On critical values concerning the evolution of the long period families

Hou, Xiyun

doi:10.1088/1674-4527/9/4/012

Cited by 1 publication

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“…This finding is interesting. It means that the global genealogy of the long-and the short-period families are same as that of the long-and the short-period families around triangular libration point of the circular restricted three-body problem (Henrard 2002;Hou 2009;Hou & Liu 2009) and also the same as that of the two periodic orbit families around the EP in the body-fixed frame of a single uniformly rotating asteroid (Feng & Hou 2017;Jiang & Baoyin 2019).…”

Section: Genealogy and Stability Of Families Of Periodic Orbitsmentioning

confidence: 91%

On the secondary’s rotation in a synchronous binary asteroid

Wang

Hou

2020

Monthly Notices of the Royal Astronomical Society

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This paper studies the secondary's rotation in a synchronous binary asteroid system in which the secondary enters the 1:1 spin-orbit resonance. The model used is the planar full two-body problem composed of a spherical primary plus a tri-axial ellipsoid secondary. Compared with classical spin-orbit work, there are two differences: (1) Influence on the mutual orbit from the secondary's rotation is considered; (2) Instead of the Hamiltonian approach, the approach of periodic orbits is adopted. Our studies find: (1) Genealogy of the two families of periodic orbits is same as that of the families around triangular libration points in the restricted three-body problem. That is, the long-period family terminates onto a short-period orbit travelling N times; (2) In the limiting case where the secondary's mass is negligible, our results can be reduced to the classical spin-orbit theory, by equating the long-period orbit with the free libration, and by equating the short-period orbit with the forced libration caused by orbit eccentricity. However, the two models show obvious differences when the secondary's mass is non-negligible. (3) By studying the stability of periodic orbits, for a specific binary asteroid system, we are able to obtain the maximum libration amplitude of the secondary (which is usually less than 90°), and the maximum mutual orbit eccentricity which does not break the secondary's synchronous state. We also find the anti-correlation between the secondary's libration amplitude and the orbit eccentricity. The (65803) Didymos system is taken as an example to show the results.

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