Planetary Spin Research Articles

Effect of planet pin position errors on the fatigue reliability of large aviation planetary systems

Effect of planet pin position errors on the fatigue reliability of large aviation planetary systems

Stable three-dimensional vortex families consistent with Jovian observations including the Great Red Spot

Detailed observations of the velocities of Jovian vortices exist at only one height in the atmosphere, so their vertical structures are poorly understood. This motivates this study that computes stable three-dimensional, long-lived planetary vortices that satisfy the equations of motion. We solve the anelastic equations with a high-resolution pseudo-spectral method using the observed Jovian atmospheric temperatures and zonal flow. We examine several families of vortices and find that constant-vorticity vortices, which have nearly uniform vorticity as a function of height, and horizontal areas that go to zero at their tops and bottoms, converge to stable vortices that look like the Great Red Spot (GRS) and other Jovian anticyclones. In contrast, the constant-area vortices proposed in previous studies, which have nearly uniform areas as a function of height, and vertical vorticities that go to zero at their tops and bottoms, are far from equilibrium, break apart, and converge to constant-vorticity vortices. Our late-time vortices show unexpected properties. Vortices that are initially non-hollow become hollow (i.e. have local minima of vertical vorticity at their centres), which is a feature of the GRS that cannot be explained with two-dimensional simulations. The central axes of the final vortices align with the planetary spin axis even if they align initially with the local direction of gravity. We present scaling laws for how vortex properties change with the Rossby number and other non-dimensional parameters. We prove analytically that the horizontal mid-plane of a stable vortex must lie at a height above the top of the convective zone.

Spin Dynamics of Planets in Resonant Chains

About a dozen exoplanetary systems have been discovered with three or more planets participating in a sequence of mean-motion resonances. The unique and complex architectures of these so-called “resonant chains” motivate efforts to characterize their planets holistically. In this work, we perform a comprehensive exploration of the spin-axis dynamics of planets in resonant chains. Planetary spin states are closely linked with atmospheric dynamics and habitability and are thus especially relevant to resonant chains like TRAPPIST-1, which hosts several temperate planets. Considering a set of observed resonant chains, we calculate the equilibrium states of the planetary axial tilts (“obliquities”). We show that high-obliquity states exist for ∼60% of planets in our sample, and many of these states can be stable in the presence of tidal dissipation. Using case studies of two observed systems (Kepler-223 and TOI-1136), we demonstrate how these high-obliquity states could have been attained during the initial epoch of disk-driven orbital migration that established the resonant orbital architectures. We show that the TRAPPIST-1 planets most likely have zero obliquities, with the possible exception of planet d. Overall, our results highlight that both the orbital and spin states of resonant chains are valuable relics of the early stages of planet formation and evolution.

Extraplanetary system under modified gravity

Abstract We investigated the properties of exoplanets using a modified gravity law. We then devised a gravitational formula that linked the radius, mass, semimajor axis, and stellar mass of the exoplanet. This formula is then validated by taking into account four different astronomical organizations (WASP, HAT, TOI, and HATS). These findings are compared to those in the exoplanet.edu database. The findings corroborated the observational data. The Einstein curvature theory was created by incorporating planet spin into Newton's planet dynamics. As a result, the spin of the planet is connected to its gravity.

The influence of a static planetary atmosphere on spin transfer during pebble accretion

Context. Pebble accretion has been used to explain the small size of Mars, the heavy element contents of the gas giants, and the size distribution of asteroids. More recently, pebble accretion has been proposed as a means to explain not only the growth but also the prograde spin preference of most larger bodies in the Solar System. Pebble accretion could induce planetary and asteroid spin equal to or exceeding the spins currently measured. However, as these planetesimals grow, they start condensing the gas of the disc around them, forming an atmosphere within their Bondi radius. Aims. We study the effect an atmosphere has on the pebble orbits and spin build-up on the planet’s surface during pebble accretion in the extreme case of a static atmosphere. Pebble feedback to the gas is not taken into account. Methods. The equations of motion for pebbles in a planar, global frame with a planet and a central star were integrated using the AIS15 integrator of REBOUND. An adiabatic atmosphere was then placed around the planet, and the spin deposited on the planet’s surface was measured. These simulations were evaluated for different distances to the star, Stokes numbers, and planet masses. Results. In general, an atmosphere dampens the spin the planet’s surface receives by absorbing part of the angular momentum of the pebbles and circularising their orbits. This could prevent the excessive spin values predicted in some 3D pebble accretion simulations without an atmosphere. For planets larger than 0.5 M⊕, a stationary atmosphere absorbs all angular momentum, leaving no spin for the surface. Significant quantities of angular momentum are stored in the inner and intermediate atmosphere (<0.3 Bondi radii). Depending on the atmospheric and disc model, this spin could be transported either to the disc through atmospheric recycling or to the planet through drag between the surface and the atmosphere. Further research is required to quantify the spin transfer within the atmosphere.

Influence of axis misalignments in stepped planetary gear stages on the excitation behavior—test rig development and simulative analysis

AbstractOne challenge in the design of automotive gearboxes is the combination of high power density, high efficiency and low noise emission. With the electrification of the powertrain, the requirements in terms of noise emission and efficiency increase additionally. Stepped planetary gear stages are a potential topology to solve the current challenges in gearbox technology. Current research shows the pronounced misalignment behavior of planetary gear stages, especially with manufacturing or assembly deviations. However, the effects of dynamic misalignment behavior on tooth contacts in stepped planetary gear stages have not been adequately investigated. This paper presents a test rig that allows the investigation of the excitation and displacement behavior of stepped planetary gear stages taking into account adjustable axis misalignments. The axis misalignment of the stepped planetary shafts is introduced with eccentric bushings in this test rig concept. To evaluate the excitation and displacement behavior the transmission error and the displacements of different components can be measured. The test rig is modeled in the dynamic multibody simulation. The tooth contact is modeled using the force module GearForce6D. The axis misalignment is varied in the simulation model and the influence on the excitation and displacement behavior is evaluated. The simulation results show that planet pin position errors have the highest influence on the sun trajectory and the load sharing. The misalignments occurring in the tooth contacts due to inclination and skew of the stepped planetary shaft lead to higher tooth flank pressures and an increase in the total transmission error.

Evidence for large disturbances of the Ediacaran geomagnetic field from West Africa

Constraining the paleogeography of the Ediacaran is crucial for understanding the extensive tectonic, biological and geochemical changes that occurred during that epoch. Paleomagnetism is an essential tool for reconstructing the Ediacaran paleogeography but it is complicated because the paleomagnetic data of that age display unusually fast and large directional oscillations. Two main competing hypotheses have been proposed: the occurrence of very fast True Polar Wander (TPW) episodes, which correspond to the motion of the planetary spin axis relative to the solid Earth, or strong geomagnetic field disturbances that could potentially be dominated by an equatorial dipole field. Their implications for paleogeographic reconstructions are radically different as TPW would result in a major latitudinal shift of continents of up to ∼ 90°. In this study, we focus on one rapid paleomagnetic change recorded in pyroclastic rocks of the Ouarzazate Group in the Anti-Atlas Belt (Morocco) that has been interpreted to reflect an exceptionally fast episode of True Polar Wander between ∼ 575 and 565 Ma. To further test this hypothesis, tight constraints on the rate of the paleomagnetic directional change are needed, as TPW is speed-limited by mantle viscosity. Here, we present high-resolution Chemical Abrasion Isotope-Dilution Thermal Ionization Mass Spectrometry (CA-ID-TIMS) U-Pb dates on zircons from seven pyroclastic levels distributed stratigraphically below, in between and above the horizons where the large paleomagnetic change is observed. Based on these new data, we estimate the associated lower bound rate of the apparent polar motion related to this abrupt paleomagnetic change to be 11.6°/Myrs [5.5 – 17.9]. This value is much higher than the TPW speed limit estimated from numerical simulations, suggesting that this large paleomagnetic change cannot be explained by TPW. It could rather be associated with intense perturbations of the Ediacaran geomagnetic field potentially oscillating from an axial to an equatorial dipole. The paleomagnetic pole that we interpret as referring to the axial dipole field would imply that West Africa was located at high latitude during the mid-Ediacaran.

On the behaviour of spin–orbit connection of exoplanets

Star–planet interactions play, among other things, a crucial role in planetary orbital configurations by circularizing orbits, aligning the star and planet spin and synchronizing stellar rotation with orbital motions. This is especially true for innermost giant planets, which can be schematized as binary systems with a very large mass ratio. Despite a few examples where spin–orbit synchronization has been obtained, there is no demographic study on synchronous regimes in those systems yet. Here we use a sample of 1,055 stars with innermost planet companions to show the existence of three observational loci of star–planet synchronization regimes. Two of them have dominant fractions of subsynchronous and supersynchronous star–planet systems, and a third less populated regime of potentially synchronized systems. No synchronous star–planet system with a period higher than 40 days has been detected yet. This landscape is different from eclipsing binary systems, most of which are synchronized. We suggest that planets in a stable asynchronous spin state belonging to star–planet systems in a supersynchronized regime offer the most favourable conditions for habitability. An analysis of 1,055 planets around main sequence stars identifies three subsamples of star–planet synchronization: subsynchronized, dominant for periods shorter than 6.2 days; supersynchronized, for periods longer than 13.5 days; and a transitional regime in between. Synchronized systems are a minority, contrary to eclipsing binaries.

Morphology of the north-western wall of Eos Chaos, Valles Marineris: Evidence for glaciation during late Amazonian high obliquity

Glacial landforms have been reported from various regions on Mars; most notably from the mid-to-high latitude regions. We studied Eos Chaos, located towards the eastern boundary of Valles Marineris, for the possible glacial processes occurring in the low-latitude areas on Mars. A thorough investigation of the morphology of the north-western wall of Eos Chaos was carried out using planetary datasets such as context camera (CTX) and High-resolution Imaging Science Experiment (HiRISE) images from NASA's Mars Reconnaissance Orbiter (MRO) mission and Mars Color Camera (MCC) images from ISRO's Mars Orbiter Mission-1 (MOM-1). We identified various geomorphological features that may have resulted from diverse geological processes. The glacial processes are manifested by the morphological features such as tongue-shaped lobate flows, alternative dark and light strata (~10-15 m thick), light-toned fragmented sediments, kettle lake-like structures, surface striations, sublimation hollows, and pit and knob structures. The flow features correspond to three stages of evolution: developing (~0.3 km length), intermediate size (1.5 km length), and mature (~15 km length). These three stages culminated in developing a model depicting the evolution of the glacial landforms of the region based on morphological features. We deduce that the glacial landforms of the region were formed during episodes of higher planetary spin axis obliquity during the late Amazonian.

One EURO for Uranus: the Elliptical Uranian Relativity Orbiter mission

ABSTRACT Recent years have seen increasing interest in sending a mission to Uranus, visited so far only by Voyager 2 in 1986. Elliptical Uranian Relativity Orbiter is a preliminary mission concept investigating the possibility of dynamically measuring the planet’s angular momentum by means of the Lense–Thirring effect affecting a putative Uranian orbiter. It is possible, at least in principle, to separate the relativistic precessions of the orbital inclination to the celestial equator and of the longitude of the ascending node of the spacecraft from its classical rates of the pericentre induced by the multipoles of the planet’s gravity field by adopting an appropriate orbital configuration. For a wide and elliptical $2000\times 100\, 000\, \mathrm{km}$ orbit, the gravitomagnetic signatures amount to tens of milliarcseconds per year, while, for a suitable choice of the initial conditions, the peak-to-peak amplitude of the range-rate shift can reach the level of ≃ 1.5 × 10−3 mm s−1 in a single pericentre passage of a few hours. By lowering the apocentre height to $10\, 000\, \mathrm{km}$, the Lense–Thirring precessions are enhanced to the level of hundreds of milliarcseconds per year. The uncertainties in the orientation of the planetary spin axis and in the inclination are major sources of systematic bias; it turns out that they should be determined with accuracies as good as ≃0.1–1 and ≃1–10 mas, respectively.

Boundary Layers of Circumplanetary Disks around Spinning Planets. I. Effects of Rossby Waves

Gas giant planets are believed to accrete from their circumplanetary disks (CPDs). The CPDs usually involve accretion through the boundary layer (BL) in the vicinity of planets. Prior studies have concentrated on the BL of nonspinning planets. We investigate the influence of planetary spin on the wave behaviors within the BL. The rotation profile in such BLs would show a sharp transition from the rigid rotation to the Keplerian rotation. We examine the angular momentum transport in these BLs in terms of linear perturbation analysis. We find that the global inertia-acoustic mode associated with spinning planets would give rise to the inflow of angular momentum and the accretion of gas. In this work, we identify a new kind of global mode, namely the Rossby mode. The Rossby mode can lead to the outflow of angular momentum and the decretion of gas from a spinning planet. The Rossby mode provides a negative feedback that regulates the planetary spin and mass. We compare the growth rate of the two modes as a function of the width of BL, the Mach number, and the spin rate of planets. Our results reveal the underlying hydrodynamic mechanism of terminal spins and asymptotic mass of the giant planets.

A dynamic gear load distribution model for epicyclic gear sets with a structurally compliant planet carrier

Structural deformations in a planet carrier under operating conditions results in misalignment of planet gears, which can significantly effect the gear mesh load distribution and load sharing of a planetary gear set. Therefore, to capture the influence of structural compliance associated with planet carrier, planet pin, and input/output shaft, a hybrid planetary dynamic load distribution model is developed in this paper. Finite element sub-structuring techniques are employed to ensure that the model is computational efficiency. The proposed model employs a simplex algorithm to iteratively solve for the elastic gear mesh contacts in conjunction with a numerical integration scheme, which enables it to inherently capture the influence of several component and system level design variations without the need for an empirical mesh stiffness formulation or transmission error excitation of the system. The developed formulation is used to study the effects of planet carrier flexibility on both the quasi-static and dynamic response of planetary gearsets. The discussed results not only illustrate the influence of carrier flexibility on the system response but also highlight the need for such computationally efficient models which could be used as design tools.

Magnetic Field Conditions Upstream of Ganymede

AbstractJupiter's magnetic field is tilted by ∼10° with respect to the planet's spin axis, and as a result the Jovian plasma sheet passes over the Galilean satellites at the jovigraphic equator twice per planetary rotation period. The plasma and magnetic field conditions near Ganymede's magnetosphere therefore change dramatically every ∼5 hr, creating a unique magnetosphere‐magnetosphere interaction, and on longer time scales as evidenced by orbit‐to‐orbit variations. In this paper, we summarize the typical magnetic field conditions and their variability near Ganymede's orbit as observed by the Galileo and Juno spacecraft. We fit Juno data from orbit 34, which included the spacecraft's close Ganymede flyby in June 2021, to a current sheet model and show that the magnetospheric conditions during orbit 34 were very close to the historical average. Our results allow us to infer the upstream conditions at the time of the Juno Ganymede flyby.

Consequences of dynamically unstable moons in extrasolar systems

ABSTRACT Moons orbiting rocky exoplanets in compact orbits about other stars experience an accelerated tidal evolution, and can either merge with their parent planet or reach the limit of dynamical instability within a Hubble time. We review the parameter space over which moons become unbound, including the effects of atmospheric tides on the planetary spin. We find that such tides can change the final outcome from merger to escape, albeit over a limited parameter space. We also follow the further evolution of unbound moons, and demonstrate that the overwhelmingly most likely long-term outcome is that the unbound moon returns to collide with its original parent planet. The dust released by such a collision is estimated to reach optical depths $\sim 10^{-3}$, exhibit characteristic temperatures of a few hundred degrees kelvin, and last for a few thousand years. These properties make such events an attractive model for the emerging class of middle-aged main-sequence stars that are observed to show transient clouds of warm dust. Furthermore, a late collision between a planet and a returning moon on a hyperbolic orbit may sterilize an otherwise habitable planet.

Tidal excitation of the obliquity of Earth-like planets in the habitable zone of M-dwarf stars

Close-in planets undergo strong tidal interactions with the parent star that modify their spins and orbits. In the two-body problem, the final stage for tidal evolution is the synchronisation of the rotation and orbital periods, and the alignment of the planet spin axis with the normal to the orbit (zero planet obliquity). The orbital eccentricity is also damped to zero, but over a much longer timescale, that may exceed the lifetime of the system. For non-zero eccentricities, the rotation rate can be trapped in spin–orbit resonances that delay the evolution towards the synchronous state. Here we show that capture in some spin–orbit resonances may also excite the obliquity to high values rather than damp it to zero. Depending on the system parameters, obliquities of 60º–80º can be maintained throughout the entire lifetime of the planet. This unexpected behaviour is particularly important for Earth-like planets in the habitable zone of M-dwarf stars, as it may help to sustain temperate environments and thus more favourable conditions for life.

0303 The Effects of Latitude on Sleep at 4300m

Abstract Introduction Worldwide, 140-million people live above 2400m and even more visit high altitudes (HA) annually. Exposure to HA is associated with hypoxia-related cognitive impairments and sleep disruptions. Additionally, both planetary axial tilt, solar gravity, and planetary spin distort the earth’s atmosphere pulling the equator’s atmosphere further from the earth’s surface when compared to the poles. These forces may have additional impacts on physiology at HA. There has yet to be a study to determine these effects of latitude on physiology at HA. Therefore, the aim of the current study was to determine if latitude exacerbates the effects of HA on sleep. Methods Similar testing protocols were utilized at 4,300m at Camp-14 on Denali at a latitude of ~63° and in the village of Dingboche on the route to Mount Everest at a latitude of ~28°. Exclusion criteria included 18-65 years, self-reported drug use, cigarette-smoking, sleep disorders, abnormal body mass index (BMI), falling asleep more than one hour or awakened more than an hour during the night. Wireless sleep recording devices recorded the sleep architecture of qualified participants. Twenty-two climbers (3 females) participated in the Denali study (age 34.0±9.7 mean±SD) and twenty-five climbers (6 females) participated in the Everest study (age 28.0±9.7 mean±SD). Participants were instructed to go to bed and wake up at their habitual bedtimes and wake times. Results Independent t-tests revealed a statistically significant decrease in total sleep (p<0.05) on Denali when compared to Mt. Everest. There were nonsignificant trends for a decrease in rapid eye movement (REM) and sleep onset latency on Denali. Other sleep stages appear relatively unaffected by latitude. Conclusion Our findings indicate that a decrease in total sleep time occurs at higher latitude with comparable altitude. Prior research has linked a decrease in total sleep time to decreased cognitive impairments and physiologic disruptions. Our findings suggest that latitude should be considered when venturing into HA environments, designing research protocols, analyzing results, and clinical applications or military operations. Support (If Any)

Dynamics of Colombo’s Top: non-trivial oblique spin equilibria of super-Earths in multiplanetary systems

ABSTRACT Many Sun-like stars are observed to host close-in super-Earths (SEs) as part of a multiplanetary system. In such a system, the spin of the SE evolves due to spin–orbit resonances and tidal dissipation. In the absence of tides, the planet’s obliquity can evolve chaotically to large values. However, for close-in SEs, tidal dissipation is significant and suppresses the chaos, instead driving the spin into various steady states. We find that the attracting steady states of the SE’s spin are more numerous than previously thought, due to the discovery of a new class of ‘mixed-mode’ high-obliquity equilibria. These new equilibria arise due to subharmonic responses of the parametrically driven planetary spin, an unusual phenomenon that arises in non-linear systems. Many SEs should therefore have significant obliquities, with potentially large impacts on the physical conditions of their surfaces and atmospheres.

The Super- and Sub-Rotation of Barotropic Atmospheres on a Rotating Planet

A statistical mechanics canonical spherical energy-enstrophy theory of the superrotation phenomenon in a quasi-2D barotropic fluid coupled by inviscid topographic torque to a rotating solid body is solved in closed form in Fourier space, with inputs on the value of the energy to enstrophy quotient of the fluid, and two planetary parameters — the radius of the planet and its rate and the axis of spin. This allows calculations that predict the following physical consequences: (A) two critical points associated with the condensation of high and low energy (resp.) states in the form of distinct superrotating and subrotating (resp.) solid-body flows, (B) only solid-body flows having wavenumbers $l=1$, $m=0$ — tiltless rotations — are excited in the ordered phases, (C) the asymmetry between the superrotating and subrotating ordered phases where the subrotation phase transition also requires that the planetary spin is sufficiently large, and thus, less commonly observed than the superrotating phase, (D) nonexcitation of spherical modes with wavenumber $l>1$ in barotropic fluids. Comparisons with other canonical, microcanonical and dynamical theories suggest that this theory complements and completes older theories by predicting the above specific outcomes.

Dynamics of Colombo’s top: tidal dissipation and resonance capture, with applications to oblique super-Earths, ultra-short-period planets and inspiraling hot Jupiters

ABSTRACT We present a comprehensive theoretical study on the spin evolution of a planet under the combined effects of tidal dissipation and gravitational perturbation from an external companion. Such a ‘spin + companion’ system (called Colombo’s top) appears in many [exo]planetary contexts. The competition between the tidal torque (which drives spin-orbit alignment and synchronization) and the gravitational torque from the companion (which drives orbital precession of the planet) gives rise to two possible spin equilibria (‘tidal Cassini Equilibria’, tCE) that are stable and attracting: the ‘simple’ tCE1, which typically has a low spin obliquity, and the ‘resonant’ tCE2, which can have a significant obliquity. The latter arises from a spin-orbit resonance and can be broken when the tidal alignment torque is stronger than the precessional torque from the companion. We characterize the long-term evolution of the planetary spin (both magnitude and obliquity) for an arbitrary initial spin orientation, and develop a new theoretical method to analytically obtain the probability of resonance capture driven by tidal dissipation. Applying our general theoretical results to exoplanetary systems, we find that a super-Earth (SE) with an exterior companion can have a substantial probability of being trapped in the high-obliquity tCE2, assuming that SEs have a wide range of primordial obliquities. We also evaluate the recently proposed ‘obliquity tide’ scenarios for the formation of ultra-short-period Earth-mass planets and for the orbital decay of hot Jupiter WASP-12b. We find in both cases that the probability of resonant capture into tCE2 is generally low and that such a high-obliquity state can be easily broken by the required orbital decay.

Boundary Layer Circumplanetary Accretion: How Fast Could an Unmagnetized Planet Spin Up through Its Disk?

Abstract Gas giant planets are expected to accrete most of their mass via a circumplanetary disk. If the planet is unmagnetized and initially slowly rotating, it will accrete gas via a radially narrow boundary layer and rapidly spin up. Radial broadening of the boundary layer as the planet spins up reduces the specific angular momentum of accreted gas, allowing the planet to find a terminal rotation rate short of the breakup rate. Here, we use axisymmetric viscous hydrodynamic simulations to quantify the terminal rotation rate of planets accreting from their circumplanetary disks. For an isothermal planet-disk system with a disk scale height h/r = 0.1 near the planetary surface, spin-up switches to spin-down at between 70% and 80% of the planet’s breakup rate. In a qualitative difference from vertically averaged models—where spin-down can coexist with mass accretion—we observe decretion accompanying solutions where angular momentum is being lost. The critical spin rate depends upon the disk thickness near the planet. For a disk scale height of h/r = 0.15, the critical spin rate drops to between 60% and 70% of the planet’s breakup rate. In the disk outside the boundary layer, we identify meridional circulation flows, which are unsteady and instantaneously asymmetric across the midplane. The simulated flows are strong enough to vertically redistribute solid material in early stage satellite formation. We discuss how exoplanetary rotation measurements, when combined with spectroscopic and variability studies of protoplanets with circumplanetary disks, could determine the role of magnetic and nonmagnetic processes in setting planet spins.