EQUATIONS OF PLANETARY SYSTEMS MOTION

The study of the dynamically evolution of planetary systems is very actually in relation with findings of exoplanet systems. free spherical bodies problem is considered in this paper, mutually gravitating according to Newton's law, with isotropically variable masses as a celestial-mechanical model of non-stationary exoplanetary systems. The dynamic evolution of planetary systems is learned, when evolution's leading factor is the masses' variability of gravitating bodies themselves. The laws of the bodies' masses varying are assumed to be known arbitrary functions of time. When doing so the rate of varying of bodies' masses is different. The planets' location is such that the orbits of planets don't intersect. Let us treat this position of planets is preserve in the evolution course. The motions are researched in the relative coordinates system with beginning in the center of the parent star, axes that are parallel to corresponding axes of the absolute coordinates system. The canonical perturbation theory is used on the base aperiodic motion over the quasi-canonical cross-section. The bodies evolution is studied in the osculating analogues of the second system of canonical Poincare elements. The canonical equations of perturbed motion in analogues of the second system of canonical Poincare elements are convenient for describing the planetary systems dynamic evolution, when analogues of eccentricities and analogues of inclinations of orbital plane are sufficiently small. It is noted that to obtain an analytical expression of the perturbing function main part through canonical osculating Poincare elements using computer algebra is preferably. If in expansions of the main part of perturbing function is constrained with precision to second orders including relatively small quantities, then the equations of secular perturbations will obtained as linear non-autonomous system. This circumstance meaningful makes much easier to study the non-autonomous canonical system of differential equations of secular perturbations of considering problem.

The unexpected narrowness of eccentric debris rings: a sign of eccentricity during the protoplanetary disc phase

This paper shows that the eccentric debris rings seen around the stars Fomalhaut and HD 202628 are narrower than expected in the standard eccentric planet perturbation scenario (sometimes referred to as ‘pericentre glow’). The standard scenario posits an initially circular and narrow belt of planetesimals at semi-major axis a , whose eccentricity is increased to e f after the gas disc has dispersed by secular perturbations from an eccentric planet, resulting in a belt of width 2 ae f . In a minor modification of this scenario, narrower belts can arise if the planetesimals are initially eccentric, which could result from earlier planet perturbations during the gas-rich protoplanetary disc phase. However, a primordial eccentricity could alternatively be caused by instabilities that increase the disc eccentricity, without the need for any planets. Whether these scenarios produce detectable eccentric rings within protoplanetary discs is unclear, but they nevertheless predict that narrow eccentric planetesimal rings should exist before the gas in protoplanetary discs is dispersed. PDS 70 is noted as a system hosting an asymmetric protoplanetary disc that may be a progenitor of eccentric debris ring systems.

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.

Twisted debris: how differential secular perturbations shape debris disks

Context. Resolved images suggest that asymmetric structures are a common feature of cold debris disks. While planets close to these disks are rarely detected, their hidden presence and gravitational perturbations provide plausible explanations for some of these features. Aims. To put constraints on the properties of yet undetected planetary companions, we aim to predict what features such a planet imprints in debris disks undergoing continuous collisional evolution. Methods. We discuss the basic equations, analytic approximations and timescales governing collisions, radiation pressure and secular perturbations. In addition, we combine our numerical model of the collisional evolution of the size and spatial distributions in debris disks with the gravitational perturbation by a single planet. Results. We find that the distributions of orbital elements in the disks are strongly dependent on grain sizes. Secular precession is differential with respect to involved semi-major axes and grain sizes. This leads to observable differences between the big grains tracing the parent belt and the small grains in the trailing halo. Observations at different wavelengths can be used to constrain the properties of a possible planet.

A First Order Automated Lie Transform

The objective of the present paper is to focus on the problem of the normalization of a Hamiltonian system via the elimination of angle variables involved using the Lie transform technique. The algorithm that we construct assumes that the Hamiltonian is periodic in [Formula: see text] angle variables, with two rates: fast and slow. If the angle variables have the same rate only one transformation is required. The equations needed to evaluate the elements of each transformation and the secular perturbations are constructed.

Dynamical evolution of near-Sun objects

The dynamical evolution of short-period objects having perihelia at small heliocentric distances is discussed. We have investigated the motion of multiple-apparition members of the Marsden and Kracht sungrazing groups. The orbital evolution of these objects on timescales < 10 Kyr is mainly determined by the Kozai-Lidov secular perturbations. These objects are dynamically connected with high-inclination near-Earth objects. On the other hand, we have found several observed near-Earth objects that evolve in the same way, reaching small perihelion distances on short timescales in the past.