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This study analyzes the secular dynamics of two extended bodies in Keplerian orbits, focusing on tidal effects. It introduces formulas for energy dissipation within each body in a binary system. The bodies can have a finite number of layers with linear viscoelastic rheology. The layers must be sufficiently coupled so that the rotation of each layer remains close to the average rotation of the body. The body is assumed to be in a "viscous regime" (though it may contain purely elastic layers), meaning that the relaxation times of the rheology are much shorter than the typical despinning time and deviations from sphericity are caused only by tidal and centrifugal stresses. The main contribution of this paper is the decomposition of orbital-averaged equations into a fast–slow system. This reduction allows the slow dynamics to be represented as sliding along a torque-free curve with occasional jumps at folding points. This greatly simplifies the analysis of the dynamics as a function of the rheological parameters. [ABSTRACT FROM AUTHOR]

Understanding of secular evolution of the Earth system is based largely on the rock and mineral archive preserved in the continental lithosphere. Based on the frequency and range of accessible data preserved in this record, we divide the secular evolution into seven phases: (a) "Proto‐Earth" (ca. 4.57–4.45 Ga); (b) "Primordial Earth" (ca. 4.45–3.80 Ga); (c) "Primitive Earth" (ca. 3.8–3.2 Ga); (d) "Juvenile Earth" (ca. 3.2–2.5 Ga); (e) "Youthful Earth" (ca. 2.5–1.8 Ga); (f) "Middle Earth" (ca. 1.8–0.8 Ga); and (g) "Contemporary Earth" (since ca. 0.8 Ga). Integrating this record with knowledge of secular cooling of the mantle and lithospheric rheology constrains the changes in the tectonic modes that operated through Earth history. Initial accretion and the Moon forming impact during the Proto‐Earth phase likely resulted in a magma ocean. The solidification of this magma ocean produced the Primordial Earth lithosphere, which preserves evidence for intra‐lithospheric reworking of a rigid lid, but which also likely experienced partial recycling through mantle overturn and meteorite impacts. Evidence for craton formation and stabilization from ca. 3.8 to 2.5 Ga, during the Primitive and Juvenile Earth phases, likely reflects some degree of coupling between the convecting mantle and a lithosphere initially weak enough to favor an internally deformable, squishy‐lid behavior, which led to a transition to more rigid, plate like, behavior by the end of the early Earth phases. The Youthful to Contemporary phases of Earth, all occurred within a plate tectonic framework with changes between phases linked to lithospheric behavior and the supercontinent cycle. Plain Language Summary: The record of Earth evolution is preserved in the continental rock archive, but is incomplete and our knowledge of it decreases with increasing age and depth of preservation. Based on secular cooling of the mantle and associated changing lithospheric properties, we recognize three dominant tectonic modes that have operated on Earth; stagnant lid, squishy lid, and plate tectonics. After solidification of the Earth's initial magma ocean (>4.45 Ga), the lithosphere was likely dominated by mafic crust that existed until ca. 3.8 Ga. The tectonic mode that operated at this time involved either no lithosphere‐mantle coupling (cf., stagnant lid), or coupling between non‐rigid lithosphere and convecting mantle (cf., squishy lid). The latter mode likely operated through most of the Archean (ca. 3.8–2.5 Ga), and was associated with the formation of the stable interior of continents, called cratons. The stabilization of these cratons in the latter half of the Archean (ca. 3.2–2.5 Ga) is associated with the development of rigid lithosphere and the transition to a plate tectonic mode that continues to the present day. Further changes, likely in response to the supercontinent cycle, lead to subdivisions of the Earth system between ca. 1.8 and 0.8 Ga. Key Points: Long‐term record of Earth evolution preserved in continental lithosphereThree main tectonic modes operated through Earth history: stagnant lid, squishy lid and rigid, active lid (plate tectonics)Stabilization of cratons at end of Archean marks transition to plate tectonics with supercontinent cycle controlling subsequent changes [ABSTRACT FROM AUTHOR]

We consider an exoplanetary system consisting of a star and two planets. The masses of the planets are significantly less than the mass of the star. The evolution of the orbital motion of exoplanets is studied within the framework of a double averaged unrestricted three-body problem. The main attention is paid to coplanar configurations, when the star and planets move in a certain plane that preserves a constant position. The possibility of reversing the orbital motion of the inner planet is noted. [ABSTRACT FROM AUTHOR]

Exploring weakly perturbed Keplerian motion within the restricted three-body problem, Lidov (Planet Space Sci 9:719-759, 1962) and, independently, Kozai (Astron J 67:591-598, 1962) discovered coupled oscillations of eccentricity and inclination (the KL cycles). Their classical studies were based on an integrable model of the secular evolution, obtained by double averaging of the disturbing function approximated with its first non-trivial term. This was the quadrupole term in the series expansion with respect to the ratio of the semimajor axis of the disturbed body to that of the disturbing body. If the next (octupole) term is kept in the expression for the disturbing function, long-term modulation of the KL cycles can be established (Ford et al. in Astrophys J 535:385-401, 2000; Naoz et al. in Nature 473:187-189, 2011; Katz et al. in Phys Rev Lett 107:181101, 2011). Specifically, flips between the prograde and retrograde orbits become possible. Since such flips are observed only when the perturber has a nonzero eccentricity, the term 'eccentric Kozai-Lidov effect' (or EKL effect) was proposed by Lithwick and Naoz (Astrophys J 742:94, 2011) to specify such behavior. We demonstrate that the EKL effect can be interpreted as a resonance phenomenon. To this end, we write down the equations of motion in terms of 'action-angle' variables emerging in the integrable Kozai-Lidov model. It turns out that for some initial values the resonance is degenerate and the usual 'pendulum' approximation is insufficient to describe the evolution of the resonance phase. Analysis of the related bifurcations allows us to estimate the typical time between the successive flips for different parts of the phase space. [ABSTRACT FROM AUTHOR]

We investigate the secular dynamics of two-planet coplanar systems evolving under mutual gravitational interactions and dissipative forces. We consider two mechanisms responsible for the planetary migration: star-planet (or planet-satellite) tidal interactions and interactions of a planet with a gaseous disc. We show that each migration mechanism is characterized by a specific law of orbital angular momentum exchange. Calculating stationary solutions of the conservative secular problem and taking into account the orbital angular momentum leakage, we trace the evolutionary routes followed by the planet pairs during the migration process. This procedure allows us to recover the dynamical history of two-planet systems and constrain parameters of the involved physical processes. [ABSTRACT FROM AUTHOR]

The author of this paper examines the influence of time variation of the gravitational constant on the evolution of the orbital elements of binary stars. The theoretical results show that the semimajor axis, eccentricity and mean longitude exhibit periodic, secular and mixed periodic variation, but the longitude of the periastron exists in periodic and mixed periodic variation, but not secular variation. The inclination and ascending node exhibit no variation. In addition, the limits of the secular evolution of the orbit of six binary stars due to time variation of the gravitational constant are estimated. The numerical results are given. The theoretical results are discussed and conclusions drawn. [ABSTRACT FROM AUTHOR]

The term “jumping” Trojan was introduced by Tsiganis et al. (Astron Astrophys 354:1091-1100, 2000) in their studies of long-term dynamics exhibited by the asteroid (1868) Thersites, which had been observed to jump from librations around L4 to librations around L5. Another example of a “jumping” Trojan was found by Connors et al. (Nature 475:481-483, 2011): librations of the asteroid 2010 TK7 around the Earth’s libration point L4 preceded by its librations around L5. We explore the dynamics of “jumping” Trojans under the scope of the restricted planar elliptical three-body problem. Via double numerical averaging we construct evolutionary equations, which allow analyzing transitions between different regimes of orbital motion. [ABSTRACT FROM AUTHOR]

Stellar bars are important internal drivers of the secular evolution of disk galaxies. Using a sample of nearby barred galaxies with weak and strong bars, we evaluate the correlations between star formation properties in different galactic structures and their associated bars, and try to interpret the complex process of bar-driven secular evolution. We find that weaker bars tend to associate with lower concentrical star formation activities, while stronger bars appear to have large scatter in the distribution of the global star formation activities. In general, the star formation activities in early- and late-type galaxies have different behavior, with similar star formation rate density distributions. In addition, there are only weak trends toward increased star formation activities in bulges and galaxies with stronger bars, which is consistent with previous works. Our results suggest that the different stages of the evolutionary sequence and many factors besides bars may contribute to the complexity of this process. Furthermore, significant correlations are found between the star formation activities in different galactic structures, in which barred galaxies with intense star formation in bulges tend to also have active star formation in their bars and disks. Most bulges have higher star formation densities than their associated bars and disks, indicating the presence of bar-driven evolution. Therefore, we derived a possible criterion (Figure 1) to quantify the different stages of a bar-driven evolutionary sequence. Future work is needed to improve on the uncertainties of this study. [ABSTRACT FROM PUBLISHER]