Exterior gravitation of a polyhedron derived and compared with harmonic and mascon gravitation representations of asteroid 4769 Castalia

Werner, Robert A.; Scheeres, Daniel J.

doi:10.1007/bf00053511

Cited by 435 publications

(371 citation statements)

References 23 publications

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“…The surface cohesive forces are proportional to the magnitude of the negative ambient gravity experienced by the surface. In particular, the gravitational acceleration, g, acting at a particular point of 1950 DA's surface, x, was determined using a polyhedral gravity field model 30 . Under asteroid rotation the ambient gravitational acceleration at that surface point will be modified by centripetal acceleration, such that…”

Section: Cohesive Force Modellingmentioning

confidence: 99%

Cohesive forces prevent the rotational breakup of rubble-pile asteroid (29075) 1950 DA

Rozitis

MacLennan

Emery

2014

Nature

180

137

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Space missions 1 and ground-based observations 2 have shown that some asteroids are loose collections of rubble rather than solid bodies. The physical behavior of such 'rubble pile' asteroids has been traditionally described using only gravitational and frictional forces within a granular material 3 . Cohesive forces in the form of small van der Waals forces between constituent grains have been recently predicted to be important for small rubble piles (10-kilometer-sized or smaller), and can potentially explain fast rotation rates in the small asteroid population 4-6 . Hitherto, the strongest evidence came from an analysis of the rotational breakup of main belt comet P/2013 R3 (ref. 7), although that was indirect and poorly constrained by present observations. Here we report that the kilometer-sized asteroid (29075) 1950 DA 8 is a rubble pile that is rotating faster than that allowed by gravity and friction. We find that cohesive forces are required to prevent surface mass shedding and structural failure, and that the strength of the forces are comparable to, though somewhat less than, that of lunar regolith.It is possible to infer the existence of cohesive forces within an asteroid by determining if it is a rubble pile with insufficient self-gravity to prevent rotational breakup by centrifugal forces. One of the largest known candidates is near-Earth asteroid 1950 DA (mean diameter of 1.3 km; ref.8), as it has a rotation period of 2.1216 hr that is just beyond the critical spin limit of ~2.2 hr estimated for a cohesionless asteroid 9 . A rubble pile structure and the degree of self-gravity can be determined by a bulk density measurement, which can be acquired through model-tomeasurement comparisons of Yarkovsky orbital drift 10 . This drift arises on a rotating asteroid with non-zero thermal inertia, and is caused by the delayed thermal emission of absorbed sunlight, which applies a small propulsion force to the asteroid's afternoon side. Thermalinfrared observations can constrain the thermal inertia value 11 , and precise astrometric position measurements conducted over several years can constrain the degree of Yarkovsky orbital drift 2 . Recently, the orbital semimajor axis of 1950 DA has been observed to be decreasing at a rate of 44.1 ± 8.5 m yr -1 because of the Yarkovsky effect 12 , which indicates that the asteroid's sense of rotation must be retrograde. Using the Advanced Thermophysical Model 13,14 , in combination with the retrograde radar shape model 8 , archival WISE thermal-infrared data 15 (Extended Data Table 1, and Extended Data Figs 1 and 2), and orbital state 12 , we determine the thermal inertia and bulk density of 1950 DA (Methods). The thermal inertia value is found to be remarkably low at 24 +20 / -14 J m -2 K -1 s -1/2 , which gives a corresponding bulk density of 1.7 ± 0.7 g cm -3 ( Fig. 1 and Extended Data Fig. 3). This bulk density is much lower than the minimum value of 3.5 g cm -3 required to prevent loss of surface material by centrifugal forces (Fig. 2).Spectral observations of 1950...

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Section: Cohesive Force Modellingmentioning

confidence: 99%

Cohesive forces prevent the rotational breakup of rubble-pile asteroid (29075) 1950 DA

Rozitis

MacLennan

Emery

2014

Nature

180

137

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“…Other gravity models, such as a polyhedron shape model (Werner and Scheeres, 1996), could be considered without impacting on the proposed guidance algorithm. Assuming the asteroid's rotational rate vector aligned with the z axis, results ω = [0, 0, ω] T .…”

Section: Problem Statementmentioning

confidence: 99%

A semi-analytical guidance algorithm for autonomous landing

Lunghi¹,

Lavagna²,

Armellín³

2015

Advances in Space Research

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One of the main challenges posed by the next space systems generation is the high level of autonomy they will require. Hazard Detection and Avoidance is a key technology in this context. An adaptive guidance algorithm for landing that updates the trajectory to the surface by means of an optimal control problem solving is here presented. A semi-analytical approach is proposed. The trajectory is expressed in a polynomial form of minimum order to satisfy a set of boundary constraints derived from initial and final states and attitude requirements. By imposing boundary conditions, a fully determined guidance profile is obtained, function of a restricted set of parameters. The guidance computation is reduced to the determination of these parameters in order to satisfy path constraints and other additional constraints not implicitly satisfied by the polynomial formulation. The algorithm is applied to two different scenarios, a lunar landing and an asteroidal landing, to highlight its general validity. verify the versatility of the algorithm in realistic cases, by the introduction of attitude control systems, thrust modulation, and navigation errors. The proposed approach proved to be flexible and accurate, granting a precision of a few meters at touchdown.

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“…For the study outside of the circumscribing sphere, the method of a spherical harmonic expansion truncated at arbitrary degree and order can be used. When the distance becomes smaller, the polyhedron method of approximation of the shape of a body with triangular faces is more valid (Werner and Scheeres 1996). Another option is to approximate the gravitational field by elementary geometrical shapes (e.g.…”

Section: Introductionmentioning

confidence: 99%

Modeling and analysis of periodic orbits around a contact binary asteroid

Feng

Noomen

Visser

et al. 2015

Astrophys Space Sci

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The existence and characteristics of periodic orbits (POs) in the vicinity of a contact binary asteroid are investigated with an averaged spherical harmonics model. A contact binary asteroid consists of two components connected to each other, resulting in a highly bifurcated shape. Here, it is represented by a combination of an ellipsoid and a sphere. The gravitational field of this configuration is for the first time expanded into a spherical harmonics model up to degree and order 8. Compared with the exact potential, the truncation at degree and order 4 is found to introduce an error of less than 10 % at the circumscribing sphere and less than 1 % at a distance of the double of the reference radius. The Hamiltonian taking into account harmonics up to degree and order 4 is developed. After double averaging of this Hamiltonian, the model is reduced to include zonal harmonics only and frozen orbits are obtained. The tesseral terms are found to introduce significant variations on the frozen orbits and distort the frozen situation. Applying the method of Poincaré sections, phase space structures of the single-averaged model are generated for different energy levels and rotation rates of the asteroid, from which the dynamics driven by the 4 × 4 harmonics model is identified and POs are found. It is found that the disturbing effect of the highly irregular gravitational field on orbital motion is Northwestern Polytechnical University, Xiaan, China weakened around the polar region, and also for an asteroid with a fast rotation rate. Starting with initial conditions from this averaged model, families of exact POs in the original non-averaged system are obtained employing a numerical search method and a continuation technique. Some of these POs are stable and are candidates for future missions.

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Exterior gravitation of a polyhedron derived and compared with harmonic and mascon gravitation representations of asteroid 4769 Castalia

Cited by 435 publications

References 23 publications

Cohesive forces prevent the rotational breakup of rubble-pile asteroid (29075) 1950 DA

Cohesive forces prevent the rotational breakup of rubble-pile asteroid (29075) 1950 DA

A semi-analytical guidance algorithm for autonomous landing

Modeling and analysis of periodic orbits around a contact binary asteroid

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