Precession Rate Research Articles

Gravitational anti-screening and predictions within the solar system

The theory of gravitational anti-screening, which has previously been applied to various astronomical observations as an alternative to dark matter, is now applied to the solar system. The effect that gravitational anti-screening has on the precession rate of the planets will be determined and compared to current observations. In addition, the effect that gravitational anti-screening will have on certain orbital parameters of long-period comets will be determined. The set of 119 long-period comets that are considered in this paper have a broad peak of aphelion distances, based on current gravitational theory, centred at approximately 50 kAU. In the case of gravitational anti-screening, these aphelion distances will be shown to be greatly reduced to a narrow distribution centred at approximately 10 kAU. It is further found from the theory that comets orbiting at this distance will have orbital speeds approximately 20% greater than that predicted from Newtonian gravitational theory.

Characteristics of a precessing flow under the influence of a convecting temperature field in a spheroidal shell

We present results from direct numerical simulations of flows in spherical and oblate spheroidal shells, driven both by precession and thermal convection, with Ekman number , non-diffusive Rayleigh numbers from to and unity Prandtl number. The applied precessional forcing spans seven orders of magnitude. Our experiments show a clear transition between a convective state and a precessing flow that can be approximated by a reduced dynamical model. The change in the flow is apparent in visualizations and a decomposition of the velocity into symmetric and antisymmetric components. For the flow dominated by precession, some parameter combinations show two stable solutions that can be realized by a hysteresis or a strong thermal forcing. An increase of the Rayleigh number at a constant precession rate exhibits established scaling properties for the heat transfer, with exponents and .

Evidence of a dynamically evolving Galactic warp

In a cosmological setting, the disc of a galaxy is expected to continuously experience gravitational torques and perturbations from a variety of sources, which can cause the disc to wobble, flare and warp. Specifically, the study of galactic warps and their dynamical nature can potentially reveal key information on the formation history of galaxies and the mass distribution of their halos. Our Milky Way presents a unique case study for galactic warps, thanks to the detailed knowledge of its stellar distribution and kinematics. Using a simple model of how the warp's orientation is changing with time, we here measure the precession rate of the Milky Way's warp using 12 million giant stars from Gaia Data Release 2, finding that it is precessing at $10.86 \pm 0.03_{stat} \pm 3.20_{sys}$ km/s/kpc in the direction of Galactic rotation, about one third the angular velocity at the Sun's position in the Galaxy. The direction and magnitude of the warp's precession rate favour the scenario that the warp is the results of a recent or ongoing encounter with a satellite galaxy, rather than the relic of the ancient assembly history of the Galaxy.

Secular evolution of close-in planets: the effects of general relativity

ABSTRACT Pairs of planets in a system may end up close to their host star on eccentric orbits as a consequence of planet–planet scattering, Kozai, or secular migration. In this scenario, general relativity and secular perturbations have comparable time-scales and may interfere with each other with relevant effects on the eccentricity and pericenter evolution of the two planets. We explore, both analytically and via numerical integration, how the secular evolution is changed by general relativity for a wide range of different initial conditions. We find that when the faster secular frequency approaches the general relativity precession rate, which typically occurs when the outer planet moves away from the inner one, it relaxes to it and a significant damping of the proper eccentricity of the inner planet occurs. The proper eccentricity of the outer planet is reduced as well due to the changes in the secular interaction of the bodies. The lowering of the peak eccentricities of the two planets during their secular evolution has important implications on their stability. A significant number of two-planet systems, otherwise chaotic because of the mutual secular perturbations, are found stable when general relativity is included.

Can orbital clustering of KBOs in the ecliptic be due to the solar toroidal field generated spacetime dragging?

The Kuiper belt objects (KBOs) exhibit an orbital clustering of the outer planets lying at perihelion distances larger than Neptune and semimajor axes greater than 150 AU from the Sun. This implies a hitherto unknown dynamical mechanism to counter randomizing of the orbital elements caused by the giant solar system planets. Using the toroidal field induced frame-dragging we deduce here the observed range of the Kuiper belt region, the semi-major axis of Sedna like objects in the Kuiper belt, as well as the orbital clustering of the KBOs in the ecliptic, without assuming dynamical effects induced by trans-Neptunian-objects (TNOs). We also calculate the orbital precession rates for the inner planets and show their correspondence, within the range of observational accuracy, with recent planetary ephemerides.

Tilting Ice Giants with a Spin–Orbit Resonance

Abstract Giant collisions can account for Uranus’s and Neptune’s large obliquities, yet generating two planets with widely different tilts and strikingly similar spin rates is a low-probability event. Trapping into a secular spin–orbit resonance, a coupling between spin and orbit precession frequencies, is a promising alternative, as it can tilt the planet without altering its spin period. We show with numerical integrations that if Uranus harbored a massive circumplanetary disk at least three times the mass of its satellite system while it was accreting its gaseous atmosphere, then its spin precession rate would increase enough to resonate with its own orbit, potentially driving the planet’s obliquity to 70°. We find that the presence of a massive disk moves the Laplace radius significantly outward from its classical value, resulting in more of the disk contributing to the planet’s pole precession. Although we can generate tilts greater than 70° only rarely and cannot drive tilts beyond 90°, a subsequent collision with an object about 0.5 M ⊕ could tilt Uranus from 70° to 98°. Minimizing the masses and number of giant impactors from two or more to just one increases the likelihood of producing Uranus’s spin states by about an order of magnitude. Neptune, by contrast, needs a less massive disk to explain its 30° tilt, eliminating the need for giant collisions altogether.

Frequency domain method of the search for the electric dipole moment in a storage ring

A new method for searching for the electric dipole moment (EDM) of the deuteron and other nuclei is presented. When trying to measure the EDM in a storage ring environment, magnetic dipole moment (MDM) spin precession due to machine imperfections becomes the primary source of systematic error. The proposed method aims at providing a solution to the machine imperfection problemas well as circumventing the geometric phase error. The method is based on estimating the combined MDM + EDM spin precession frequency, in which the MDM contribution is due only to field imperfections. The MDM term is canceled in the final statistic by adding frequency estimates from cycles with counter-circulating beams. Spin precession rate depends on the particle’s effective Lorentz factor; the proposed method’s core feature is a procedure for equalizing the effective Lorentz factors of the clockwise and counter-clockwise circulating beams, thus enabling the cancelation.

On the Lynden-Bell Bar Formation Mechanism in Galactic Disks

One of the possible bar formation mechanisms in the disks of galaxies was proposed by Lynden-Bell (1979). The presumed amplification of a weak seed oval stellar surface density perturbation in the central regions of the galaxy through the alignment of the major axes of precessing elliptical orbits underlies it. According to his qualitative reasoning, the orbits are aligned along the perturbation if the precession rate diminishes with decreasing angular momentum at a constant adiabatic invariant. Using a rigorous approach based on finding the system’s stable stationary points, we show that this condition is not the only one that determines the orbit alignment orientation. The orbit precession direction in the unperturbed potential and the rate of decrease of the bar potential amplitude with radius also turn out to be important. In some cases, the latter can even be more important.

Frequency domain method of the search for the electric dipole moment in a storage ring

A new method for searching for the electric dipole moment (EDM) of the deuteron and other nuclei is presented. When trying to measure the EDM in a storage ring environment, magnetic dipole moment (MDM) spin precession due to machine imperfections becomes the primary source of systematic error. The proposed method aims at providing a solution to the machine imperfection problemas well as circumventing the geometric phase error. The method is based on estimating the combined MDM + EDM spin precession frequency, in which the MDM contribution is due only to field imperfections. The MDM term is canceled in the final statistic by adding frequency estimates from cycles with counter-circulating beams. Spin precession rate depends on the particle’s effective Lorentz factor; the proposed method’s core feature is a procedure for equalizing the effective Lorentz factors of the clockwise and counter-clockwise circulating beams, thus enabling the cancelation.

Secular Eccentricity Oscillations in Axisymmetric Disks of Eccentric Orbits

Abstract Massive bodies undergo orbital eccentricity oscillations when embedded in an axisymmetric disk of smaller mass orbits. These eccentricity oscillations are driven by secular torques that seek to equalize the apsidal precession rates of all the orbits in the disk. We investigate this mechanism within the context of detached objects in the outer solar system, but we find that the oscillation timescale is too long for it to be dynamically important. It could however be interesting for phenomenon a bit farther from home, namely, feeding supermassive black holes and polluting the surfaces of white dwarf stars.

A record of the final phase of giant planet migration fossilized in the asteroid belt’s orbital structure

ABSTRACT The asteroid belt is characterized by an extreme low total mass of material on dynamically excited orbits. The Nice model explains many peculiar qualities of the Solar system, including the belt’s excited state, by invoking an orbital instability between the outer planets. However, previous studies of the Nice model’s effect on the belt’s structure struggle to reproduce the innermost asteroids’ orbital inclination distribution. Here, we show how the final phase of giant planet migration sculpts the asteroid belt, in particular its inclination distribution. As interactions with leftover planetesimals cause Saturn to move away from Jupiter, its rate of orbital precession slows as the two planets’ mutual interactions weaken. When the planets approach their modern separation, where Jupiter completes just short of five orbits for every two of Saturn’s, Jupiter’s eccentric forcing on Saturn strengthens. We use numerical simulations to show that the absence of asteroids with orbits that precess between 24 and 28 arcsec yr−1 is related to the inclination problem. As Saturn’s precession speeds back up, high-inclination asteroids are excited on to planet crossing orbits and removed from the inner main belt. Through this process, the asteroid belt’s orbital structure is reshaped, leading to markedly improved simulation outcomes.

Effects of Nonlinearity on the Angular Drift Error of an Electrostatic MEMS Rate Integrating Gyroscope

Electrostatic MEMS coriolis vibratory gyroscopes (CVG) are essentially nonlinear because of the capacitive transducers employed for the excitation and detection of resonance vibration. This paper investigates the influence of nonlinearity on the precession angle dependent bias error of a MEMS rate integrating gyroscope (RIG) and proposes a novel correction to minimize this effect. A linear model of CVGs is commonly used in the dynamic analysis and control of MEMS RIGs. The linear model predicts a 2nd harmonic angular drift error due mainly to non-proportional damping. However, experimental results from previous work demonstrate the existence of an additional 4th harmonic component in the precession rate, and in the resonant frequency and quadrature control. The analysis and removal of this high-order error term will further improve the accuracy of the RIG. Here, it is shown that high-order angularly modulated drift error is the result of nonlinear damping, and the stiffness nonlinearity is responsible for the 4th harmonics present in the fluctuation of the operating frequency and in the control for quadrature nulling. It is understood that nonlinear damping may be introduced electrically by the energy sustain state feedback control that uses nonlinear capacitive measurements. Nonlinearity correction is proposed to the capacitive displacement detection that significantly reduces the high-order drift error. Simulation and experimental results are provided to validate the analysis. A DSP controlled MEMS RIG with nonlinearity correction exhibits an angular drift error of less than 0.2 deg/s.

Observational investigation of the 2013 near-Earth encounter by asteroid (367943) Duende

On 15 February 2013, the asteroid 367943 Duende (2012 DA14) experienced a near-Earth encounter at an altitude of 27,700 km or 4.2 Earth radii. We present here the results of an extensive, multi-observatory campaign designed to probe for spectral and/or rotational changes to Duende due to gravitational interactions with the Earth during the flyby. Our spectral data reveal no changes within systematic uncertainties. Post-flyby lightcurve photometry places strong constraints on the rotation state of Duende, showing that it is in non-principal axis rotation with fundamental periods of P1 = 8.71 ± 0.03 and P2 = 23.7 ± 0.2 h. Multiple lightcurve analysis techniques, coupled with theoretical considerations and delay-Doppler radar imaging, allow us to assign these periods to specific rotational axes of the body. In particular we suggest that Duende is now in a non-principal, short axis mode rotation state with a precessional period equal to P1 and oscillation about the symmetry axis at a rate equal to P2. Temporal and signal-to-noise limitations inherent to the pre-flyby photometric dataset make it difficult to definitively diagnose whether these periods represent a change imparted due to gravitational torques during the flyby. However, based on multiple analysis techniques and a number of plausibility arguments, we suggest that Duende experienced a rotational change during the planetary encounter with an increase in its precessional rotation period. Our preferred interpretation of the available data is that the precession rate increased from 8.4 h prior to the flyby to 8.7 h afterwards. A companion paper by Benson et al. (2019) provides a more detailed dynamical analysis of this event and compares the data to synthetic lightcurves computed from a simple shape model of Duende. The interpretation and results presented in these two works are consistent with one another. The ultimate outcome of this campaign suggests that the analytic tools we employed are sufficient to extract detailed information about solid-body rotation states given data of high enough quality and temporal sampling. As current and future discovery surveys find more near-Earth asteroids, the opportunities to monitor for physical changes during planetary encounters will increase.

On systematic and GR effects on muon g − 2 experiments

We derive in full generality the equations that govern the time dependence of the energy ℰ of the decay electrons in a muon g − 2 experiment. We include both electromagnetic and gravitational effects and we estimate possible systematics on the measurements of a ≡ (g − 2)/2, whose experimental uncertainty will soon reach ∆a/a ≈ 10−7. In addition to the standard modulation of ℰ when the motion is orthogonal to a constant magnetic field B, with angular frequency ωa = ea|B|/m, we study effects due to: (1) a non constant muon γ factor, in presence of electric fields E, (2) a correction due to a component of the muon velocity along B (the “pitch correction”), (3) corrections to the precession rate due to E fields, (4) non-trivial spacetime metrics. Oscillations along the radial and vertical directions of the muon lead to oscillations in ℰ with a relative size of order 10−6, for the BNL g − 2 experiment. We then find a subleading effect in the “pitch” correction, leading to a frequency shift of ∆ωa/ωa≈ mathcal{O} (10−9) and subleading effects of about ∆ωa/ωa≈ few × mathcal{O} (10−8–10−9) due to E fields. Finally we show that GR effects are dominated by the Coriolis force, due to the Earth rotation with angular frequency ωT, leading to a correction of about ∆ωa/ωa≈ ωT/(γωa) ≈ mathcal{O} (10−12). A similar correction might be more appreciable for future electron g − 2 experiments, being of order ∆ωa/ωa,el≈ ωT/(ωa,el) ≈ 7 × 10−13, compared to the present experimental uncertainty, ∆ael/ael≈ 10−10, and forecasted to reach soon ∆ael/ael≈ 10−11.

Planetary orbital precession in pseudo-Newtonian potentials: reproduction of the general relativity orbital effect

In this paper, pseudo-Newtonian potentials are used to study the problem of orbital precession. The precession rates are found to have the same dependence on GM/cL, where M is the mass of the star and L the angular momentum per unit mass of the planet, comparable to the result obtained in Einstein’s general relativity (GR). Moreover, a specific form of pseudo-Newtonian potential (i.e. equation () in the text) is constructed to have the same precession rate with the GR result to the lowest order. Finally, we give a brief discussion for this potential form, as well.

Lunar Tide in the F Region Ionosphere

AbstractIn this paper the magnetic latitude (±50°) and longitude, local solar time (LST), and month‐to‐month variability of the M2 lunar semidiurnal tide in the ionosphere is revealed through analysis of topside F region electron density measurements by the Planar Langmuir Probe instrument on the CHAMP satellite during the two 5‐year periods 2001–2005 and 2005–2009. The local time precession rate of CHAMP is such that 5 years is required to obtain full LST coverage for every month of the year at each latitude of interest. Thus, each 5‐year period is compressed into one equivalent year. M2 amplitudes, expressed in terms of percent residuals from a background value, range between about 3% and 20% and vary considerably with LST and magnetic longitude. Longitude variations in principle arise from zonal asymmetries in lunar tidal forcing due to Earth and ocean tides, as well as magnitude of Earth's magnetic field. The O1 diurnal tide is also discussed in the context of CHAMP and other measurements of the F region ionosphere.

Spontaneous CPT breaking and fermion propagation in the Schwarzschild geometry

The Schwarzschild solution is used as a background metric to analyze the effects of a vector field undergoing spontaneous symmetry breaking in a Standard Model Extension Bumblebee Model. The corresponding back-reaction of the background field expectation value on the metric is calculated, yielding a consistent model for describing CPT-violating effects within the context of pseudo-Riemannian geometry. The Bianchi identities of general relativity and the gauge theory are found to be mutually consistent and yield no conflicts with Riemannian geometry. This fact is demonstrated to second-order in the background field. Fermions with a spin-dependent, CPT-violating coupling to this background field experience altered geodesics relative to the conventional black hole orbital solutions. The spin-dependent corrections to the orbital velocity and precession rate are calculated.

Inverse Lidov-Kozai resonance for an outer test particle due to an eccentric perturber

Aims. We analyze the behavior of the argument of pericenter ω2 of an outer particle in the elliptical restricted three-body problem, focusing on the ω2 resonance or inverse Lidov-Kozai resonance. Methods. First, we calculated the contribution of the terms of quadrupole, octupole, and hexadecapolar order of the secular approximation of the potential to the outer particle’s ω2 precession rate (dω2∕dτ). Then, we derived analytical criteria that determine the vanishing of the ω2 quadrupole precession rate (dω2/dτ)quad for different values of the inner perturber’s eccentricity e1. Finally, we used such analytical considerations and described the behavior of ω2 of outer particles extracted from N-body simulations developed in a previous work. Results. Our analytical study indicates that the values of the inclination i2 and the ascending node longitude Ω2 associated with the outer particle that vanish (dω2/dτ)quad strongly depend on the eccentricity e1 of the inner perturber. In fact, if e1 < 0.25 (>0.40825), (dω2/dτ)quad is only vanished for particles whose Ω2 circulates (librates). For e1 between 0.25 and 0.40825, (dω2/dτ)quad can be vanished for any particle for a suitable selection of pairs (Ω2, i2). Our analysis of the N-body simulations shows that the inverse Lidov-Kozai resonance is possible for small, moderate, and high values of e1. Moreover, such a resonance produces distinctive features in the evolution of a particle in the (Ω2, i2) plane. In fact, if ω2 librates and Ω2 circulates, the extremes of i2 at Ω2 = 90° and 270° do not reach the same value, while if ω2 and Ω2 librate, the evolutionary trajectory of the particle in the (Ω2, i2) plane shows evidence of an asymmetry with respect to i2 = 90°. The evolution of ω2 associated with the outer particles of the N-body simulations can be very well explained by the analytical criteria derived in our investigation.

Secular spin-axis dynamics of exoplanets

Context. Seasonal variations and climate stability of a planet are very sensitive to the planet obliquity and its evolution. This is of particular interest for the emergence and sustainability of land-based life, but orbital and rotational parameters of exoplanets are still poorly constrained. Numerical explorations usually realised in this situation are therefore in heavy contrast with the uncertain nature of the available data. Aims. We aim to provide an analytical formulation of the long-term spin-axis dynamics of exoplanets, linking it directly to physical and dynamical parameters, but still giving precise quantitative results if the parameters are well known. Together with bounds for the poorly constrained parameters of exoplanets, this analysis is designed to enable a quick and straightforward exploration of the spin-axis dynamics. Methods. The long-term orbital solution is decomposed into quasi-periodic series and the spin-axis Hamiltonian is expanded in powers of eccentricity and inclination. Chaotic zones are measured by the resonance overlap criterion. Bounds for the poorly known parameters of exoplanets are obtained from physical grounds (rotational breakup) and dynamical considerations (equipartition of the angular momentum deficit). Results. This method gives accurate results when the orbital evolution is well known. The detailed structure of the chaotic zones for the solar system planets can be retrieved from simple analytical formulas. For less-constrained planetary systems, the maximal extent of the chaotic regions can be computed, requiring only the mass, the semi-major axis, and the eccentricity of the planets present in the system. Additionally, some estimated bounds of the precession constant allow to classify which observed exoplanets are necessarily out of major spin-orbit secular resonances (unless the precession rate is affected by the presence of massive satellites).

A straightforward method for deriving the Fermi–Walker transport law

A mathematically and conceptually simple approach that allows one to recover the Fermi–Walker transport law is proposed. The method is based on defining the Fermi–Walker transport law as the one for which the moving vector undergoes in its instantaneous rest frame only an infinitesimal Lorentz boost. The general Lorentz boosts are represented by 3 × 3 matrices, which significantly simplifies calculations. Also, a comment elucidating that the celebrated formula for the Thomas precession rate is not directly encapsulated in the expression representing this law is provided.