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

Dirkx, Dominic; Mooij, Erwin; Root, Bart

doi:10.1007/s10509-019-3521-4

Cited by 11 publications

(6 citation statements)

References 65 publications

(120 reference statements)

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“…J2000). We stress that, in a general formulation, the states y need not be translational states, but may be any type of dynamics, of any number of bodies (see Mazarico et al (2017); Dirkx et al (2019) for an example of coupled translational-rotational dynamics estimation of multiple bodies).…”

Section: Variational Equations Formulationmentioning

confidence: 99%

Decoupled and coupled moons’ ephemerides estimation strategies application to the JUICE mission

Fayolle

Dirkx

Lainey

et al. 2022

Planetary and Space Science

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Section: Variational Equations Formulationmentioning

confidence: 99%

Decoupled and coupled moons’ ephemerides estimation strategies application to the JUICE mission

Fayolle

Dirkx

Lainey

et al. 2022

Planetary and Space Science

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“…Consequently, no tidal model for Phobos is applied, and the time-varying influence of the longitudinally-asymmetric C 22 is omitted. Properly capturing the rotational-orbital-tidal coupling of Phobos would require the estimation of many libration amplitudes [32,37], the estimation of a dynamical rotational state [38], or the fully dynamical modelling (including tides) as proposed in [39]. Each of these approaches is beyond the scope of the current work, which focuses on comparing the RS and CAI instruments for Phobos gravity field determination.…”

Section: Dynamical Model and Orbit Designmentioning

confidence: 99%

“…Modelling the long-term improvement in Phobos' ephemeris requires data fusion of astrometric data [42] and the radiometric data simulated here, which is beyond the scope of this analysis. Moreover, properly accounting for the influence of Phobos' rotational dynamics on its ephemeris over both the short-term (during the mission; see Section 3) and the long-term would ideally require a coupled translational-rotational model for the propagation and estimation of Phobos' dynamics [38,75]. At the very least, it would require the estimation of a spectrum of libration amplitudes.…”

Section: Ephemeris and Librationmentioning

confidence: 99%

Cold Atom Interferometry for Enhancing the Radio Science Gravity Experiment: A Phobos Case Study

Plumaris

Dirkx²,

Siemes³

et al. 2022

Remote Sensing

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Interplanetary missions have typically relied on Radio Science (RS) to recover gravity fields by detecting their signatures on the spacecraft trajectory. The weak gravitational fields of small bodies, coupled with the prominent influence of confounding accelerations, hinder the efficacy of this method. Meanwhile, quantum sensors based on Cold Atom Interferometry (CAI) have demonstrated absolute measurements with inherent stability and repeatability, reaching the utmost accuracy in microgravity. This work addresses the potential of CAI-based Gradiometry (CG) as a means to strengthen the RS gravity experiment for small-body missions. Phobos represents an ideal science case as astronomic observations and recent flybys have conferred enough information to define a robust orbiting strategy, whilst promoting studies linking its geodetic observables to its origin. A covariance analysis was adopted to evaluate the contribution of RS and CG in the gravity field solution, for a coupled Phobos-spacecraft state estimation incorporating one week of data. The favourable observational geometry and the small characteristic period of the gravity signal add to the competitiveness of Doppler observables. Provided that empirical accelerations can be modelled below the nm/s2 level, RS is able to infer the 6 × 6 spherical harmonic spectrum to an accuracy of 0.1–1% with respect to the homogeneous interior values. If this correlates to a density anomaly beneath the Stickney crater, RS would suffice to constrain Phobos’ origin. Yet, in event of a rubble pile or icy moon interior (or a combination thereof) CG remains imperative, enabling an accuracy below 0.1% for most of the 10 × 10 spectrum. Nevertheless, technological advancements will be needed to alleviate the current logistical challenges associated with CG operation. This work also reflects on the sensitivity of the candidate orbits with regard to dynamical model uncertainties, which are common in small-body environments. This brings confidence in the applicability of the identified geodetic estimation strategy for missions targeting other moons, particularly those of the giant planets, which are targets for robotic exploration in the coming decades.

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“…Additionally, the gravitational fields of oblate planets have been of interest to understand the motion of satellites, in particular artificial satellites orbiting around the Earth (Vinti, 1966;Lara, 2020). More recently, general shapes have been considered with the aim of providing accurate dynamics of interacting gravitational bodies that can be monitored experimentally to high precision (Dirkx, Mooij, & Root, 2019;Celletti, Gales, & Lhotka, 2020). In such problems, multipolar expansions of the gravitational potential play a key role in the analysis.…”

Section: Introductionmentioning

confidence: 99%

Surface Gravity of Rotating Dumbbell Shapes

Lam,

Gidea,

Zypman

2021

Preprint

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We investigate the problem of determining the shape of a rotating celestial object -e.g., a comet or an asteroid -under its own gravitational field. More specifically, we consider an object symmetric with respect to one axis -such as a dumbbell -that rotates around a second axis perpendicular to the symmetry axis. We assume that the object can be modeled as an incompressible fluid of constant mass density, which is regarded as a first approximation of an aggregate of particles.In the literature, the gravitational field of a body is often described as a multipolar expansion involving spherical coordinates (Kaula, 1966). In this work we describe the shape in terms of cylindrical coordinates, which are most naturally adapted to the symmetry of the body, and we express the gravitational potential generated by the rotating body as a simple formula in terms of elliptic integrals. An equilibrium shape occurs when the gravitational potential energy and the rotational kinetic energy at the surface of the body balance each other out. Such an equilibrium shape can be derived as a solution of an optimization problem, which can be found via the variational method. We give an example where we apply this method to a two-parameter family of dumbbell shapes, and find approximate numerical solutions to the corresponding optimization problem.

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

Cited by 11 publications

References 65 publications

Decoupled and coupled moons’ ephemerides estimation strategies application to the JUICE mission

Decoupled and coupled moons’ ephemerides estimation strategies application to the JUICE mission

Cold Atom Interferometry for Enhancing the Radio Science Gravity Experiment: A Phobos Case Study

Surface Gravity of Rotating Dumbbell Shapes

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