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 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

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 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 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 Long-term postmerger simulations of relativistic star coalescence: Formation of toroidal remnants and gravitational wave afterglow

2019 ◽  
Vol 28 (01) ◽  
pp. 1950026 ◽  
Author(s):  
Xuefeng Zhang ◽  
Zhoujian Cao ◽  
He Gao
Keyword(s):  
Gravitational Wave ◽  
Rotational Symmetry ◽  
Significant Proportion ◽  
Low Frequency ◽  
Equal Mass ◽  
Fluid Equation ◽  
Binary Neutron Star ◽  
Double Peaks ◽  
Test Models

It has been estimated that a significant proportion of binary neutron star merger events produce long-lived massive remnants supported by differential rotation and subject to rotational instabilities. To examine formation and oscillation of rapidly rotating neutron stars (NS) after merger, we present an exploratory study of fully general-relativistic hydrodynamic simulations using the public code Einstein Toolkit. The attention is focused on qualitative aspects of long-term postmerger evolution under [Formula: see text]-rotational symmetry. As simplified test models, we use a moderately stiff [Formula: see text] ideal-fluid equation-of-state and unmagnetized irrotational equal-mass binaries with three masses well below the threshold for prompt collapse. Our high resolution simulations generate postmerger “ringdown” gravitational wave (GW) signals of 170 ms, sustained by rotating massive NS remnants without collapsing to black holes. We observe that the high-density double-core structure inside the remnants gradually turns into a quasi-axisymmetric toroidal shape. It oscillates in a quasi-periodic manner and shrinks in size due to gravitational radiation. In the GW spectrograms, dominant double peaks persist throughout the postmerger simulations and slowly drift to higher frequencies. A new low-frequency peak emerges at about 100 ms after merger, owing to the growth of GW-driven unstable oscillation modes. The long-term effect of grid resolution is also investigated using the same initial model. Moreover, we comment on physical conditions that are favorable for the transient toroidal configuration to form, and discuss implication of our findings on future GW observation targeting rapidly rotating NS remnants.

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 Mapping the Distributions of Exoplanet Populations with NICI and GPI

2015 ◽  
Vol 10 (S314) ◽  
pp. 220-225
Author(s):  
Eric L. Nielsen ◽  
Michael C. Liu ◽  
Zahed Wahhaj ◽  
Beth A. Biller ◽  
Thomas L. Hayward ◽  
...  
Keyword(s):  
Low Frequency ◽  
Major Axis ◽  
Giant Planets ◽  
Direct Imaging ◽  
Semi Major Axis ◽  
Solar Systems ◽  
Test Models ◽  
Nearby Stars ◽  
Formation And Evolution ◽  
Band Contrast

AbstractWhile more and more long-period giant planets are discovered by direct imaging, the distribution of planets at these separations (≳5 AU) has remained largely uncertain, especially compared to planets in the inner regions of solar systems probed by RV and transit techniques. The low frequency, the detection challenges, and heterogeneous samples make determining the mass and orbit distributions of directly imaged planets at the end of a survey difficult. By utilizing Monte Carlo methods that incorporate the age, distance, and spectral type of each target, we can use all stars in the survey, not just those with detected planets, to learn about the underlying population. We have produced upper limits and direct measurements of the frequency of these planets with the most recent generation of direct imaging surveys. The Gemini NICI Planet-Finding Campaign observed 220 young, nearby stars at a median H-band contrast of 14.5 magnitudes at 1”, representing the largest, deepest search for exoplanets by the completion of the survey. The Gemini Planet Imager Exoplanet Survey is in the process of surveying 600 stars, pushing these contrasts to a few tenths of an arcsecond from the star. With the advent of large surveys (many hundreds of stars) using advanced planet-imagers we gain the ability to move beyond measuring the frequency of wide-separation giant planets and to simultaneously determine the distribution as a function of planet mass, semi-major axis, and stellar mass, and so directly test models of planet formation and evolution.

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