Orientation Of Rotation Axis Research Articles

INFLUENCE OF CONTROL CURRENT WAVEFORM ON ROTOR NUTATION OF THREE-DEGREES-OF-FREEDOM ELECTRIC MACHINE

The design of the electric machine with three degrees of freedom of the rotor with an external magnetic core, containing permanent magnets, and an internal magnetic core is considered. The both magnetic cores are rotating. The stator windings (control winding and two-phase rotation winding) are located in the air gap between the magnetic cores. The windings are powered by alternating current of corresponding phase. The positive property of rotor gyrostabilization in such structure is shown. At the same time, the negative fact consists in the nutation under the conditions of forced change in the orientation of rotation axis. There are no magnetic losses in the structure due to synchronous rotation of both external and internal magnetic cores. The immobility of the center of mass is assumed. There are no losses that give a non-conservative mechanical system. The mathematical model of the mechanic system and magnetic field is developed to compute the electromagnetic torques acting on the rotor. The expressions for electromagnetic torque components are obtained to use them in the Comsol Multiphysics interface. The effect of the sinusoidal and pulse currents in the control winding on the nutation swing is studied. The optimality of the control winding supplied by undisturbed sinusoidal current or the pulse current having square-wave length of about one-third of the period is revealed. References 15, figures 6, table 1.

A modified 6-DOF hybrid serial–parallel platform for ship wave compensation

This study proposes a modified six-degrees of freedom (6-DOF) hybrid serial–parallel platform (HSPP) for ship wave compensation. This HSPP is proposed based on the three universal-prismatic-universal_universal-prismatic (3UPU_UP) parallel module (PM), constructed by three UPU limbs and one UP limb. The serial module (SM) consists of a XY table and a rotational table. First, to better understand the compensation motions of the 6-DOF HSPP, the position and orientation of rotational axes and translational axes in this system are analyzed in detail by using the screw theory. Second, the position and velocity of the HSPP are systematically analyzed. Third, differences between the HSPP and its PM in singularity and reachable workspace are analyzed. The results show that the PM includes three characteristics: larger workspace, poorer orientation adjustment ability, and stronger coupling in the position and orientation. The HSPP inherits the characteristics of PM and adds SM to improve the deficiency of PM. The proposed HSPP can use PM for coupling compensation and can also use PM and SM for decoupling compensation. Compared with the Stewart platform, the HSPP has more advantages in terms of workspace and decoupling, which provides a new idea for the study of wave compensation.

Rotational Components of Normal Modes Measured at a Natural Sandstone Tower (Kane Springs Canyon, Utah, U.S.A.)

AbstractModal analysis of freestanding rock formations is crucial for evaluating their vibrational response to external stimuli, aiding accurate assessment of associated geohazards. Whereas conventional seismometers can be used to measure the translational components of normal modes, recent advances in rotational seismometer technology now allow direct measurement of the rotational components. We deployed a portable, three-component rotational seismometer for a short-duration experiment on a 36 m high sandstone tower located near Moab, Utah, in addition to conducting modal analysis using conventional seismic data and numerical modeling. Spectral analysis of rotation rate data resolved the first three natural frequencies of the tower (2.1, 3.1, and 5.9 Hz), and polarization analysis revealed the orientations of the rotation axes. Modal rotations were the strongest for the first two eigenmodes, which are mutually perpendicular, full-height bending modes with horizontal axes of rotation. The third mode is torsional with rotation about a subvertical axis. Measured natural frequencies and the orientations of displacements and rotation axes match our numerical models closely for these first three modes. In situ measurements of modal rotations are valuable at remote field sites with limited access, and contribute to an improved understanding of modal deformation, material properties, and landform response to vibration stimuli.

Characterising the orbit and circumstellar environment of the high-mass binary MWC 166 A

Context. Stellar evolution models are highly dependent on accurate mass estimates, especially for highly massive stars in the early stages of stellar evolution. The most direct method for obtaining model-independent stellar masses is derivation from the orbit of close binaries. Aims. Our aim was to derive the first astrometric plus radial velocity orbit solution for the single-lined spectroscopic binary star MWC 166 A, based on near-infrared interferometry over multiple epochs and ∼100 archival radial velocity measurements, and to derive fundamental stellar parameters from this orbit. A supplementary aim was to model the circumstellar activity in the system from K band spectral lines. Methods. The data used include interferometric observations from the VLTI instruments GRAVITY and PIONIER, as well as the MIRC-X instrument at the CHARA Array. We geometrically modelled the dust continuum to derive relative astrometry at 13 epochs, determine the orbital elements, and constrain individual stellar parameters at five different age estimates. We used the continuum models as a base to examine differential phases, visibilities, and closure phases over the Br γ and He I emission lines in order to characterise the nature of the circumstellar emission. Results. Our orbit solution suggests a period of P = 367.7 ± 0.1 d, approximately twice as long as found with previous radial velocity orbit fits. We derive a semi-major axis of 2.61 ± 0.04 au at d = 990 ± 50 pc, an eccentricity of 0.498 ± 0.001, and an orbital inclination of 53.6 ± 0.3°. This allowed the component masses to be constrained to M1 = 12.2 ± 2.2 M⊙ and M2 = 4.9 ± 0.5 M⊙. The line-emitting gas was found to be localised around the primary and is spatially resolved on scales of ∼11 stellar radii, where the spatial displacement between the line wings is consistent with a rotating disc. Conclusions. The large spatial extent and stable rotation axis orientation measured for the Br γ and He I line emission are inconsistent with an origin in magnetospheric accretion or boundary-layer accretion, but indicate an ionised inner gas disc around this Herbig Be star. We observe line variability that could be explained either with generic line variability in a Herbig star disc or V/R variations in a decretion disc scenario. We have also constrained the age of the system, with relative flux ratios suggesting an age of ∼(7 ± 2)×105 yr, consistent with the system being composed of a main-sequence primary and a secondary still contracting towards the main-sequence stage.

The Intercalated Segment: Does the Triquetrum Move in Synchrony With the Lunate?

To quantify the relative motion between the lunate and triquetrum during functional wrist movements and to examine the impact of wrist laxity on triquetral motion. A digital database of wrist bone anatomy and carpal kinematics for 10 healthy volunteers in 10 different positions was used to study triquetral kinematics. The orientation of radiotriquetral (RT) and radiolunate rotation axes was compared during a variety of functional wrist movements, including radioulnar deviation (RUD) and flexion-extension (FE), and during a hammering task. The motion of the triquetrum relative to the radius during wrist RUD was compared with passive FE range of motion measurements (used as a surrogate measure for wrist laxity). The difference in the orientation of the radiolunate and RT rotation axes was less than 20° during most of the motions studied, except for radial deviation and for the first stage of the hammering task. During wrist RUD, the orientation of the RT rotation axis varied as a function of passive FE wrist range of motion. The suggestion that the lunate and triquetrum move together as an intercalated segment may be an oversimplification. We observed synchronous movement during some motions, but as the wrist entered RUD, the lunate and triquetrum no longer moved synchronously. These findings challenge the assumptions behind models describing the mechanical function of the carpals. Individual-specific differences in the amount of relative motion between the triquetrum and lunate may contribute to the variability in outcomes following lunotriquetral arthrodesis. Variation in triquetral motion patterns may also have an impact on the ability of the triquetrum to extend the lunate, affecting the development of carpal instability.

The AGN fuelling/feedback cycle in nearby radio galaxies – III. 3D relative orientations of radio jets and CO discs and their interaction

ABSTRACT This is the third paper of a series exploring the multifrequency properties of a sample of eleven nearby low-excitation radio galaxies (LERGs) in the southern sky. We are conducting an extensive study of different galaxy components (stars, dust, warm and cold gas, radio jets) with the aim of better understanding the AGN fuelling/feedback cycle in LERGs. Here, we present new, deep, sub-kpc resolution Karl G. Jansky Very Large Array (JVLA) data for five sample sources at 10 GHz. Coupling these data with previously acquired Atacama Large Millimetre/submillimetre Array (ALMA) CO(2–1) observations and measurements of comparable quality from the literature, we carry out for the first time a full 3D analysis of the relative orientations of jet and disc rotation axes in six FR I LERGs. This analysis shows (albeit with significant uncertainties) that the relative orientation angles span a wide range (≈30○–60○). There is no case where both axes are accurately aligned and there is a marginally significant tendency for jets to avoid the disc plane. Our study also provides further evidence for the presence of a jet-CO disc interaction (already inferred from other observational indicators) in at least one source, NGC 3100. In this case, the limited extent of the radio jets, along with distortions in both the molecular gas and the jet components, suggest that the jets are young, interacting with the surrounding matter and rapidly decelerating.

Outgassing-induced acceleration of comet 67P/Churyumov-Gerasimenko

Context. Cometary activity affects the orbital motion and rotation state through sublimation-induced forces. The availability of precise rotation-axis orientation and position data from the Rosetta mission allows us to accurately determine the outgassing of comet Churyumov-Gerasimenko/67P (67P). Aims. We derived the observed non-gravitational acceleration of 67P directly from the trajectory of the Rosetta spacecraft. From the non-gravitational acceleration, we recovered the diurnal outgassing variations and study a possible delay of the sublimation response with respect to the peak of the solar illumination. This allowed us to compare the non-gravitational acceleration of 67P with expectations based on empirical models and common assumptions about the sublimation process. Methods. We used an iterative orbit refinement and Fourier decomposition of the diurnal activity to derive the outgassing-induced non-gravitational acceleration. The uncertainties of the data reduction were established by a sensitivity analysis of an ensemble of best-fit orbits for comet 67P. Results. We find that the Marsden non-gravitational acceleration parameters reproduce part of the non-gravitational acceleration, but need to be augmented by an analysis of the nucleus geometry and surface illumination to draw conclusions about the sublimation process on the surface. The non-gravitational acceleration closely follows the subsolar latitude (seasonal illumination), with a small lag angle with respect to local noon around perihelion. The observed minor changes of the rotation axis do not favor forced precession models for the non-gravitational acceleration. Conclusions. In contrast to the sublimation-induced torques, the non-gravitational acceleration does not place strong constraints on localized active areas on the nucleus. We find a close agreement of the orbit-deduced non-gravitational acceleration and the water production that is independently derived from Rosetta in situ measurements.

Decadal Polar Motion of the Earth Excited by the Convective Outer Core From Geodynamo Simulations

AbstractLong time geodetic observation records show that the orientation of the Earth's rotation axis with respect to the terrestrial reference frame, or polar motion, changes on a broad range of timescales. Apart from external torques from the luni‐solar tides, these changes are excited by interactions among different components of the Earth system. The convective fluid outer core has long been conjectured a likely contributor to the observed polar motion on timescales upward of decades, such as the ∼30 year Markowitz wobble. We investigated the electromagnetic coupling scenario across the core‐mantle boundary via numerical geodynamo simulation for different geodynamo parameters (Rayleigh numbers and magnetic Rossby numbers). Our simulated polar motion varies strongly with the dynamo parameters, while its excitation on decadal timescales appear to converge asymptotically within the adopted range of numerical Rossby numbers. Three strongest asymptotic modes emerge from numerical results, with periods around 30, 40, and 60 years for the prograde excitation and around 24, 30, and 60 years for the retrograde excitation. Their amplitudes are all larger than 5 × 10−8, or approximately 10 milliseconds of arc. The results suggest that the electromagnetic core‐mantle coupling could explain a substantial portion, if not all, of the observed decadal polar motion. In particular, the predicted 60 year polar motion deserves special attention for future observations and studies.

Referencing the Polarization Orientation to the Emission-Region Magnetic Field

AbstractUsing the proper-motion as a proxy for a pulsar’s rotation-axis orientation, the emission polarization can be related to the magnetic field direction in the emission region, providing a much more physical foundation for understanding orthogonal mode radiation.

In-vivo analysis of sternal angle, sternal and sternocostal kinematics in supine humans during breathing.

This paper aims at contributing to the understanding of the combination of in vivo sternum displacement, sternal angle variations and sternocostal joints (SCJ) kinematics of the seven first rib pairs over the inspiratory capacity (IC). Retrospective codified spiral-CT data obtained at total lung capacity (TLC), middle of inspiratory capacity (MIC) and at functional residual capacity (FRC) were used to compute kinematic parameters of the bones and joints of interest in a sample of 12 asymptomatic subjects. 3D models of rib, thoracic vertebra, manubrium and sternum were processed to determine anatomical landmarks (ALs) on each bone. These ALs were used to create local coordinate system and compute spatial transformation of ribs and manubrium relative to sternum, and sternum relative to thoracic vertebra. The rib angular displacements and associated orientation of rotation axes and joint pivot points (JPP), the sternal angle variations and the associated displacement of the sternum relative to vertebra were computed between each breathing pose at the three lung volumes. Results can be summarized as following: (1) sternum cephalic displacement ranged between 17.8 and 19.2mm over the IC; (2) the sternal angle showed a mean variation of 4.4°±2.7° over the IC; (3) ranges of rib rotation relative to sternum decreased gradually with increasing rib level; (4) axes of rotation were similarly oriented at each SCJ; (5) JPP spatial displacements showed less variations at first SCJ compared to levels underneath; (6) linear relation was demonstrated between SCJ ROMs and sternum cephalic displacement over the IC.

Spin states of asteroids in the Eos collisional family

Eos family was created during a catastrophic impact about 1.3 Gyr ago. Rotation states of individual family members contain information about the history of the whole population. We aim to increase the number of asteroid shape models and rotation states within the Eos collision family, as well as to revise previously published shape models from the literature. Such results can be used to constrain theoretical collisional and evolution models of the family, or to estimate other physical parameters by a thermophysical modeling of the thermal infrared data. We use all available disk-integrated optical data (i.e., classical dense-in-time photometry obtained from public databases and through a large collaboration network as well as sparse-in-time individual measurements from a few sky surveys) as input for the convex inversion method, and derive 3D shape models of asteroids together with their rotation periods and orientations of rotation axes. We present updated shape models for 15 asteroids and new shape model determinations for 16 asteroids. Together with the already published models from the publicly available DAMIT database, we compiled a sample of 56 Eos family members with known shape models that we used in our analysis of physical properties within the family. Rotation states of asteroids smaller than ∼ 20 km are heavily influenced by the YORP effect, whilst the large objects more or less retained their rotation state properties since the family creation. Moreover, we also present a shape model and bulk density of asteroid (423) Diotima, an interloper in the Eos family, based on the disk-resolved data obtained by the Near InfraRed Camera (Nirc2) mounted on the W.M. Keck II telescope.

Energy of low angle grain boundaries based on continuum dislocation structure

In this paper, we present a continuum model to compute the energy of low angle grain boundaries for any given degrees of freedom (arbitrary rotation axis, rotation angle and boundary plane orientation) based on a continuum dislocation structure. In our continuum model, we minimize the grain boundary energy associated with the dislocation structure subject to the constraint of Frank's formula for dislocations with all possible Burgers vectors. This constrained minimization problem is solved by the penalty method by which it is turned into an unconstrained minimization problem. The grain boundary dislocation structure is approximated by a network of straight dislocations that predicts the energy and dislocation densities of the grain boundaries. The grain boundary energy based on the calculated dislocation structure is able to incorporate its anisotropic nature. We use our continuum model to systematically study the energy of <111> low angle grain boundaries in fcc Al with any boundary plane orientation and all six possible Burgers vectors. Comparisons with atomistic simulation results show that our continuum model is able to give excellent predictions of the energy and dislocation densities of low angle grain boundaries. We also study the energy of low angle grain boundaries in fcc Al with varying rotation axis while the remaining degrees of freedom are fixed. With modifications, our model can also apply to dislocation structures and energy of heterogeneous interfaces.

Disentangling rotational velocity distribution of stars

AbstractRotational speed is an important physical parameter of stars: knowing the distribution of stellar rotational velocities is essential for understanding stellar evolution. However, rotational speed cannot be measured directly and is instead the convolution between the rotational speed and the sine of the inclination angle vsin(i). The problem itself can be described via a Fredhoml integral of the first kind. A new method (Curé et al. 2014) to deconvolve this inverse problem and obtain the cumulative distribution function for stellar rotational velocities is based on the work of Chandrasekhar &amp; Münch (1950). Another method to obtain the probability distribution function is Tikhonov regularization method (Christen et al. 2016). The proposed methods can be also applied to the mass ratio distribution of extrasolar planets and brown dwarfs (in binary systems, Curé et al. 2015).For stars in a cluster, where all members are gravitationally bounded, the standard assumption that rotational axes are uniform distributed over the sphere is questionable. On the basis of the proposed techniques a simple approach to model this anisotropy of rotational axes has been developed with the possibility to “disentangling” simultaneously both the rotational speed distribution and the orientation of rotational axes.

New and updated convex shape models of asteroids based on optical data from a large collaboration network

Asteroid modeling efforts in the last decade resulted in a comprehensive dataset of almost 400 convex shape models and their rotation states. This amount already provided a deep insight into physical properties of main-belt asteroids or large collisional families. We aim to increase the number of asteroid shape models and rotation states. Such results are an important input for various further studies such as analysis of asteroid physical properties in different populations, including smaller collisional families, thermophysical modeling, and scaling shape models by disk-resolved images, or stellar occultation data. This provides, in combination with known masses, bulk density estimates, but constrains also theoretical collisional and evolutional models of the Solar System. We use all available disk-integrated optical data (i.e., classical dense-in-time photometry obtained from public databases and through a large collaboration network as well as sparse-in-time individual measurements from a few sky surveys) as an input for the convex inversion method, and derive 3D shape models of asteroids, together with their rotation periods and orientations of rotation axes. The key ingredient is the support of more that one hundred observers who submit their optical data to publicly available databases. We present updated shape models for 36 asteroids, for which mass estimates are currently available in the literature or their masses will be most likely determined from their gravitational influence on smaller bodies, which orbital deflection will be observed by the ESA Gaia astrometric mission. This was achieved by using additional optical data from recent apparitions for the shape optimization. Moreover, we also present new shape model determinations for 250 asteroids, including 13 Hungarias and 3 near-Earth asteroids.

ACHANDRASEARCH FOR THE PULSAR WIND NEBULA AROUND PSR B1055–52

The nearby, middle-aged PSR B1055-52 has many properties in common with the Geminga pulsar. Motivated by the Geminga's enigmatic and prominent pulsar wind nebula (PWN), we searched for extended emission around PSR B1055-52 with Chandra ACIS. For an energy range 0.3-1 keV, we found a 4 sigma flux enhancement in a 4.9-20 arcsec annulus around the pulsar. There is a slight asymmetry in the emission close, 1.5-4 arcsec, to the pulsar. The excess emission has a luminosity of about 10^{29} erg s^{-1} in an energy range 0.3-8 keV for a distance of 350 pc. Overall, the faint extended emission around PSR B1055-52 is consistent with a PWN of an aligned rotator moving away from us along the line of sight with supersonic velocity, but a contribution from a dust scattering halo cannot be excluded. Comparing the properties of other nearby, middle-aged pulsars, we suggest that the geometry -- the orientations of rotation axis, magnetic field axis, and the sight-line -- is the deciding factor for a pulsar to show a prominent PWN. For PSR B1055-52, we also report on a flux decrease of at least 30% between the 2000 XMM-Newton and our 2012 Chandra observation. We tentatively attribute this flux decrease to a cross-calibration problem, but further investigations of the pulsar are required to exclude actual intrinsic flux changes.

TRIGGERING COLLAPSE OF THE PRESOLAR DENSE CLOUD CORE AND INJECTING SHORT-LIVED RADIOISOTOPES WITH A SHOCK WAVE. IV. EFFECTS OF ROTATIONAL AXIS ORIENTATION

Both astronomical observations of the interaction of Type II supernova remnants (SNR) with dense interstellar clouds as well as cosmochemical studies of the abundances of daughter products of short-lived radioisotopes (SLRIs) formed by supernova nucleosynthesis support the hypothesis that the Solar Systems SLRIs may have been derived from a supernova. This paper continues a series devoted to examining whether such a shock wave could have triggered the dynamical collapse of a dense, presolar cloud core and simultaneously injected sufficient abundances of SLRIs to explain the cosmochemical evidence. Here we examine the effects of shock waves striking clouds whose spin axes are oriented perpendicular, rather than parallel, to the direction of propagation of the shock front. The models start with 2.2 solar mass cloud cores and shock speeds of 20 or 40 km/sec. Central protostars and protoplanetary disks form in all models, though with disk spin axes aligned somewhat randomly. The disks derive most of their angular momentum not from the initial cloud rotation, but from the Rayleigh-Taylor fingers that also inject shock wave SLRIs. Injection efficiencies, fi, the fraction of the incident shock wave material injected into the collapsing cloud core, are 0.04 - 0.1 in these models, similar to when the rotation axis is parallel to the shock propagation direction. Evidently altering the rotation axis orientation has only a minor effect on the outcome, strengthening the case for this scenario as an explanation for the Solar Systems SLRIs.

Characteristics of Friedel pairs and diffraction contrast tomography with non-perpendicular rotation axis.

The characteristics of Friedel pairs in diffraction contrast tomography (DCT) are studied in the condition that the rotation axis of the sample is not exactly perpendicular to the incident X-ray direction. For the rotation axis approximately aligned along the vertical direction, the Friedel pairs close to the horizontal plane are insensitive to the non-perpendicularity of the rotation axis, and can be used to refine the sample-to-detector distance and X-ray energy, while the Friedel pairs close to the vertical direction are sensitive to the non-perpendicularity of the rotation axis, and can be used to determine the rotation axis orientation. The correct matching proportion of Friedel pairs decreases with increasing non-perpendicularity of the rotation axis. A method of data processing considering rotation axis misalignment is proposed, which significantly increases the correct matching and indexing proportions of the diffraction spots. A pure aluminium polycrystalline sample is investigated using DCT at beamline 4W1A of Beijing Synchrotron Radiation Facility. Based on the analysis of Friedel pairs, the sample-to-detector distance and X-ray energy are refined to be 8.67 mm and 20.04 keV, respectively. The non-perpendicular angle of the rotation axis is calculated to be 0.10°. With these refined geometric parameters, the matching proportion of the spatial position of diffraction spots is 90.62%. Three-dimensional reconstruction of the sample with 13 grains is realised using the algebraic reconstruction technique. It is demonstrated that the precise correction of the orientation of the sample rotation axis is effective in DCT suffering from rotation axis misalignment, and the higher accuracy in determining the rotation axis is expected to improve the reconstruction precision of grains.

A large anisotropy in the sky distribution of 3CRR quasars and other radio galaxies

We report the presence of large anisotropies in the sky distributions of powerful extended quasars as well as some other sub-classes of radio galaxies in the 3CRR survey, the most reliable and most intensively studied complete sample of strong steep-spectrum radio sources. The anisotropies lie about a plane passing through the equinoxes and the north celestial pole. Out of a total of 48 quasars in the sample, 33 of them lie in one half of the observed sky and the remaining 15 in the other half. The probability that in a random distribution of 3CRR quasars in the sky, statistical fluctuations could give rise to an asymmetry in observed numbers up to this level is only $\sim 1\%$. Also only about 1/4th of Fanaroff-Riley 1 (FR1) type of radio galaxies lie in the first half of the observed sky and the remainder in the second half. If we include all the observed asymmetries in the sky distributions of quasars and radio galaxies in the 3CRR sample, the probability of their occurrence by a chance combination reduces to $\sim 2 \times 10^{-5}$. Two pertinent but disturbing questions that could be raised here are -- firstly why should there be such large anisotropies present in the sky distribution of some of the strongest and most distant discrete sources, implying inhomogeneities in the universe at very large scales (covering a fraction of the universe)? Secondly why should such anisotropies lie about a great circle decided purely by the orientation of earth's rotation axis and/or the axis of its revolution around the sun? Are these alignments a mere coincidence or do they imply that these axes have a preferential placement in the larger scheme of things, implying an apparent breakdown of the Copernican principle or its more generalization, cosmological principle, upon which the standard cosmological model is based upon?

The climate system

An overview of what we know about the climate of the planet Earth up to 5.5 millions of years from now is presented first, with the air temperature in proximity to the surface as the main, and more feasible, parameter to be followed. The behavior of this parameter exhibits a distinct periodicity with more internal fluctuations. This overview prompts us to a description of the physical basis of the climate system, capable of explaining such fluctuations. The system is the star-planet, initially described as a lamp-billiard ball simple system. Astronomical causes affect the distance lamp-billiard ball (star-planet) and the ball (Earth) rotation axis orientation, while astronomical causes affect the intensity of radiation emitted from the lamp (Sun). The complication introduced by the atmosphere is then explained, essentially through the triatomic gas molecules, aerosol and clouds. Atmospheric composition affects incoming solar radiation and outgoing infrared one. The compartments relevant for climate definition are examined: lithosphere, hydrosphere, cryosphere, biosphere including vegetation and humans. However due to space limitations the interactions between the different compartments are not treated here and we restrict ourselves to the treatment of the atmosphere.

The Occurrence and Architecture of Exoplanetary Systems

The basic geometry of the Solar System—the shapes, spacings, and orientations of the planetary orbits—has long been a subject of fascination as well as inspiration for planet-formation theories. For exoplanetary systems, those same properties have only recently come into focus. Here we review our current knowledge of the occurrence of planets around other stars, their orbital distances and eccentricities, the orbital spacings and mutual inclinations in multiplanet systems, the orientation of the host star's rotation axis, and the properties of planets in binary-star systems.