scholarly journals Secular spin-axis dynamics of exoplanets

2019 ◽  
Vol 623 ◽  
pp. A4 ◽  
Author(s):  
M. Saillenfest ◽  
J. Laskar ◽  
G. Boué
Keyword(s):  
Major Axis ◽  
Orbital Evolution ◽  
Spin Axis ◽  
Semi Major Axis ◽  
Resonance Overlap ◽  
Climate Stability ◽  
Dynamical Parameters ◽  
Analytical Formulas ◽  
Quantitative Results

Context. Seasonal variations and climate stability of a planet are very sensitive to the planet obliquity and its evolution. This is of particular interest for the emergence and sustainability of land-based life, but orbital and rotational parameters of exoplanets are still poorly constrained. Numerical explorations usually realised in this situation are therefore in heavy contrast with the uncertain nature of the available data. Aims. We aim to provide an analytical formulation of the long-term spin-axis dynamics of exoplanets, linking it directly to physical and dynamical parameters, but still giving precise quantitative results if the parameters are well known. Together with bounds for the poorly constrained parameters of exoplanets, this analysis is designed to enable a quick and straightforward exploration of the spin-axis dynamics. Methods. The long-term orbital solution is decomposed into quasi-periodic series and the spin-axis Hamiltonian is expanded in powers of eccentricity and inclination. Chaotic zones are measured by the resonance overlap criterion. Bounds for the poorly known parameters of exoplanets are obtained from physical grounds (rotational breakup) and dynamical considerations (equipartition of the angular momentum deficit). Results. This method gives accurate results when the orbital evolution is well known. The detailed structure of the chaotic zones for the solar system planets can be retrieved from simple analytical formulas. For less-constrained planetary systems, the maximal extent of the chaotic regions can be computed, requiring only the mass, the semi-major axis, and the eccentricity of the planets present in the system. Additionally, some estimated bounds of the precession constant allow to classify which observed exoplanets are necessarily out of major spin-orbit secular resonances (unless the precession rate is affected by the presence of massive satellites).

scholarly journals Dynamical evolution of objects on highly elliptical orbits near high-order resonance zones

2014 ◽  
Vol 9 (S310) ◽  
pp. 168-169
Author(s):  
Eduard D. Kuznetsov ◽  
Stanislav O. Kudryavtsev
Keyword(s):  
Dynamical Evolution ◽  
Major Axis ◽  
Orbital Evolution ◽  
High Order ◽  
Semi Major Axis ◽  
Order Resonance ◽  
High Order Resonance ◽  
Elliptical Orbits ◽  
Pass Through

AbstractBoth analytical and numerical results are used to study high-order resonance regions in the vicinity of Molnya-type orbits. Based on data of numerical simulations, long-term orbital evolution are studied for objects in highly elliptical orbits depending on their area-to-mass ratio. The Poynting–Robertson effect causes a secular decrease in the semi-major axis of a spherically symmetrical satellite. Under the Poynting–Robertson effect, objects pass through the regions of high-order resonances. The Poynting–Robertson effect and secular perturbations of the semi-major axis lead to the formation of weak stochastic trajectories.

scholarly journals Dynamical properties of the Molniya satellite constellation: long-term evolution of the semi-major axis

2021 ◽  
Author(s):  
Jérôme Daquin ◽  
Elisa Maria Alessi ◽  
Joseph O’Leary ◽  
Anne Lemaitre ◽  
Alberto Buzzoni
Keyword(s):  
Major Axis ◽  
Long Term Evolution ◽  
Semi Major Axis ◽  
Satellite Constellation ◽  
Term Evolution ◽  
Dynamical Properties

scholarly journals The orbital evolution of meteor streams at the 2/1 resonance with Jupiter

1985 ◽  
Vol 83 ◽  
pp. 179-180
Author(s):  
Cl. Froeschlé
Keyword(s):  
Major Axis ◽  
Orbital Evolution ◽  
The Sun ◽  
Orbital Elements ◽  
Meteor Stream ◽  
Semi Major Axis ◽  
Meteor Streams ◽  
Gravitational Forces ◽  
Resonant Effect

We investigated the orbital evolution of Quadrantid-like meteor streams situated in the vicinity of the 2/1 resonance with Jupiter. For the starting orbital elements we took the values of the orbital elements of the Quadrantid meteor stream except for the semi-major axis which was varied between a = 3.22 and a = 3.34 AU. We considered these meteor streams as a ring and we investigated the resonant effect on the dispersion of this ring over a period of 13 000 years. Only gravitational forces due to the Sun and due to Jupiter were taken into account.

Reachable domain of spacecraft with a single normal impulse

2019 ◽  
Vol 91 (7) ◽  
pp. 977-986 ◽  
Author(s):  
Junhua Zhang ◽  
Jianping Yuan ◽  
Wei Wang ◽  
Jiao Wang
Keyword(s):  
Major Axis ◽  
Emergency Evacuation ◽  
Semi Major Axis ◽  
Content Type ◽  
Orbital Transfers ◽  
Ellipsoid Of Revolution ◽  
Rendezvous And Docking ◽  
Practical Implications ◽  
Initial Orbit

Purpose The purpose of this paper is to obtain the reachable domain (RD) for spacecraft with a single normal impulse while considering both time and impulse constraints. Design/methodology/approach The problem of RD is addressed in an analytical approach by analyzing for either the initial maneuver point or the impulse magnitude being arbitrary. The trajectories are considered lying in the intersection of a plane and an ellipsoid of revolution, whose family can be determined analytically. Moreover, the impulse and time constraints are considered while formulating the problem. The upper bound of impulse magnitude, “high consumption areas” and the change of semi-major axis and eccentricity are discussed. Findings The equations of RD with a single normal impulse are analytically obtained. The equations of three scenarios are obtained. If normal impulse is too large, the RD cannot be obtained. The change of the semi-major axis and eccentricity with large normal impulse is more obvious. For long-term missions, the change of semi-major axis and eccentricity leaded by multiple normal impulses should be considered. Practical implications The RD gives the pre-defined region (all positions accessible) for a spacecraft under a given initial orbit and a normal impulse with certain magnitude. Originality/value The RD for spacecraft with normal impulse can be used for non-coplanar orbital transfers, emergency evacuation after failure of rendezvous and docking and collision avoidance.

scholarly journals Orbital effects of a monochromatic plane gravitational wave with ultra-low frequency incident on a gravitationally bound two-body system

2014 ◽  
Author(s):  
Lorenzo Iorio
Keyword(s):  
Gravitational Wave ◽  
Extrasolar Planets ◽  
A Priori ◽  
Low Frequency ◽  
Major Axis ◽  
Characteristic Size ◽  
Body System ◽  
Semi Major Axis ◽  
Plane Gravitational Wave

We analytically compute the long-term orbital variations of a test particle orbiting a central body acted upon by an incident monochromatic plane gravitational wave. We assume that the characteristic size of the perturbed two-body system is much smaller than the wavelength of the wave. Moreover, we also suppose that the wave's frequency νg is much smaller than the particle's orbital one nb. We make neither a priori assumptions about the direction of the wavevector k nor on the orbital configuration of the particle. While the semi-major axis a is left unaffected, the eccentricity e, the inclination I, the longitude of the ascending node Ω, the longitude of pericenter ϖ and the mean anomaly ℳ undergo non-vanishing long-term changes of the form dΨ/dt=F(Kij;e,I,Ω,ω),Ψ=e,I,Ω,ϖ,M, where Kij, i,j=1,2,3 are the coefficients of the tidal matrix K. Thus, in addition to the variations of its orientation in space, the shape of the orbit would be altered as well. Strictly speaking, such effects are not secular trends because of the slow modulation introduced by K and by the orbital elements themselves: they exhibit peculiar long-term temporal patterns which would be potentially of help for their detection in multidecadal analyses of extended data records of planetary observations of various kinds. In particular, they could be useful in performing independent tests of the inflation-driven ultra-low gravitational waves whose imprint may have been indirectly detected in the Cosmic Microwave Background by the Earth-based experiment BICEP2. Our calculation holds, in general, for any gravitationally bound two-body system whose orbital frequency nb is much larger than the frequency νg of the external wave, like, e.g., extrasolar planets and the stars orbiting the Galactic black hole. It is also valid for a generic perturbation of tidal type with constant coefficients over timescales of the order of the orbital period of the perturbed particle.

scholarly journals Orbital effects of a monochromatic plane gravitational wave with ultra-low frequency incident on a gravitationally bound two-body system

2014 ◽  
Author(s):  
Lorenzo Iorio
Keyword(s):  
Gravitational Wave ◽  
Extrasolar Planets ◽  
A Priori ◽  
Low Frequency ◽  
Major Axis ◽  
Characteristic Size ◽  
Body System ◽  
Semi Major Axis ◽  
Plane Gravitational Wave

We analytically compute the long-term orbital variations of a test particle orbiting a central body acted upon by an incident monochromatic plane gravitational wave. We assume that the characteristic size of the perturbed two-body system is much smaller than the wavelength of the wave. Moreover, we also suppose that the wave's frequency νg is much smaller than the particle's orbital one nb. We make neither a priori assumptions about the direction of the wavevector k nor on the orbital configuration of the particle. While the semi-major axis a is left unaffected, the eccentricity e, the inclination I, the longitude of the ascending node Ω, the longitude of pericenter ϖ and the mean anomaly ℳ undergo non-vanishing long-term changes of the form dΨ/dt=F(Kij;e,I,Ω,ω),Ψ=e,I,Ω,ϖ,M, where Kij, i,j=1,2,3 are the coefficients of the tidal matrix K. Thus, in addition to the variations of its orientation in space, the shape of the orbit would be altered as well. Strictly speaking, such effects are not secular trends because of the slow modulation introduced by K and by the orbital elements themselves: they exhibit peculiar long-term temporal patterns which would be potentially of help for their detection in multidecadal analyses of extended data records of planetary observations of various kinds. In particular, they could be useful in performing independent tests of the inflation-driven ultra-low gravitational waves whose imprint may have been indirectly detected in the Cosmic Microwave Background by the Earth-based experiment BICEP2. Our calculation holds, in general, for any gravitationally bound two-body system whose orbital frequency nb is much larger than the frequency νg of the external wave, like, e.g., extrasolar planets and the stars orbiting the Galactic black hole. It is also valid for a generic perturbation of tidal type with constant coefficients over timescales of the order of the orbital period of the perturbed particle.

scholarly journals High Order Resonances in the Evolution of the Lunar Orbit

1983 ◽  
Vol 74 ◽  
pp. 3-17
Author(s):  
J. Kovalevsky
Keyword(s):  
Major Axis ◽  
Lunar Theory ◽  
The Moon ◽  
Tidal Effects ◽  
Semi Major Axis ◽  
Natural Satellite ◽  
Variation Of Constants ◽  
The Mean ◽  
Mean Elements

AbstractThis paper deals with the long term evolution of the motion of the Moon or any other natural satellite under the combined influence of gravitational forces (lunar theory) and the tidal effects. We study the equations that are left when all the periodic non-resonant terms are eliminated. They describe the evolution of the-mean elements of the Moon. Only the equations involving the variation of the semi-major axis are considered here. Simplified equations, preserving the Hamiltonian form of the lunar theory are first considered and solved. It is shown that librations exist only for those terms which have a coefficient in the lunar theory larger than a quantity A which is function of the magnitude of the tidal effects. The solution of the general case can be derived from a Hamiltonian solution by a method of variation of constants. The crossing of a libration region causes a retardation in the increase of the semi-major axis. These results are confirmed by numerical integration and orders of magnitude of this retardation are given.

scholarly journals The Formation and Evolution of the Perseid Meteoroid Stream

1996 ◽  
Vol 150 ◽  
pp. 101-104
Author(s):  
Nathan W. Harris
Keyword(s):  
Orbital Stability ◽  
Direct Consequence ◽  
Major Axis ◽  
Orbital Evolution ◽  
Meteoroid Stream ◽  
Semi Major Axis ◽  
Meteoroid Streams ◽  
Integration Techniques ◽  
Formation And Evolution ◽  
Direct Numerical Integration

AbstractThe orbital evolution of two modelled ‘Perseid’ meteoroid streams is investigated using direct numerical integration techniques. We conclude that, in the absence of significant meteoroid velocity determination errors, the observed meteoroid orbital semi-major axis distribution is a direct consequence of the cometary ejection process and not due to subsequent orbital evolution. A high ejection-velocity (~ 0.6 km s-1) model stream succeeds in reproducing the observations. Conclusions are made concerning how the orbital stability of Earth-orbit-intersecting Perseid metecroids varies with initial orbital semi-major axis.

scholarly journals Dynamical Behaviour of Asteroids in the 4:1 Resonance

1999 ◽  
Vol 172 ◽  
pp. 377-378 ◽  
Author(s):  
Francisco López-García ◽  
Adrian Brunini
Keyword(s):  
Time Scale ◽  
Initial Conditions ◽  
Major Axis ◽  
Orbital Evolution ◽  
Dynamical Behaviour ◽  
Three Dimensions ◽  
Symplectic Integrators ◽  
Minor Planets ◽  
Semi Major Axis ◽  
Secular Resonance

We study the dynamics of mean motion resonance with Jupiter in the 4:1 gap using only gravitational methods. This mechanism is capable of explaining this Kirkwood gap in an uniform way (see Ferraz-Mello, 1994; Ferraz-Mello et al., 1994; Moons, 1997; Yoshikawa, 1989). We considered the asteroidal motion in two and three dimensions and we carried out our investigations integrating numerically the full equations of motion and taking into account Mars, Jupiter and Saturn as disturbing planets. The orbital evolution of asteroids was obtained considering the elements variation. The numerical investigations were carried out using symplectic integrators. These integrations were stopped when the asteroid had close encouters with Mars or Jupiter, this occurs when the distance between the planet and the asteroid is of the order of 0.01 AU or less, or when the eccentricity increases up to 0.9. We studied real and fictitious asteroids on a time scale of 5 × 107 yr. The initial osculating elements of perturbing planets and their inverse masses were taken from the Ephemerides of Minor Planets (EMP) at the epoch of JD 2450000.5. The initial data corresponding to the real asteroids were also taken from the EMP. The starting elements of fictitious asteroids were, in all analyzed cases, a = acrit = 2.064; AU, i = 2°.5 and e = 0.01 (in the majority of cases). The other initial elements are shown in Table II. We have also studied fictitious asteroids with i = 0°, a = acrit and e = 0.01 (Table I). The present analysis leads to the following results: (1) The motions are unstable. The eccentricity, in the majority of cases, has very large increase. It may grow up to 0.9 in 106 yr. The semi major axis has large variations then, owing to both effects some fictitious asteroids reach the 3:1 resonance while others reach 7:2 resonance in a few million years, they are very chaotic regions. (2) The eccentricities of fictitious asteroids become large by the effect of the secular resonance v6, i.e. when (ϖ − ϖSat) ≅ 0, the rate of this resonance is 26.217”/year with period ~ 4.9 × 104 years (Bretagnon, 1974). (3) The fictitious asteroids studied with a = acrit, e < 0.05 and i < 3° are removed of this gap mainly by the effects of the secular resonances v6 and v16 (see Moons and Morbidelli, 1995; Williams, 1969). (4) There are close encounters with Mars or eventually with the Earth (not considered here) in a time scale of 106 - 107 yr. (5) For certain initial conditions some fictitious asteroids are temporally captured by Mars and in some cases for a long time. (6) If a = acrit,e = 0.3 and the inclination is less than 3°, Mars and asteroid’s perihelion are very close ( ~ 0.06AU ). This situation helps the capture. (7) The (a,e)-plane was used to determine the dynamical behaviour of all asteroids and we found that the 4:1 resonance is very strong. The Lyapunov times are very short.

scholarly journals Evolution of star–planet systems under magnetic braking and tidal interaction

2019 ◽  
Vol 621 ◽  
pp. A124 ◽  
Author(s):  
M. Benbakoura ◽  
V. Réville ◽  
A. S. Brun ◽  
C. Le Poncin-Lafitte ◽  
S. Mathis
Keyword(s):  
Ab Initio ◽  
Stellar Wind ◽  
Structural Changes ◽  
Rotation Period ◽  
Major Axis ◽  
Orbital Evolution ◽  
Open Clusters ◽  
Stellar Rotation ◽  
Semi Major Axis ◽  
Tidal Interaction

Context.With the discovery over the last two decades of a large diversity of exoplanetary systems, it is now of prime importance to characterize star–planet interactions and how such systems evolve.Aims.We address this question by studying systems formed by a solar-like star and a close-in planet. We focus on the stellar wind spinning down the star along its main-sequence phase and tidal interaction causing orbital evolution of the systems. Despite recent significant advances in these fields, all current models use parametric descriptions to study at least one of these effects. Our objective is to introduce ab initio prescriptions of the tidal and braking torques simultaneously, so as to improve our understanding of the underlying physics.Methods.We develop a one-dimensional (1D) numerical model of coplanar circular star–planet systems taking into account stellar structural changes, wind braking, and tidal interaction and implement it in a code called ESPEM. We follow the secular evolution of the stellar rotation and of the semi-major axis of the orbit, assuming a bilayer internal structure for the former. After comparing our predictions to recent observations and models, we perform tests to emphasize the contribution of ab initio prescriptions. Finally, we isolate four significant characteristics of star–planet systems: stellar mass, initial stellar rotation period, planetary mass and initial semi-major axis; and browse the parameter space to investigate the influence of each of them on the fate of the system.Results.Our secular model of stellar wind braking accurately reproduces the recent observations of stellar rotation in open clusters. Our results show that a planet can affect the rotation of its host star and that the resulting spin-up or spin-down depends on the orbital semi-major axis and on the joint influence of magnetic and tidal effects. The ab initio prescription for tidal dissipation that we used predicts fast outward migration of massive planets orbiting fast-rotating young stars. Finally, we provide the reader with a criterion based on the characteristics of the system that allows us to assess whether or not the planet will undergo orbital decay due to tidal interaction.

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