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

Hou, Xiyun

doi:10.1007/s10509-018-3254-9

Cited by 2 publications

(3 citation statements)

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“…The full two-body dynamics of the system was studied in detail by Fahnestock and Scheeres (2008). The dynamics of this system was later used as a test case for models of the F2BP by (e.g., Boué and Laskar, 2009;Compère and Lemaître, 2014;Boué, 2017;Hou, 2018).…”

Section: Kw4mentioning

confidence: 99%

“…Our focus is on the development of an explicit link between the F2BP formulation and the formulations used in orbit determination/ephemeris generation, while ensuring a computational efficiency not prohibitive from a practical point of view. Our goal is not to improve the current state of the art in terms of computational performance (Boué, 2017;Hou, 2018).…”

Section: Introductionmentioning

confidence: 99%

“…Recently, an efficient representation of this problem was introduced by Boué (2017) by applying angular momentum theory. An equivalent formulation of the problem, in terms of inertia integrals instead of mass multipole moments, was developed by Paul (1988), Tricarico (2008, , with a highly efficient implementation presented by Hou (2018). In an alternative approach, a formulation of the mutual interaction of homogeneous bodies is derived by Werner and Scheeres (2005); Fahnestock and Scheeres (2006); Hirabayashi and Scheeres (2013) based on polyhedron shape models, which is highly valuable for the simulation of small bodies, such as binary asteroids (Fahnestock and Scheeres, 2008).…”

Section: Introductionmentioning

confidence: 99%

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Propagation and estimation of the dynamical behaviour of gravitationally interacting rigid bodies

Dirkx

Mooij

Root

2019

Astrophys Space Sci

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Next-generation planetary tracking methods, such as interplanetary laser ranging (ILR) and same-beam interferometry (SBI) promise an orders-of-magnitude increase in the accuracy of measurements of solar system dynamics. This requires a reconsideration of modelling strategies for the translational and rotational dynamics of natural bodies, to ensure that model errors are well below the measurement uncertainties.The influence of the gravitational interaction of the full mass distributions of celestial bodies, the so-called figure-figure effects, will need to be included for selected future missions. The mathematical formulation of this problem to arbitrary degree is often provided in an elegant and compact manner that is not trivially relatable to the formulation used in space geodesy and ephemeris generation. This complicates the robust implementation of such a model in operational software packages. We formulate the problem in a manner that is directly compatible with the implementation used in typical dynamical modelling codes: in terms of spherical harmonic coefficients and Legendre polynomials. An analytical formulation for the associated variational equations for both translational and rotational motion is derived.We apply our methodology to both Phobos and the KW4 binary asteroid system, to analyze the influence of figure-figure effects during estimation from next-generation tracking data. For the case of Phobos, omitting these effects during estimation results in relative errors of 0.42% and 0.065% for theC 20 andC 22 spherical harmonic gravity field coefficients, respectively. These values are below current uncertainties, but orders of magnitude larger than those obtained from past simulations for accurate tracking of a future Phobos lander, showing the need to apply the methodology outlined in this manuscript for selected future missions.

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