Search

A new analytical model (R-toroid), representing a 3D generalization of the precessing Gaussian ring, is constructed for the study of secular perturbations in celestial mechanics. Our approach is based on triple averaging of the motion of a material point and is reduced to a chain of transformations: 1D Gaussian ring–2D R-ring–3D R-toroid. The figure, structure and gravitational potential of the R-toroid are studied. We obtained the expression for the mutual energy of the R-toroid and the outer Gaussian ring to study the motion of bodies in the gravitational field of the model in two forms (in the integral and in the form of a power-law series). Two equation systems of the secular evolution of osculating orbits (Gaussian rings), in the gravitational field of an R-toroid and in the field of a central precessing star, are derived using the mutual energy. The periods of nodal TΩ and apsidal Tω orbital precession were obtained. Examples of three hot Jupiters with a known period of nodal precession are considered. For the exoplanet Kepler-413b, the R-toroid describes the evolution of any orbit with a ≥ 5.48 AU, and for the exoplanet PTFO 8-8695b, the critical value of the semi-major axis turned out to be only amin ≈ 0.2 AU. The frequency profile of the precession of the test orbit in the field of the star and planet PTFO 8-8695b has been calculated. The minimum value of the period of nodal precession was TΩ ≈ (26.1 ± 3.0) × 103 years.

The problem of the secular evolution of a thin ring around a rapidly rotating triaxial celestial body is formulated and solved. The technology for calculating secular perturbations is based on two formulas: the azimuthally averaged force field of the central body and the mutual energy $${{W}_{{{\text{mut}}}}}$$ of this body and a Gaussian ring. With $${{W}_{{{\text{mut}}}}}$$ instead of the usual perturbing function, a system of differential equations for the osculating elements of the ring is obtained. An equation is obtained that allows one to find the coefficients of the zonal harmonics of the azimuthally averaged potential of an inhomogeneous ellipsoid using a unified scheme. The method is applied to dwarf planet Haumea with refined masses of the rocky core and the ice shell and the coefficients $${{C}_{{20}}}$$ and $${{C}_{{40}}}$$ of the po-tential’s zonal harmonics. According to new data, the ring around Haumea has a slight obliquity and must precess. It was established that the period of the retrograde nodal precession of the Haumea’s ring (without regard to self-gravity) is $${{T}_{\Omega }} = 12.9 \pm 0.7$$ days and the period of the forward of the apside line precession is $${{T}_{\omega }} \approx 8.{\text{08}}\;{\text{days}}$$ . It is proven that the 3:1 orbital resonance for the particles of the Haumea’s ring is fulfilled only approximately and the averaging time of additional perturbations at a nonsharp resonance turned out to be an order of magnitude smaller than $${{T}_{\Omega }}$$ . This confirms the adequacy of the method.

$\pi$ Men hosts a transiting super Earth ($P\approx6.27$ d, $m\approx4.82$ $M_{\oplus}$, $R\approx2.04$ $R_{\oplus}$) discovered by TESS and a cold Jupiter ($P\approx2093$ d, $m \sin I\approx10.02$ $M_{\rm{Jup}}$, $e\approx0.64$) discovered from radial velocity. We use Gaia DR2 and Hipparcos astrometry to derive the star's velocity caused by the orbiting planets and constrain the cold Jupiter's sky-projected inclination ($I_b=41-65^{\circ}$). From this we derive the mutual inclination ($\Delta I$) between the two planets, and find that $49^{\circ}< \Delta I < 131^{\circ}$ (1$\sigma$), and $28^{\circ} < \Delta I < 152^{\circ}$ (2$\sigma$). We examine the dynamics of the system using $N$-body simulations, and find that potentially large oscillations in the super Earth's eccentricity and inclination are suppressed by general relativistic precession. However, nodal precession of the inner orbit around the invariable plane causes the super Earth to only transit between 7-22 per cent of the time, and to usually be observed as misaligned with the stellar spin axis. We repeat our analysis for HAT-P-11, finding a large $\Delta I$ between its close-in Neptune and cold Jupiter and similar dynamics. $\pi$ Men and HAT-P-11 are prime examples of systems where dynamically hot outer planets excite their inner planets, with the effects of increasing planet eccentricities, planet-star misalignments, and potentially reducing the transit multiplicity. Formation of such systems likely involves scattering between multiple giant planets or misaligned protoplanetary discs. Future imaging of the faint debris disc in $\pi$ Men and precise constraints on the stellar spin orientation would provide strong tests for these formation scenarios., Comment: Corrected Fig 7 and Sec 6.1.1 (HAT-P-11 also weak planet-star coupling). Published as MNRAS 497, 2096-2118 (2020)

Satellite relative motion around the Earth has been thoroughly studied during the last two decades. However, considerably less attention has been given to the study of satellite relative motion around Mars. As the cost of space technologies decreases and more space missions are within reach, formation flying missions around Mars have the potential to benefit future exploration missions launched to the Red Planet. A key parameter in such missions will be the frequency at which the spacecraft need to perform formation-keeping maneuvers to compensate for unwanted drifts due to differential perturbations. The Martian $$J_3$$ and $$J_4$$ gravitational harmonics are significant enough to warrant a dedicated investigation of bounded satellite relative motion configurations. In this study, we derive conditions for bounded satellite relative motion in non-critical inclinations around Mars, while considering its gravitational harmonics up to $$J_4$$ . We first introduce a family of stable frozen orbits facilitating the implementation of formation flying and then apply differential nodal precession negation and differential periapsis rotation negation methods while considering the gravitational harmonics up to $$J_4$$ . Using this procedure, we demonstrate how the secular growth of the relative distance can be arrested during long time intervals.

Even sub-millimeter-size debris could cause a fatal damage on a spacecraft. Such tiny debris cannot be followed up or tracked from the ground. Therefore, Kyushu University has initiated IDEA the project for In-situ Debris Environmental Awareness, which conducts in-situ measurements of sub-millimeter-size debris. One of the objectives is to estimate the location of on-orbit satellite fragmentations from in-situ measurements. The previous studies revealed that it is important to find out the right nodal precession rate to estimate the orbital parameters of a broken-up object properly. Therefore, this study derives a constraint equation that applies to the nodal precession rate of the broken-up object. This study also establishes an effective procedure to estimate properly the orbital parameters of a broken-up object with the constraint equation.

The discovery of numerous circumprimary planets in the last few years has brought to the fore the question of planet formation in binary systems. The significant dynamical influence, during the protoplanetary disk phase, of a binary companion on a giant planet has previously been highlighted for wide binary stars. In particular, highly inclined binary companion can induce perturbations on the disk and the planets, through the Lidov-Kozai resonance, which could inhibit the formation process. In this work, we aim to study how the disk gravitational potential acting on the planet and the nodal precession \textbf{induced by the wide binary companion with separation of 1000 AU} on the disk act to suppress the Lidov-Kozai perturbations on a migrating giant planet. We derive new approximate formulas for the evolution of the disk's inclination and longitude of the ascending node, in the case of a rigidly precessing disk with a decreasing mass and perturbed by a wide binary companion, which are suitable for $N$-body simulations. We carry out 3200 simulations with several eccentricity and inclination values for the binary companion. The gravitational and damping forces exerted by the disk on the planet tend to keep the latter in the midplane of the former, and suppress the effect of the binary companion by preventing the planet from getting locked in the Lidov-Kozai resonance during the disk phase. We also confirm that because of nodal precession induced by the binary, a primordial spin-orbit misalignment could be generated for circumprimary planets with an inclined binary companion., Comment: 11 pages, 10 figures, to be published in MNRAS

To fulfill its operational function, the Sun-synchronous satellite needs to have a specific nodal precession value of 360°/year. This nodal precession value is mainly affected by semi-major axis, eccentricity, and inclination. However, in fact, semi-major axis and inclination of an orbit often drift over a long period of operation. Thus, the nodal precession of the orbit will be no longer 360°/year. This paper discusses the simulation of inclination maneuver to correct the nodal precession of Sun-synchronous satellite by using a non-impulsive thruster approach. Data from LAPAN Sun-synchronous satellite was used for simulation. The results of the simulation show that there are no significant changes to other orbital parameters for inclination maneuver for every 1, 2, 3, 4, and 6 months. Also, the results of the simulation are compared to the analytical results (impulsive thruster approach), which turns out that the analytical approach still gives a good accuracy of inclination changes for that maneuver interval with accuracy up to 0.001°. The results can be used as a recommendation for the thruster operation of the next LAPAN Sun-synchronous satellite.

We investigate the formation mechanism for the observed nearly polar aligned (perpendicular to the binary orbital plane) debris ring around the eccentric orbit binary 99 Herculis. An initially inclined nonpolar debris ring or disc will not remain flat and will not evolve to a polar configuration, due to the effects of differential nodal precession that alter its flat structure. However, a gas disc with embedded well coupled solids around the eccentric binary may evolve to a polar configuration as a result of pressure forces that maintain the disc flatness and as a result of viscous dissipation that allows the disc to increase its tilt. Once the gas disc disperses, the debris disc is in a polar aligned state in which there is little precession. We use three-dimensional hydrodynamical simulations, linear theory, and particle dynamics to study the evolution of a misaligned circumbinary gas disc and explore the effects of the initial disc tilt, mass, and size. We find that for a wide range of parameter space, the polar alignment timescale is shorter than the lifetime of the gas disc. Using the observed level of alignment of 3 deg. from polar, we place an upper limit on the mass of the gas disc of about 0.014 M_sun at the time of gas dispersal. We conclude that the polar debris disc around 99 Her can be explained as the result of an initially moderately inclined gas disc with embedded solids. Such a disc may provide an environment for the formation of polar planets., Comment: 13 pages, 12 figures, accepted for publication in MNRAS

When a star passes close to a supermassive black hole (BH), the BH's tidal forces rip it apart into a thin stream, leading to a tidal disruption event (TDE). In this work, we study the post-disruption phase of TDEs in general relativistic hydrodynamics (GRHD) using our GPU-accelerated code H-AMR. We carry out the first grid-based simulation of a deep-penetration TDE ($\beta$=7) with realistic system parameters: a black-hole-to-star mass ratio of $10^6$, a parabolic stellar trajectory, and a nonzero BH spin. We also carry out a simulation of a tilted TDE whose stellar orbit is inclined relative to the BH midplane. We show that for our aligned TDE, an accretion disk forms due to the dissipation of orbital energy with $\sim$20 percent of the infalling material reaching the BH. The dissipation is initially dominated by violent self-intersections and later by stream-disk interactions near the pericenter. The self-intersections completely disrupt the incoming stream, resulting in five distinct self-intersection events separated by approximately 12 hours and a flaring in the accretion rate. We also find that the disk is eccentric with mean eccentricity e$\approx$0.88. For our tilted TDE, we find only partial self-intersections due to nodal precession near pericenter. Although these partial intersections eject gas out of the orbital plane, an accretion disk still forms with a similar accreted fraction of the material to the aligned case. These results have important implications for disk formation in realistic tidal disruptions. For instance, the periodicity in accretion rate induced by the complete stream disruption may explain the flaring events from Swift J1644+57., Comment: Accepted to MNRAS on November 23rd, 2021, 23 pages, 25 figures, uses mnras.cls. Comments welcome. Movies available at https://www.youtube.com/playlist?list=PL7YbfRC6zxzAqIPXWbJgXpr4Wq_nwHiDu

Finding satellite relative orbits that are resilient to differential gravitational perturbations has received much attention in the literature. In particular, detecting “invariant” relative orbits ...

Many protostellar gapped and binary discs show misalignments between their inner and outer discs; in some cases, $\sim70$ degree misalignments have been observed. Here we show that these misalignments can be generated through a "secular precession resonance" between the nodal precession of the inner disc and the precession of the gap-opening (stellar or massive planetary) companion. An evolving protostellar system may naturally cross this resonance during its lifetime due to disc dissipation and/or companion migration. If resonance crossing occurs on the right timescale, of order a few Myrs, characteristic for young protostellar systems, the inner and outer discs can become highly misaligned ($\gtrsim 60$ degrees). When the primary star has a mass of order a solar mass, generating a significant misalignment typically requires the companion to have a mass of $\sim 0.01-0.1$ M$_\odot$ and an orbital separation of tens of AU. The recently observed companion in the cavity of the gapped, highly misaligned system HD 142527 satisfies these requirements, indicating that a previous resonance crossing event misaligned the inner and outer discs. Our scenario for HD 142527's misaligned discs predicts that the companion's orbital plane is aligned with the outer disc's; this prediction should be testable with future observations as the companion's orbit is mapped out. Misalignments observed in several other gapped disc systems could be generated by the same secular resonance mechanism., 12 pages, 8 figures, submitted to MNRAS

We analyse the evolution of a mildly inclined circumbinary disc that orbits an eccentric orbit binary by means of smoother particle hydrodynamic (SPH) simulations and linear theory. We show that the alignment process of an initially misaligned circumbinary disc around an eccentric orbit binary is significantly different than around a circular orbit binary and involves tilt oscillations. The more eccentric the binary, the larger the tilt oscillations and the longer it takes to damp these oscillations. A circumbinary disc that is only mildly inclined may increase its inclination by a factor of a few before it moves towards alignment. The results of the SPH simulations agree well with those of linear theory. We investigate the properties of the circumbinary disc/ring around KH 15D. We determine disc properties based on the observational constraints imposed by the changing binary brightness. We find that the inclination is currently at a local minimum and will increase substantially before setting to coplanarity. In addition, the nodal precession is currently near its most rapid rate. The recent observations that show a reappearance of Star B impose constraints on the thickness of the layer of obscuring material. Our results suggest that disc solids have undergone substantial inward drift and settling towards to disc midplane. For disc masses $\sim 0.001 M_\odot$, our model indicates that the level of disc turbulence is low $\alpha \ll 0.001$. Another possibility is that the disc/ring contains little gas., Comment: 16 pages, 16 figures; accepted for publication in MNRAS

A Neptune-sized exomoon candidate was recently announced by Teachey & Kipping, orbiting a 287 day gas giant in the Kepler-1625 system. However, the system is poorly characterized and needs more observations to be confirmed, with the next potential transit in 2019 May. In this Letter, we aid observational follow up by analyzing the transit signature of exomoons. We derive a simple analytic equation for the transit probability and use it to demonstrate how exomoons may frequently avoid transit if their orbit is larger than the stellar radius and sufficiently misaligned. The nominal orbit for the moon in Kepler-1625 has both of these characteristics, and we calculate that it may only transit roughly 40% of the time. This means that approximately six non-transits would be required to rule out the moon's existence at 95% confidence. When an exomoon's impact parameter is displaced off the star, the planet's impact parameter is displaced the other way, so larger planet transit durations are typically positively correlated with missed exomoon transits. On the other hand, strong correlations do not exist between missed exomoon transits and transit timing variations of the planet. We also show that nodal precession does not change an exomoon's transit probability and that it can break a prograde-retrograde degeneracy., Accepted at ApJ Letters

Recent studies suggest that ultra-short period planets (USPs), Earth-sized planets with sub-day periods, constitute a statistically distinct sub-sample of {\it Kepler} planets: USPs have smaller radii ($1-1.4R_\oplus$) and larger mutual inclinations with neighboring planets than nominal {\it Kepler} planets, and their period distribution is steeper than longer-period planets. We study a "low-eccentricity" migration scenario for the formation of USPs, in which a low-mass planet with initial period of a few days maintains a small but finite eccentricity due to secular forcings from exterior companion planets, and experiences orbital decay due to tidal dissipation. USP formation in this scenario requires that the initial multi-planet system have modest eccentricities ($\gtrsim 0.1$) or angular momentum deficit. During the orbital decay of the inner-most planet, the system can encounter several apsidal and nodal precession resonances that significantly enhance eccentricity excitation and increase the mutual inclination between the inner planets. We develop an approximate method based on eccentricity and inclination eigenmodes to efficiently evolve a large number of multi-planet systems over Gyr timescales in the presence of rapid (as short as $\sim 100$~years) secular planet-planet interactions and other short-range forces. Through a population synthesis calculation, we demonstrate that the "low-$e$ migration" mechanism can naturally produce USPs from the large population of {\it Kepler} multis under a variety of conditions, with little fine tuning of parameters. This mechanism favors smaller inner planets with more massive and eccentric companion planets, and the resulting USPs have properties that are consistent with observations., Comment: submitted to Monthly Notices

We measured the Rossiter-McLaughlin effect of WASP-107b during a single transit with Keck/HIRES. We found the sky-projected inclination of WASP-107b's orbit, relative to its host star's rotation axis, to be $|\lambda| = {118}^{+38}_{-19}$ degrees. This confirms the misaligned/polar orbit that was previously suggested from spot-crossing events and adds WASP-107b to the growing population of hot Neptunes in polar orbits around cool stars. WASP-107b is also the fourth such planet to have a known distant planetary companion. We examined several dynamical pathways by which this companion could have induced such an obliquity in WASP-107b. We find that nodal precession and disk dispersal-driven tilting can both explain the current orbital geometry while Kozai-Lidov cycles are suppressed by general relativity. While each hypothesis requires a mutual inclination between the two planets, nodal precession requires a much larger angle which for WASP-107 is on the threshold of detectability with future Gaia astrometric data. As nodal precession has no stellar type dependence, but disk dispersal-driven tilting does, distinguishing between these two models is best done on the population level. Finding and characterizing more extrasolar systems like WASP-107 will additionally help distinguish whether the distribution of hot-Neptune obliquities is a dichotomy of aligned and polar orbits or if we are uniformly sampling obliquities during nodal precession cycles., Comment: 13 pages, 6 figures, to be published in The Astronomical Journal

This paper proposes a method for deploying a nanosatellite constellation to several orbital planes from a single launch vehicle. The method is based on commercially available deorbit devices that are used to lower the initial orbit, and that are discarded after the correct altitude has been reached. Nodal precession of the right ascension of the ascending node at different altitudes results in spreading the orbital planes of the satellites. Maneuvering all satellites to a similar final altitude freezes the relative separation of the orbital planes. Calculations and simulations of the method are presented, and the results indicate that with a launch of 6 satellites to an initial 800 km sun-synchronous orbit, orbital plane separation of approximately 30° between each satellite can be achieved within 5 years, with each satellite in its own final 600 km orbital plane. Such a constellation could provide continuous global coverage, while requiring only one launch vehicle. Due to the timescales required by the method, it is best suited for nanosatellite missions designed for long lifetimes. Possible applications of such constellations are also discussed.

Aims: We aim to determine whether Jupiter's obliquity is bound to remain exceptionally small in the Solar System, or if it could grow in the future and reach values comparable to those of the other giant planets. Methods: The spin axis of Jupiter is subject to the gravitational torques from its regular satellites and from the Sun. These torques evolve over time due to the long-term variations of its orbit and to the migration of its satellites. With numerical simulations, we explore the future evolution of Jupiter's spin axis for different values of its moment of inertia and for different migration rates of its satellites. Analytical formulas show the location and properties of all relevant resonances. Results: Because of the migration of the Galilean satellites, Jupiter's obliquity is currently increasing, as it adiabatically follows the drift of a secular spin-orbit resonance with the nodal precession mode of Uranus. Using the current estimates of the migration rate of the satellites, the obliquity of Jupiter can reach values ranging from 6{\deg} to 37{\deg} after 5 Gyrs from now, according to the precise value of its polar moment of inertia. A faster migration for the satellites would produce a larger increase in obliquity, as long as the drift remains adiabatic. Conclusions: Despite its peculiarly small current value, the obliquity of Jupiter is no different from other obliquities in the Solar System: It is equally sensitive to secular spin-orbit resonances and it will probably reach comparable values in the future., Comment: Published in Astronomy & Astrophysics

While mantle convection is a fundamental ingredient of geodynamics, the driving mechanism of plate tectonics remains elusive. Are plates driven only from the thermal cooling of the mantle or are there further astronomical forces acting on them? GPS measurements are now accurate enough that, on long baselines, both secular plate motions and periodic tidal displacements are visible. The now >20 year-long space geodesy record of plate motions allows a more accurate analysis of the contribution of the horizontal component of the body tide in shifting the lithosphere. We review the data and show that lithospheric plates retain a non-zero horizontal component of the solid Earth tidal waves and their speed correlates with tidal harmonics. High-frequency semidiurnal Earth's tides are likely contributing to plate motions, but their residuals are still within the error of the present accuracy of GNSS data. The low-frequency body tides rather show horizontal residuals equal to the relative motion among plates, proving the astronomical input on plate dynamics. Plates move faster with nutation cyclicities of 8.8 and 18.6 years that correlate to lunar apsides migration and nodal precession. The high-frequency body tides are mostly buffered by the high viscosity of the lithosphere and the underlying mantle, whereas low-frequency horizontal tidal oscillations are compatible with the relaxation time of the low-velocity zone and can westerly drag the lithosphere over the asthenospheric mantle. Variable angular velocities among plates are controlled by the viscosity anisotropies in the decoupling layer within the low-velocity zone. Tidal oscillations also correlate with the seismic release.

Planet-planet perturbations can cause planets' orbital elements to change on secular timescales. Previous work has evaluated the nodal precession rate for planets in the limit of low $\alpha$ (semi-major axis ratio, 0$, Comment: 18 pages, 11 figures, submitted to AJ

We study the orbital evolution of black hole (BH) binaries in quadruple systems, where the tertiary binary excites large eccentricity in the BH binary through Lidov-Kozai (LK) oscillations, causing the binary BHs to merge via gravitational radiation. For typical BH binaries with masses $m_{1,2}\simeq 20M_\odot-30M_\odot$ and initial semimajor axis $a_0\sim100$ AU (such that the binaries have no chance of merging by themselves within $\sim10^{10}$ yrs), we show that binary-binary interactions can significantly increase the LK window for mergers (the range of companion inclinations that allows the BH binary to merge within 10~Gyrs). This increase arises from a secular resonance between the LK oscillation of the BH binary and the nodal precession of the outer (binary-binary) orbit driven by the tertiary binary. Therefore, in the presence of tertiary binary, the BH merger fraction is increased to $10-30\%$, an order of magnitude larger than the merger fraction found in similar triple systems. Our analysis (with appropriate scalings) can be easily adapted to other configurations of systems, such as relatively compact BH binaries and moderately hierarchical triples, which may generate even higher merger fractions. Since the occurrence rate of stellar quadruples in the galactic fields is not much smaller than that of stellar triples, our result suggests that dynamically induced BH mergers in quadruple systems may be an important channel of producing BH mergers observed by LIGO/VIRGO., 12 pages, 8 figures, accepted for publication in MNRAS

HAT-P-11 is a mid-K dwarf that hosts one of the first Neptune-sized planets found outside the solar system. The orbit of HAT-P-11b is misaligned with the star's spin --- one of the few known cases of a misaligned planet orbiting a star less massive than the Sun. We find an additional planet in the system based on a decade of precision radial velocity (RV) measurements from Keck/HIRES. HAT-P-11c is similar to Jupiter in its mass ($M_P \sin{i} = 1.6\pm0.1$ $M_J$) and orbital period ($P = 9.3^{+1.0}_{-0.5}$ year), but has a much more eccentric orbit ($e=0.60\pm0.03$). In our joint modeling of RV and stellar activity, we found an activity-induced RV signal of $\sim$7 m s$^{-1}$, consistent with other active K dwarfs, but significantly smaller than the 31 m s$^{-1}$ reflex motion due to HAT-P-11c. We investigated the dynamical coupling between HAT-P-11b and c as a possible explanation for HAT-P-11b's misaligned orbit, finding that planet-planet Kozai interactions cannot tilt planet b's orbit due to general relativistic precession; however, nodal precession operating on million year timescales is a viable mechanism to explain HAT-P-11b's high obliquity. This leaves open the question of why HAT-P-11c may have such a tilted orbit. At a distance of 38 pc, the HAT-P-11 system offers rich opportunities for further exoplanet characterization through astrometry and direct imaging., Comment: 16 pages, 11 figures, 4 tables. Accepted to AJ

Although most of the circumbinary planets detected by the Kepler spacecraft are on orbits that are closely aligned with the binary orbital plane, the systems Kepler-413 and Kepler-453 exhibit small misalignments of $\sim 2.5^\circ$. One possibility is that these planets formed in a circumbinary disc whose midplane was inclined relative to the binary orbital plane. Such a configuration is expected to lead to a warped and twisted disc, and our aim is to examine the inclination evolution of planets embedded in these discs. We employed 3D hydrodynamical simulations that examine the disc response to the presence of a modestly inclined binary with parameters that match the Kepler-413 system, as a function of disc parameters and binary inclinations. The discs all develop slowly varying warps, and generally display very small amounts of twist. Very slow solid body precession occurs because a large outer disc radius is adopted. Simulations of planets embedded in these discs resulted in the planet aligning with the binary orbit plane for disc masses close to the minimum mass solar nebular, such that nodal precession of the planet was controlled by the binary. For higher disc masses, the planet maintains near coplanarity with the local disc midplane. Our results suggest that circumbinary planets born in tilted circumbinary discs should align with the binary orbit plane as the disc ages and loses mass, even if the circumbinary disc remains misaligned from the binary orbit. This result has important implications for understanding the origins of the known circumbinary planets., accepted in MNRAS

Accretion discs are common in binary systems, and they are often found to be misaligned with respect to the binary orbit. The gravitational torque from a companion induces nodal precession in misaligned disc orbits. We calculate whether this precession is strong enough to overcome the internal disc torques communicating angular momentum. For typical parameters precession wins: the disc breaks into distinct planes that precess effectively independently. We run hydrodynamical simulations to check these results, and confirm that disc breaking is widespread and generally enhances accretion on to the central object. This applies in many cases of astrophysical accretion, e.g. supermassive black hole binaries and X--ray binaries., 8 pages, 6 figures, accepted for publication in MNRAS

We present analytical formulae for the orbital and epicyclic frequencies in orbits around Maclaurin spheroids in Newtonian gravity. The Laplace equation for the gravitational potential implies that the orbital frequency squared is the arithmetic mean of the squares of the epicyclic frequencies, $\omega _r^2 + \omega _z^2 = 2\Omega _{\rm o}^2$. The radial epicyclic frequency has a maximum at radius $r=\sqrt{2}ae$ for spheroid ellipticities $e>1/\sqrt{2}$, while for e = 0.834 583 18 it vanishes at the stellar equator (at r = a). For still larger ellipticities the innermost stable circular orbit (ISCO) is separated from the surface of the spheroid by a gap and has radius r ms = 1.198 203 ae. The vertical epicyclic frequency is always larger than the orbital one, and always by a factor of $\sqrt{2}$ in the marginally stable orbit. The presence of periastron motion, nodal precession (whose sense is the same as in retrograde orbits in the Kerr metric) and of the ISCO makes the properties of orbital motion around Maclaurin spheroids analogous to those in the Kerr metric. We find that the condition for the existence of circular orbits in test-particle motion is $\omega _r^2 + \omega _z^2 >0$, equally for the Maclaurin spheroid and for the Kerr metric.

NSV 1907, formerly listed as an irregular variable in variability catalogues, was classified as an Algol-type eclipsing binary in the Catalina Surveys Periodic Variable Star Catalogue. We have identified NSV 1907 as an ultraviolet (UV) bright source using measurements from the GALEX space telescope and detected obvious out-of-eclipse variability in archival photometric data from the Catalina Sky Survey, which instigated a closer examination of the object. A spectrum and extensive multicolour photometric observations were acquired, from which we deduce that NSV 1907 is a deeply eclipsing, nova-like cataclysmic variable. Apart from the orbital variations (deep eclipses with a period of P ~ 6.63 hours), changes in mean brightness and irregular short-term variability (flickering) were observed. The presence of a secondary minimum at phase phi ~ 0.5 was established, which indicates a significant contribution of the companion star to the optical flux of the system. We find possible evidence for sinusoidal variations with a period of P ~ 4.2 d, which we interpret as the nodal precession period of the accretion disc. No outbursts or VY Scl-like drops in brightness were detected either by the CSS or during our photometric monitoring. Because of its spectral characteristics and the observed variability pattern, we propose NSV 1907 as a new moderately bright long-period SW Sextantis star. Further photometric and spectroscopic observations are encouraged., 7 pages, 12 figures

Frequencies of the three quasi-periodic oscillation (QPO) modes observed simultaneously in the accreting black hole GRO J1655-40 are compared with the predictions of models. Models in which all three QPO signals are produced at the same radius are considered: these include different versions of relativistic precession, epicyclic resonance, tidal disruption, and warped disc models. Models that were originally proposed to interpret only the twin high-frequency QPOs are generalized here to interpret also the low-frequency QPO in terms of relativistic nodal precession. Inferred values of the black hole mass and spin from each QPO model are compared with the mass measured from optical observations and the spin inferred from X-ray spectroscopy techniques. We find that along with the relativistic precession model predicting $M=(5.3\pm0.1)~M_{\odot}, a=0.286\pm0.004$, the so-called total precession model ($M=(5.5\pm0.1)~M_{\odot}, a=0.276\pm0.003$), and the resonance epicyclic model with beat frequency ($M=(5.1\pm0.1)~M_{\odot}, a=0.274\pm0.003$) also satisfy the optical mass test. We compare our results with those inferred from X-ray spectral measurements.

An analytic form of the accelerations due to the luni-solar perturbations resolved along the rotating Euler-Hill frame is devised by using the expansion method. The addition of higher order terms to the main gravity gradient term linear in the spacecraft radial distance, carried out to the third order, provides a very high level of accuracy in accounting for the gravity perturbations experienced by a vehicle in orbit due to the sun and the moon. The nodal precession as well as the perigee advance of the lunar orbit is taken into account analytically by using the analytic lunar theory of de Pontecoulant. The analytic description of the apparent solar orbit and the motion of the moon remove the need to call an epherneris generator at each integration step during the numerical integration of the spacecraft trajectory, leading to the self-contained software for rapid and efficient optimal trajectory generation through iterations. Equinoctial elements are used to describe the spacecraft state and the luni-solar accelerations are given in terms of the apparent solar and lunar longitudes as well as Eulerian angles of the spacecraft orbit with respect to the inertial ecliptic system. The analysis is useful in optimal low-thrust orbit transfers complementing previous analyses carried out by this author, in which thrust and Earth zonal perturbations such as J2, J3 and J4 in terms of the nonsingular equinoctial elements are included.

We explore the effects of an undetected outer giant planet on the dynamics, observability, and stability of Systems with Tightly-packed Inner Planets (STIPs). We use direct numerical simulations along with secular theory and synthetic secular frequency spectra to analyze how analogues of Kepler-11 and Kepler-90 behave in the presence of a nearly co-planar, Jupiter-like outer perturber with semi-major axes between 1 and 5.2 au. Most locations of the outer perturber do not affect the evolution of the inner planetary systems, apart from altering precession frequencies. However, there are locations at which an outer planet causes system instability due to, in part, secular eccentricity resonances. In Kepler-90, there is a range of orbital distances for which the outer perturber drives planets b and c, through secular interactions, onto orbits with inclinations that are $\sim16^\circ$ away from the rest of the planets. Kepler-90 is stable in this configuration. Such secular resonances can thus affect the observed multiplicity of transiting systems. We also compare the synthetic apsidal and nodal precession frequencies with the secular theory and find some misalignment between principal frequencies, indicative of strong interactions between the planets (consistent with the system showing TTVs). First-order libration angles are calculated to identify MMRs in the systems, for which two near-MMRs are shown in Kepler-90, with a 5:4 between b and c, as well as a 3:2 between g and h., 17 pages, accepted for publication in AJ

We study the circularization of tidally disrupted stars on bound orbits around spinning supermassive black holes by performing three-dimensional smoothed particle hydrodynamic simulations with Post-Newtonian corrections. Our simulations reveal that debris circularization depends sensitively on the efficiency of radiative cooling. There are two stages in debris circularization if radiative cooling is inefficient: first, the stellar debris streams self-intersect due to relativistic apsidal precession; shocks at the intersection points thermalize orbital energy and the debris forms a geometrically thick, ring-like structure around the black hole. The ring rapidly spreads via viscous diffusion, leading to the formation of a geometrically thick accretion disk. In contrast, if radiative cooling is efficient, the stellar debris circularizes due to self-intersection shocks and forms a geometrically thin ring-like structure. In this case, the dissipated energy can be emitted during debris circularization as a precursor to the subsequent tidal disruption flare. The possible radiated energy is up to ~2*10^{52} erg for a 1 Msun star orbiting a 10^6 Msun black hole. We also find that a retrograde (prograde) black hole spin causes the shock-induced circularization timescale to be shorter (longer) than that of a non-spinning black hole in both cooling cases. The circularization timescale is remarkably long in the radiatively efficient cooling case, and is also sensitive to black hole spin. Specifically, Lense-Thirring torques cause dynamically important nodal precession, which significantly delays debris circularization. On the other hand, nodal precession is too slow to produce observable signatures in the radiatively inefficient case. We also discuss the relationship between our simulations and the parabolic TDEs that are characteristic of most stellar tidal disruptions., 23 pages, 18 figures, 1 appendix, accepted for publication in MNRAS (with significant improvement)

This work shows the dynamical instability that can happen to close-in satellites when planet oblateness is not accounted for in non-coplanar multiplanet systems. Simulations include two secularly interacting Jupiter-mass planets mutually inclined by 10 degrees, with the host planet either oblate or spherical. With a spherical host planet, moons within a critical planetocentric distance experience high inclinations and in some cases high eccentricities, while more distant moons orbit stably with low inclinations and eccentricities, as expected. These counter-intuitive dynamical phenomena disappear with an oblate host planet, in which case the moons' Laplace plane transitions from the host planet's equatorial plane to the host planet's precessing orbital plane as their semi-major axes increase, and all moons are dynamically stable with very mild changes in orbits. Direct perturbation from the perturbing planet has been investigated and ruled out as an explanation for the behavior of the innermost satellites, therefore leaving the central star's perturbation as the cause. Instability occurs while the nodal precession of the satellite and the central star (as seen from the host planet's frame) approaches the 1:1 secular resonance. In non-coplanar systems, around a non-oblate planet, the nodal precession of the moon becomes slow and comparable to that of the planet, giving rise to resonant configurations. The above effect needs to be taken into account in setting up numerical simulations., Comment: 7 pages, 6 figures. Accepted for publication in MNRAS

The dynamics of synchronous rotation and physical librations are revisited in order to establish a conceptually simple and general theoretical framework applicable to a variety of problems. Our motivation comes from disagreements between the results of numerical simulations and those of previous theoretical studies, and also because different theoretical studies disagree on basic features of the dynamics. We approach the problem by decomposing the orientation matrix of the body into perfectly synchronous rotation and deviation from the equilibrium state. The normal modes of the linearized equations are computed in the case of a circular satellite orbit, yielding both the periods and the eigenspaces of three librations. Libration in longitude decouples from the other two, vertical modes. There is a fast vertical mode with a period very close to the average rotational period. It corresponds to tilting the body around a horizontal axis while retaining nearly principal-axis rotation. In the inertial frame, this mode appears as nutation and free precession. The other vertical mode, a slow one, is the free wobble. The effects of the nodal precession of the orbit are investigated from the point of view of Cassini states. We test our theory using numerical simulations of the full equations of the dynamics and discuss the disagreements among our study and previous ones. The numerical simulations also reveal that in the case of eccentric orbits large departures from principal-axis rotation are possible due to a resonance between free precession and wobble. We also revisit the history of the Moon's rotational state and show that it switched from one Cassini state to another when it was at 46.2 Earth radii. This number disagrees with the value 34.2 derived in a previous study.

The orbital inclinations of a bounded, self-gravitating particle population subject to secular perturbations from an inclined planet are studied. The particle disk is shown to have discrete modes and pattern speeds in which the wave behavior is very pronounced compared with the nonwave behavior. The response is in the form of a standing wave pattern produced by wave reflection at the finite outer edge of the disk. In the absence of dissipation, the perpendicular torque between disk and perturber vanishes, with equal incoming and outgoing angular momentum fluxes carried by the wave trains. This resonant cavity theory is applied to Neptune perturbations of the primordial Kuiper belt. If the nodal precession rate of Neptune was near one of the disk's mode frequencies, very high inclinations could be produced for this population. There are a number of mechanisms in the early solar system that could have tuned the system to pass through one or more resonant states.

We derive a formula for the nodal precession frequency and the Keplerian period of a particle at an arbitrarily inclined orbit (with a minimum latitudinal angle reached at the orbit) in the post-Newtonian approximation in the external field of an oblate rotating neutron star (NS). We also derive formulas for the nodal precession and periastron rotation frequencies of slightly inclined low-eccentricity orbits in the field of a rapidly rotating NS in the form of asymptotic expansions whose first terms are given by the Okazaki--Kato formulas. The NS gravitational field is described by the exact solution of the Einstein equation that includes the NS quadrupole moment induced by rapid rotation. Convenient asymptotic formulas are given for the metric coefficients of the corresponding space-time in the form of Kerr metric perturbations in Boyer--Lindquist coordinates., 12 pages

Many exoplanetary systems containing hot Jupiters are found to possess significant misalignment between the spin axis of the host star and the planet's orbital angular momentum axis. A possible channel for producing such misaligned hot Jupiters involves Lidov-Kozai oscillations of the planet's orbital eccentricity and inclination driven by a distant binary companion. In a recent work (Storch, Anderson & Lai 2014), we have shown that a proto-hot Jupiter undergoing Lidov-Kozai oscillations can induce complex, and often chaotic, evolution of the spin axis of its host star. Here we explore the origin of the chaotic spin behavior and its various features in an idealized non-dissipative system where the secular oscillations of the planet's orbit are strictly periodic. Using Hamiltonian perturbation theory, we identify a set of secular spin-orbit resonances in the system, and show that overlaps of these resonances are responsible for the onset of wide-spread chaos in the evolution of stellar spin axis. The degree of chaos in the system depends on the adiabaticity parameter $\epsilon$, proportional to the ratio of the Lidov-Kozai nodal precession rate and the stellar spin precession rate, and thus depends on the planet mass, semi-major axis and the stellar rotation rate. For systems with zero initial spin-orbit misalignment, our theory explains the occurrence (as a function of $\epsilon$) of "periodic islands" in the middle of a "chaotic ocean" of spin evolution, and the occurrence of restricted chaos in middle of regular/periodic spin evolution. Finally, we discuss a novel "adiabatic resonance advection" phenomenon, in which the spin-orbit misalignment, trapped in a resonance, gradually evolves as the adiabaticity parameter slowly changes. This phenomenon can occur for certain parameter regimes when tidal decay of the planetary orbit is included., Comment: 15 pages, 17 figures, submitted to MNRAS

Exploration of the inner planets of the Solar System is vital to significantly enhance the understanding of the formulation of the Earth and other planets. This paper therefore considers the development of novel orbits of Mars, Mercury and Venus to enhance the opportunities for remote sensing of these planets. Continuous acceleration is used to extend the critical inclination of highly elliptical orbits at each planet and is shown to require modest thrust magnitudes. This paper also presents the extension of existing sun-synchronous orbits around Mars. However, unlike Earth and Mars, natural sun-synchronous orbits do not exist at Mercury or Venus. This research therefore also uses continuous acceleration to enable circular and elliptical sun-synchronous orbits, by ensuring that the orbit's nodal precession rate matches the planets mean orbital rate around the Sun, such that the lighting along the ground-track remains approximately constant over the mission duration. This property is useful both in terms of spacecraft design, due to the constant thermal conditions, and for comparison of images. Considerably high thrust levels are however required to enable these orbits, which are prohibitively high for orbits with inclinations around 90°. These orbits therefore require some development in electric propulsion systems before becoming feasible.

Kilohertz QPOs can be used as a probe of the inner regions of accretion disks in compact stars and hence also of the properties of the central object. Most models of kHz QPOs involve epicyclic frequencies to explain their origin. We compute the epicyclic frequencies of nearly circular orbits around rotating strange quark stars. The MIT bag model is used to model the equation of state of quark matter and the uniformly rotating stellar configurations are computed in full general relativity. The vertical epicyclic frequency and the related nodal precession rate of inclined orbits are very sensitive to the oblateness of the rotating star. For slowly rotating stellar models of moderate and high mass strange stars, the sense of the nodal precession changes at a certain rotation rate. At lower stellar rotation rates the orbital nodal precession is prograde, as it is in the Kerr metric, while at higher rotation rates the precession is retrograde, as it is for Maclaurin spheroids. Thus, qualitatively, the orbits around rapidly rotating strange quark stars are affected more strongly by the effects of stellar oblateness than by the effects of general relativity. We show that epicyclic and orbital frequencies calculated numerically for small mass strange stars are in very good agreement with analytical formulae for Maclaurin spheroids., Comment: 9 pages, 8 figures, submitted to Physical Review D

At the beginning of this chapter, we will review the way the Earth moves with respect to a Galilean frame. By composing the two motions, we will then be able to follow the motion of the satellite relative to the Earth, which was indeed our original aim. We shall then study the apparent motion of the Sun relative to the Earth, so that we may subsequently study the cycles of the satellite in relation to the Sun. The aim here will ultimately be to specify the geometry of the satellite, its target, and the Sun: we consider a point on the Earth’s surface and determine how this point is seen by the satellite and under what conditions of solar illumination. In the last two sections, we examine two types of satellite orbit for which two of the quantities studied here play a key role. These quantities are the mean motion n and the nodal precession rate \(\dot{\varOmega }\). We shall find that they can take certain values of particular importance for the satellite. The first quantity n determines the geosynchronous orbits, and the second \(\dot{\varOmega }\) the Sunsynchronous orbits.

The effect of the diurnal cycle when monitoring the climate from low earth orbit is examined briefly. Equations are derived that relate the harmonics of the diurnal cycle to temporal sampling error and drift rates in that error. Special attention is given to nodal precession of satellite orbits. Using an insolated blackbody as a simple model for the diurnal cycle, roughly simulating subtropical desert surface temperature, the effects of orbital precession are examined numerically. From an initial configuration, wherein satellites are evenly spaced in nodal crossing time, minor differences in precession rates lead to biases proportional to the amplitude of the semidiurnal cycle and inversely to the square root of the number of satellites. Overall biases for a single mission can be dramatically reduced by flying in a formation wherein the satellites' orbits are evenly distributed in their equator-crossing times. To monitor surface temperature, it is suggested that at least six satellites be flown i...

Even-degree zonal gravitational variations due to mass redistribution within the Earth's system, especially in the atmosphere, hydrosphere, and oceans will lead to variations in the nodal precession rate of satellite orbit. The accurately measured nodal variation for LAGEOS 1 provides a means to study planetary-scale mass redistributions and gravitational variations from the space. In this paper, we investigate atmospheric and hydrologic contributions to the LAGEOS 1 nodal changes using barometric pressure, soil moisture, and snow accumulation values from data-assimilating numerical models. Oceanic effects are estimated from nonsteric sea level change determined by TOPEX/Poseidon satellite radar altimeter observation and a simple model for steric sea level changes. The results are compared with the LAGEOS 1 nodal change time series observed by satellite laser ranging. At annual and semiannual time scales, the atmosphere and hydrosphere provide significant contributions. The atmosphere provides broadband excitation of nodal changes at intraseasonal timescales. Seasonal and intraseasonal nontidal oceanic effects are also significant. General agreement between predicted and observed nodal precession rate residuals is improved relative to earlier studies, in part because of the better estimation of hydrological effects and new assessment of nontidal oceanic effects.

The main aim of the present paper is the very first analysis of the binary-orbit precession out of our Galaxy. The light curves of an eclipsing binary MACHO 82.8043.171 in the Large Magellanic cloud (LMC) were studied in order to analyse the long-term evolution of its orbit. It is a detached system that is undergoing rapid orbit precession. The inclination of the orbit towards the observer has been changing, which has caused the eclipse depth to become lower over the past decade, and this is ongoing. The period of this effect was derived as only about 77 years, so it is the second fastest nodal motion known amongst such systems nowadays. This is the first analysis of an extragalactic binary with nodal precession. This effect is probably caused by a distant third body orbiting the pair, which could potentially be detected via spectroscopy. Some preliminary estimates of this body are presented. However, even such a result can tell us something about the multiplicity fraction in other galaxies., 5 pages, 4 figures, 2 tables, published in 2013A&A...559A..41Z

PTFO 8-8695b represents the first transiting exoplanet candidate orbiting a pre-main-sequence star. We find that the unusual lightcurve shapes of PTFO 8-8695 can be explained by transits of a planet across an oblate, gravity-darkened stellar disk. We simultaneously and self-consistently fit two separate lightcurves observed in 2009 December and 2010 December. Our two self-consistent fits yield M_p = 3.0 M_Jup and M_p = 3.6 M_Jup for assumed stellar masses of M_* = 0.34 M_Sun and M_* = 0.44 M_Sun respectively. The two fits have precession periods of 293 days and 581 days. These mass determinations (consistent with previous upper limits) along with the strength of the gravity-darkened precessing model together validate PTFO 8-8695b as just the second Hot Jupiter known to orbit an M-dwarf. Our fits show a high degree of spin-orbit misalignment in the PTFO 8-8695 system: 69 +/- 2 or 73.1 +/- 0.5 degrees, in the two cases. The large misalignment is consistent with the hypothesis that planets become Hot Jupiters with random orbital plane alignments early in a system's lifetime. We predict that as a result of the highly misaligned, precessing system, the transits should disappear for months at a time over the course of the system's precession period. The precessing, gravity-darkened model also predicts other observable effects: changing orbit inclination that could be detected by radial velocity observations, changing stellar inclination that would manifest as varying v sin i, changing projected spin-orbit alignment that could be seen by the Rossiter-McLaughlin effect, changing transit shapes over the course of the precession, and differing lightcurves as a function of wavelength. Our measured planet radii of 1.64 R_Jup and 1.68 R_Jup in each case are consistent with a young, hydrogen-dominated planet that results from a hot-start formation mechanism., Accepted at ApJ

We have carried out general relativistic particle simulations of stars tidally disrupted by massive black holes. When a star is disrupted in a bound orbit with moderate eccentricity instead of a parabolic orbit, the temporal behavior of the resulting stellar debris changes qualitatively. The debris is initially all bound, returning to pericenter in a short time ~ the original stellar orbital timescale. The resulting fallback rate can thus be much higher than the Eddington rate. Furthermore if the star is disrupted close to the hole, in a regime where general relativity is important, the stellar and debris orbits display general relativistic precession. Apsidal precession can make the debris stream cross itself after several orbits, likely leading to fast debris energy dissipation. If the star is disrupted in an inclined orbit around a spinning hole, nodal precession reduces the probability of self-intersection, and circularization may take many dynamical timescales, delaying the onset of flare activity. An examination of the particle dynamics suggests that quasi-periodic flares with short durations, produced when the center of the tidal stream passes pericenter, may occur in the early-time light curve. The late-time light curve may still show power-law behavior which is generic to disk accretion processes. The detection triggers for future surveys should be extended to capture such "non-standard" short-term flaring activity before the event enters the asymptotic decay phase, as this activity is likely to be more sensitive to physical parameters such as the black hole spin., Comment: 19 pages, 5 figures, Accepted for publication in ApJL

We investigate whether the recently discovered Phoenix stream may be part of a much longer structure that includes the previously discovered Hermus stream. Using a simple model of the Galaxy with a disk, bulge, and a spherical dark matter halo, we show that a nearly circular orbit, highly inclined with respect to the disk, can be found that fits the positions, orientations, and distances of both streams. While the two streams are somewhat misaligned in the sense that they do not occupy the same plane, nodal precession due to the Milky Way disk potential naturally brings the orbit into line with each stream in the course of half an orbit. We consequently consider a common origin for the two streams as plausible. Based on our best fitting orbit, we make predictions for the positions, distances, radial velocities, and proper motions along each stream. If our hypothesis is borne out by measurements, then at ~183 degrees (~235 degrees with respect to the Galactic center) and ~76 kpc in length, Phoenix-Hermus would become the longest cold stream yet found. This would make it a particularly valuable new probe of the shape and mass of the Galactic halo out to ~20 kpc., Comment: 8 pages, 4 figures, accepted for publication in ApJ Letters

The observed properties of transiting exoplanets are an exceptionally rich source of information that allows us to understand and characterize their physical properties. Unfortunately, only a relatively small fraction of the known exoplanets discovered using the radial velocity technique are known to transit their host, due to the stringent orbital geometry requirements. For each target, the transit probability and predicted transit time can be calculated to great accuracy with refinement of the orbital parameters. However, the transit probability of short period and eccentric orbits can have a reasonable time dependence due to the effects of apsidal and nodal precession, thus altering their transit potential and predicted transit time. Here we investigate the magnitude of these precession effects on transit probabilities and apply this to the known radial velocity exoplanets. We assess the refinement of orbital parameters as a path to measuring these precessions and cyclic transit probabilities., 6 pages, 4 figures, accepted for publication in ApJ, fixed references

In transiting planetary systems, the angle between the orbital angular momentum and the stellar spin is usually constrained through the Rossiter-McLaughlin effect observed in radial velocity and can be subject to large uncertainties, especially for hot stars (T_eff > 6250 K). It is thus interesting to have an alternative method to constrain the value of the obliquity and to detect companions that might have disturbed the orbit of the planet. We show how the long-term variations in the transit duration (TDV) can be used to constrain the obliquity of the stellar rotation axis. We introduce a simple theory to express the secular variations in the orbital elements and their effects on the TDVs with a general formulation valid for both oblique and eccentric systems. Parameters or orbital elements that cannot be directly measured, such as the longitude of the ascending node of the orbit, are avoided thus allowing us a straightforward application. We compute the expected TDVs for the presently known transiting systems, adopting their parameters found in the literature. Considering the capabilities of the present or next generation space-borne telescopes, we point out the systems that could be readily observed and discuss the constraints derivable on their fundamental parameters. TDVs can be used to constrain the obliquity of the stars (and possibly of the planets in systems younger than 10 -- 100 Myr), giving information about the formation scenarios, the strength of the tidal coupling, and the internal structure of both the stars and the planets. Moreover, they can provide an indirect indication of the presence of other bodies, even with a mass comparable with that of the Earth, because they give rise to additional contributions to the nodal precession., 8 pages, 1 figure, accepted by A&A

Planets have been observed in tight binary systems with separations less than 20 AU. A likely formation scenario for such systems involves a dynamical capture, after which high relative inclinations are likely and may lead to Kozai oscillations. We numerically investigate the fate of an initially coplanar double-planet system in a class of binaries with separation ranging between $12 - 20 $ AU. Dynamical integrations of representative four-body systems are performed, each including a hot Jupiter and a second planet on a wider orbit. We find that, although such systems can remain stable at low relative inclinations ($\lesssim 40^\circ$), high relative inclinations are likely to lead to instabilities. This can be avoided if the planets are placed in a \emph{Kozai-stable zone} within which mutual gravitational perturbations can suppress the Kozai mechanism. We investigate the possibility of inducing Kozai oscillations in the inner orbit by a weak coupling mechanism between the planets in which the coplanarity is broken due to a differential nodal precession. Propagating perturbations from the stellar companion through a planetary system in this manner can have dramatic effects on the dynamical evolution of planetary systems, especially in tight binaries and can offer a reasonable explanation for eccentricity trends among planets observed in binary systems. We find that inducing such oscillations into the orbit of a hot Jupiter is more likely in tight binaries and an upper limit can be set on the binary separation above which these oscillations are not observed.

Many recent observational studies have concluded that planetary systems commonly exist in multiple-star systems. At least ~20% of the known extrasolar planetary systems are associated with one or more stellar companions. The orbits of stellar binaries hosting planetary systems are typically wider than 100 AU and often highly inclined with respect to the planetary orbits. The effect of secular perturbations from such an inclined binary orbit on a coupled system of planets, however, is little understood theoretically. In this paper we investigate various dynamical classes of double-planet systems in binaries through numerical integrations and we provide an analytic framework based on secular perturbation theories. Differential nodal precession of the planets is the key property that separates two distinct dynamical classes of multiple planets in binaries: (1) dynamically-rigid systems in which the orbital planes of planets precess in concert as if they were embedded in a rigid disk, and (2) weakly-coupled systems in which the mutual inclination angle between initially coplanar planets grows to large values on secular timescales. In the latter case, the quadrupole perturbation from the outer planet induces additional Kozai cycles and causes the orbital eccentricity of the inner planet to oscillate with large amplitudes. The cyclic angular momentum transfer from a stellar companion propagating inward through planets can significantly alter the orbital properties of the inner planet on shorter timescales. This perturbation propagation mechanism may offer important constraints on the presence of additional planets in known single-planet systems in binaries., Comment: 14 pages, 14 figures, to appear in ApJ

*A charged particle moving relative to a magnetic field accelerates in a direction perpendicular to its velocity and the magnetic field due to the Lorentz force. Although a negligible force for spacecraft potentials due to natural charging, this effect can be seen, for example, in the unusual celestial mechanics of dust particles in the rings of Saturn and Jupiter. This study evaluates the use of the Lorentz force as a means of orbit control for finite bodies, including small spacecraft. Although the Hamiltonian is constant in a frame that rotates with the earth, the co-rotational electrical field (associated with the rotating geomagnetic field) can do work, increasing or decreasing the orbit’s semimajor axis. A number of intriguing applications are offered, including earth escape, drag compensation, new stable satellite formations, inclination control, nodal precession control, new sunsynchronous orbits, and non-Keplerian orbits for polar satellites. A candidate spacecraft design is offered based on lessons learned from decades of research in spacecraft charging and plasma interactions. The performance of this design is demonstrated by simulation. Closed-form equations for actuator sizing are provided.

The relativistic precession model for quasi periodic oscillations, QPOs, in low mass X-ray binaries is reviewed. The behaviour of three simultaneous types of QPOs is well matched in terms of the fundamental frequencies for geodesic motion in the strong field of the accreting compact object for reasonable star masses and spin frequencies. The model works for neutron star as well as black hole candidate systems, as it ascribes the higher frequency kHz QPOs, the lower frequency kHz QPOs and the horizontal branch oscillations to the Keplerian, periastron precession and nodal precession frequencies of matter orbiting close to the inner edge of the accretion disk. The remarkable correlation between the centroid frequency of QPOs in both neutron star and black hole candidate low mass X-ray binaries is very well fit by the model. Some testable predictions are described. QPOs from low mass X-ray binaries might provide an unprecedented laboratory to test strong field general relativity.

We consider the evolution of a warped disc around a Kerr black hole, under conditions such that the warp propagates in a wavelike manner. This occurs when the dimensionless effective viscosity, alpha, that damps the warp is less than the characteristic angular semi-thickness, H/R, of the disc. We adopt linearized equations that are valid for warps of sufficiently small amplitude in a Newtonian disc, but also account for the apsidal and nodal precession that occur in the Kerr metric. Through analytical and time-dependent studies, we confirm the results of Demianski & Ivanov, and of Ivanov & Illarionov, that such a disc takes on a characteristic warped shape. The inner part of the disc is not necessarily aligned with the equator of the hole, even in the presence of dissipation. We draw attention to the fact that this might have important implications for the directionality of jets emanating from discs around rotating black holes., 8 pages, 6 figures, to be published in MNRAS