Initial Inclination Research Articles

The influence of inclinations on the dynamical stability of multi-planet systems

ABSTRACT A type of compactly spaced and comparably sized multi-exoplanet system similar to TRAPPIST-1 has been discovered recently. The stability of these systems is an important issue, requiring further study. We examined how the initial inclinations influence the stability of multi-planet systems and derived an empirical formula describing the dependence of the instability time-scale on planetary mass, space separation and initial inclination. We find the following. (i) If space separations between planets are greater than 12RH (mutual Hill radius), coplanar multi-planet systems with 10−6 ≤ μ ≤ 10−3 (reduced planetary mass μ = m/M*) will remain stable within 1010Tin (the innermost orbital period). (ii) If initial inclinations of planets are smaller than 10° and space separations are greater than 10RH, multi-planet systems consisting of ≥5 planets with μ ≥ 10−5 will remain stable within 1010Tin. (iii) Initial inclinations in [0°, 10°] have inconsequential effects on the instability time-scales of massive multi-planet systems (μ ≥ 10−5), because eccentricities (excited during evolution) dominate the stability of these systems. (iv) If the initial inclinations are large enough (≥10°), sharp increases of instability time-scales in groups with 10−3 ≥ μ ≥ 10−5 will be moderated. This article presents a comprehensive study of the influence of inclination on the stability of multi-planet systems and discusses critical space separations for a multi-planet system becoming unstable.

Luni-solar resonances and effect on long-term evolution of inclined geostationary transfer orbits

In this paper, a singly-averaged, semi-analytical orbital dynamic model in terms of Milankovitch elements is given for geostationary transfer orbits (GTOs), which includes the Earth's oblateness, luni-solar perturbations, atmospheric drag and solar radiation pressure (SRP). The orbital dynamic model is verified through a numerical simulation compared with the Semi-analytic Tool for End of Life Analysis software (STELA) by CNES. We find that if the area-to-mass ratio of the object is relatively large, the SRP will have a significant impact on the long-term evolution of GTOs. Then, the long-term dynamical evolution and orbital resonances of rocket upper stages in inclined geostationary transfer orbits (IGTOs) are studied. It has been found that the luni-solar secular resonances, which are inclination-dependent-only, play a leading role in the long-term evolution of IGTOs. By comparing and analyzing long-term dynamical evolution of orbits with different initial inclinations, the effects of luni-solar secular resonances are studied in details. Finally, a mitigation method for IGTO objects by utilizing luni-solar secular resonances is proposed, in which the eccentricity growth caused by the resonances is used for an early atmospheric re-entry.

Magnetorheological elastomers with particle chain orientation: modelling and experiments

This work describes a new model of the magneto-induced shear storage modulus to simulate the shear behavior of magnetorheological elastomers (MRE) with particle chain orientation. The directionality of the chains is here described by using as a parameter the tilt angle with the external magnetic field. The magnetized particles within the MRE are described as magnetic dipoles. The model takes into consideration the dipole–dipole interaction and the magnetic field coupling between the particles in the chain. Magneto-rheological samples with different particle sizes and initial inclination angles have also been prepared and subjected to shear tests in a rheometer facility. The simulations from the model show that the magneto-induced modulus strongly depends on the initial inclination angle of the particle chain. The experimental data are also consistent with the results provided by the model, and confirm that the change of the initial tilt angle of the particle chain is an effective tool to improve the mechanical properties of magneto-rheological elastomers.

Sedimentation of an elliptic rigid particle in a yield-stress fluid: A Lattice-Boltzmann simulation

Sedimentation of a single, two-dimensional, rigid, elliptic particle in a biviscous fluid contained in a finite, closed-ended channel is studied in this work using the lattice-Boltzmann method. The main objective of the work is to numerically investigate the role played by a fluid’s yield stress on the trajectory, orientation, and terminal velocity of such a particle for different density and aspect ratios. Numerical results suggest that a new mode of settling might emerge for yield-stress fluids, which is nonexistent for Newtonian fluids. That is, a particle released from the rest state at the midplane with a prescribed, nonzero, inclination angle (with respect to the horizontal line) migrates toward the left side-wall (if the inclination angle is positive) soon after it is released but changes course after a short while and moves back toward the centerline where the voyage started. However, while for Newtonian fluids the particle eventually returns to the centerline and continues its free fall with a horizontal orientation, for yield-stress fluids, the particle might finally lodge at a specific distance away from the centerline and continue its fall assuming a nonhorizontal orientation. The offset position is predicted to be a function of the Bingham number and the density ratio but independent of the initial inclination angle.

Long-Term Evolution of Highly-Elliptical Orbits: Luni-Solar Perturbation Effects for Stability and Re-entry

This paper investigates the long-term evolution of spacecraft in Highly Elliptical Orbits (HEOs). The single averaged disturbing potential due to luni-solar perturbations, zonal harmonics of the Earth gravity field is written in mean Keplerian elements. The double averaged potential is also derived in the Earth-centered equatorial system. Maps of long-term orbit evolution are constructed by measuring the maximum variation of the orbit eccentricity to identify conditions for quasi-frozen, long-lived libration orbits or initial orbit conditions that naturally evolve toward re-entry in the Earth’s atmosphere. The behavior of these long-term orbit maps is studied for increasing values of the initial orbit inclination and anomaly of the perigee with respect to the Moon’s orbital plane. In addition, to allow meeting specific mission constraints, quasi-frozen orbits can be selected as graveyard orbits for the end-of-life of HEO missions. On the opposite side, unstable conditions can be exploited to target Earth re-entry at the end-of-mission.

NGC 7457: evidence for merger-driven cylindrical rotation in disc galaxies

ABSTRACT We construct Schwarzschild orbit-based models of NGC 7457, known as a peculiar low-mass lenticular galaxy. Our best-fitting model successfully retrieves most of the unusual kinematics behaviours of this galaxy, in which, the orbital distribution of stars is dominated by warm and hot orbits. The reconstructed surface brightness of the hot component matches fairly well the photometric bulge and the reconstructed LOSVD map of this component shows clear rotation around the major photometric axis of the galaxy. In the absence of a dominant cold component, the outer part of our model is dominated by warm orbits, representing an exponential thick disc. Our orbital analysis also confirms the existence of a counter-rotating orbital substructure in the very centre, reported in previous observational studies. By comparing our model with a variety of simulation studies, and considering the stellar kinematics and populations properties of this galaxy, we suggest that the thick disc is most likely a dynamically heated structure, formed through the interactions and accretion of satellite(s) with near-polar initial inclination. We also suggest a merger-driven process as the most plausible scenario to explain the observed and dynamically modelled properties of the bulge of NGC 7457. We conclude that both the high level of cylindrical rotation and unusually low velocity dispersion reported for the NGC 7457 have most likely external origins. Therefore, NGC 7457 could be considered as a candidate for merger-driven cylindrical rotation in the absence of a strong bar in disc galaxies.

Orbital lifetime and collision risk reduction for inclined geosynchronous disposal orbits

A growing number of satellites are operating on inclined geosynchronous orbits (IGSOs) with inclination typically much higher than that of traditional geosynchronous orbits (GEOs). Several recent studies have considered the long-term evolution of IGSOs. Unlike traditional GEO disposal orbits, IGSO disposal orbits can undergo large excursions in eccentricity due to the effect of luni-solar gravity perturbations. For specific ranges of initial orbital elements, perigee can reach the Earth's atmosphere, resulting in vehicle reentry. A previously published study by the authors on Tundra orbits, a specific class of IGSO with critical inclination and moderate eccentricity, demonstrated that orbital lifetime can be reduced below 200 years (in some cases below 25 years) and that the corresponding collision probability with background objects can be significantly reduced below that for traditional GEO disposal orbits. This paper presents a study of a broad range of IGSO disposal orbits. Three cases of IGSO disposal orbit were considered: (1) near circular orbits (motivated by the BeiDou and IRNSS constellations); (2) orbits with intermediate eccentricity (motivated by the QZS constellation); and (3) orbits with larger eccentricity (motivated by the Sirius Tundra constellation). For each case, a large number of long-term propagations using the high-precision code TRACE were performed. Disposal orbit initial inclination and right ascension of ascending node (RAAN) were parametrically varied. The Aerospace Debris Environment Projection Tool (ADEPT) suite was used to determine collision probability with inactive background objects and with operational satellites in GEO, medium Earth orbit (MEO), and low Earth orbit (LEO). Study results show that orbital lifetime of IGSOs can be reduced to less than 200 years for all three IGSO cases considered if initial inclination is high enough. The minimum required inclination depends on initial RAAN. An orbital lifetime less than 200 years offers effective reduction of probability of collision with inactive background objects (by 0.7–1.8 orders of magnitude) and can be achieved in a wider disposal orbit design space than would be needed to reduce orbital lifetime to less than 25 years. For near circular IGSOs, collision probability with operational satellites will be higher at high inclinations than at low inclinations, but there are options for mitigation. When inclination is not high enough to achieve reentry, a high eccentricity storage disposal orbit may be a consideration if collision probability is lower than for other options.

Black hole mergers from quadruples

With the hundreds of merging binary black hole (BH) signals expected to be detected by LIGO/Virgo, LISA and other instruments in the next few years, the modeling of astrophysical channels that lead to the formation of compact-object binaries has become of fundamental importance. In this paper, we carry out a systematic statistical study of quadruple BHs consisting of two binaries in orbit around their center of mass, by means of high-precision direct $N$-body simulations including Post-Newtonian (PN) terms up to 2.5PN order. We found that most merging systems have high initial inclinations and the distributions peak at $\sim 90^\circ$ as for triples, but with a more prominent broad distribution tail. We show that BHs merging through this channel have a significant eccentricity in the LIGO band, typically much larger than BHs merging in isolated binaries and in binaries ejected from star clusters, but comparable to that of merging binaries formed via the GW capture scenario in clusters, mergers in hierarchical triples, or BH binaries orbiting intermediate-mass black holes in star clusters. We show that the merger fraction can be up to $\sim 3$--$4\times$ higher for quadruples than for triples. Thus even if the number of quadruples is $20\%$--$25\%$ of the number of triples, the quadruple scenario can represent an important contribution to the events observed by LIGO/VIRGO.

Will Medical Students Cadaver Dissection Experience Influence their Proclivity toward Body Donation?

ObjectivePrevious work suggests that human dissection in medical school enhances a student's knowledge of and appreciation for the human body1. While most students report predominantly positive feelings toward their experiences in anatomy lab2, we do not currently understand the impact of cadaver dissection on a student's inclination to donate her own body. In this study we aim to determine whether human cadaver dissection impacts medical students' proclivity to donate their own bodies postmortem and whether initial inclination varies based on demographic factors.MethodsWe surveyed 140 first‐year medical students at the Baylor College of Medicine before they began anatomical dissection of human cadavers. The survey included items regarding race, religion, hometown, previous experience with human dissection, organ donor status, initial proclivity to donate one's own body and reasons underlying this proclivity. We employed Pearson's chi‐squared analyses to determine whether initial inclination to donate one's body varied based on the aforementioned factors. Students will be administered a similar survey again after completion of their anatomy course in February 2019. We will use this data to determine whether their experiences in lab influence their likelihood to donate their body.ResultsBefore beginning cadaver dissection, nearly equivalent proportions of the class said that they would vs. would not donate their body for medical education (48% yes vs. 52% no). We found no correlation between race, religion, or age and proclivity toward body donation. Fifty‐five percent (55%) of those who are registered organ donors indicated they would donate their body vs. 29% of those who are not registered organ donors (OR=2.88, p=0.0002). Additionally, the proportion of reasons underlying proclivity varied significantly between those who would vs. would not be inclined to donate their bodies. Fifty‐two percent (52%) of those who said they would donate their body cited ethical reasons vs. 4% of those who said they would not (p<0.0001). In contrast, 12% of those who said they would donate their body cited religious reasons vs. 24% of those who said they would not (p=0.012).ConclusionsWe found that the best predictor of a student's initial proclivity toward body donation is organ donor status. While we found no correlation between demographic factors and proclivity toward body donation, we did find that the reasons underlying one's inclination toward or against donating her body varied significantly between the groups. Those who said they would donate their body were far more likely to cite ethical reasons, while those who said they would not donate were more likely to cite religious reasons. Come February we will finish analyses on the post‐lab survey to determine the effects of human dissection on inclination to donate one's body to medical education.This abstract is from the Experimental Biology 2019 Meeting. There is no full text article associated with this abstract published in The FASEB Journal.

An agentive focus may limit learning about complex causality and systems dynamics: A study of seventh graders' explanations of ecosystems

AbstractAgent‐oriented pedagogies have been used in teaching concepts related to complex systems dynamics. However, little research has systematically explored the role of a strong agency‐oriented focus on understanding of complex, dynamic ecological systems. This study analyzed seventh graders' (n = 216) explanations of a complex ecological scenario. The findings show that students were more likely to generate agentive than nonagentive explanations and students who adopted an agentive framing were least likely to understand the complex causal dynamics of two environmental scenarios, eutrophication in a pond and acid rain in a forest. Furthermore, students' initial inclination toward agency‐oriented explanation on the assessment was predictive of their performance on a postassessment following an instructional opportunity to learn about ecosystems dynamics; a strong agency orientation corresponded to less complex interpretations of the dynamics of the ecosystems. The results suggest that a strongly agentive perspective may limit students' ability to learn complex systems dynamics and that the pedagogical advantages of agent‐based approaches may not be without limitations.

A new way to introduce geometrically nonlinear stiffness and damping with an application to vibration suppression

The single-degree-of-freedom linear oscillator (LO) under the action of harmonic forcing is coupled to a light attachment that acts, in essence, as a nonlinear energy sink (NES). The complex dynamics of this two-degree-of-freedom system is investigated. Strong stiffness and damping nonlinearity in this system is introduced by coupling the LO and NES by two inclined linear spring-damper elements. The inclination of the coupling elements during the motion introduces strongly nonlinear geometric effects in the forced dynamics. A slow/fast partition of the dynamics is introduced by applying a complexification-averaging method, based on which a bifurcation analysis is performed. The effects of the initial angle, i.e., the initial inclination angle of the spring-damper elements, are thoroughly studied. The topology of the trajectories on the slow manifold of the dynamics is studied, and the different steady-state response regimes are predicted analytically. The conditions for existence of strongly modulated responses and of “folding singularities” are studied, and their effects on the nonlinear dynamical responses are revealed. Comparisons between analytical and numerical results indicate a good agreement between the two and provide a means of verification of the analytical findings. The analytical results show that, by increasing the initial angle of inclination, one can shrink, and even completely eliminate, unwanted high-amplitude steady-state responses of the LO that co-exist with desirable low-amplitude forced responses over definitive frequency ranges. This finding has significant practical implications for the vibration mitigation efficiency and robustness of the proposed NES, enhancing drastically the vibration suppression of the forced response of the LO. The presented results and the associated analytical modeling can be used to design and enhance the performance of nonlinear vibration absorbers as vibration mitigating devices.

WASP-92, WASP-93, and WASP-118: transit timing variations and long-term stability of the systems

We studied three exoplanetary systems with transiting planets: WASP-92, WASP-93 and WASP-118. Using ground-based photometric observations of WASP-92 and WASP-93 and Kepler-K2 observations of WASP-118, we redetermined the orbital and physical parameters of these planets. The precise times of all transits were determined. We constructed O-C diagrams of transits and analysed possible transit timing variations. We did not observe any significant deviation from a linear ephemeris for any of the selected exoplanets. We put upper-mass limits for other hypothetical planets in these systems. Using long-term numerical simulation, we looked for stable regions where another planet could exist for a long time. We used the maximum eccentricity method for this purpose. We discuss the influence of values of initial inclination and eccentricity on the shape and size of regions of stability.

Analysis of lifetime extension capabilities for CubeSats equipped with a low-thrust propulsion system for Moon missions

In this paper, we analyze the mission lifetime extension capability for a CubeSat smaller than 3U in a circular lunar orbit at a 100-km altitude, assuming the utilization of a state-of-the-art low-thrust electric propulsion system such as pulsed plasma thrusters with an impulse bit (Ibit) and velocity change (ΔV) below 60 μNs and 120 m/s, respectively. Because of the non-spherical gravity field of the Moon and its strong influence on low-altitude lunar orbits, a long orbital lifetime is achievable only within a set of stable orbits which mainly depends on initial inclination and right ascension of the ascending node (RAAN); moreover, as a piggyback on a main mission, the deployment of CubeSats in those stable orbits is not guaranteed. For this reason, we propose an orbit correction strategy whose performance is constrained to the initial orbital parameters of the CubeSat (i.e., inclination and RAAN), its solar power generation capacity, its attitude control strategy, and its propulsion subsystem features, such as the thruster Ibit and budgeted ΔV. By analyzing the required time to perform the orbit correction maneuvers to extend the orbital lifetime and the minimum altitude achieved throughout the mission lifetime of the spacecraft, we demonstrated that a one-year mission can be achieved within initial orbital inclination values greater than 65°. For unstable orbits bounded by initial orbital inclination values smaller than 65°, the orbit lifetime can also be extended from a few days to up to one year. Better performance with our proposed orbit correction strategy can be achieved by using an electric propulsion system featuring Ibit and ΔV values greater than 40 μNs and 80 m/s, respectively. Our results show the feasibility of performing any orbit correction maneuver for the enhancement of the mission lifetime of a CubeSat, expanding the performance capabilities of CubeSats to any mission in a lunar orbit by reducing the limitation of deploying them in unstable orbits.

Misaligned accretion disc formation via Kozai–Lidov oscillations

We investigate the formation and evolution of misaligned accretion discs around the secondary component of a binary through mass transfer driven by Kozai-Lidov oscillations of the circumprimary disc's eccentricity and inclination. We perform SPH simulations to study the amount of mass transferred to the secondary star as a function of both the disc and binary parameters. For the range of parameters we explore, we find that increasing the disc aspect ratio, viscosity parameter and initial inclination as well as decreasing the binary mass ratio leads to larger amount of mass transfer, up to a maximum of about ten per cent of the initial mass of the primary disc. The circumsecondary disc forms with a high eccentricity and a high inclination and is also able to undergo KL oscillations. The circumsecondary disc oscillations have a shorter period than those in the disc around the primary. We find that some of the material that escapes the Roche-lobe of the two components forms a narrow misaligned circumbinary accretion disc. This study has implications for disc evolution in young binary star systems.

Rational design of additively manufactured Ti6Al4V implants to control Staphylococcus aureus biofilm formation

Bacterial attachment and subsequent biofilm formation on medical implants presents a serious infection risk. The precision, personalisation and superior functionality of additive manufacturing techniques, such as selective laser melting (SLM), enables the fabrication of metallic implants with patient specific customisation. An unexpected outcome of this process, however, is a hitherto unachievable fine control over the bio-interface in a single manufacturing step. Here, for the first time, we report on how the SLM build inclination angle can be utilised to modify the surface topography of metallic implants for directed Staphylococcus aureus biofilm restriction. From an initial build inclination angle of 90°, lowering the angle gave metallic surfaces with lower roughness, lower hydrophobicity, higher surface energy, and fewer partially melted metal particles without altering the bulk surface chemistry. This directly correlated with significantly lower biofilm coverage and an associated reduction in biomass without compromising mammalian cell viability and attachment. This work provides facile single step method at the manufacturing stage for the development of additively manufactured metallic implants with superior, inherent protection against implant associated infection.

Numerical analysis of fatigue performance of CFRP–repaired steel plates with central inclined cracks

Previous experimental and numerical studies on central inclined cracked steel plates demonstrated that when the initial crack inclination angles range from 0° to 60°, fatigue lives are similar if the initial crack projection lengths on the direction perpendicular to the loading direction are the same. This is applicable to both unrepaired and repaired specimens. This numerical study extended the inclination angle range from 60° to 80° and was conducted on the stress intensity factor (SIF) and fatigue life of CFRP–repaired steel plates with inclined central cracks subjected to tensile fatigue loading. In the case of unrepaired specimens with a crack inclination angle of 0–70° and double-sided repaired specimens with a crack inclination angle of 0–60°, it was concluded that the crack projection length on the direction perpendicular to the loading axis is the main influence of fatigue life, even though the projection length is calculated from the crack length and inclination angle. Beyond these limits, there is an obvious increase of fatigue life as the crack inclination angle rises. To minimize the effect of mode II component of SIF on the crack tip, two tail slots perpendicular to the loading axis were induced in the front of the inclined crack tips. The tail slots caused the effective SIF to increase and this led to a reduction of fatigue life. However, the limits of the initial crack angle of fatigue life calculation did not change. The results of previous research were also compared to the findings of this study; they supported the conclusions to some extent.

Climate Vibrations and Chaotic Behavior of Earth’s Inclination in the Laskar’s Model of a Moonless Earth

The model of the moonless Earth, introduced by J. Laskar, has the form of a non-autonomous Hamiltonian system of differential equations for two variables: the cosine of the angle of inclination and the longitude of the axis of rotation of the Earth. The system describes the rotational dynamics of the Earth under the influence of the sun and planets. Earth perturbations from other planets of the solar system are considered periodic and are taken into account using the first four terms of the Fourier expansion of the corresponding part of the Hamilton function with known amplitudes and frequencies. The initial inclination of the Earth is considered as a parameter of the problem. The system was numerically integrated over a time period of 18 million years for various values of the initial inclination from 0 to 180 degrees. Three chaotic gaps of the initial inclination were found. During the bifurcation study, singular points were found and special segments of the non-autonomous system were obtained. A bifurcation diagram of the system is constructed by the initial inclination parameter. Poincare cartographic maps are constructed. The system is written in variations on the initial conditions for the Laskar system, and with its help the dependences of the problem parameter of the senior Lyapunov exponent and the averaged MEGNO indicator are calculated. The results confirm the presence of three chaotic and one regular region of variation of the bifurcation parameter of the problem.

Secular Transport during Disk Dispersal: The Case of Kepler-419

Abstract Due to fortuitous circumstances, the two giant planets around Kepler-419 have well characterized three-dimensional orbits. They are nearly coplanar to each other; the inner one has a large eccentricity (≃0.82); and the apses of the two orbits librate around anti-alignment. Such a state defies available proposals for large eccentricities. We argue that it is instead uniquely produced by a decaying protoplanetary disk. When the disk was massive, its precessional effect on the planets forced the two apses to center around an anti-aligned state. And as the disk is gradually eroded, the pair of planets are adiabatically transported to a new state where most of the eccentricity (or rather, the angular momentum deficit) is transferred to the inner planet, and the two apses are largely anti-aligned. During this transport, any initial mutual inclination may be reduced or enhanced; either may be compatible with the current constraints. So a primordial disk can drive up planet eccentricities both in resonant planet pairs (as has been shown for GJ 876) and in secularly-interacting, non-resonant pairs. The mechanism discussed here may be relevant for forming hot Jupiters and for explaining the observed eccentricities of warm and cold giant planets.

The motion of a buoyant vortex filament

We investigate the motion of a thin vortex filament in the presence of buoyancy. The asymptotic model of Moore & Saffman (Phil. Trans. R. Soc. Lond.A, vol. 272, 1972, pp. 403–429) is extended to take account of buoyancy forces in the force balance on a vortex element. The motion of a buoyant vortex is given by the transverse component of force balance, while the tangential component governs the dynamics of the structure in the core. We show that the local acceleration of axial flow is generated by the external pressure gradient due to gravity. The equations are then solved for vortex rings. An analytic solution for a buoyant vortex ring at a small initial inclination is obtained and asymptotically agrees with the literature.

Performance and Applicability of Orbital Transfer with Bare Electrodynamic Tether

Electrodynamic tether technology is a novel way to perform spacecraft orbital transfers. This paper focuses on a bare electrodynamic tether (BEDT) system and evaluates its orbital transfer performance and mission applicability. A nonsingular dynamic model of the BEDT orbital transfer system is developed. In particular, the ambient perturbation forces, including the atmospheric drag and Earth oblateness effect, are taken into account. Numerical simulations are then performed to investigate the orbital transfer performance under various mission parameters involving the initial orbital altitude, initial orbital inclination, tether length, tether diameter, spacecraft mass, and power voltage. An orbital transfer scheme is designed to raise and regulate the orbit. Furthermore, to verify its practicability, the mission applicability of the BEDT system is analyzed for Ariane-4’s H10 upper stage by comparison with the conventional chemical propulsion method. Finally, the conclusions and some discussions are presented to support conducting BEDT-based orbital transfer mission planning in practice.