Interaction of free-floating planets with a star–planet pair

The recent discovery of free-floating planets and their theoretical interpretation as celestial bodies, either condensed independently or ejected from parent stars in tight clusters, introduced an intriguing possibility. Namely, that some exoplanets are not condensed from the protoplanetary disk of their parent star. In this novel scenario a free-floating planet interacts with an already existing planetary system, created in a tight cluster, and is captured as a new planet. In the present work we study this interaction process by integrating trajectories of planet-sized bodies, which encounter a binary system consisting of a Jupiter-sized planet revolving around a Sun-like star. To simplify the problem we assume coplanar orbits for the bound and the free-floating planet and an initially parabolic orbit for the free-floating planet. By calculating the uncertainty exponent, a quantity that measures the dependence of the final state of the system on small changes of the initial conditions, we show that the interaction process is a fractal classical scattering. The uncertainty exponent is in the range (0.2–0.3) and is a decreasing function of time. In this way we see that the statistical approach we follow to tackle the problem is justified. The possible final outcomes of this interaction are only four, namely flyby, planet exchange, capture or disruption. We give the probability of each outcome as a function of the incoming planet’s mass. We find that the probability of exchange or capture (in prograde as well as retrograde orbits and for very long times) is non-negligible, a fact that might explain the possible future observations of planetary systems with orbits that are either retrograde (see e.g. Queloz et?al. Astron. Astrophys. 417, L1, 2010) or tight and highly eccentric.     

Chaotic Scattering in the Restricted Three‐Body Problem II. Small mass parameters

We study the scattering motion of the planar restricted three‐body problem for small mass parameters μ. We consider the symmetric periodic orbits of this system with μ = 0 that collide with the singularity together with the circular and parabolic solutions of the Kepler problem. These divide the parameter space in a natural way and characterize the main features of the scattering problem for small non‐vanishing μ. Indeed, continuation of these orbits yields the primitive periodic orbits of the system for small μ. For different regions of the parameter space, we present scattering functions and discuss the structure of the chaotic saddle. We show that for μ < μc and any Jacobi integral there exist departures from hyperbolicity due to regions of stable motion in phase space. Numerical bounds for μc are given. This revised version was published online in July 2006 with corrections to the Cover Date.     

The restricted problem of n+ν bodies

The simplest, conventional, and original form of the circular restricted problem of three bodies is briefly described in sidereal and synodic systems using dimensional and non-dimensional variables. This dynamical system is generalized to n2 primary bodies (from n=2) with masses M_i, 1in, interacting with arbitrary force laws (instead of only gravitational forces). The number of bodies of small mass mM_i not perturbing the primaries is increased from =1 to 1 where 1 and the minor bodies are allowed to interact with one another under arbitrary force laws. While the minor bodies (m) do not affect the motions of the primaries (M_i), the primaries influence the motions of the minor bodies with arbitrary force laws.For the case where n=2, 1, and only gravitational forces act on the system, an integral of the system is derived. It is shown that the energy integral of the general problem of N bodies and the Jacobian integral of the classical restricted problem of three bodies are limiting cases of this integral. The role of the integral in bounding the motion of the minor bodies is discussed. Several applications of this system are given.     

Chaotic Feature in the Light Curve of 3C 273

Some nonlinear dynamical techniques, including state-space reconstruction and correlation integral, are used to analyze the light curve of 3C 273. The result is compared with a chaotic model. The similarities between them suggest there is a low-dimension chaotic attractor in the light curve of 3C 273.     

Spectroscopy of K-complex asteroids: Parent bodies of carbonaceous meteorites?

This is the first focused study of non-Eos K asteroids. We have observed a total of 30 K-complex objects (12 K-2 Sk- and 13 Xk-type asteroids (from the Bus taxonomy), plus 3 K-candidates from previous work) and we present an analysis of their spectral properties from 0.4 to 2.5 μm. We targeted these asteroids because their previous observations are spectrally similar enough to suggest a possible compositional relationship. All objects have exhibited spectral redness in the visible wavelengths and minor absorptions near 1 micron. If, as suggested, K-complex asteroids (including K, Xk, and Sk) are the parent bodies of carbonaceous meteorites, knowledge of K-asteroid properties and distribution is essential to our understanding of the cosmochemical importance of some of the most primitive meteorite materials in our collection. This paper presents initial results of our analysis of telescopic data, with supporting analysis of laboratory measurements of meteorite analogs. Our results indicate that K-complex asteroids are distinct from other main belt asteroid types (S, B, C, F, and G). They do not appear to be a subset of these other types. K asteroids nearly span the range of band center positions and geometric albedos exhibited by the carbonaceous chondrites (CO, CM, CV, CH, CK, CR, and CI). We find that B-, C-, F- and G-type asteroids tend to be darker than meteorites, and can have band centers longer than any of the chondrites measured here. This could indicate that K-complex asteroids are better spectral analogues for the majority of our carbonaceous meteorites than the traditional B-, C-, F- and G-matches suggested in the literature. This paper present first results of our ongoing survey to determine K-type mineralogy, meteorite linkages, and significance to the geology of the asteroid regions.     

Against all odds? Forming the planet of the HD 196885 binary

HD 196885 Ab is the most ??extreme?? planet-in-a-binary discovered to date, whose orbit places it at the limit for orbital stability. The presence of a planet in such a highly perturbed region poses a clear challenge to planet-formation scenarios. We investigate this issue by focusing on the planet-formation stage that is arguably the most sensitive to binary perturbations: the mutual accretion of kilometre-sized planetesimals. To this effect we numerically estimate the impact velocities dv amongst a population of circumprimary planetesimals. We find that most of the circumprimary disc is strongly hostile to planetesimal accretion, especially the region around 2.6 AU (the planet??s location) where binary perturbations induce planetesimal-shattering dv of more than 1 kms^?1. Possible solutions to the paradox of having a planet in such accretion-hostile regions are (1) that initial planetesimals were very big, at least 250 km (2) that the binary had an initial orbit at least twice the present one, and was later compacted due to early stellar encounters (3) that planetesimals did not grow by mutual impacts but by sweeping of dust (the ??snowball?? growth mode identified by Xie et al., in Astrophys J 724:1153, 2010b), or (4) that HD 196885 Ab was formed not by core-accretion but by the concurrent disc instability mechanism. All of these 4 scenarios remain however highly conjectural.     

Detection of λ = 2 cm emission from minor planet 704 Interamnia

λ = 2 cm emission from 704 Interamnia was detected on June 28, 1984, using the VLA. At this time, 704 Interamnia was 2.0 AU distant from Earth. A flux density of 953±53 μJy was measured at 14.9 GHz (50-MHz bandwidth). If 338 km is adopted for the diameter, a disk temperature of 190±15°K results. This temperature is consistent with a rapidly rotating black sphere with 704 Interamnia's diameter. Using published 20-μm infrared data, we infer that a dust-like layer (depth ≥3 cm) covers 704 Interamnia. Most probably, the bulk composition of this layer is identical to that of the outermost shell of the asteroid. Comparison with observations of 15 Eunomia reported earlier suggest that smaller main belt asteroids are covered by a few centimeters of impact gardened material. The physical properties of this layer (especially its depth) make it impossible to infer the dielectric properties of the underlying surface with radio measurements at frequencies above 8 GHz.     

Could G-class asteroids be the parent bodies of the CM chondrites?

Abstract— I review the dynamical and compositional evidence for possibly linking CM chondrites and asteroids having G-class taxonomic designations. Three G asteroids have been identified through previous theoretical studies as being likely meteorite source bodies due to their locations near resonances. Two of these objects, 19 Fortuna and 13 Egeria, have spectral properties that are consistent with such a linkage with CM chondrites. Fortuna has a similar strength 0.7 μm absorption feature and near-infrared spectral slope to CM chondrites but a weaker ultraviolet feature. Egeria also has the characteristic 0.7 μm feature of CM chondrite spectra but does not match as well in the near-infrared. However, since the 0.7 μm feature is apparent in the spectra of approximately one-half of measured C-type asteroids, no definitive statement about any linkages can be made. Ceres is spectrally different from known meteorites in the 3 μm wavelength region and cannot be convincingly linked with any meteorite group.     

A semi-analytical model of the Galilean satellites’ dynamics

The Galilean satellites’ dynamics has been studied extensively during the last century. In the past it was common to use analytical expansions in order to get simple models to integrate, but with the new generation of computers it became prevalent the numerical integration of very sophisticated and almost complete equations of motion. In this article we aim to describe the resonant and secular motion of the Galilean satellites through a Hamiltonian, depending on the slow angles only, obtained with an analytical expansion of the perturbing functions and an averaging operation. In order to have a model as near as possible to the actual dynamics, we added perturbations and we considered terms that in similar studies of the past were neglected, such as the terms involving the inclinations and the Sun’s perturbation. Moreover, we added the tidal dissipation into the equations, in order to investigate how well the model captures the evolution of the system.     

Asymmetric periodic solutions of the averaged Hill problem with allowance for a planet’s oblateness

We consider asymmetric periodic solutions of the double-averaged Hill problem by taking into account oblateness of the central planet. They are generated by steady-state solutions, which are stable in the linear approximation and correspond to satellite orbits orthogonal to the line of intersection of the planet’s equatorial plane with the orbital plane of a disturbing point. For two model systems [(Sun+Moon)-Earth-satellite] and [Sun-Uranus-satellite], these periodic solutions are numerically continued from a small vicinity of the equilibrium position. The results are illustrated by projecting the solutions onto the (pericenter argument-eccentricity) and (longitude-inclination) planes.     

The asymptotic limit of the form-factors α and β product for celestial bodies

The applicability of the properties of central configurations proceeding from the many-body problem to study of gaseous sphere cloud evolution during its gravitational contraction is justified. It is shown that the product runs to a constant value in the asymptotic time limit of simultaneous collision of all the particles of the cloud where is a form-factor of the potential energy and is a form-factor of the moment of inertia.The spherical bodies as well as ellipsoids of rotation and general ellipsoids with a one-dimensional mass distribution (k),k[0, 1] are found to possess the property =const.

---

. , - , , ., , - =const., , (k),k[0, 1].

     

On the structure of Saturn's rings and the ‘real’ rotational period for the planet

An analysis of the Lowell Observatory photographic plates of Saturn gave the following results: (1) ring A and B show peculiar brightness distributions around the planet, from which we conclude that both are composed of particles in synchronous rotation. (2) The leading side of the particles in ring A is brighter than the trailing side by about 4%, which may indicate an interaction between such particles and the interplanetary medium. (3) Scans of the rings across the major axis show a small (～0.3″) region of enhanced brightness, from which we derive a value ofT _s =10^h13 _. ^m 8±5 _. ^m 4 for the actual planetary rotational period of Saturn. (4) In order to explain the synchronous rotation, the particles in ring A have to be at least 42 m in diameter.     

Nonlinear dynamics of Landau damped kinetic Alfvén waves

In the present paper we have studied the nonlinear dynamical equation of Landau damped kinetic Alfvén wave (KAW) to investigate the nonlinear evolution of KAW and the resulting turbulent spectra in solar wind plasmas. We have introduced a parameter g which governs the coupling between the amplitude of the pump KAW and the density perturbation. The numerical solution has been carried out to see the dependence on the parameter g in the nonlinear part of our equation. Our results reveal the formation of damped localized structures of KAW as well as steepening of the turbulent spectra by increasing g when damping is taken into account. The power spectra of magnetic field fluctuations indicate the redistribution of energy among the higher wave numbers. Each power spectrum with and without damping splits up into two different scaling ranges, Kolmogorov scaling followed by a steeper scaling. The steepening in the power spectra with Landau damping is more than without Landau damping case (for the same value of g). This type of steeper spectra has also been observed in the solar wind and is attributed to the Landau damping effects.     

Robe’s restricted problem of 2+2 bodies with one of the primaries an oblate body

In this problem, one of the primaries of mass \(m^{*}_{1}\) is a rigid spherical shell filled with a homogeneous incompressible fluid of density ρ ₁. The smaller primary of mass m ₂ is an oblate body 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 the third and the fourth body are infinitesimal. We assume that m ₂ is describing a circle around \(m^{*}_{1}\) . The masses m ₃ and m ₄ mutually attract each other, do not influence the motions of \(m^{*}_{1}\) and m ₂ but are influenced by them. We also assume that masses m ₃ and m ₄ are moving in the plane of motion of mass m ₂. In the paper, equilibrium solutions of m ₃ and m ₄ and their linear stability are analyzed. There are two collinear equilibrium solutions for the system. The non collinear equilibrium solutions exist only when ρ ₃=ρ ₄. There exist an infinite number of non collinear equilibrium solutions of the system, provided they lie inside the spherical shell. In a system where the primaries are considered as earth-moon and m ₃,m ₄ as submarines, the collinear equilibrium solutions thus obtained are unstable for the mass parameters μ,μ ₃,μ ₄ and oblateness factor A. In this particular case there are no non-collinear equilibrium solutions of the system.     

Investigation of heliogeoactivity impact on the dynamics of orbital parameters of Earth’s artificial satellites. I

The influence of active processes on the Sun and their response on the dynamics of Earth’s artificial satellites has been investigated. The relationship between the characteristics of solar activity and variations of the periods P of the orbital motion of Earth’s artificial satellites has been found. These variations mainly indicate the variations in the Earth’s atmosphere density caused by solar activity (index F_10.7) and geomagnetic activity (ΣK_p index). High values of the correlation coefficients between P and ^F_10.7 (–0.77…–0.91) and between P and ΣK_p (–0.67…–0.89) exhibit significant effect of solar and geomagnetic activity on the orbital periods of satellites.     

On the existence of periodic solutions of Poincaré's second sort in the general problem of three bodies moving in plane

In his Méthodes Nouvelles de la Mécanique Cèlèste (Sections 42–47), Poincaré envisaged the existence of a class (the second sort) of periodic solutions of the general problem of three bodies, arising by analytical continuation from unperturbed elliptic motion of two bodies about a primary, in which the two orbits are of commensurable period, and of non-zero eccentricity. Existence proofs have been given for the restricted problem case (in which the mass of the third body remains zero) by Arenstorf and Barrar, and for the lunar theory case by Arenstorf. A proof is offered here for the general problem, making use of the symmetry of the equations of motion (with use of the Mirror Theorem of Roy and Ovenden) in an extension of the approach used by Barrar for the restricted problem, and using a device proposed by Poincaré himself which enables the extension to the general problem to be made.Proceedings of the Sixth Conference on Mathematical Methods in Celestial Mechanics held at Oberwolfach (West Germany) from 14 to 19 August, 1978.     

Regions of a satellite��s motion in a Maxwell��s ring system of?N?bodies

The study of a dynamical system comprises a variety of processes, each one of which requires careful analysis. A fundamental preliminary step is to detect and limit the regions where solutions may exist. In the case of the ring problem of (N+1)-bodies or, otherwise, the regular polygon problem of (N+1) bodies, the existence of a Jacobian-type integral of motion constitutes the key for the investigation of the areas where the motions of the small particle are realized. Based on the aforementioned integral, we present an extended study of the parametric evolution of the regions where 3-D particle motions may exist.     

IR spectroscopy of COmosphere dynamics with the CO ?rst overtone band

We discuss observations of the weak ?rst overtone (Δν = 2) CO absorption band near 2300 nm with the U.S. National Solar Observatory Array Camera (NAC), a modern mid‐infrared detector. This molecular band provides a thermal diagnostic that forms lower in the atmosphere than the stronger fundamental band near 4600 nm. The observed center‐to‐limb increase in CO line width qualitatively agrees with the proposed higher temperature shocks or faster plasma motions higher in the COmosphere. The spatial extent of chromospheric shock waves is currently at or below the diffraction limit of the available CO lines at existing telescopes. Five minute period oscillations in line strength and measured Doppler shifts are consistent with the p‐mode excitation of the photospheric gas. We also show recent efforts at direct imaging at 4600 nm. We stress that future large‐aperture solar telescopes must be teamed with improved, dynamic mid‐infrared instruments, like the NAC, to capitalize on the features that motivate such facilities (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Band parameters for self-broadened ammonia gas in the range 0.74 to 5.24 μm to support measurements of the atmosphere of the planet Jupiter

We present new measurements and modelling of low-resolution transmission spectra of self-broadened ammonia gas, one of the most important absorbers found in the near-infrared spectrum of the planet Jupiter. These new spectral measurements were specifically designed to support measurements of Jupiter's atmosphere made by the Near-Infrared Mapping Spectrometer (NIMS) which was part of the Galileo mission that orbited Jupiter from 1995 to September 2003. To reach approximate jovian conditions in the lab, a new gas spectroscopy facility was developed and used to measure self-broadened ammonia spectra from 0.74 to 5.2 μm, virtually the complete range of the NIMS instrument, for the first time. Spectra were recorded at temperatures varying from 300 to 215 K, pressures from 1000 to 33 mb and using three different path lengths (10.164, 6.164 and 2.164 m). The spectra were then modelled using a series of increasingly complex physically based transmittance functions.