The Gravity Field of a Cube

Chappell, James M.; Chappell, Mark; Iqbal, Azhar; Abbott, Derek

doi:10.3844/pisp.2012.50.57

Cited by 14 publications

(8 citation statements)

References 35 publications

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“…For forces in the x-direction these are: a flat plane of any arbitrary orientation; a surface (flat or singly curved) whose normal meets the requirements = ȷ ·n 0 n or = ·n k 0; n or a surface (flat or singly curved) whose normal meets the requirement = ·n ı 0 n . Clearly in the third case equation (5) evaluates to zero and the other cases reduce to single integrals as solved below. For doubly curved surfaces we cannot reduce the surface integral to a single integral without triangular meshing.…”

Section: Theorymentioning

confidence: 99%

A vector field approach to calculating gravitational forces

Stirling¹

2017

New J. Phys.

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Calculation of gravitational forces is essential for many fundamental measurements, such as determining the gravitational constant or investigating violations of the inverse square law. These calculations, even with modern computational power, are slow and tedious. Improved calculation efficiency allows an experimentalist to easily check the effect of possible systematic biases and to ease the process of instrument design. Many gravitational measurements are expanded in terms of multipole moments for efficient calculations, however for many experimental geometries these do not converge, leaving awkward sextuple integrals. In this work we introduce a modified approach to the calculation which reduces the force between a point mass and any arbitrary object to a sum of single integrals. The force between any two objects can then be calculated as a quadruple rather than a sextuple integral.

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Section: Theorymentioning

confidence: 99%

A vector field approach to calculating gravitational forces

Stirling¹

2017

New J. Phys.

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“…Li et al [33] have investigated the locations and linear stability of equilibrium points as well as periodic orbits around equilibrium points in the vicinity of a rotating dumbbell-shaped body. These simply shaped bodies and potential fields, including the logarithmic gravity field [34], the straight segment [6][8] [13] [35], the solid circular ring [29] [36], the triangular plate and the square plate [14], the homogeneous annulus disk [30][31], the homogeneous cube [32,[37][38][39], the dumbbell-shaped body [33], the classical rotating dipole model [40][41][42], and the dipole segment model [43] are all plane-symmetric. The relative equilibria of spacecrafts in the second degree and order-gravity field [44][45] are different from the equilibria in the above studies.…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Stability and motion around equilibrium points in the rotating plane-symmetric potential field

et al. 2018

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This study presents a study of equilibrium points, periodic orbits, stabilities, and manifolds in a rotating plane-symmetric potential field. It has been found that the dynamical behaviour near equilibrium points is completely determined by the structure of the submanifolds and subspaces. The non-degenerate equilibrium points are classified into twelve cases. The necessary and sufficient conditions for linearly stable, non-resonant unstable and resonant equilibrium points are established. Furthermore, the results show that a resonant equilibrium point is a Hopf bifurcation point. In addition, if the rotating speed changes, two non-degenerate equilibria may collide and annihilate each other. The theory developed here is lastly applied to two particular cases, motions around a rotating, homogeneous cube and the asteroid 1620 Geographos. We found that the mutual annihilation of equilibrium points occurs as the rotating speed increases, and then the first surface shedding begins near the intersection point of the -x axis and the surface. The results can be applied to planetary science, including the birth and evolution of the minor bodies in the Solar system, the rotational breakup and surface mass shedding of asteroids, etc.

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“…Michalodimitrakis and Bozis [9] studied the two-body problem with a massive point particle and a homogeneous cube and proved the existence of a ring-type bounded motion. The gravitational field around a cube was also analyzed by Chappell et al [10]. The search for periodic orbits around a fixed homogeneous cube and the potential based on the polyhedron method for a cube given by a volume integral were studied by Liu et al [11,12].…”

Section: Introductionmentioning

confidence: 99%

Mapping Orbits regarding Perturbations due to the Gravitational Field of a Cube

Venditti

Prado

2015

Mathematical Problems in Engineering

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The orbital dynamics around irregular shaped bodies is an actual topic in astrodynamics, because celestial bodies are not perfect spheres. When it comes to small celestial bodies, like asteroids and comets, it is even more import to consider the nonspherical shape. The gravitational field around them may generate trajectories that are different from Keplerian orbits. Modeling an irregular body can be a hard task, especially because it is difficult to know the exact shape when observing it from the Earth, due to their small sizes and long distances. Some asteroids have been observed, but it is still a small amount compared to all existing asteroids in the Solar System. An approximation of their shape can be made as a sum of several known geometric shapes. Some three-dimensional figures have closed equations for the potential and, in this work, the formulation of a cube is considered. The results give the mappings showing the orbits that are less perturbed and then have a good potential to be used by spacecrafts that need to minimize station-keeping maneuvers. Points in the orbit that minimizes the perturbations are found and they can be used for constellations of nanosatellites.

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The Gravity Field of a Cube

Cited by 14 publications

References 35 publications

A vector field approach to calculating gravitational forces

A vector field approach to calculating gravitational forces

Stability and motion around equilibrium points in the rotating plane-symmetric potential field

Mapping Orbits regarding Perturbations due to the Gravitational Field of a Cube

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