body. The Earth-Moon system is considered as a binary planet rotating around their barycenter. Numerical values of the period and amplitudes of oscillations of the poles are obtained by estimating the elastic deformation of the Earth and the variation of its inertia tensor, and they agree well with observational data. An evolution model of the Earth-Moon-Sun system is constructed by taking into account tidal forces of dissipation character. By means of the method of averaging, the qualitative properties of motion on asymptotically large intervals of time (comparable and essentially longer than the period of precession of the Earth's axis) are established and commented on.     

A Qualitative Calculus for Three-Dimensional Rotations

We have developed a qualitative calculus for three-dimensional directions and rotations. A direction is characterized in terms of the signs of its components relative to an absolute coordinate system. A rotation is characterized in terms of the signs of the components of the associated 3 × 3 rotation matrix.

A system has been implemented that can solve the following problems: 1. Given the signs of direction and rotation matrix P, find the possible signs of the image of under P. Moreover, for each possible sign vector of · P, generate numerical instantiations of and P that yields that result.

2. Given the signs of rotation matrices P and Q, find the possible signs of the composition P · Q. Moreover, for each possible sign matrix for the composition, generate numerical instantiations of P and Q that yield that result.

We have also proved some related complexity and expressivity results. The satisfiability problem for a qualitative rotation constraint network is NP-complete in two dimensions and NP-hard in three dimensions. In three dimensions, any two directions are distinguishable by a qualitative rotation constraint network.     

Evolution of Motion of a Binary Planet

A model of a binary planet, consisting of a material point of small mass and a deformable viscoelastic sphere, is suggested. The center of mass of the binary planet moves in the gravitational field of a central body in the plane, which contains planets forming the binary planet. A deformable spherical planet rotates around the axis orthogonal to the plane of planetary motion. Planet deformations are described by the linear theory of viscoelasticity. It is shown that with an appropriate approximation of the gravitational potential, there is a class of quasicircular orbits, when the eccentricities of an orbit of the center of mass of a binary planet and an orbit, describing mutual planet motion, are equal to zero. The further evolution of motion is investigated in this class of orbits with the use of the canonical Poincare–Andoyer variables. Corresponding averaged equations are found, and phase pictures are constructed; the stability of stationary solutions is investigated on the basis of equations in variations. For the Solar system planets with their satellites, forming binary planets, the application of the presented model allows us to conclude that satellites sooner or later will fall on the corresponding planets.     

Distortions of rectangular pulse with linear frequency modulation during trans-ionospheric sounding of the Martian surface

Specific features of propagation of a wideband rectangular pulse along the route spacecraft-Martian surface-spacecraft caused by the influence of the planetary ionosphere are considered as applied to the problem of radio pulse sounding of the subsurface Martian soil from the Mars-Express satellite. The night Martian ionosphere considerably reduces the energy of the pulse, but does not lead to degradation of its envelope or uncertainty function. When sounding a two-layer surface, the influence of the ionosphere is also manifested in limitation from below of the thickness of the upper layer accessible for measurement, which is more essential than when sounding with the use of a wideband Gaussian pulse. It is demonstrated that the surface sounding is possible through the dayside planet ionosphere at the parameters of operating pulse of the MARSIS radar.     

What makes a planet habitable, and how to search for habitable planets in other solar systems

The availability of liquid water is the most important factor that makes a planet habitable, because water is a very effective polar molecule and hence an excellent solvent and facilitator for the complex chemistry of life. Its presence presupposes a planet with a significant mass that guarantees the presence of a substantial atmosphere, and a reasonable spinning rate to avoid overheating. It also implies that the planet is at moderate distances from its central star, a range that is called the Ecosphere or the Habitable Zone. Since the evolution of life to high intelligence seems to take billions of years, it requires also that the central star must be neither too massive, that will produce a lot of lethal UV radiation and will have too short a life-span to allow life to evolve, nor of very small mass which will be producing too feeble a radiation to sustain life. The detection of free Oxygen in the atmosphere of a planet is a very strong evidence for the presence of life, because Oxygen is highly reactive and would rapidly disappear by combining with other elements, unless it is continuously replenished by life as the by-product of the process of photosynthesis that builds food for life (sugars) from CO2 and H2O.     

Translational–Rotational Motion of a Viscoelastic Sphere in Gravitational Field of an Attracting Center and a Satellite

We study the translational–rotational motion of a planet modeled by a viscoelastic sphere in the gravitational fields of an immovable attracting center and a satellite modeled as material points. The satellite and the planet move with respect to their common center of mass that, in turn, moves with respect to the attracting center. The exact system of equations of motion of the considered mechanical system is deduced from the D'Alembert–Lagrange variational principle. The method of separation of motions is applied to the obtained system of equations and an approximate system of ordinary differential equations is deduced which describes the translational–rotational motion of the planet and its satellite, taking into account the perturbations caused by elasticity and dissipation. An analysis of the deformed state of the viscoelastic planet under the action of gravitational forces and forces of inertia is carried out. It is demonstrated that in the steady-state motion, when energy dissipation vanishes, the planet's center of mass and the satellite move along circular orbits with respect to the attracting center, being located on a single line with it. The viscoelastic planet in its steady-state motion is immovable in the orbital frame of reference. It is demonstrated that this steady-state motion is unstable.     

M stars as targets for terrestrial exoplanet searches and biosignature detection

The changing view of planets orbiting low mass stars, M stars, as potentially hospitable worlds for life and its remote detection was motivated by several factors, including the demonstration of viable atmospheres and oceans on tidally locked planets, normal incidence of dust disks, including debris disks, detection of planets with masses in the 5-20 M() range, and predictions of unusually strong spectral biosignatures. We present a critical discussion of M star properties that are relevant for the long- and short-term thermal, dynamical, geological, and environmental stability of conventional liquid water habitable zone (HZ) M star planets, and the advantages and disadvantages of M stars as targets in searches for terrestrial HZ planets using various detection techniques. Biological viability seems supported by unmatched very long-term stability conferred by tidal locking, small HZ size, an apparent short-fall of gas giant planet perturbers, immunity to large astrosphere compressions, and several other factors, assuming incidence and evolutionary rate of life benefit from lack of variability. Tectonic regulation of climate and dynamo generation of a protective magnetic field, especially for a planet in synchronous rotation, are important unresolved questions that must await improved geodynamic models, though they both probably impose constraints on the planet mass. M star HZ terrestrial planets must survive a number of early trials in order to enjoy their many Gyr of stability. Their formation may be jeopardized by an insufficient initial disk supply of solids, resulting in the formation of objects too small and/or dry for habitability. The small empirical gas giant fraction for M stars reduces the risk of formation suppression or orbit disruption from either migrating or nonmigrating giant planets, but effects of perturbations from lower mass planets in these systems are uncertain. During the first approximately 1 Gyr, atmospheric retention is at peril because of intense and frequent stellar flares and sporadic energetic particle events, and impact erosion, both enhanced, the former dramatically, for M star HZ semimajor axes. Loss of atmosphere by interactions with energetic particles is likely unless the planetary magnetic moment is sufficiently large. For the smallest stellar masses a period of high planetary surface temperature, while the parent star approaches the main sequence, must be endured. The formation and retention of a thick atmosphere and a strong magnetic field as buffers for a sufficiently massive planet emerge as prerequisites for an M star planet to enter a long period of stability with its habitability intact. However, the star will then be subjected to short-term fluctuations with consequences including frequent unpredictable variation in atmospheric chemistry and surficial radiation field. After a review of evidence concerning disks and planets associated with M stars, we evaluate M stars as targets for future HZ planet search programs. Strong advantages of M stars for most approaches to HZ detection are offset by their faintness, leading to severe constraints due to accessible sample size, stellar crowding (transits), or angular size of the HZ (direct imaging). Gravitational lensing is unlikely to detect HZ M star planets because the HZ size decreases with mass faster than the Einstein ring size to which the method is sensitive. M star Earth-twin planets are predicted to exhibit surprisingly strong bands of nitrous oxide, methyl chloride, and methane, and work on signatures for other climate categories is summarized. The rest of the paper is devoted to an examination of evidence and implications of the unusual radiation and particle environments for atmospheric chemistry and surface radiation doses, and is summarized in the Synopsis. We conclude that attempts at remote sensing of biosignatures and nonbiological markers from M star planets are important, not as tests of any quantitative theories or rational arguments, but instead because they offer an inspection of the residues from a Gyr-long biochemistry experiment in the presence of extreme environmental fluctuations. A detection or repeated nondetections could provide a unique opportunity to partially answer a fundamental and recurrent question about the relation between stability and complexity, one that is not addressed by remote detection from a planet orbiting a solar-like star, and can only be studied on Earth using restricted microbial systems in serial evolution experiments or in artificial life simulations. This proposal requires a planet that has retained its atmosphere and a water supply. The discussion given here suggests that observations of M star exoplanets can decide this latter question with only slight modifications to plans already in place for direct imaging terrestrial exoplanet missions.     

Uncontrollable Rotational Motion of the Mir Orbital Station

The results of determining the rotational motion of the Mir orbital station are presented for four long segments of its unmanned uncontrolled flight in 1999–2000. The determination was carried out using the data of onboard measurements of the Earth's magnetic field intensity. These data, taken for a time interval of several hours, were jointly processed by the least squares method with the help of integration of the equations of station motion relative to its center of mass. As a result of this processing, the initial conditions of motion and the parameters of the mathematical model used were evaluated. The technique of processing is verified using the telemetry data on angular velocity of the station and its attitude parameters. Two types of motion were applied on the investigated segments. One of them (three segments) presents a rotation around the axis of the minimum moment of inertia. This axis executes small oscillations with respect to a normal to the orbit plane. Such a motion was used for the first time on domestic manned orbital complexes. The second type of motion begins with a biaxial rotation which, in a few weeks, goes over into a motion very similar to the rotation around the normal to the orbit plane, but around the axis of the maximum moment of inertia.     

Did evolution select a nonrandom "alphabet" of amino acids?

The last universal common ancestor of contemporary biology (LUCA) used a precise set of 20 amino acids as a standard alphabet with which to build genetically encoded protein polymers. Considerable evidence indicates that some of these amino acids were present through nonbiological syntheses prior to the origin of life, while the rest evolved as inventions of early metabolism. However, the same evidence indicates that many alternatives were also available, which highlights the question: what factors led biological evolution on our planet to define its standard alphabet? One possibility is that natural selection favored a set of amino acids that exhibits clear, nonrandom properties-a set of especially useful building blocks. However, previous analysis that tested whether the standard alphabet comprises amino acids with unusually high variance in size, charge, and hydrophobicity (properties that govern what protein structures and functions can be constructed) failed to clearly distinguish evolution's choice from a sample of randomly chosen alternatives. Here, we demonstrate unambiguous support for a refined hypothesis: that an optimal set of amino acids would spread evenly across a broad range of values for each fundamental property. Specifically, we show that the standard set of 20 amino acids represents the possible spectra of size, charge, and hydrophobicity more broadly and more evenly than can be explained by chance alone.     

Circumstellar habitable zones: an overview

We review aspects of circumstellar habitable zones based on results reported at the First International Conference on Circumstellar Habitable Zones (held in 1994 at NASA Ames Research Center). Recent advances in atmospheric radiative transfer modeling have shown that circumstellar habitable zones are wider than previously thought. New considerations may allow a much shorter time scale both for the origin as well as the evolution of biological forms. The most abundant M dwarf stars, contrary to previous views, appear to be able to support the necessary conditions for a habitable zone around them. New planet formation models indicate that at least one planet should form within the circumstellar habitable zone of single dwarf stars regardless of mass. Biogenic materials also appear to be widespread and delivery to terrestrial planets via cometary impacts may be a viable mechanism. Finally, biology will modify a planet and provide positive feedback, in general, to increase the habitability of a planet. Overall, new astronomical, planetary, and biological considerations each seem to indicate that habitable zones around other stars may be both more widespread and more stable than previous research had indicated.