Perihelion Precession Research Articles

Role of the Rossiter-McLaughlin effect in the study of close binaries

This paper is devoted to binary stars belonging to the class of eclipsing-variable systems. Photometric and spectroscopic analysis of eclipses allows us to determine geometric parameters of the orbit and physical characteristics of stellar components as well as inclinations of stellar equators to the orbital plane. Estimations of inclinations can be obtained from measurement of the Rossiter-McLaughlin effect, which is discussed using examples of some eccentric binaries with an anomalous apsidal effect. Our task is to find the complete spectrum of solutions of the equation of apsidal motion, depending on the inclinations of the polar axes of the components to the orbital one for these systems, based on their individual spectroscopic and photometric observational data. The matrix of solutions allows us to select those pairs of polar inclinations that provide agreement with the observational apsidal period.

Apsidal Motion and Absolute Parameters of 21 Early-type Small Magellanic Cloud Eccentric Eclipsing Binaries

Abstract We present the apsidal motion and light-curve analyses of 21 eccentric eclipsing binaries located in the Small Magellanic Cloud. Most of these systems have never been studied before, hence their orbital and physical properties as well as the apsidal motion parameters are given here for the first time. All the systems are of early spectral type, having orbital periods up to 4 days. The apsidal motion periods were derived to be from 7.2 to 200 yr (OGLE-SMC-ECL-2194 having the shortest apsidal period among known main-sequence systems). The orbital eccentricities are usually rather mild (median of about 0.06), the maximum eccentricity being 0.33. For the period analysis using O − C diagrams of eclipse timings, in total 951 minima were derived from survey photometry as well as our new data. Moreover, six systems show some additional variation in their O − C diagrams, which should indicate the presence of hidden additional components in them. According to our analysis these third-body variations have periods from 6.9 to 22 yr.

Late Delivery of Nitrogen to the Earth

Atmospheric nitrogen may be a necessary ingredient for the habitability of a planet since its presence helps to prevent water loss from a planet. The present day nitrogen isotopic ratio, $^{15}$N/$^{14}$N, in the Earth's atmosphere is a combination of the primitive Earth's ratio and the ratio that might have been delivered in comets and asteroids. Asteroids have a nitrogen isotopic ratio that is close to the Earth's. This indicates either a similar formation environment to the Earth or that the main source of nitrogen was delivery by asteroids. However, according to geological records, the Earth's atmosphere could have been enriched in $^{15}$N during the Archean era. Comets have higher a $^{15}$N/$^{14}$N ratio than the current atmosphere of the Earth and we find that about $5\%$ $\sim$ $10\%$ of nitrogen in the atmosphere of the Earth may have been delivered by comets to explain the current Earth's atmosphere or the enriched $^{15}$N Earth's atmosphere. We model the evolution of the radii of the snow lines of molecular nitrogen and ammonia in a protoplanetary disk and find that both have radii that put them farther from the Sun than the main asteroid belt. With an analytic secular resonance model and N--body simulations we find that the $\nu_8$ apsidal precession secular resonance with Neptune, which is located in the Kuiper belt, is a likely origin for the nitrogen-delivering comets that impact the Earth.

Constraining Yukawa gravity from planetary motion in the solar system

In this work we used the observed additional perihelion precession in the Solar System, obtained from the observations of planets and spacecrafts, to study the possible existence of Yukawa correction term to the Newtonian gravitational potential. Our study was motivated by previous analyses which indicated the possible discrepancies from Newtonian gravity in this form and at wide range of astrophysical scales. Yukawa gravity was introduced to cure some shortcomings of General Relativity (GR) at galactic and extragalactic scales. We demonstrated that this form of gravity can give the values for orbital precession which are comparable or even in better agreement with observations than the corresponding predictions of GR. The obtained results can be used for setting stronger constraints on variation of the gravitational constant G, as well as on the fundamental constant δ of Yukawa gravity. Moreover, Yukawa gravity could be used to improve the results for the motion of planets, other Solar System bodies, as well as spacecrafts, and as a consequence, it can help us to get more reliable predictions for natural hazards in the Solar System, such as potential impacts by near-Earth objects.

Perihelion precession in binary systems: higher order corrections

Higher order corrections (up to n-th order) are obtained for the perihelion precession in binary systems like OJ287 using the Schwarzschild metric and complex integration. The corrections are performed considering the third root of the motion equation and developing the expansion in terms of $r_{s}/ (a(1-e^{2}) )$ .The results are compared with other expansions that appear in the literature giving corrections to second and third order. Finally, we simulate the shape of relativistic orbits for binary systems with different masses.

Solar system tests in constraining parameters of dyon black holes

In the present paper we examine the possibility of constraining dyon black holes based on the available observational data at the scale of the Solar system. For this we consider the classical tests of general relativity, viz., the perihelion precession of the planet Mercury and the deflection of light by the Sun. In connection to mathematical analysis we are considering static and spherically symmetric dyon black hole which carries both the electric and magnetic charge simultaneously, which are encoded it by the parameters lambda _0 and beta _0. We constrain these two parameters using the Solar system tests and obtain the permissible range from theoretical analysis based on our model and later on compare them with the available observational data.

Understanding WASP-12b

The orbital period of the hot Jupiter WASP-12b is apparently changing. We study whether this reflects orbital decay due to tidal dissipation in the star, or apsidal precession of a slightly eccentric orbit. In the latter case, a third body or other perturbation would be needed to sustain the eccentricity against tidal dissipation in the planet itself. We have analyzed several such perturbative scenarios, but none is satisfactory. Most likely therefore, the orbit really is decaying. If this is due to a dynamical tide, then WASP-12 should be a subgiant without a convective core as Weinberg et al. (2017) have suggested. We have modeled the star with the MESA code. While no model fits all of the observational constraints, including the luminosity implied by the GAIA DR2 distance, main-sequence models are less discrepant than subgiant ones.

Theory of The Three Fields of Space


 This article is a logical and rational analysis of the physical phenomena produced by the three fields that are generated in space: gravity field; field of terrestrial nuclear magnetism; and orbital field.
 Eduardo Guimarães, through the studies of the three nuclear masses of the Sun's nucleus, the three nuclear masses of the moon's nucleus, and the three nuclear masses of the Earth's nucleus.
 We discover the three spatial fields that are generated in the solar system and in the planets.
 Then, from the general theory of the three fields of space, we can understand all the mechanics that generate the dynamics and kinematics of celestial bodies.
 So now we can understand why the smaller celestial bodies orbit the orbital field of the largest celestial bodies.
 So now we can understand why the planets produce orbits of elliptical motions, around the orbital field of the Sun.
 Then we understand the orbital mechanics of the little planet Mercury, and its abnormal orbit around the orbiting field of the Sun.
 Then Mercury has a perihelion precession of 2 degrees per century, due to an approximation of the perihelion of Mercury which is attracted by the micro-gravity of the Sun, generating an orbital deviation of 2 degrees per century.
 In the future the planet Mercury will lose energy from its nucleus and will not be able to make the orbital curve of the perihelion because it will have been attracted by the gravitational field of the Sun's nucleus.
 The fall of Mercury on the Sun will generate two thermonuclear explosions of SUPERNOVA.
 The first thermonuclear explosion of SUPERNOVA will be generated by the thermonuclear collision of the gravity mass attraction of Mercury debris with the Sun's nucleus.
 The second thermonuclear explosion of SUPERNOVA will be generated by the thermonuclear collision of attraction of the mass of orbital attraction of Mercury debris with the nucleus of the Sun.
 These two thermonuclear explosions of SUPERNOVA will generate two immense thermonuclear shockwaves that will devastate the entire fragile geo-biome of the solar system.
 

Black Hole Disks in Galactic Nuclei.

Gravitational torques among objects orbiting a supermassive black hole drive the rapid reorientation of orbital planes in nuclear star clusters (NSCs), a process known as vector resonant relaxation. In this Letter, we determine the statistical equilibrium of systems with a distribution of masses, semimajor axes, and eccentricities. We average the interaction over the apsidal precession time and construct a MonteCarlo Markov chain method to sample the microcanonical ensemble of the NSC. We examine the case of NSCs formed by 16 episodes of star formation or globular cluster infall. We find that the massive stars and stellar mass black holes form a warped disk, while low mass stars resemble a spherical distribution with a possible net rotation. This explains the origin of the clockwise disk in the Galactic center and predicts a population of black holes (BHs) embedded within this structure. The rate of mergers among massive stars, tidal disruption events of massive stars by BHs, and BH-BH mergers are highly increased in such disks. The first two may explain the origin of the observed G1 and G2 clouds, the latter may be important for gravitational wave detections with LIGO and VIRGO. More generally, black holes are expected to settle in disks in all dense spherical stellar systems assembled by mergers of smaller systems including globular clusters.

Orbital dynamics of a two-body system in the context of a nonlocally mixed IR–UV field theory of gravity

We have recently suggested a set of nonlocally extended field equations in which Newton’s constant [Formula: see text] was promoted to a covariant differential operator [Formula: see text] composed by two different contributions. These two terms independently operate in the infrared (IR) and ultraviolet (UV) energy regimes. Considering the recent spectacular direct gravitational radiation measurements, we aim to compute the nonlocally modified orbital dynamics of a two-body system. In a first attempt, we determine the effective Newtonian potential from the nonlocal UV-wave equation to work out the modified Kepler orbits. In addition, we use data obtained from the perihelion precession of Mercury in order to derive an upper bound for the dimensionless UV-parameter [Formula: see text]. Finally, we determine the energy per unit time (power) released by a binary system in the form of gravitational waves. In this context, we observe that in the limit of vanishing UV-parameters, we eventually recover the result obtained in the context of the standard quadrupole formula.

Is it possible to measure new general relativistic third-body effects on the orbit of Mercury with BepiColombo?

Recently, Will calculated an additional contribution to the Mercury’s precession of the longitude of perihelion varpi of the order of {dot{varpi }}_text {W}simeq 0.22~text {milliarcseconds per century} (text {mas cty}^{-1}). It is partly a direct consequence of certain 1pN third-body accelerations entering the planetary equations of motion, and partly an indirect, mixed effect due to the simultaneous interplay of the standard 1pN pointlike acceleration of the primary with the Newtonian N-body acceleration, to the quadrupole order, in the analytical calculation of the secular perihelion precession with the Gauss equations. We critically discuss the actual measurability of the mixed effects with respect to direct ones. The current uncertainties in either the magnitude of the Sun’s angular momentum S_odot and the orientation of its spin axis {varvec{hat{S}}}_odot impact the precessions {dot{varpi }}_{J_2^odot },~{dot{varpi }}_text {LT} induced by the Sun’s quadrupole mass moment and angular momentum via the Lense–Thirring effect to a level which makes almost impossible to measure {dot{varpi }}_text {W}, even in the hypothesis that it comes entirely from the aforementioned 1pN third-body accelerations. On the other hand, from the point of view of the Lense–Thirring effect itself, the mismodeled quadrupolar precession delta {dot{varpi }}_{J_2^odot } due to the uncertainties in {varvec{hat{S}}}_odot corresponds to a bias of simeq 9% of the relativistic one. The resulting simulated mismodeled range and range-rate times series of BepiColombo are at about the per cent level of the nominal gravitomagnetic ones.

Computation of the General Relativistic Perihelion Precession and of Light Deflection via the Laplace-Adomian Decomposition Method

We study the equations of motion of the massive and massless particles in the Schwarzschild geometry of general relativity by using the Laplace-Adomian Decomposition Method, which proved to be extremely successful in obtaining series solutions to a wide range of strongly nonlinear differential and integral equations. After introducing a general formalism for the derivation of the equations of motion in arbitrary spherically symmetric static geometries and of the general mathematical formalism of the Laplace-Adomian Decomposition Method, we obtain the series solution of the geodesics equation in the Schwarzschild geometry. The truncated series solution, containing only five terms, can reproduce the exact numerical solution with a high precision. In the first order of approximation we reobtain the standard expression for the perihelion precession. We study in detail the bending angle of light by compact objects in several orders of approximation. The extension of this approach to more general geometries than the Schwarzschild one is also briefly discussed.

Dynamic portrait of the region occupied by the Hungaria asteroids: the influence of Mars

The region occupied by the Hungaria asteroids has a high dynamical complexity. In this paper, we analyse the main dynamic structures and their influence on the known asteroids through the construction of maps of initial conditions. We evolve a set of test particles placed on a perfectly rectangular grid of initial conditions during 3 Myr under the gravitational influence of the Sun and eight planets, from Mercury to Neptune. Moreover, we use the method MEGNO in order to obtain a complete dynamical portrait of the region. A comparison of our maps with the distribution of real objects allows us to detect the main dynamical mechanisms acting in the domain under study such as mean-motion and secular resonances. Our main results is the existence of a small area inside a stable region where are placed the Hungaria asteroids. We found that the influence of Mars has an important role for the dynamic structure of the region, defining the limits for this population of asteroids. Our result is in agreement with previous studies, which have indicated the importance of the eccentricity of Mars for the stability of Hungaria asteroids. However, we found that the secular resonance resulting from the precession of perihelion due to a coupling with that of Jupiter proposed as limit for the Hungaria region could not be determinant for this population of asteroids.

Einstein's Rocket Ship, the Deflection of Light and the Precession of the Orbital Perihelion

The nature of the principle of equivalence is explored. The light ray travel path in an accelerated reference frame, a rocket ship, is described and the rocket ship model is used to derive the deflection of light by a massive body. By accounting for the effect of the velocity of the accelerated observer relative to an inertial frame, the additional deflection angle is obtained due to the aberration of the light beam. This model is applied to the deflection of light by a central gravitational field, giving the total deflection angle in agreement with the standard result. Also, a novel approach is given by considering the deflection of light by a massive body to obtain the precession of the perihelion of a planet.

The dark-baryonic matter mass relation for observational verification in Verlinde’s emergent gravity

Recently, a new interesting idea of origin of gravity has been developed by Verlinde. In this scheme of emergent gravity, where horizon entropy, microscopic de Sitter states and relevant contribution to gravity are involved, an entropy displacement resulting from matter behaves as a memory effect and can be exhibited at sub-Hubble scales, namely, the entropy displacement and its “elastic” response would lead to emergent gravity, which gives rise to an extra gravitational force. Then galactic dark matter effects may origin from such extra emergent gravity. We discuss some concepts in Verlinde’s theory of emergent gravity and point out some possible problems or issues, e.g., the gravitational potential caused by Verlinde’s emergent apparent dark matter may no longer be continuous in spatial distribution at ordinary matter boundary (such as a massive sphere surface). In order to avoid the unnatural discontinuity of the extra emergent gravity of Verlinde’s apparent dark matter, we suggest a modified dark-baryonic mass relation (a formula relating Verlinde’s apparent dark matter mass to ordinary baryonic matter mass) within this framework of emergent gravity. The modified mass relation is consistent with Verlinde’s result at relatively small scales (e.g., $$R<3h_{70}^{-1}$$ Mpc). However, it seems that, compared with Verlinde’s relation, at large scales (e.g., gravitating systems with $$R>3h_{70}^{-1}$$ Mpc), the modified dark-baryonic mass relation presented here might be in better agreement with the experimental curves of weak lensing analysis in the recent work of Brouwer et al. Galactic rotation curves are compared between Verlinde’s emergent gravity and McGaugh’s recent model of MOND (Modified Newtonian Dynamics established based on recent galaxy observations). It can be found that Verlinde rotational curves deviate far from those of McGaugh MOND model when the MOND effect (or emergent dark matter) dominates. Some applications of the modified dark-baryonic mass relation inspired by Verlinde’s emergent gravity will be addressed for galactic and solar scales. Potential possibilities to test this dark-baryonic mass relation as well as apparent dark matter effects, e.g., planetary perihelion precession at Solar System scale, will be considered. This may enable to place some constraints on the magnitudes of the MOND characteristic acceleration at the small solar scale.

Relative influence of precession and obliquity in the early Holocene: Topographic modulation of subtropical seasonality during the Asian summer monsoon

On orbital timescales, higher summer insolation is thought to strengthen the continental monsoon while weakening the maritime monsoon in the Northern hemisphere. Through simulations using the Community Earth System Model, we evaluated the relative influence of perihelion precession and high obliquity in the early Holocene during the Asian summer monsoon. The major finding was that precession dominates the atmospheric heating change over the Tibetan Plateau–Himalayas and Maritime Continent, whereas obliquity is responsible for the heating change over the equatorial Indian Ocean. Thus, precession and obliquity can play contrasting roles in driving the monsoons on orbital timescales.In late spring–early summer, interior Asian continental heating drives the South and East Asian monsoons. The broad-scale monsoonal circulation further expands zonally in July–August, corresponding to the development of summer monsoons in West Africa and the subtropical Western North Pacific (WNP) as well as a sizable increase in convection over the equatorial Indian Ocean. Tropical and oceanic heating becomes crucial in late summer. Over South Asia–Indian Ocean (50°E−110°E), the precession maximum intensifies the monsoonal Hadley cell (heating with an inland/highland origin), which is opposite to the meridional circulation change induced by high obliquity (heating with a tropical origin). The existence of the Tibetan Plateau–Himalayas intensifies the precessional impact. During the late-summer phase of the monsoon season, the effect of obliquity on tropical heating can be substantial. In addition to competing with Asian continental heating, obliquity-enhanced heating over the equatorial Indian Ocean also has a Walker-type circulation impact, resulting in suppression of precession-enhanced heating over the Maritime Continent.

KMTNet Time-series Photometry of the Doubly Eclipsing Binary Stars Located in the Large Magellanic Cloud

We report the results of photometric observations for doubly eclipsing binaries OGLE-LMC-ECL-15674 and OGLE-LMC-ECL-22159, both of which are composed of two pairs (designated A&B) of a detached eclipsing binary located in the Large Magellanic Cloud. The light curves were obtained by high-cadence time-series photometry using the Korea Microlensing Telescope Network 1.6 m telescopes located at three southern sites (CTIO, SAAO, and SSO) between 2016 September and 2017 January. The orbital periods were determined to be 1.433 and 1.387 days for components A and B of OGLE-LMC-ECL-15674, respectively, and 2.988 and 3.408 days for OGLE-LMC-ECL-22159A and B, respectively. Our light curve solutions indicate that the significant changes in the eclipse depths of OGLE-LMC-ECL-15674A and B were caused by variations in their inclination angles. The eclipse timing diagrams of the A and B components of OGLE-LMC-ECL-15674 and OGLE-LMC-ECL-22159 were analyzed using 28, 44, 28, and 26 new times of minimum light, respectively. The apsidal motion period of OGLE-LMC-ECL-15674B was estimated by detailed analysis of eclipse timings for the first time. The detached eclipsing binary OGLE-LMC-ECL-15674B shows a fast apsidal period of 21.5 ± 0.1 years.

The 1.5 post-Newtonian radiative quadrupole moment in the context of a nonlocal field theory of gravity

We recently suggested a nonlocal modification of Einstein’s field equations in which Newton’s constant G was promoted to a covariant differential operator . The latter contains two independent contributions which operate respectively in the infrared (IR) and ultraviolet (UV) energy regimes. In the light of the recent direct gravitational radiation measurements we aim to determine the UV-modified 1.5 post-Newtonian radiative quadrupole moment of a generic n-body system. We eventually use these preliminary results in the context of a binary system and observe that in the limit vanishing UV parameters we precisely recover the corresponding general relativistic results. Moreover we notice that the leading order deviation of the UV-modified radiative quadrupole moment numerically coincides with findings obtained in the framework of calculations performed previously in the context of the perihelion precession of Mercury.

The Dynamics of Tightly-packed Planetary Systems in the Presence of an Outer Planet: Case Studies Using Kepler-11 and Kepler-90

Abstract We explore the effects of an undetected outer giant planet on the dynamics, observability, and stability of Systems with Tightly-packed Inner Planets (STIPs). We use direct numerical simulations along with secular theory and synthetic secular frequency spectra to analyze how analogues of Kepler-11 and Kepler-90 behave in the presence of a nearly co-planar, Jupiter-like outer perturber with semimajor axes between 1 and 5.2 au. Most locations of the outer perturber do not affect the evolution of the inner planetary systems, apart from altering precession frequencies. However, there are locations at which an outer planet causes system instability due to, in part, secular eccentricity resonances. In Kepler-90, there is a range of orbital distances for which the outer perturber drives planets b and c, through secular interactions, onto orbits with inclinations that are ∼16° away from the rest of the planets. Kepler-90 is stable in this configuration. Such secular resonances can thus affect the observed multiplicity of transiting systems. We also compare the synthetic apsidal and nodal precession frequencies with the secular theory and find some misalignment between principal frequencies, indicative of strong interactions between the planets (consistent with the system showing TTVs). First-order libration angles are calculated to identify MMRs in the systems, for which two near-MMRs are shown in Kepler-90, with a 5:4 between b and c, as well as a 3:2 between g and h.

Null geodesics and observables around the Kerr–Sen black hole

We investigate the geodesic motion in the background of the Kerr–Sen black hole arising in heterotic string theory. The nature of the effective potential is discussed in the radial, as well as latitudinal, direction. A special class of spherical photon orbits is obtained along with an expression for the turning point for the radial photons. Dependence of photon motion within this class of solution is discussed explicitly in view of the different black hole parameters. We have discussed the allowed regions for the geodesic motion of massless test particles around the Kerr–Sen black hole in a more generalised way by considering non-equatorial motion of the photons into account. The conditions for different types of possible orbits are discussed with specific parameter values along with the corresponding orbit structure. No terminating orbits are possible for photons due to non-zero black hole charge. Observables on the angular plane (viz. bending of light and perihelion precession for massive test particles) are analysed as special cases. We have also calculated the rotation and mass parameters for the Kerr–Sen black hole in terms of the red/blue shifts of the photons in circular and equatorial orbits emitted by the massive test particles which represent stars or other probable sources of photons.