Perihelion Precession Research Articles

The influence of obliquity in the early Holocene Asian summer monsoon

AbstractThe early Holocene climatic optimum is associated with perihelion precession and high obliquity, though most studies emphasize the former over the latter. Asian monsoon proxy records only decisively show the precessional impact. To explore the obliquity effect, four climate simulations are conducted by fixing orbital parameters of present‐day (0K), early Holocene (11K), the lowest obliquity (31K), and 11K's precession and eccentricity with 31K's obliquity (11Kp31Ko). We show that high obliquity significantly augments the precessional impact by shifting the Asian monsoon farther north than present. By contrast, the present‐day monsoon seasonality can still be identified in the simulations with low obliquity. We argue that the upper tropospheric (South Asian) and lower tropospheric (North Pacific) high‐pressure systems are affected by the subtropical atmospheric heating changes responding to obliquity. As a consequence, associated with the changes in meridional gradients of geopotential height and temperature made by the heating, midlatitude transient eddies and monsoon‐midlatitude interactions are modulated.

Pericenter precession induced by a circumstellar disk on the orbit of massive bodies: comparison between analytical predictions and numerical results

Context. Planetesimals and planets embedded in a circumstellar disk are dynamically perturbed by the disk gravity. It causes an apsidal line precession at a rate that depends on the disk density profile and on the distance of the massive body from the star. Aims. Different analytical models are exploited to compute the precession rate of the perihelion ϖ . We compare them to verify their equivalence, in particular after analytical manipulations performed to derive handy formulas, and test their predictions against numerical models in some selected cases. Methods. The theoretical precession rates were computed with analytical algorithms found in the literature using the Mathematica symbolic code, while the numerical simulations were performed with the hydrodynamical code FARGO. Results. For low-mass bodies (planetesimals) the analytical approaches described in Binney & Tremaine (2008, Galactic Dynamics, p. 96), Ward (1981, Icarus, 47, 234), and Silsbee & Rafikov (2015a, ApJ, 798, 71) are equivalent under the same initial conditions for the disk in terms of mass, density profile, and inner and outer borders. They also match the numerical values computed with FARGO away from the outer border of the disk reasonably well. On the other hand, the predictions of the classical Mestel disk (Mestel 1963, MNRAS, 126, 553) for disks with p = 1 significantly depart from the numerical solution for radial distances beyond one-third of the disk extension because of the underlying assumption of the Mestel disk is that the outer disk border is equal to infinity. For massive bodies such as terrestrial and giant planets, the agreement of the analytical approaches is progressively poorer because of the changes in the disk structure that are induced by the planet gravity. For giant planets the precession rate changes sign and is higher than the modulus of the theoretical value by a factor ranging from 1.5 to 1.8. In this case, the correction of the formula proposed by Ward (1981) to account for the presence of a gap is a better approximation, at least in predicting a positive precession rate. Conclusions. Analytical modeling of the precession rate of massive bodies embedded in a circumstellar disk is accurate for planetesimals and terrestrial planets, but it becomes inaccurate when Jupiter-sized planets are considered. The changes they induce in the disk reverse the precession rate and increase it by more than 50%. This discrepancy can be partly solved by including the effects of a gap in the disk density profile in the analytical equations, as done in Ward (1981).

Disruption of planetary orbits through evection resonance with an external companion: circumbinary planets and multiplanet systems

Planets around binary stars and those in multiplanet systems may experience resonant eccentricity excitation and disruption due to perturbations from a distant stellar companion. This "evection resonance" occurs when the apsidal precession frequency of the planet, driven by the quadrupole associated with the inner binary or the other planets, matches the orbital frequency of the external companion. We develop an analytic theory to study the effects of evection resonance on circumbinary planets and multiplanet systems. We derive the general conditions for effective eccentricity excitation or resonance capture of the planet as the system undergoes long-term evolution. Applying to circumbinary planets, we show that inward planet migration may lead to eccentricity growth due to evection resonance with an external perturber, and planets around shrinking binaries may not survive the resonant eccentricity growth. On the other hand, significant eccentricity excitation in multiplanet systems occurs in limited parameter space of planet and binary semimajor axes, and requires the planetary migration to be sufficiently slow.

Noncircular features in Saturn’s rings III: The Cassini Division

We have conducted a comprehensive survey of 22 sharp-edged ringlets and gaps in the Cassini Division of Saturn’s rings, making use of nearly 200 high-SNR stellar and radio occultation chords obtained by the Cassini VIMS, UVIS, and RSS instruments between 2005 and 2013. We measure eccentricities from as small as ae=80 m to nearly 30 km, free normal modes with amplitudes from ∼ 0.1 to 4.1 km, and detectable inclinations as small as asini=0.2 km. Throughout the entire region, the Mimas 2.1 ILR (inner Lindblad resonance) produces systematic forced m=2 distortions that quantitatively match the expected amplitudes, phases, and pattern speed. The narrow Russell, Jeffreys, Kuiper, Bessel, and Barnard gaps are simplest, and do not contain dense ringlets. Their outer edges are generally quite sharp and four of them are circular to within ∼0.25 km, whereas most of the inner gap edges have significant eccentricities. Three gaps are more complex, containing one or more isolated ringlets. First among these is the 361 km-wide Huygens gap, containing two ringlets. The wider Huygens ringlet has nearly identical eccentricities on the two edges, in addition to OLR-type (outer Lindblad resonance) normal modes on the inner edge and ILR-type modes on the outer edge. A secondary m=1 (eccentric) mode is present on the outer edge of the ringlet, with a pattern speed similar to that of the B ring’s outer edge. Variations in the ringlet’s width are complex, but are statistically consistent with the expected magnitudes resulting from the random superposition of the multiple normal modes on the two edges. Also present in the Huygens gap is the very narrow so-called Strange ringlet, with a substantial eccentricity and inclination, as well as both ILR- and OLR-type normal modes. The 100 km-wide Herschel gap’s inner edge is highly eccentric, with at least seven ILR-type normal modes. The outer gap edge is also eccentric, and hosts four OLR-type normal modes, and a secondary m=1 mode with a pattern speed quite close to that of the B ring’s outer edge. The Herschel ringlet itself is eccentric and inclined, but neither the pericenters nor the nodes are well-aligned. The third of the complex gaps is the 241 km-wide Laplace gap, containing the Laplace ringlet. Both gap edges are eccentric, with very similar pericenter longitudes and apsidal precession rates, in spite of their large radial separation. The Laplace ringlet has eccentric edges and an abundance of normal modes. Like the Herschel ringlet, the Laplace ringlet does not precess rigidly and does not conform to the usual dynamical picture of an eccentric ringlet. Normal modes are abundant in the Cassini Division. Consistently, we find free ILR-type normal modes (m > 0) at the outer edges of ringlets and the inner edges of gaps, and free OLR-type normal modes (m ≤ 0) at inner ringlet edges and outer edges of gaps, as expected from the resonant cavity model of normal modes. We estimate the surface density of ring features from the resonance locations of the normal modes. The Cassini Division exhibits apsidal precession rates that are anomalously large, compared to the predicted values based on Saturn’s zonal gravity field. The overall radial trend matches the secular contribution expected from the nearby B ring, assuming a surface mass density of Σ=100 gm cm−2. However, the outer edges of the Huygens and Laplace gaps, and the outer edge of the Laplace ringlet, have conspicuously large residuals, exceeding their predicted precession rates by more than 0.03∘d−1. These patterns are probably the result of forcing by nearby ring material, but at present we cannot account for them in detail.

JUMPING JUPITER CAN EXPLAIN MERCURY’S ORBIT

ABSTRACT The orbit of Mercury has large values of eccentricity and inclination that cannot be easily explained if this planet formed on a circular and coplanar orbit. Here, we study the evolution of Mercury’s orbit during the instability related to the migration of the giant planets in the framework of the jumping-Jupiter model. We found that some instability models are able to produce the correct values of Mercury’s eccentricity and inclination, provided that relativistic effects are included in the precession of Mercury’s perihelion. The orbital excitation is driven by the fast change of the normal oscillation modes of the system corresponding to the perihelion precession of Jupiter (for the eccentricity) and the nodal regression of Uranus (for the inclination).

Departure from the constant-period ephemeris for the transiting exoplanet WASP-12 b

Most hot Jupiters are expected to spiral in towards their host stars due to transfering of the angular momentum of the orbital motion to the stellar spin. Their orbits can also precess due to planet-star interactions. Calculations show that both effects could be detected for the very-hot exoplanet WASP-12 b using the method of precise transit timing over a timespan of the order of 10 yr. We acquired new precise light curves for 29 transits of WASP-12 b, spannning 4 observing seasons from November 2012 to February 2016. New mid-transit times, together with literature ones, were used to refine the transit ephemeris and analyse the timing residuals. We find that the transit times of WASP-12 b do not follow a linear ephemeris with a 5 sigma confidence level. They may be approximated with a quadratic ephemeris that gives a rate of change in the orbital period of -2.56 +/- 0.40 x 10^{-2} s/yr. The tidal quality parameter of the host star was found to be equal to 2.5 x 10^5 that is comparable to theoretical predictions for Sun-like stars. We also consider a model, in which the observed timing residuals are interpreted as a result of the apsidal precession. We find, however, that this model is statistically less probable than the orbital decay.

Nonlocal gravity in the solar system

The implications of the recent classical nonlocal generalization of Einstein’s theory of gravitation for gravitational physics in the solar system are investigated. In this theory, the nonlocal character of gravity appears to simulate dark matter. Nonlocal gravity in the Newtonian regime involves a reciprocal kernel with three spatial parameters, of which two have already been determined from the rotation curves of spiral galaxies and the internal dynamics of clusters of galaxies. However, the short-range parameter a0 remains to be determined. In this connection, the nonlocal contribution to the perihelion precession of a planetary orbit is estimated and a preliminary lower limit on a0 is determined.

Uncertainty relations and precession of perihelion

We compute the corrections to the Schwarzschild metric necessary to reproduce the Hawking temperature derived from a Generalized Uncertainty Principle (GUP), so that the GUP deformation parameter is directly linked to the deformation of the metric. Using this modified Schwarzschild metric, we compute corrections to the standard General Relativistic predictions for the perihelion precession for planets in the solar system, and for binary pulsars. This analysis allows us to set bounds for the GUP deformation parameter from well-known astronomical measurements.

Does Newton’s gravitational constant vary sinusoidally with time? Orbital motions say no

A sinusoidally time-varying pattern of the values of Newton’s constant of gravitation G measured in Earth-based laboratories over the last few decades has been recently reported in the literature. We put to the test the hypothesis that the aforementioned harmonic variation may pertain to G itself in a direct and independent way. We numerically integrated the ad hoc modified equations of motion of the major bodies of the Solar System, finding that the orbits of the planets would be altered by an unacceptably larger amount in view of the present-day high accuracy astrometric measurements. In the case of Saturn, its geocentric right ascension α, declination δ and range ρ would be affected by up to milliarcseconds and 105 km, respectively; the present-day residuals of such observables are as little as about 4 milliarcseconds and 10−1 km, respectively. We analytically calculated the long-term orbital effects induced by the putative harmonic variation of G at hand, finding non-zero rates of change for the semimajor axis a, the eccentricity e and the argument of pericenter ω of a test particle. For the LAGEOS satellite, an orbital increase as large as 3.9 m yr−1 is predicted, in contrast with the observed decay of −0.203 ± 0.035 m yr−1. An anomalous perihelion precession as large as 14 arcseconds per century is implied for Saturn, while latest observations constrain it to the 10−4 arcseconds per century level. The rejection level provided by the Mercury’s perihelion rate is of the same order of magnitude.

The dynamical structure of the MEO region: long-term stability, chaos, and transport

It has long been suspected that the Global Navigation Satellite Systems exist in a background of complex resonances and chaotic motion; yet, the precise dynamical character of these phenomena remains elusive. Recent studies have shown that the occurrence and nature of the resonances driving these dynamics depend chiefly on the frequencies of nodal and apsidal precession and the rate of regression of the Moon's nodes. Woven throughout the inclination and eccentricity phase space is an exceedingly complicated web-like structure of lunisolar secular resonances, which become particularly dense near the inclinations of the navigation satellite orbits. A clear picture of the physical significance of these resonances is of considerable practical interest for the design of disposal strategies for the four constellations. Here we present analytical and semi-analytical models that accurately reflect the true nature of the resonant interactions, and trace the topological organization of the manifolds on which the chaotic motions take place. We present an atlas of FLI stability maps, showing the extent of the chaotic regions of the phase space, computed through a hierarchy of more realistic, and more complicated, models, and compare the chaotic zones in these charts with the analytical estimation of the width of the chaotic layers from the heuristic Chirikov resonance-overlap criterion. As the semi-major axis of the satellite is receding, we observe a transition from stable Nekhoroshev-like structures at three Earth radii, where regular orbits dominate, to a Chirikov regime where resonances overlap at five Earth radii. From a numerical estimation of the Lyapunov times, we find that many of the inclined, nearly circular orbits of the navigation satellites are strongly chaotic and that their dynamics are unpredictable on decadal timescales.

Variations in Titan’s dune orientations as a result of orbital forcing

Wind-blown dunes are a record of the climatic history in Titan’s equatorial region. Through modeling of the climatic conditions associated with Titan’s historical orbital configurations (arising from apsidal precessions of Saturn’s orbit), we present evidence that the orientations of the dunes are influenced by orbital forcing. Analysis of 3 Titan general circulation models (GCMs) in conjunction with a sediment transport model provides the first direct intercomparison of results from different Titan GCMs. We report variability in the dune orientations predicted for different orbital epochs of up to 70°. Although the response of the GCMs to orbital forcing varies, the orbital influence on the dune orientations is found to be significant across all models. Furthermore, there is near agreement among the two models run with surface topography, with 3 out of the 5 dune fields matching observation for the most recent orbital cycle. Through comparison with observations by Cassini, we find situations in which the observed dune orientations are in best agreement with those modeled for previous orbital configurations or combinations thereof, representing a larger portion of the cycle. We conclude that orbital forcing could be an important factor in governing the present-day dune orientations observed on Titan and should be considered when modeling dune evolution.

Net Force <i>F</i> = <i>γ</i><sup>3</sup><i>ma</i> at High Velocity

Newton’s theory of gravitation has been outdated by relativity theory explaining specific phenomena like perihelion precession of Mercury, light deflection and very recently the detection of gravitational waves. But the disappearance of the obvious gravitational force and the variation of time are arguable concepts difficult to directly prove. Present methodology is based on hypotheses as expressed in a previous article: a universal time and an inertial mass variable according to the Lorentz factor (which could not be envisioned at Newton’s age). Because this methodology is mainly stood on Newtonian mechanics, it will be called neo-Newtonian mechanics. This theory is in coherence with the time of the Quantum Mechanics. In Newtonian mechanics, all forces, including gravitational force, are deducted from the linear momentum. Introducing the variable inertial mass, the result of the demonstration is an updated expression of the net force at high velocity: F = γ3mga. If such a factor in γ3 can look a bit strange at first sight for a force, let us remind that the lost energy in a synchrotron is already measured in γ4. Next article will be on the perihelion precession of Mercury within neo-Newtonian mechanics.

The Hypergeometrical Universe: Cosmogenesis, Cosmology and Standard Model

This paper presents a simple and purely geometrical Grand Unification Theory. Quantum Gravity, Electrostatic and Magnetic interactions are shown in a unified framework. Newton’s Gravitational Law, Gauss’ Electrostatics Law and Biot-Savart’s Electromagnetism Law are derived from first principles. Gravitational Lensing, Mercury Perihelion Precession are replicated within the theory. Unification symmetry is defined for all the existing forces. This alternative model does not require Strong and Electroweak forces. A 4D Shock-Wave Hyperspherical topology is proposed for the Universe which together with a Quantum Lagrangian Principle and a Dilator based model for matter result in a quantized stepwise expansion for the whole Universe along a radial direction within a 4D spatial manifold. The Hypergeometrical Standard Model for matter, Universe Topology, Simple Cosmogenesis and a new Law of Gravitation are presented. Type 1A Supernova Survey HU results is provided. A New de-Broglie Force is proposed.

On the Intrinsic Precession of the Perihelion of Planets of the Solar System

By analytically solving a corrected balance between the force given by the Newton’s 2nd law and the Newton gravitational force in polar coordinates, an equation for the intrinsic (i.e. two-body problem) perihelion precession of the planets of the solar sys...

Merging compact binaries in hierarchical triple systems: Resonant excitation of binary eccentricity

We study the secular dynamics of compact binaries (consisting of white dwarfs, neutron stars or black holes) with tertiary companions in hierarchical triple systems. As the inner binary (with initially negligible eccentricity) undergoes orbital decay due to gravitational radiation, its eccentricity can be excited by gravitational forcing from the tertiary. This excitation occurs when the triple system passes through an ``apsidal precession resonance,'' when the precession rate of the inner binary, driven by the gravitational perturbation of the external companion and general relativity, matches the precession rate of the outer binary. The eccentricity excitation requires the outer companion to be on an eccentric orbit, with the mutual inclination between the inner and outer orbits less than $\ensuremath{\sim}40\ifmmode^\circ\else\textdegree\fi{}$. Gravitational wave (GW) signals from the inner binary can be significantly modified as the system evolves through the apsidal precession resonance. For some system parameters (e.g., a white dwarf binary with a brown dwarf tertiary), the resonance can happen when the binary emits GWs in the ${10}^{\ensuremath{-}4}\ensuremath{-}{10}^{\ensuremath{-}1}\text{ }\text{ }\mathrm{Hz}$ range (the sensitivity band of LISA).

Analytical Computation of the Perihelion Precession in General Relativity via the Homotopy Perturbation Method

Analytical Computation of the Perihelion Precession in General Relativity via the Homotopy Perturbation Method

Disc formation from tidal disruptions of stars on eccentric orbits by Schwarzschild black holes

The potential of tidal disruption of stars to probe otherwise quiescent supermassive black holes cannot be exploited, if their dynamics is not fully understood. So far, the observational appearance of these events has been derived from analytical extrapolations of the debris dynamical properties just after disruption. By means of hydrodynamical simulations, we investigate the subsequent fallback of the stream of debris towards the black hole for stars already bound to the black hole on eccentric orbits. We demonstrate that the debris circularize due to relativistic apsidal precession which causes the stream to self-cross. The circularization timescale varies between 1 and 10 times the period of the star, being shorter for more eccentric and/or deeper encounters. This self-crossing leads to the formation of shocks that increase the thermal energy of the debris. If this thermal energy is efficiently radiated away, the debris settle in a narrow ring at the circularization radius with shock-induced luminosities of $\sim 10-10^3 \, L_{\rm Edd}$. If instead cooling is impeded, the debris form an extended torus located between the circularization radius and the semi-major axis of the star with heating rates $\sim 1-10^2 \, L_{\rm Edd}$. Extrapolating our results to parabolic orbits, we infer that circularization would occur via the same mechanism in $\sim 1$ period of the most bound debris for deeply penetrating encounters to $\sim 10$ for grazing ones. We also anticipate the same effect of the cooling efficiency on the structure of the disc with associated luminosities of $\sim 1-10 \, L_{\rm Edd}$ and heating rates of $\sim 0.1-1 \, L_{\rm Edd}$. In the latter case of inefficient cooling, we deduce a viscous timescale generally shorter than the circularization timescale. This suggests an accretion rate through the disc tracing the fallback rate, if viscosity starts acting promptly.

Periodic mass extinctions and the Planet X model reconsidered

Abstract The 27 Myr period in the fossil extinction record has been confirmed in modern data bases dating back 500 Myr, which is twice the time interval of the original analysis from 30 years ago. The surprising regularity of this period has been used to reject the Nemesis model. A second model based on the Sun's vertical Galactic oscillations has been challenged on the basis of an inconsistency in period and phasing. The third astronomical model originally proposed to explain the periodicity is the Planet X model in which the period is associated with the perihelion precession of the inclined orbit of a trans-Neptunian planet. Recently, and unrelated to mass extinctions, a trans-Neptunian super-Earth planet has been proposed to explain the observation that the inner Oort cloud objects Sedna and 2012VP113 have perihelia that lie near the ecliptic plane. In this Letter, we reconsider the Planet X model in light of the confluence of the modern palaeontological and outer Solar system dynamical evidence.

Analytical Computation of the Perihelion Precession in General Relativity via the Homotopy Perturbation Method

We propose a new approach in studying the planetary orbits and the perihelion precession in General Relativity by means of the Homotopy Perturbation Method (HPM).For this purpose, we give a brief review of the nonlinear geodesic equations in the spherical symmetry spacetime which are to be studied in our work. On the basis of the main idea of HPM, we construct the appropriate homotopy what leads to the problem of solving the set of linear equations. First of all, we consider the simple example of the Schwarzschild metric for which the approximate geodesics solutions are known, in order to compare the HPM solution for orbits with those obtained earlier. Moreover, we obtain an approximate HPM solution for the Reissner-Nordstorm spacetime of a charged star.

Apsidal precession, disc breaking and viscosity in warped discs

Abstract We demonstrate the importance of general relativistic apsidal precession in warped black hole accretion discs by comparing three-dimensional smoothed particle hydrodynamic simulations in which this effect is first neglected, and then included. If apsidal precession is neglected, we confirm the results of an earlier magnetohydrodynamic simulation which made this assumption, showing that at least in this case the α viscosity model produces very similar results to those of simulations where angular momentum transport is due to the magnetorotational instability. Including apsidal precession significantly changes the predicted disc evolution. For moderately inclined discs thick enough that tilt is transported by bending waves, we find a disc tilt which is non-zero at the inner disc edge and oscillates with radius, consistent with published analytic results. For larger inclinations, we find disc breaking.