A class of E. Stromgren's direct orbits in the restricted problem

Szebehely, V.; Nacozy, P. E.

doi:10.1086/110215

Cited by 20 publications

(10 citation statements)

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“…In particular their work gave new insights into the orbit structure of the circular restricted three body problem (CRTBP), a problem already immortalized by Poincaré. Interest in the CRTBP was reinvigorated in the 1960's with the inauguration of the space race and a number of authors including Szebehely, Nacozy, and Flandern [4,5] harnessed the newly available power of digital computing to settle some questions raised by Strömgren. The interested reader will find a delightful retelling of this story with many additional references in the book of Szebhely [6].…”

Section: Introductionmentioning

confidence: 99%

“…We adapt this scheme for the CRFBP, and compute atlases for the local stable/unstable manifolds attached to a saddle-focus equilibrium. By an atlas we mean a collection of analytic maps or charts of the form, P : [−1, 1] 2 → R 4 , where the image of P lies in the stable or unstable manifold. The union of these charts is a piecewise approximation for a large portion of the manifold away from the equilibrium.…”

Section: Introductionmentioning

confidence: 99%

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Homoclinic dynamics in a restricted four-body problem: transverse connections for the saddle-focus equilibrium solution set

Kepley

James

2019

Celest Mech Dyn Astr

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We describe a method for computing an atlas for the stable or unstable manifold attached to an equilibrium point, and implement the method for the saddle-focus libration points of the planar equilateral restricted four body problem. We employ the method at the maximally symmetric case of equal masses, where we compute atlases for both the stable and unstable manifolds. The resulting atlases are comprised of thousands of individual chart maps, with each chart represented by a two variable Taylor polynomial. Post-processing the atlas data yields approximate intersections of the invariant manifolds, which we refine via a shooting method for an appropriate two point boundary value problem. Finally, we apply numerical continuation to some of the BVP problems. This breaks the symmetries and leads to connecting orbits for some non-equal values of the primary masses.Keywords Gravitational 4-body problem • invariant manifolds • high-order Taylor methods • automatic differentiation • numerical continuation

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Homoclinic dynamics in a restricted four-body problem: transverse connections for the saddle-focus equilibrium solution set

Kepley

James

2019

Celest Mech Dyn Astr

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“…Broucke (1968) presented results for orbit families in the Earth-Moon system. Szebehely and Nacozy (1967) worked on these same sets of periodic obits. Szebehely's book Theory of Orbits (Szebehely 1967) indeed remains to date a classic reference with an extensive study on different families in the CR3BP, mostly for equal masses (the so-called Copenhagen problem), but also reviewing and completing Darwin's and Broucke's work.…”

Section: Families Of Planar Symmetric Periodic Orbits In the Cr3bp Anmentioning

confidence: 99%

On the $$a$$ a and $$g$$ g families of orbits in the Hill problem with solar radiation pressure and their application to asteroid orbiters

Yárnoz

Scheeres

McInnes

2015

Celest Mech Dyn Astr

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. (2015) On the a and g families of orbits in the Hill problem with solar radiation pressure and their application to asteroid orbiters. Celestial Mechanics and Dynamical Astronomy, 121(4) ABSTRACTThe focus of this paper is on the exploration of the a and g-g' families of planar symmetric periodic orbits around minor bodies under the effect of solar radiation pressure. An extended Hill problem with solar radiation pressure (SRP) allows the study of spacecraft trajectories in the vicinity of asteroids orbiting the Sun. The evolution of the a and g-g' families is presented with SRP increasing from the classical Hill problem to levels characteristic of current and future planned missions to minor bodies, as well as one extreme case with very large SRP for a small asteroid. In addition, the implications of considering a spherical body are analysed, in terms of trajectories colliding with the asteroid and eclipses, which limits the feasibility of various family branches. Finally, the influence of SRP on the linear stability of feasible orbits is calculated.

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“…Szebehely worked on these same sets of periodic obits. 8 His book Theory of Orbits 9 is still a classic reference with an extensive study on different families in the CR3BP, mostly for equal masses (the so-called Copenhagen problem), but also reviewing and completing Darwin's and Broucke's work. Hénon had also studied prior to Hill problem planar symmetric families in the Copenhagen problem as the other limiting case of the CR3BP.…”

Section: A Families Of Symmetric Periodic Orbits In the Cr3bpmentioning

confidence: 99%

On the a and g Families of Symmetric Periodic Orbits in the Photogravitational Hill Problem and Their Application to Asteroids

Yárnoz

Scheeres

McInnes

2014

AIAA/AAS Astrodynamics Specialist Conference

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This paper focuses on the exploration of families of planar symmetric periodic orbits around minor bodies under the effect of solar radiation pressure. For very small asteroids and comets, an extension of the Hill problem with Solar Radiation Pressure (SRP) perturbation is a particularly well-suited dynamical model. The evolution of the a and g families of symmetric periodic orbits has been studied in this model when SRP is increased from the classical problem with no SRP to levels corresponding to current and future planned missions to minor bodies, as well as one extreme case with very large SRP. In addition, the feasibility an applicability of these orbits for the case of asteroids was analysed, and the effect of SRP in their stability is presented.

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A class of E. Stromgren's direct orbits in the restricted problem

Cited by 20 publications

References 0 publications

Homoclinic dynamics in a restricted four-body problem: transverse connections for the saddle-focus equilibrium solution set

Homoclinic dynamics in a restricted four-body problem: transverse connections for the saddle-focus equilibrium solution set

On the $$a$$ a and $$g$$ g families of orbits in the Hill problem with solar radiation pressure and their application to asteroid orbiters

On the a and g Families of Symmetric Periodic Orbits in the Photogravitational Hill Problem and Their Application to Asteroids

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