Continued studies of planetary motion about nearby binary star systems with restricted elliptic three body motion

1986 ◽  
Author(s):  
W. KELLY
Keyword(s):  
Binary Star ◽  
Body Motion ◽  
Planetary Motion ◽  
Three Body

scholarly journals Impact flux of asteroids and water transport to the habitable zone in binary star systems

2014 ◽  
Vol 9 (S310) ◽  
pp. 86-87
Author(s):  
D. Bancelin ◽  
E. Pilat-Lohinger ◽  
S. Eggl ◽  
R. Dvorak
Keyword(s):  
Binary Star ◽  
Stellar System ◽  
Terrestrial Planet ◽  
Solar Neighborhood ◽  
Planetary Motion ◽  
Habitable Zone ◽  
Star System ◽  
Single Star ◽  
Multiple Systems ◽  
Binary Star System

AbstractBy now, observations of exoplanets have found more than 50 binary star systems hosting 71 planets. We expect these numbers to increase as more than 70% of the main sequence stars in the solar neighborhood are members of binary or multiple systems. The planetary motion in such systems depends strongly on both the parameters of the stellar system (stellar separation and eccentricity) and the architecture of the planetary system (number of planets and their orbital behaviour). In case a terrestrial planet moves in the so-called habitable zone (HZ) of its host star, the habitability of this planet depends on many parameters. A crucial factor is certainly the amount of water. We investigate in this work the transport of water from beyond the snow-line to the HZ in a binary star system and compare it to a single star system.

Euler, Leonhard (1707–1783)

2018 ◽  
Author(s):  
Jeremy Gray
Keyword(s):  
Eighteenth Century ◽  
Quadratic Forms ◽  
Body Problem ◽  
History Of Mathematics ◽  
Body Motion ◽  
Integral Calculus ◽  
History Of ◽  
The Subject ◽  
High Level ◽  
Three Body

Leonhard Euler’s importance for the history of mathematics is undoubted. Not only was he the most prolific mathematician ever – his collected works so far run to 76 volumes and further editions of his correspondence are planned – he dominated the eighteenth century. He combined an extraordinary memory, a capacity for a huge range of interests, an exceptional technical facility, and an ability to work to a high level of abstraction with a natural clarity of expression. His importance extends beyond his many profound innovations in many fields, of which three can be mentioned here: - mechanics, which he built up from the motion of point masses through the theory of rigid body motion to aero- and hydrodynamics, with applications to ship design, gunnery, optics, and celestial mechanics, where he did important work on the motion of the Moon and the three body problem; - the calculus, where he successfully introduced the concept of a function as fundamental; and - number theory, including the theory of quadratic forms and the zeta function. It was also the force of his example that established the culture of publishing in mathematics, and replaced the markedly more secretive habits of Newton and Leibniz. His widespread correspondence stimulated others, his work at the head of the Academy of St Petersburg helped develop mathematics in Russia, and his textbooks on the differential and integral calculus and on algebra made the subject accessible to generations of students.

Modeling and Analysis of the Ground Experiment for Restricted Three-Body Problem

2014 ◽  
Vol 926-930 ◽  
pp. 3084-3087
Author(s):  
Hao Yang Li ◽  
Zhi Kun She ◽  
Bai Xue ◽  
Wang Jie Qiu ◽  
Zhi Ming Zheng
Keyword(s):  
Mathematical Model ◽  
Body Problem ◽  
Test System ◽  
Body Motion ◽  
Ideal Condition ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Ground Test ◽  
Three Body ◽  
The Ideal

This paper analyzes the restricted three-body problems in the ground test systems. First, under the ideal condition, after analyzing the forces on the spacecraft in the rotating coordinates, a mathematical model of elliptic restricted three-body motion is founded. Second, for the restricted three-body problem in the ground test system, the forces on the test ball are analyzed and the corresponding elliptic mathematical model apart from the perturbation is founded. Then, based on the two models founded above, the similarity between the ideal spatial model and the ground simulation model is analyzed.

Discussion on Geodynamics of Three-body Motion

2015 ◽  
Vol 89 (6) ◽  
pp. 1858-1864
Author(s):  
LIU Quanwen ◽  
YAN Lingling ◽  
CHEN Guomin
Keyword(s):  
Body Motion ◽  
Three Body

scholarly journals The orbital stability of a test body motion in the field of two massive bodies

2018 ◽  
Vol 168 ◽  
pp. 04001
Author(s):  
Medeu Abishev ◽  
Saken Toktarbay ◽  
Aigerim Abylayeva ◽  
Amanhan Talkhat
Keyword(s):  
Body Problem ◽  
Orbital Stability ◽  
Test Body ◽  
Body Motion ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Test Particles ◽  
The Stability ◽  
Three Body ◽  
Insight Into

We investigate the orbital stability of a test particle motion in the restricted three-body problem where all bodies have their own rotation. We have shown that it is possible to get some insight into the stability properties of the motion of test particles in restricted three-body problem, without knowing the exact solutions of the relativistic motion equations.

scholarly journals An Extra-Solar Planet in a Double Stellar System: The Modelling of Insufficient Orbital Elements

2011 ◽  
Vol 7 (S282) ◽  
pp. 127-128
Author(s):  
Eva Plávalová ◽  
Nina A. Solovaya ◽  
Eduard M. Pittich
Keyword(s):  
Initial Conditions ◽  
Binary Star ◽  
Stellar System ◽  
Orbital Evolution ◽  
Orbital Elements ◽  
Mutual Inclination ◽  
The Stability ◽  
The Masses ◽  
Three Body ◽  
Binary Star System

AbstractThe modelling of the insufficient orbital elements of extra-solar planets (EPs) revolving around one component in a binary star system is investigated in the present paper. This problem is considered in the frame of the three-body problem using the analytical theory of Orlov & Solovaya (1998). In the general case, the motion is defined by the masses of the components and by the six pairs of the initial values of the Keplerian elements. For EPs, it is not possible to obtain the complete set of elements for the orbit, in particular, the ascending node and the angle of the inclination. So, it is possible the two different variants of orbital evolution of EPs depend on the initial conditions. In one case, the orbit is unstable. Using the stability conditions of Solovaya & Pittich (2004), which are presented by the angle of the mutual inclination of the orbits between the EP and distant star, we varied unknown angular elements and defined the regions with possible values of the elements for which the motion of EP stays stable. We applied these calculations to the particular specific EPs: HD19994b, HD196885Ab and HD222404b.

scholarly journals Binary Gravitational Perturbations and Their Influence on the Habitability of Circumstellar Planets

2021 ◽  
Vol 8 ◽  
Author(s):  
Elke Pilat-Lohinger ◽  
Ákos Bazsó
Keyword(s):  
Binary Stars ◽  
Binary Star ◽  
Giant Planet ◽  
Planetary Motion ◽  
Atmospheric Conditions ◽  
Orbital Parameters ◽  
Gravitational Perturbations ◽  
Planetary Orbits

In order to assess the habitability of planets in binary star systems, not only astrophysical considerations regarding stellar and atmospheric conditions are needed, but orbital dynamics and the architecture of the system also play an important role. Due to the strong gravitational perturbations caused by the presence of the second star, the study of planetary orbits in double star systems requires special attention. In this context, we show the important role of the main gravitational perturbations (resonances) and review our recently developed methods which allow a quick determination of locations of secular resonances (SRs) in binary stars for circumstellar planetary motion where a giant planet has to move exterior to the habitable zone (HZ). These methods provide the basis for our online-tool ShaDoS which allows a quick check of circumstellar HZs regarding secular perturbations. It is important to know the locations of SRs since they can push a dynamically quiet HZ into a high-eccentricity state which will change the conditions for habitability significantly. Applications of SHaDoS to the wide binary star HD106515 AB and the tight system HD41004 AB reveal a quiet HZ for both systems. However, the study of these systems indicates only for the tight binary star a possible change of the HZ's dynamical state if the orbital parameters change due to new observational data.

scholarly journals Rendezvous in Cis-Lunar Space near Rectilinear Halo Orbit: Dynamics and Control Issues

Aerospace ◽  
2021 ◽  
Vol 8 (3) ◽  
pp. 68
Author(s):  
Giordana Bucchioni ◽  
Mario Innocenti
Keyword(s):  
Body Motion ◽  
Stable And Unstable Manifolds ◽  
Actuator Dynamics ◽  
Guidance And Control ◽  
Dynamics And Control ◽  
Critical Phases ◽  
Three Body ◽  
And Control ◽  
In Cis ◽  
Selection Of

The paper presents the development of a fully-safe, automatic rendezvous strategy between a passive vehicle and an active one orbiting around the Earth–Moon L2 Lagrangian point. This is one of the critical phases of future missions to permanently return to the Moon, which are of interest to the majority of space organizations. The first step in the study is the derivation of a suitable full 6-DOF relative motion model in the Local Vertical Local Horizontal reference frame, most suitable for the design of the guidance. The main dynamic model is approximated using both the elliptic and circular three-body motion, due to the contribution of Earth and Moon gravity. A rather detailed set of sensors and actuator dynamics was also implemented in order to ensure the reliability of the guidance algorithms. The selection of guidance and control is presented, and evaluated using a sample scenario as described by ESA’s HERACLES program. The safety, in particular the passive safety, concept is introduced and different techniques to guarantee it are discussed that exploit the ideas of stable and unstable manifolds to intrinsically guarantee some properties at each hold-point, in which the rendezvous trajectory is divided. Finally, the rendezvous dynamics are validated using available Ephemeris models in order to verify the validity of the results and their limitations for future more detailed design.

scholarly journals Triple Collision as an Unstable Equilibrium

1978 ◽  
Vol 41 ◽  
pp. 356-356
Author(s):  
Jörg Waldvogel
Keyword(s):  
Free Fall ◽  
Order Theory ◽  
Triple Collision ◽  
Body Motion ◽  
Three Body Problem ◽  
Close Encounters ◽  
First Order Theory ◽  
The Family ◽  
Three Body ◽  
Almost All

AbstractThe family of trajectories near a triple collision solution in the planar problem of three bodies is investigated by means of linearization in the neighborhood of the parabolic free fall. The local topological structure of this family is found to be that of a saddle point in the R8. The corresponding stable manifold is the set of all triple collision solutions, whereas the instable manifold is formed by the parabolic solutions.In important cases of nonzero total energy the family of close encounters is quantitatively described in terms of hypergeometric functions. By means of homothetic transformations the close triple encounters are then related to three-body motion with zero energy and zero angular momentum. In this way almost all close encounters near a homothetic solution can be treated by using a small number of particular solutions of the three-body problem that may be calculated once for all.In practical examples the first order theory presented here predicts the escape velocity after a close triple encounter with a relative accuracy comparable to the closeness of the encounter.

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