Applications of Symplectic Topology to Orbit Uncertainty and Spacecraft Navigation

Scheeres, Daniel J.; Gosson, Maurice de; Maruskin, Jared M.

doi:10.1007/s40295-013-0006-5

Cited by 8 publications

(9 citation statements)

References 14 publications

(26 reference statements)

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“…We are grateful to the referee for his/her constructive criticism of the manuscript which helped improve the exposition, and also for pointing out to us references [45,46] of which we were completely unaware at the time of development and writing of this manuscript. The second author is grateful to Professor Anastasios Bountis for his support, without which this work would have never been possible.…”

Section: Acknowledgementmentioning

confidence: 99%

Irreversibility from staircases in symplectic embeddings

Creaco

Kalogeropoulos

2019

Physica A: Statistical Mechanics and its Applications

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We present an argument whose goal is to trace the origin of the macroscopically irreversible behavior of Hamitonian systems of many degrees of freedom. We use recent flexibility and rigidity results of symplectic embeddings, quantified via the (stabilized) Fibonacci and Pell staircases, to encode the underlying breadth of the possible initial conditions, which alongside the multitude of degrees of freeedom of the underlying system give rise to time-irreversibility.

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Section: Acknowledgementmentioning

confidence: 99%

Irreversibility from staircases in symplectic embeddings

Creaco

Kalogeropoulos

2019

Physica A: Statistical Mechanics and its Applications

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“…This fact is of course strongly reminiscent of the uncertainty principle of quantum mechanics, of which it is in fact a classical version; we have discussed this analogy in detail in de Gosson [ 4 , 10 ]. Scheeres et al [ 9 ] used our results to study orbit uncertainty in space craft navigation.…”

Section: Subsystems Of Hamiltonian Systemsmentioning

confidence: 99%

“…[ 6 ]). This theorem plays an essential role in quantum mechanics, and also in the study of entropy [ 7 ], aeronautics [ 8 , 9 ], and statistical mechanics [ 10 ]. Its importance and potential applications have however not yet been fully exploited in physics.…”

Section: Introductionmentioning

confidence: 99%

The Symplectic Camel and Poincaré Superrecurrence: Open Problems

Gosson

2018

Entropy

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Poincaré's Recurrence Theorem implies that any isolated Hamiltonian system evolving in a bounded Universe returns infinitely many times arbitrarily close to its initial phase space configuration. We discuss this and related recurrence properties from the point of view of recent advances in symplectic topology which have not yet reached the Physics community. These properties are closely related to Emergent Quantum Mechanics since they belong to a twilight zone between classical (Hamiltonian) mechanics and its quantization.

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“…When studying the dynamics around it a short time interval, we can assume that during this time interval, the position of the Sun is "frozen" in the inertial space. The formulation of Hill's problem taking into account the effect of SRP was presented by Scheeres & Marzari (2002). However, in the body-fixed frame of the asteroid, as represented in Fig.…”

Section: Zero Velocity Curves and Equilibriamentioning

confidence: 99%

“…In this paper, we analyze the stability of both homogeneous and inhomogeneous mass distribution and the effects of solar radiation pressure in equatorial orbits in the proximity of the asteroid (101955) Bennu. This will be attended using the mascon gravitation model and the solar radiation pressure force defined by Scheeres & Marzari (2002) and Xin et al (2016) for the dynamical model. First, we show the general properties of (101955) Bennu in Section 2.…”

Section: Introductionmentioning

confidence: 99%

Dynamics in the vicinity of (101955) Bennu: solar radiation pressure effects in equatorial orbits

Chanut

Aljbaae

Prado

et al. 2017

Monthly Notices of the Royal Astronomical Society

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Here we study the dynamical effects of the solar radiation pressure (SRP) on a spacecraft that will survey the near-Earth rotating asteroid (101955) Bennu when the projected shadow is accounted for. The spacecraft's motion near (101955) Bennu is modelled in the rotating frame fixed at the centre of the asteroid, neglecting the sun gravity effects. We calculate the solar radiation pressure at the perihelion, semi-major axis and aphelion distances of the asteroid from the Sun. The goals of this work are to analyse the stability for both homogeneous and inhomogeneous mass distribution and study the effects of the solar radiation pressure in equatorial orbits close to the asteroid (101955) Bennu. As results, we find that the mascon model divided into ten equal layers seems to be the most suitable for this problem. We can highlight that the centre point E8, which was linearly stable in the case of the homogeneous mass distribution, becomes unstable in this new model changing its topological structure. For a Sun initial longitude ψ 0 = −180 o , starting with the spacecraft longitude λ = 0, the orbits suffer fewer impacts and some (between 0.4 and 0.5 km), remaining unwavering even if the maximum solar radiation is considered. When we change the initial longitude of the Sun to ψ 0 = −135 o , the orbits with initial longitude λ = 90 0 appear to be more stable. Finally, when the passage of the spacecraft in the shadow is accounted for, the effects of solar radiation pressure are softened, and we find more stable orbits.

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Applications of Symplectic Topology to Orbit Uncertainty and Spacecraft Navigation

Cited by 8 publications

References 14 publications

Irreversibility from staircases in symplectic embeddings

Irreversibility from staircases in symplectic embeddings

The Symplectic Camel and Poincaré Superrecurrence: Open Problems

Dynamics in the vicinity of (101955) Bennu: solar radiation pressure effects in equatorial orbits

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