Limits on the Orbits of Possible Eccentric and Inclined Moons of Extrasolar Planets Orbiting Single Stars

Limits are placed on the range of orbits and masses of possible moons orbiting extrasolar planets which orbit single central stars. The Roche limiting radius determines how close the moon can approach the planet before tidal disruption occurs; while the Hill stability of the star–planet–moon system determines stable orbits of the moon around the planet. Here the full three-body Hill stability is derived for a system with the binary composed of the planet and moon moving on an inclined, elliptical orbit relative the central star. The approximation derived here in Eq. (17) assumes the binary mass is very small compared with the mass of the star and has not previously been applied to this problem and gives the criterion against disruption and component exchange in a closed form. This criterion was applied to transiting extrasolar planetary systems discovered since the last estimation of the critical separations (Donnison in Mon Not R Astron Soc 406:1918, 2010a) for a variety of planet/moon ratios including binary planets, with the moon moving on a circular orbit. The effects of eccentricity and inclination of the binary on the stability of the orbit of a moon is discussed and applied to the transiting extrasolar planets, assuming the same planet/moon ratios but with the moon moving with a variety of eccentricities and inclinations. For the non-zero values of the eccentricity of the moon, the critical separation distance decreased as the eccentricity increased in value. Similarly the critical separation decreased as the inclination increased. In both cases the changes though very small were significant.     

从云南最近三次强震看天体位置对地震的影响

本文详细分析了近期云南连续发生的三次强震与天体位置的关系。这三次大震都在期望期，又出现很多天文奇点，表明天体的引潮力影响也是这三次大震发震的重要因素。     

How common are Earth-Moon planetary systems?

The Earth’s comparatively massive moon, formed via a giant impact on the proto-Earth, has played an important role in the development of life on our planet, both in the history and strength of the ocean tides and in stabilizing the chaotic spin of our planet. Here we show that massive moons orbiting terrestrial planets are not rare. A large set of simulations by Morishima et al. (Morishima, R., Stadel, J., Moore, B. [2010]. Icarus. 207, 517-535), where Earth-like planets in the habitable zone form, provides the raw simulation data for our study. We use limits on the collision parameters that may guarantee the formation of a circumplanetary disk after a protoplanet collision that could form a satellite and study the collision history and the long term evolution of the satellites qualitatively. In addition, we estimate and quantify the uncertainties in each step of our study. We find that giant impacts with the required energy and orbital parameters for producing a binary planetary system do occur with more than 1 in 12 terrestrial planets hosting a massive moon, with a low-end estimate of 1 in 45 and a high-end estimate of 1 in 4.     

The precession and nutation of deformable bodies

The aim of the present paper will be to derive from the fundamental equations of hydrodynamics the explicit form of the Eulerian equations which govern the motion about the centre of gravity of self-gravitating bodies, consisting of compressible fluid of arbitrary viscosity, in an arbitrary external field of force. If the problem is particularized so that the external field of force represents the attaction of the sun and the moon, this motion would represent the luni-solar precession and nutation of a fluid viscous earth; if, on the other hand, the external field of force were governed by the earth (and the sun), the motion would define the physical librations of the moon regarded as a deformable body. The same equations are, moreover, equally applicable to the phenomena of precession and nutation of rotating fluid components in close binary systems, distorted by mutual tidal action; and the present paper contains the first formulation of the effects of viscosity on such phenomena.Investigation supported in part by the U.S. National Aeronautics and Space Administration under Contract No. NASW-1470.     

The motion of a lunar satellite

Presented in this theory is a semianalytical solution for the problem of the motion of a satellite in orbit around the moon. The principal perturbations on such a body are due to the nonspherical gravity field of the moon, the attraction of the earth, and, to a lesser degree, the attraction of the sun. The major part of the problem is solved by means of the celebrated von Zeipel Method, first successfully applied to the motion of an artificial earth satellite by Brouwer in 1959. After eliminating from the Hamiltonian all terms with the period of the satellite and those with the period of the moon, it is suggested to solve the remaining problem with the aid of numerical integration of the modified equations of motion.This theory was written in 1964 and presented as a dissertation to Yale University in 1965. Since then a great deal has been learned about the gravity field of the moon. It seems that quite a number of recently determined gravity coefficients would qualify as small quantities of order two. Hence, according to the truncation criteria employed, they should be considered in the present theory. However, the author has not endeavored to update the work accordingly. The final results, therefore, are incomplete in the lunar gravitational perturbations. Nevertheless, the theory does give the largest such variations and it does present the methods by which perturbations may be derived for any gravity terms not actually developed.     

What makes a planet habitable?

This work reviews factors which are important for the evolution of habitable Earth-like planets such as the effects of the host star dependent radiation and particle fluxes on the evolution of atmospheres and initial water inventories. We discuss the geodynamical and geophysical environments which are necessary for planets where plate tectonics remain active over geological time scales and for planets which evolve to one-plate planets. The discoveries of methane–ethane surface lakes on Saturn’s large moon Titan, subsurface water oceans or reservoirs inside the moons of Solar System gas giants such as Europa, Ganymede, Titan and Enceladus and more than 335 exoplanets, indicate that the classical definition of the habitable zone concept neglects more exotic habitats and may fail to be adequate for stars which are different from our Sun. A classification of four habitat types is proposed. Class I habitats represent bodies on which stellar and geophysical conditions allow Earth-analog planets to evolve so that complex multi-cellular life forms may originate. Class II habitats includes bodies on which life may evolve but due to stellar and geophysical conditions that are different from the class I habitats, the planets rather evolve toward Venus- or Mars-type worlds where complex life-forms may not develop. Class III habitats are planetary bodies where subsurface water oceans exist which interact directly with a silicate-rich core, while class IV habitats have liquid water layers between two ice layers, or liquids above ice. Furthermore, we discuss from the present viewpoint how life may have originated on early Earth, the possibilities that life may evolve on such Earth-like bodies and how future space missions may discover manifestations of extraterrestrial life.     

Emission of cyclotron radiation by interstellar planets

In the solar system all planets that have significant magnetic fields also emit electron cyclotron radiation, usually near the auroral regions around the magnetic poles. In this study we use scaling laws based on solar system data to estimate the power and frequency of the auroral cyclotron emissions from interstellar planets (or sub-brown dwarfs). The emission can be powered either by motion of the planet through the interstellar plasma or by unipolar induction due to a moon. According to our results, in interstellar space the unipolar induction mechanism is potentially more effective than the motional emission mechanism. Typical emission power is around 10¹⁰-10¹² W, but significantly stronger emissions are obtained in the most optimistic estimates. We have to conclude that detection of a rogue Jupiter would be very difficult, if not impossible with the radio telescopes available now or in the near future, but in very favorable conditions a much more massive and rapidly rotating (or otherwise strongly magnetized) gas giant with a large nearby moon could be detected up to ∼57 pc distance with the square kilometer array. There may be a few thousand large enough interstellar planets this close to the solar system. For reference, we point out that according to previous studies some known hot Jupiters are expected to emit up to 10¹⁴-10¹⁶ W of cyclotron radiation, orders of magnitude more than the typical interstellar planets discussed here. However, these emissions have not yet been detected.     

Deep versus shallow origin of gravity anomalies, topography and volcanism on Earth, Venus and Mars

The relation between gravity anomalies, topography and volcanism can yield important insights about the internal dynamics of planets. From the power spectra of gravity and topography on Earth, Venus and Mars we infer that gravity anomalies have likely predominantly sources below the lithosphere up to about spherical harmonic degree l=30 for Earth, 40 for Venus and 5 for Mars. To interpret the low-degree part of the gravity spectrum in terms of possible sublithospheric density anomalies we derive radial mantle viscosity profiles consistent with mineral physics. For these viscosity profiles we then compute gravity and topography kernels, which indicate how much gravity anomaly and how much topography is caused by a density anomaly at a given depth. With these kernels, we firstly compute an expected gravity-topography ratio. Good agreement with the observed ratio indicates that for Venus, in contrast to Earth and Mars, long-wavelength topography is largely dynamically supported from the sublithospheric mantle. Secondly, we combine an empirical power spectrum of density anomalies inferred from seismic tomography in Earth’s mantle with gravity kernels to model the gravity power spectrum. We find a good match between modeled and observed gravity power spectrum for all three planets, except for 2?l?4 on Venus. Density anomalies in the Venusian mantle for these low degrees thus appear to be very small. We combine gravity kernels and the gravity field to derive radially averaged density anomaly models for the Martian and Venusian mantles. Gravity kernels for l?5 are very small on Venus below ≈800 km depth. Thus our inferences on Venusian mantle density are basically restricted to the upper 800 km. On Mars, gravity anomalies for 2?l?5 may originate from density anomalies anywhere within its mantle. For Mars as for Earth, inferred density anomalies are dominated by l=2 structure, but we cannot infer whether there are features in the lowermost mantle of Mars that correspond to Earth’s Large Low Shear Velocity Provinces (LLSVPs). We find that volcanism on Mars tends to occur primarily in regions above inferred low mantle density, but our model cannot distinguish whether or not there is a Martian analog for the finding that Earth’s Large Igneous Provinces mainly originate above the margins of LLSVPs.     

Model bond albedos of extrasolar giant planets

The atmospheres of extrasolar giant planets are modeled with various effective temperatures and gravities, with and without clouds. Bond albedos are computed by calculating the ratio of the flux reflected by a planet (integrated over wavelength) to the total stellar flux incident on the planet. This quantity is useful for estimating the effective temperature and evolution of a planet. We find it is sensitive to the stellar type of the primary. For a 5 M_Jup planet the Bond albedo varies from 0.4 to 0.3 to 0.6 as the primary star varies from A5V to G2V to M2V in spectral type. It is relatively insensitive to the effective temperature and gravity for cloud-free planets. Water clouds increase the reflectivity of the planet in the red, which increases the Bond albedo. The Bond albedo increases by an order of magnitude for a 13 M_Jup planet with an M2V primary when water clouds are present. Silicate clouds, on the other hand, can either increase or decrease the Bond albedo, depending on whether there are many small grains (the former) or few large grains (the latter).     

The interaction of the stellar wind with an extrasolar planet—3D hybrid and drift-kinetic simulations

To be able to simulate the interaction of extrasolar planets with the stellar wind, a number of planetary parameters are required. Some of these (like planetary mass and radius) can be obtained directly from observational data. Other properties are not known very precisely. For example, up to now, there is no observation providing information on the strength of planetary magnetic moments. However, there is good reason to expect only very small magnetic moments for planets in very close orbits around their stars (like HD 209458 b and OGLE-TR-56 b). Thus, as a first step towards a more complete treatment, it seems reasonable to treat the interaction of the stellar wind with an unmagnetized planet. Calculations were performed for a nonconducting as well as for a weakly conducting planet. The interaction with the stellar wind and the resulting induced magnetosphere was simulated using a three dimensional hybrid code as well as in the drift-kinetic approximation. The effect of a interplanetary magnetic field oriented perpendicular to the incoming stellar wind was included. In the case of a weakly conducting body an asymmetrical Mach cone is formed, whereas for a nonconducting body no Mach cone is observed. These investigations will serve as the first step in the search for particular effects occurring at extrasolar planets, which could possibly lead to observable effects, e.g. radio emission. The results are also relevant for plasma structures near weakly conducting, unmagnetized bodies like the Earth's moon.     

Another mechanism of restricting the lifetime of orbiting satellites

Apsidal resonance causes long periodic variation of large amplitude in the eccentricity of the minor bodies of the solar system (asteroids, natural satellites, artificial satellites of the planets and the moon). Especially for a large-inclination orbiting satellite the increased eccentricity may cause its pericentric distance to decrease below the radius of the primary. This effect, completely different from the dissipative effect of the earth's atmosphere, will be analysed theoretically and illustrated with numerical examples in this paper.     

Problems of asteroid–comet hazard

The most relevant tasks associated with the problem of asteroid–comet hazard are discussed. A review is given of the respective research at the Institute of Applied Astronomy. The institute is currently implementing a project to create an information center whose tasks include the collection and processing of optical and radar observations of small solar system bodies, determination of their orbits, and assessment of the impact hazard of the newly discovered small bodies with respect to the earth, moon, and the other major planets and their satellites.     

Mathematical investigation of bode's law and quantilization of gravity

A non-static General Relativistic mathematical solution for the gravitational field around a star is obtained. From this mathematical solution, the orbits of the planets around the Sun are calculated and compared with Bode's law and the mean distances of the orbits, the origin of the Moon is deduced, and a theory for quantilization of gravity is concluded.     

Planet formation: Compositional mixing and lunar compositional anomalies

Significant fractions of each planet's late-accreted mass originated not at its own distance from the Sun, but from a neighboring planet's orbit, according to results that follow from calculations by Wetherill (1975). “Late-accreted” refers to a loosely defined period after planets acquired most of their present mass. In an idealized model, Mercury, Venus, Earth, and Mars received 47, 45, 37, and 52% of their late-accreted mass from planetesimals formed closer to other planets. Resulting compositional anomalies in outer parts of early planets could be significant; atmospheric tests of Lewis's predicted S deficiency on Venus may be inconclusive.The Moon's orbit around Earth puts it in a special category: sorting occurs between Moon-impacting and Earth-impacting material according to approach velocity. In the above model, the moon receives 60% of its late-accreted mass from planetesimals formed near Venus' orbit. Distant planetesimals could be perturbed into the Earth-Moon system and cause major changes in the Moon's composition with only minor effect on Earth. The entire lunar bulk composition anomaly could be explained by plausible reservoirs of distant low-density material.     

制约卫星轨道寿命的另一种机制

近点共振会导致太阳系小天体(小行星,自然卫星以及大行星和月球的人造卫星)的轨道偏心率出现变幅较大的长周期变化,特别是以月球和大行星为中心天体的大倾角轨道(确切地说是倾角接近90°的极轨道)卫星,由于类似的原因,偏心率的增大而导致近星距rp=a(1-e)≤ae(ae是中心天体的赤道半径),使其落到中心天体上,结束轨道寿命,这与耗散机制大不相同,因此将对其作理论分析,并以计算实例加以证实.     

系外类地行星的内部结构及大气成分研究进展

系外类地行星是目前搜寻地外生命的主要目标.随着观测仪器的发展,现在已经能探测到低于10个地球质量的系外行星.该文简要回顾了系外类地行星的形成与演化,介绍了当前研究它们内部结构的模型和方法,以及由此得出的类地行星质量-半径关系.同时,对应不同的行星初始物质成分,讨论了各种可能的大气结构.最后介绍了未来的空间任务在相关方面的工作.     

An algorithm for photometric identification of transiting circumbinary planets

Transiting planets manifest themselves by a periodic dimming of their host star by a fixed amount. On the other hand, light curves of transiting circumbinary (CB) planets are expected to be neither periodic nor to have a single depth while in transit. These propertied make the popular transit-finding algorithm Box Least Squares (BLS) almost ineffective so a modified version of BLS for the identification of CB planets was developed – CB-BLS. We show that using this algorithm it is possible to find CB planets in the residuals of light curves of eclipsing binaries that have noise levels of 1 per cent and more – quality that is routinely achieved by current ground-based transit surveys. Previous searches for CB planets using variation in eclipse times minima of CM Dra and elsewhere are more closely related to radial velocity than to transit searches and so are quite distinct from CB-BLS. Detecting CB planets is expected to have significant impact on our understanding of exoplanets in general, and exoplanet formation in particular. Using CB-BLS will allow to easily harness the massive ground- and space-based photometric surveys in operation to look for these hard-to-find objects.     

An analytic study of impact ejecta trajectories in the atmospheres of Venus,Mars, and Earth

Calculations have been made to determine the effects of atmospheric drag and gravity on impact ejecta trajectories on Venus, Mars, and the Earth. The equations of motion were numerically integrated for a broad range of body sizes, initial velocities, and initial elevation angles. A dimensionless parameter was found from approximate analytic solutions which correlated the ejecta range, final impact angle, and final impact velocity for all three planets.     

Forthcoming close angular approaches of planets to radio sources and possibilities to use them as GR tests

During close angular approaches of solar system planets to astrometric radio sources, the apparent positions of these sources shift due to relativistic effects and, thus, these events may be used for testing the theory of general relativity; this fact was successfully demonstrated in the experiments on the measurements of radio source position shifts during the approaches of Jupiter carried out in 1988 and 2002. An analysis, performed within the frames of the present work, showed that when a source is observed near a planet’s disk edge, i.e., practically in the case of occultation, the current experimental accuracy makes it possible to measure the relativistic effects for all planets. However, radio occultations are fairly rare events. At the same time, only Jupiter and Saturn provide noticeable relativistic effects approaching the radio sources at angular distances of about a few planet radii. Our analysis resulted in the creation of a catalog of forthcoming occultations and approaches of planets to astrometric radio sources for the time period of 2008–2050, which can be used for planning experiments on testing gravity theories and other purposes. For all events included in the catalog, the main relativistic effects are calculated both for ground-based and space (Earth-Moon) interferometer baselines.