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We study the perturbed-from-synchronous librational state of a double asteroid, modeled by the Full Two Rigid Body Problem (F2RBP), with primary emphasis on deriving analytical formulas which describe the system's evolution after deflection by a kinetic impactor. To this end, both linear and nonlinear (canonical) theories are developed. We make the simplifying approximations (to be relaxed in a forthcoming paper) of planar binary orbit and axisymmetric shape of the primary body. To study the effect of a DART-like hit on the secondary body, the momentum transfer enhancement parameter β is introduced and retained as a symbolic variable throughout all formulas derived, either by linear or nonlinear theory. Our approach can be of use in the context of the analysis of the post-impact data from kinetic impactor missions, by providing a precise modeling of the impactor's effect on the seconadry's librational state as a function of β . [ABSTRACT FROM AUTHOR]

We revisit the problem of secular resonance sweeping during the dissipation of a protoplanetary disk and its possible role in exciting the orbits of primordial asteroids, in light of recent models of Solar system evolution. We develop an integrator that incorporates the gravitational effect of a uniformly (or not) depleting, axisymmetric disk with arbitrary surface density profile; its performance is verified by analytical calculations. The secular response of fictitious asteroids, under perturbations from Jupiter, Saturn and a decaying disk, is thoroughly studied. Note that the existence of a symmetry plane induced by the disk lifts the inherent degeneracy of the two-planet system, such that the ' s 5 ' nodal frequency can also play a major role. We examine different resonant configurations for the planets (2:1, 3:2, 5:3), disk models and depletion scenarios. For every case, we compute the corresponding time paths of secular resonances, which show when and where resonance crossing occurs. The excitation of asteroids, particularly in inclination, is studied in the various models and compared to analytical estimates. We find that inclination excitation in excess of ∼ 10 ∘ is possible in the asteroid belt, but the nearly uniform spread of Δ i ∼ 20 ∘ observed calls for the combined action of secular resonance sweeping with other mechanisms (e.g., scattering by Mars-sized embryos) that would be operating during terrestrial planet formation. Our results are also applicable to extrasolar planetary systems. [ABSTRACT FROM AUTHOR]

The recent discovery of free-floating planets and their theoretical interpretation as celestial bodies, either condensed independently or ejected from parent stars in tight clusters, introduced an intriguing possibility. Namely, that some exoplanets are not condensed from the protoplanetary disk of their parent star. In this novel scenario a free-floating planet interacts with an already existing planetary system, created in a tight cluster, and is captured as a new planet. In the present work we study this interaction process by integrating trajectories of planet-sized bodies, which encounter a binary system consisting of a Jupiter-sized planet revolving around a Sun-like star. To simplify the problem we assume coplanar orbits for the bound and the free-floating planet and an initially parabolic orbit for the free-floating planet. By calculating the uncertainty exponent, a quantity that measures the dependence of the final state of the system on small changes of the initial conditions, we show that the interaction process is a fractal classical scattering. The uncertainty exponent is in the range (0.2-0.3) and is a decreasing function of time. In this way we see that the statistical approach we follow to tackle the problem is justified. The possible final outcomes of this interaction are only four, namely flyby, planet exchange, capture or disruption. We give the probability of each outcome as a function of the incoming planet's mass. We find that the probability of exchange or capture (in prograde as well as retrograde orbits and for very long times) is non-negligible, a fact that might explain the possible future observations of planetary systems with orbits that are either retrograde (see e.g. Queloz et al. Astron. Astrophys. 417, L1, 2010) or tight and highly eccentric. [ABSTRACT FROM AUTHOR]

We study the establishment of three-planet resonances-similar to the Laplace resonance in the Galilean satellites-and their effects on the mutual inclinations of the orbital planes of the planets, assuming that the latter undergo migration in a gaseous disc. In particular, we examine the resonance relations that occur, by varying the physical and initial orbital parameters of the planets (mass, initial semi-major axis and eccentricity) as well as the parameters of the migration forces (migration rate and eccentricity damping rate), which are modeled here through a simplified analytic prescription. We find that, in general, for planetary masses below 1.5 M, multiple-planet resonances of the form n : n : n = 1 : 2 : 4 and 1:3:6 are established, as the inner planets, m and m, get trapped in a 1:2 resonance and the outer planet m subsequently is captured in a 1:2 or 1:3 resonance with m. For mild eccentricity damping, the resonance pumps the eccentricities of all planets on a relatively short time-scale, to the point where they enter an inclination-type resonance (as in Libert and Tsiganis ); then mutual inclinations can grow to ~35°, thus forming a ' 3-D system'. On the other hand, we find that trapping of m in a 2:3 resonance with m occurs very rarely, for the range of masses used here, so only two cases of capture in a respective three-planet resonance were found. Our results suggest that trapping in a three-planet resonance can be common in exoplanetary systems, provided that the planets are not very massive. Inclination pumping could then occur relatively fast, provided that eccentricity damping is not very efficient so that at least one of the inner planets acquires an orbital eccentricity higher than e = 0.3. [ABSTRACT FROM AUTHOR]

In this paper, we study the long-term dynamical evolution of highly elliptical orbits in the medium-Earth orbit region around the Earth. The real population consists primarily of Geosynchronous Transfer Orbits (GTOs), launched at specific inclinations, Molniya-type satellites and related debris. We performed a suite of long-term numerical integrations (up to 200 years) within a realistic dynamical model, aimed primarily at recording the dynamical lifetime of such orbits (defined as the time needed for atmospheric reentry) and understanding its dependence on initial conditions and other parameters, such as the area-to-mass ratio (A / m). Our results are presented in the form of 2-D lifetime maps, for different values of inclination, A / m, and drag coefficient. We find that the majority of small debris (>70%, depending on the inclination) can naturally reenter within 25-90 years, but these numbers are significantly less optimistic for large debris (e.g., upper stages), with the notable exception of those launched from high latitude (Baikonur). We estimate the reentry probability and mean dynamical lifetime for different classes of GTOs and we find that both quantities depend primarily and strongly on initial perigee altitude. Atmospheric drag and higher A / m values extend the reentry zones, especially at low inclinations. For high inclinations, this dependence is weakened, as the primary mechanisms leading to reentry are overlapping lunisolar resonances. This study forms part of the EC-funded (H2020) "ReDSHIFT" project. [ABSTRACT FROM AUTHOR]