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Carlos B Briozzo - One of the best experts on this subject based on the ideXlab platform.
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extension of fast periodic Transfer Orbits from the earth moon rtbp to the sun earth moon quasi bicircular problem
Celestial Mechanics and Dynamical Astronomy, 2008Co-Authors: A M Leiva, Carlos B BriozzoAbstract:Starting from 80 families of low-energy fast periodic Transfer Orbits in the Earth–Moon planar circular Restricted Three Body Problem (RTBP), we obtain by analytical continuation 11 periodic Orbits and 25 periodic arcs with similar properties in the Sun–Earth–Moon Quasi-Bicircular Problem (QBCP). A novel and very simple procedure is introduced giving the solar phases at which to attempt continuation. Detailed numerical results for each periodic orbit and arc found are given, including their stability parameters and minimal distances to the Earth and Moon. The periods of these Orbits are between 2.5 and 5 synodic months, their energies are among the lowest possible to achieve an Earth–Moon Transfer, and they show a diversity of circumlunar trajectories, making them good candidates for missions requiring repeated passages around the Earth and the Moon with close approaches to the last.
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the earth moon cr3bp a full atlas of low energy fast periodic Transfer Orbits
arXiv: Astrophysics, 2006Co-Authors: A M Leiva, Carlos B BriozzoAbstract:In the framework of the planar CR3BP for mass parameter mu=0.0121505, corresponding to the Earth-Moon system, we identify and describe 80 families of periodic Orbits encircling both the Earth and the Moon ("Transfer" Orbits). All the Orbits in these families have very low energies, most of them corresponding to values of the Jacobi constant C for which the Hill surface is closed at the Lagrangian point L2. All of these Orbits have also short period T, generally under six months. Most of the families are composed of Orbits that are asymmetric with respect to the Earth-Moon axis. The main results presented for each family are: (i) the characteristic curves T(h), y(h), v_y(h), and v_x(h) on the Poincare section Sigma_1={x=0.836915310,y,v_x>0,v_y} normal to the Earth-Moon axis at the Lagrangian point L1, parameterized by their energy h=-C/2 in the synodic coordinate system; (ii) the stability parameter along each family; (iii) the intersections x_i(h) of the Orbits with the Earth-Moon axis, on the Poincare section Sigma_2={x,y=0,v_x},v_y>0}; (iv) plots of some selected Orbits and details of their circumlunar region; and (v) numerical data for the intersection of an orbit with Sigma_1 at a reference value of h. Some possible extensions and applications of this work are also discussed.
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control of chaos and fast periodic Transfer Orbits in the earth moon cr3bp
Acta Astronautica, 2006Co-Authors: A M Leiva, Carlos B BriozzoAbstract:Abstract We find sets of initial conditions leading to unstable periodic Orbits in the Earth–Moon CR3BP, having values of the Jacobi constant - 1.59407 h - 1.58617 and periods shorter than 180 days, which perform periodic Transfers around the primary masses. All of these initial conditions lie in the chaotic region of the problem, and some belong to stability islands inside it. We develop a realistic control algorithm allowing to stabilize the unstable periodic Orbits over long periods, requiring very modest Δ v .
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fast periodic Transfer Orbits in the sun earth moon quasi bicircular problem
Celestial Mechanics and Dynamical Astronomy, 2005Co-Authors: A M Leiva, Carlos B BriozzoAbstract:Starting from the identification and classification of a family of fast periodic Transfer Orbits in the Earth–Moon planar circular Restricted Three Body Problem (RTBP), and using analytic continuation techniques, we find two unstable periodic Orbits in the Sun–Earth–Moon Quasi-Bicircular Problem (QBCP). The Orbits found perform periodic Earth–Moon Transfers with a period of approximately 29.5 days.
V Carruba - One of the best experts on this subject based on the ideXlab platform.
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chaos and the effects of planetary migration on the orbit of s 2000 s5 kiviuq
The Astronomical Journal, 2004Co-Authors: V Carruba, David Nesvorny, Joseph A Burns, Matija Cuk, K TsiganisAbstract:Among the many new irregular satellites that have been discovered in the last 5 years, five or more are in the so-called Kozai resonance. Because of solar perturbations, the argument of pericenter ! of a satellite usually precesses from 0 � to 360 � . However, at inclinations higher than ’39N3 and lower than ’140N7, a new kind of behavior occurs for which the argument of pericenter oscillates around � 90 � . In this work we concentrate on the orbital history of the Saturnian satellite S/2000 S5 Kiviuq, one of the satellites currently known to be in such resonance. Kiviuq’s orbit is very close to the separatrix of the Kozai resonance. Because of perturbations from the other Jovian planets, it is expected that Orbits near the Kozai separatrix may show significant chaotic behavior. This is important because chaotic diffusion may Transfer Orbits from libration to circulation, and vice versa. To identify chaotic Orbits, we used two well-known methods: the frequency analysis method of Laskar and the maximum Lyapunov exponents method of Benettin and coworkers. Our results show that the Kozai resonance is crossed by a web of secondary resonances, whose arguments involve combinations of the argument of pericenter, the argument of the Great Inequality (GI) (2kJ � 5kS), the longitude of the node � , and other terms related to the secular frequencies g5, g6 ,a nds6. Many test Orbits whose precession period are close to the period of the GI (883 yr), or some of its harmonics, are trapped by these secondary resonances and show significant chaotic behavior. Because the GI’s period is connected to the semimajor axes of Jupiter and Saturn and because the positions of the Jovian planets have likely changed since their formation, the phase-space location of these secondary resonances should have been different in the past. By simulating the effect of planetary migration, we show that a mechanism of sweeping secondary resonances, similar to the one studied by Ferraz-Mello and coworkers. for the asteroids in the 2:1 mean motion resonance with Jupiter, could significantly deplete a primordial population of Kozai resonators and push several circulators near the Kozai separatrix. This mechanism is not limited to Kiviuq’s region and could have worked to destabilize any initial population of satellites in the Kozai resonance around Saturn and Jupiter.
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chaos and the effects of planetary migration on the orbit of s 2000 s5 kiviuq
arXiv: Astrophysics, 2004Co-Authors: V Carruba, David Nesvorny, Joseph A Burns, Matija Cuk, K TsiganisAbstract:Among the many new irregular satellites that have been discovered in the last five years, at least six are in the so-called Kozai resonance. Due to solar perturbations, the argument of pericenter of a satellite usually precesses from 0 to 360 degrees. However, at inclinations higher than 39.3 degrees and lower than 140.7 degrees a new kind of behavior occurs for which the argument of pericenter oscillates around +/-90 degrees. In this work we will concentrate on the orbital history of the saturnian satellite S/2000 S5 Kiviuq, one of the satellites currently known to be in such resonance Kiviuq's orbit is very close to the separatrix of the Kozai resonance. Due to perturbations from the other jovian planets, it is expected that Orbits near the Kozai separatrix may show significant chaotic behavior. This is important because chaotic diffusion may Transfer Orbits from libration to circulation, and vice versa. To identify chaotic Orbits we used two well-known methods: the Frequency Analysis Method (Laskar 1990) and Maximum Lyapunov Exponents (Benettin et al. 1980). Our results show that the Kozai resonance is crossed by a web of secondary resonances, whose arguments involve combinations of the argument of pericenter, the argument of the Great Inequality, longitude of the node, and other terms related to the secular frequencies g5, g6, and s6. Many test Orbits whose precession period is close to the period of the Great Inequality (883 yrs), or some of its harmonics, are trapped by these secondary resonances, and show significant chaotic behavior. Planetary migration, by moving the locations of these secondary resonances, may have depleted an original population of Kozai resonators.
A M Leiva - One of the best experts on this subject based on the ideXlab platform.
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extension of fast periodic Transfer Orbits from the earth moon rtbp to the sun earth moon quasi bicircular problem
Celestial Mechanics and Dynamical Astronomy, 2008Co-Authors: A M Leiva, Carlos B BriozzoAbstract:Starting from 80 families of low-energy fast periodic Transfer Orbits in the Earth–Moon planar circular Restricted Three Body Problem (RTBP), we obtain by analytical continuation 11 periodic Orbits and 25 periodic arcs with similar properties in the Sun–Earth–Moon Quasi-Bicircular Problem (QBCP). A novel and very simple procedure is introduced giving the solar phases at which to attempt continuation. Detailed numerical results for each periodic orbit and arc found are given, including their stability parameters and minimal distances to the Earth and Moon. The periods of these Orbits are between 2.5 and 5 synodic months, their energies are among the lowest possible to achieve an Earth–Moon Transfer, and they show a diversity of circumlunar trajectories, making them good candidates for missions requiring repeated passages around the Earth and the Moon with close approaches to the last.
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the earth moon cr3bp a full atlas of low energy fast periodic Transfer Orbits
arXiv: Astrophysics, 2006Co-Authors: A M Leiva, Carlos B BriozzoAbstract:In the framework of the planar CR3BP for mass parameter mu=0.0121505, corresponding to the Earth-Moon system, we identify and describe 80 families of periodic Orbits encircling both the Earth and the Moon ("Transfer" Orbits). All the Orbits in these families have very low energies, most of them corresponding to values of the Jacobi constant C for which the Hill surface is closed at the Lagrangian point L2. All of these Orbits have also short period T, generally under six months. Most of the families are composed of Orbits that are asymmetric with respect to the Earth-Moon axis. The main results presented for each family are: (i) the characteristic curves T(h), y(h), v_y(h), and v_x(h) on the Poincare section Sigma_1={x=0.836915310,y,v_x>0,v_y} normal to the Earth-Moon axis at the Lagrangian point L1, parameterized by their energy h=-C/2 in the synodic coordinate system; (ii) the stability parameter along each family; (iii) the intersections x_i(h) of the Orbits with the Earth-Moon axis, on the Poincare section Sigma_2={x,y=0,v_x},v_y>0}; (iv) plots of some selected Orbits and details of their circumlunar region; and (v) numerical data for the intersection of an orbit with Sigma_1 at a reference value of h. Some possible extensions and applications of this work are also discussed.
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control of chaos and fast periodic Transfer Orbits in the earth moon cr3bp
Acta Astronautica, 2006Co-Authors: A M Leiva, Carlos B BriozzoAbstract:Abstract We find sets of initial conditions leading to unstable periodic Orbits in the Earth–Moon CR3BP, having values of the Jacobi constant - 1.59407 h - 1.58617 and periods shorter than 180 days, which perform periodic Transfers around the primary masses. All of these initial conditions lie in the chaotic region of the problem, and some belong to stability islands inside it. We develop a realistic control algorithm allowing to stabilize the unstable periodic Orbits over long periods, requiring very modest Δ v .
-
fast periodic Transfer Orbits in the sun earth moon quasi bicircular problem
Celestial Mechanics and Dynamical Astronomy, 2005Co-Authors: A M Leiva, Carlos B BriozzoAbstract:Starting from the identification and classification of a family of fast periodic Transfer Orbits in the Earth–Moon planar circular Restricted Three Body Problem (RTBP), and using analytic continuation techniques, we find two unstable periodic Orbits in the Sun–Earth–Moon Quasi-Bicircular Problem (QBCP). The Orbits found perform periodic Earth–Moon Transfers with a period of approximately 29.5 days.
K Tsiganis - One of the best experts on this subject based on the ideXlab platform.
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chaos and the effects of planetary migration on the orbit of s 2000 s5 kiviuq
The Astronomical Journal, 2004Co-Authors: V Carruba, David Nesvorny, Joseph A Burns, Matija Cuk, K TsiganisAbstract:Among the many new irregular satellites that have been discovered in the last 5 years, five or more are in the so-called Kozai resonance. Because of solar perturbations, the argument of pericenter ! of a satellite usually precesses from 0 � to 360 � . However, at inclinations higher than ’39N3 and lower than ’140N7, a new kind of behavior occurs for which the argument of pericenter oscillates around � 90 � . In this work we concentrate on the orbital history of the Saturnian satellite S/2000 S5 Kiviuq, one of the satellites currently known to be in such resonance. Kiviuq’s orbit is very close to the separatrix of the Kozai resonance. Because of perturbations from the other Jovian planets, it is expected that Orbits near the Kozai separatrix may show significant chaotic behavior. This is important because chaotic diffusion may Transfer Orbits from libration to circulation, and vice versa. To identify chaotic Orbits, we used two well-known methods: the frequency analysis method of Laskar and the maximum Lyapunov exponents method of Benettin and coworkers. Our results show that the Kozai resonance is crossed by a web of secondary resonances, whose arguments involve combinations of the argument of pericenter, the argument of the Great Inequality (GI) (2kJ � 5kS), the longitude of the node � , and other terms related to the secular frequencies g5, g6 ,a nds6. Many test Orbits whose precession period are close to the period of the GI (883 yr), or some of its harmonics, are trapped by these secondary resonances and show significant chaotic behavior. Because the GI’s period is connected to the semimajor axes of Jupiter and Saturn and because the positions of the Jovian planets have likely changed since their formation, the phase-space location of these secondary resonances should have been different in the past. By simulating the effect of planetary migration, we show that a mechanism of sweeping secondary resonances, similar to the one studied by Ferraz-Mello and coworkers. for the asteroids in the 2:1 mean motion resonance with Jupiter, could significantly deplete a primordial population of Kozai resonators and push several circulators near the Kozai separatrix. This mechanism is not limited to Kiviuq’s region and could have worked to destabilize any initial population of satellites in the Kozai resonance around Saturn and Jupiter.
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chaos and the effects of planetary migration on the orbit of s 2000 s5 kiviuq
arXiv: Astrophysics, 2004Co-Authors: V Carruba, David Nesvorny, Joseph A Burns, Matija Cuk, K TsiganisAbstract:Among the many new irregular satellites that have been discovered in the last five years, at least six are in the so-called Kozai resonance. Due to solar perturbations, the argument of pericenter of a satellite usually precesses from 0 to 360 degrees. However, at inclinations higher than 39.3 degrees and lower than 140.7 degrees a new kind of behavior occurs for which the argument of pericenter oscillates around +/-90 degrees. In this work we will concentrate on the orbital history of the saturnian satellite S/2000 S5 Kiviuq, one of the satellites currently known to be in such resonance Kiviuq's orbit is very close to the separatrix of the Kozai resonance. Due to perturbations from the other jovian planets, it is expected that Orbits near the Kozai separatrix may show significant chaotic behavior. This is important because chaotic diffusion may Transfer Orbits from libration to circulation, and vice versa. To identify chaotic Orbits we used two well-known methods: the Frequency Analysis Method (Laskar 1990) and Maximum Lyapunov Exponents (Benettin et al. 1980). Our results show that the Kozai resonance is crossed by a web of secondary resonances, whose arguments involve combinations of the argument of pericenter, the argument of the Great Inequality, longitude of the node, and other terms related to the secular frequencies g5, g6, and s6. Many test Orbits whose precession period is close to the period of the Great Inequality (883 yrs), or some of its harmonics, are trapped by these secondary resonances, and show significant chaotic behavior. Planetary migration, by moving the locations of these secondary resonances, may have depleted an original population of Kozai resonators.
Matija Cuk - One of the best experts on this subject based on the ideXlab platform.
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chaos and the effects of planetary migration on the orbit of s 2000 s5 kiviuq
The Astronomical Journal, 2004Co-Authors: V Carruba, David Nesvorny, Joseph A Burns, Matija Cuk, K TsiganisAbstract:Among the many new irregular satellites that have been discovered in the last 5 years, five or more are in the so-called Kozai resonance. Because of solar perturbations, the argument of pericenter ! of a satellite usually precesses from 0 � to 360 � . However, at inclinations higher than ’39N3 and lower than ’140N7, a new kind of behavior occurs for which the argument of pericenter oscillates around � 90 � . In this work we concentrate on the orbital history of the Saturnian satellite S/2000 S5 Kiviuq, one of the satellites currently known to be in such resonance. Kiviuq’s orbit is very close to the separatrix of the Kozai resonance. Because of perturbations from the other Jovian planets, it is expected that Orbits near the Kozai separatrix may show significant chaotic behavior. This is important because chaotic diffusion may Transfer Orbits from libration to circulation, and vice versa. To identify chaotic Orbits, we used two well-known methods: the frequency analysis method of Laskar and the maximum Lyapunov exponents method of Benettin and coworkers. Our results show that the Kozai resonance is crossed by a web of secondary resonances, whose arguments involve combinations of the argument of pericenter, the argument of the Great Inequality (GI) (2kJ � 5kS), the longitude of the node � , and other terms related to the secular frequencies g5, g6 ,a nds6. Many test Orbits whose precession period are close to the period of the GI (883 yr), or some of its harmonics, are trapped by these secondary resonances and show significant chaotic behavior. Because the GI’s period is connected to the semimajor axes of Jupiter and Saturn and because the positions of the Jovian planets have likely changed since their formation, the phase-space location of these secondary resonances should have been different in the past. By simulating the effect of planetary migration, we show that a mechanism of sweeping secondary resonances, similar to the one studied by Ferraz-Mello and coworkers. for the asteroids in the 2:1 mean motion resonance with Jupiter, could significantly deplete a primordial population of Kozai resonators and push several circulators near the Kozai separatrix. This mechanism is not limited to Kiviuq’s region and could have worked to destabilize any initial population of satellites in the Kozai resonance around Saturn and Jupiter.
-
chaos and the effects of planetary migration on the orbit of s 2000 s5 kiviuq
arXiv: Astrophysics, 2004Co-Authors: V Carruba, David Nesvorny, Joseph A Burns, Matija Cuk, K TsiganisAbstract:Among the many new irregular satellites that have been discovered in the last five years, at least six are in the so-called Kozai resonance. Due to solar perturbations, the argument of pericenter of a satellite usually precesses from 0 to 360 degrees. However, at inclinations higher than 39.3 degrees and lower than 140.7 degrees a new kind of behavior occurs for which the argument of pericenter oscillates around +/-90 degrees. In this work we will concentrate on the orbital history of the saturnian satellite S/2000 S5 Kiviuq, one of the satellites currently known to be in such resonance Kiviuq's orbit is very close to the separatrix of the Kozai resonance. Due to perturbations from the other jovian planets, it is expected that Orbits near the Kozai separatrix may show significant chaotic behavior. This is important because chaotic diffusion may Transfer Orbits from libration to circulation, and vice versa. To identify chaotic Orbits we used two well-known methods: the Frequency Analysis Method (Laskar 1990) and Maximum Lyapunov Exponents (Benettin et al. 1980). Our results show that the Kozai resonance is crossed by a web of secondary resonances, whose arguments involve combinations of the argument of pericenter, the argument of the Great Inequality, longitude of the node, and other terms related to the secular frequencies g5, g6, and s6. Many test Orbits whose precession period is close to the period of the Great Inequality (883 yrs), or some of its harmonics, are trapped by these secondary resonances, and show significant chaotic behavior. Planetary migration, by moving the locations of these secondary resonances, may have depleted an original population of Kozai resonators.