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Ellipsoidal Full Two Body Problem: An Application to Binary Asteroids
,
Ph.D. Dissertation
Sharif University of Technology
;
Asadian, Nima
(Supervisor)
Abstract
Chaotic and resonant Dynamics of full two body problem are investigated through the sphere-ellipsoid and ellipsoid-ellipsoid models. The fourth-order mutual gravitational potential function is derived in terms of the first-order moment of inertia for both models. Employing Hamiltonian formulation and elliptical expansion, the resonant angles appear in the equations which include secondary’s attitude and mean anomaly for sphere-ellipsoid model and attitude of both bodies and mean anomaly for ellipsoid-ellipsoid model. In first step, resonances overlapping criteria is applied to the first-order resonances of sphere-ellipsoid model and the effect of the asphericity and orbital eccentricity on...
Widespread chaos in rotation of the secondary asteroid in a binary system
, Article Nonlinear Dynamics ; Volume 81, Issue 4 , September , 2015 , Pages 2031-2042 ; 0924090X (ISSN) ; Assadian, N ; Sharif University of Technology
Kluwer Academic Publishers
2015
Abstract
The chaotic behavior of the secondary asteroid in a system of binary asteroids due to the asphericity and orbital eccentricity is investigated analytically and numerically. The binary asteroids are modeled with a sphere–ellipsoid model, in which the secondary asteroid is ellipsoid. The first-order resonance is studied for different values of asphericity and eccentricity of the secondary asteroid. The results of the Chirikov method are verified by Poincare section which show good agreement between analytical and numerical methods. It is also shown that asphericity and eccentricity affect the size of resonance regions such that beyond the threshold value, the resonance overlapping occurs and...
Continuous-thrust Trajectory Optimization in the Binary Asteroids System
, M.Sc. Thesis Sharif University of Technology ; Asadian, Nima (Supervisor)
Abstract
In this thesis, the optimal trajectories of a spacecraft in the binary asteroids system is studied. The objective functions of optimal trajectories in these system are the maximum coverage of the asteroids surface and minimum time and fuel consumption. For this purpose, the dynamic of binary system is modeled. The binary system of 1999 KW4 is selected as a case study. The ellipsoid-sphere model is a good approximation for the case of this study. In this model, the asteroids orbit in a circular orbit around each other in a spin-spin-orbit resonance configuration, in which the asteroids’ rotational velocity is equal to orbital mean motion. Then, the equations of motion of the spacecraft as the...
Dynamics of Tethered Satellite Formation Around Binary Asteroids
, M.Sc. Thesis Sharif University of Technology ; Assadian, Nima (Supervisor)
Abstract
Studying of binary asteroids because of achieving data of existence sources in the world persuades to investigate about tethered satellite formation around binary asteroids in future missions. About 20 percent of asteroids around the sun are binary asteroids. It is going to analyse dynamics of tethered satellite around Didymos binary asteroid. Light mass of the asteroid is good reason to consider gravitational harmonic perturbation, and leads to attention about solar radiation pressure depends on distance in modelling of the dynamical system. It will be zonal harmonics up to second order and sectoral. Satellites are such a particle as an assumption; that is why attitude motion of satellites...
Chirikov diffusion in the sphere–ellipsoid binary asteroids
, Article Nonlinear Dynamics ; 2016 , Pages 1-12 ; 0924090X (ISSN) ; Assadian, N ; Sharif University of Technology
Springer Netherlands
2016
Abstract
The Chirikov diffusion in the sphere–ellipsoid binary asteroids through the spin–orbit resonance model is analytically and numerically studied. The primary and the secondary of the binary system are considered sphere and ellipsoid, respectively. The gravitational potential function is expanded up to the fourth-order. The geography of the first- and second-order resonances is derived and studied for different values of asphericity and dynamical flattening of the secondary asteroid and the semimajor axis and eccentricity of the mutual orbit. The Chirikov diffusion due to overlapping of the first- and second-order resonances is examined. For this end, the previously derived criterion for...