Mutual potential between two rigid bodies with arbitrary shapes and mass distributions

Hou, Xiyun; Scheeres, Daniel J.; Xin, Xiaodong

doi:10.1007/s10569-016-9731-y

Cited by 64 publications

(57 citation statements)

References 36 publications

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“…In this case, force models and solutions truncated at the 2nd order may be not accurate enough [9]. Higher order non-spherical terms should be considered.…”

Section: Remarkmentioning

confidence: 99%

“…(31) still applies, but the expressions of F A , F B should change accordingly by incorporating higher order non-spherical terms of each primary. The mutual orbit and rotations of the F2BP can be firstly numerically integrated [9]. A Fourier transformation can be applied to the two bodies' mutual orbit and rotations to extract periodic terms of D,Ḋ,D, r AB , C A , C B which are necessary in Eq.…”

Section: Remarkmentioning

confidence: 99%

“…The mutual dynamics of the system is governed by the mutual potential between the two rigid bodies which depends on their relative orbit and relative attitude [2,3]. Generally, except for some special cases [4], there is no closed form for the mutual potential [5][6][7][8][9]. As a result, except some studies on the qualitative description of the system [3,[10][11][12][13], works on the motions of the system [14][15][16][17][18] are usually carried out for potentials truncated at finite orders.…”

Section: Introductionmentioning

confidence: 99%

“…The two ellipsoids are rotating along their primary principal axis and the orbital plane is coincident with the rotational planes of the two bodies. This model is often used to qualitatively describe the fission process of binary asteroids [9,18,20], and is the model that will be analytically treated in this work.…”

Section: Introductionmentioning

confidence: 99%

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A note on the full two-body problem and related restricted full three-body problem

Hou

Xin

2017

Astrodyn

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Truncating at the second order of the mutual potential between two rigid bodies, timeexplicit first order solutions to the rotations and the orbital motion of the two bodies in the planar full two-body problem (F2BP) are constructed. Based on this analytical solution, equations of motion (EOMs) for the related restricted full three-body problem are given.In the case of the synchronous or double synchronous states for the full two-body problem, EOMs for the related restricted full three-body problem (RF3BP) are also given. At last, one example-the "collinear libration point" in the binary asteroid system-is given.

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“…In this case, force models and solutions truncated at the 2nd order may be not accurate enough [9]. Higher order non-spherical terms should be considered.…”

Section: Remarkmentioning

confidence: 99%

Section: Remarkmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A note on the full two-body problem and related restricted full three-body problem

Hou

Xin

2017

Astrodyn

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“…Both studies provided valuable insight into the dynamical behavior of binaries, however they were limited by the computational burden or limited expansion order inherent to their implementation of the F2BP. Recently Hou et al derived a recursive approach to the F2BP which enables much more computationally efficient simulation of the F2BP [11]. The improvements in computationally efficiency also open the door to study mass distribution sensitivity of binary system dynamics.…”

Section: Introductionmentioning

confidence: 99%

Doubly synchronous binary asteroid mass parameter observability

Davis

Scheeres

2020

Icarus

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The full two-body problem (F2BP) is often used to model binary asteroid systems, representing the bodies as two finite mass distributions whose dynamics are influenced by their mutual gravity potential. The emergent behavior of the F2BP is highly coupled translational and rotational mutual motion of the mass distributions. A large fraction of characterized binary asteroids appear to be at, or near, the doubly synchronous equilibrium, which occurs when both bodies are tidally-locked and in a circular co-orbit. Stable oscillations about this equilibrium can be shown, for the nonplanar system, to be combinations of seven fundamental frequencies of the system and the mutual orbit rate. The fundamental frequencies arise as the linear periods of center manifolds identified about the equilibrium which are heavily influenced by each body's mass parameters. We leverage these eight dynamical constraints to investigate the observability of binary asteroid mass parameters via dynamical observations. This is accomplished by deriving a relationship between the fundamental frequencies and mass parameters for doubly synchronous systems. This relationship allows us to show the sensitivity of the dynamics to changes in the mass parameters, first for the planar dynamics, and then for the nonplanar dynamics. In so doing we are able to predict the idealized estimation covariance of the mass parameters based on obser-$ vation quality and define idealized observation accuracies for desired mass parameter certainties. We apply these tools to 617 Patroclus, a doubly synchronous Trojan binary and flyby target of the LUCY mission, as well as the Pluto and Charon system in order to predict mutual behaviors of these doubly synchronous systems and to provide observational requirements for these systems mass parameters.

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Integration of the full two-body problem by using generalized inertia integrals

Hou

2018

Astrophys Space Sci

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Mutual potential between two rigid bodies with arbitrary shapes and mass distributions

Cited by 64 publications

References 36 publications

A note on the full two-body problem and related restricted full three-body problem

A note on the full two-body problem and related restricted full three-body problem

Doubly synchronous binary asteroid mass parameter observability

Integration of the full two-body problem by using generalized inertia integrals

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