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1.
Przemysław Bartczak Sławomir Breiter 《Celestial Mechanics and Dynamical Astronomy》2003,86(2):131-141
We propose a new, simple model to describe the gravity field of irregular, nonspherical celestial bodies, like small moons or minor asteroids. The simple idea of Duboshin to use a material straight segment for such bodies is extended by combining two perpendicular segments of different lengths and masses. In typical situations, when the longest axis of the body coincides with one segment, the remaining segment must have an imaginary length. The potential remains a real function even if one segment is imaginary. The new model is confronted with the exact form of an ellipsoid's potential and with two alternative simple models for a two-axial and a three-axial ellipsoid. 相似文献
2.
Peter J. Brown Alice A. Breeveld Stephen Holland Paul Kuin Tyler Pritchard 《Astrophysics and Space Science》2014,353(1):89-96
This paper studies the motion of an infinitesimal mass in the framework of Robe’s circular restricted three-body problem in two cases; the first case is when the hydrostatic equilibrium figure of the first primary is an oblate spheroid, the shape of the second primary is considered as an oblate spheroid with oblateness coefficients up to the second zonal harmonic, while the first primary is a Roche ellipsoid in the second case and the full buoyancy of the fluid is taken into account. In case one; it is observed that there are two axial libration points on the line joining the centres of the primaries, points on the circle within the first primary are also libration points under certain conditions. It is further found that the first axial point is stable, while the second one is conditionally stable, and the circular points are unstable. It is found in case two that there is exist only one libration point (0,0,0) this point is stable. 相似文献
3.
Triaxial ellipsoid dimensions and rotational poles of seven asteroids from Lick Observatory adaptive optics images, and of Ceres 总被引：1，自引：0，他引：1
Seven main belt asteroids, 2 Pallas, 3 Juno, 4 Vesta, 16 Psyche, 87 Sylvia, 324 Bamberga, and 707 Interamnia, were imaged with the adaptive optics system on the 3 m Shane telescope at Lick Observatory in the near infrared, and their triaxial ellipsoid dimensions and rotational poles have been determined with parametric blind deconvolution. In addition, the dimensions and pole for 1 Ceres are derived from resolved images at multiple epochs, even though it is an oblate spheroid. 相似文献
4.
Philip J. Stooke 《Earth, Moon, and Planets》1994,65(1):31-54
Topographic models of Neptune's small inner satellites Larissa and Proteus were derived from the shapes of limbs and terminators in Voyager images, modified locally to accomodate large craters and ridges. The models are presented here in tabular and graphic form, including the first map of Larissa and the first detailed relief map of Proteus. The shape of Larissa is approximated by a triaxial ellipsoid with axes of 208, 192 and 178 km, but is only weakly constrained by the single available view. The volume is estimated to be 3.5 ± 1.0 × 106 km3. The surface is heavily cratered and may be crossed by one or two poorly seen linear ridges. Proteus is approximated by a triaxial ellipsoid with axes of 424, 390 and 396 km (the latter being the rotation axis dimension). The volume is estimated to be 3.4 ± 0.4 × 107 km3. Its surface appears to be very heavily cratered and extensive evidence for linear fractures is observed despite very low image quality. 相似文献
5.
This paper examines the existence and stability of the out-of-plane equilibrium points of a third body of infinitesimal mass when the equations of motion are written in the three dimensional form under the set up of the Robe’s circular restricted three-body problem, in which the hydrostatic equilibrium figure of the first primary is an oblate spheroid and the second one is a triaxial rigid body under the full buoyancy force of the fluid. The existence of the out of orbital plane equilibrium points lying on the xz-plane is noticed. These points are however unstable in the linear sense. 相似文献
6.
Predictions of two widely-used regolith reflectance models, a numerically exact computer code and an approximate analytic equation, based on the equation of radiative transfer were tested against the measured reflectance of a medium of close-packed spheres, whose properties supposedly can be well-characterized. Surprisingly, the approximate analytic model was a better match to the experimental data than the numerically exact computer solution. Other approximate regolith models were tested briefly with similar results. Discrepancies between the two models and between models and experiment can be explained if the phase functions and albedos of the spheres are not the same as when the particles are isolated. Differences include the absence of the Fraunhoffer diffraction peak, which is an intrinsic assumption of the approximate analytical model but not the exact numerical model, and increased scattering in the mid-range of phase angles, which the approximate analytic model fortuitously describes more accurately than the exact numerical model. These changes may be caused by the close proximity of surrounding particles. If they are taken into account, models based on the radiative transfer equation appear able to quantitatively predict the reflectances of regoliths and other particulate media. Interparticle perturbations are also predicted to cause a coherent backscatter opposition effect in the backward direction that was observed, but its angular width was found to be much larger than predicted by theories for sparsely-packed media. 相似文献
7.
Stability of Surface Motion on a Rotating Ellipsoid 总被引：2，自引：0，他引：2
The dynamical environment on the surface of a rotating, massive ellipsoid is studied, with applications to surface motion on an asteroid. The analysis is performed using a combination of classical dynamics and geometrical analysis. Due to the small sizes of most asteroids, their shapes tend to differ from the classical spheroids found for the planets. The tri-axial ellipsoid model provides a non-trivial approximation of the gravitational potential of an asteroid and is amenable to analytical computation. Using this model, we study some properties of motion on the surface of an asteroid. We find all the equilibrium points on the surface of a rotating ellipsoid and we show that the stability of these points is intimately tied to the conditions for a Jacobi or MacLaurin ellipsoid of equilibria. Using geometrical analysis we can define global constraints on motion as a function of shape, rotation rate, and density, we find that some asteroids should have accumulation of material at their ends, while others should have accumulation of surface material at their poles. This study has implications for motion of a rover on an asteroid, and for the distribution of natural material on asteroids, and for a spacecraft hovering over an asteroid. 相似文献
8.
Takeo Sakurai 《Astrophysics and Space Science》1976,41(1):15-25
We give an analytic expression of the braking torque on a Jacobian ellipsoid rotating steadily in an environmental gas, based on the assumption that the ellipsoid rotates around its shortest principal axis with an angular momentum slightly larger than that at the bifurcation point of the Maclaurin spheroid. This braking torque is effected by the gravitational interaction between the ellipsoid matter and a spiral density configuration in the environmental gas. This spiral configuration, which we call a tidal acoustic wave, is caused by the zone of silence effect in a supersonic flow. With respect to a coordinates system rotating with the ellipsoid, a supersonic region appears outside a certain radius. In this supersonic region, the effect of the non-axisymmetric fluctuation in the ellipsoid potential propagates only along the downstream branches of the Mach waves. This one-sided response of the supersonic part causes the tidal acoustic wave. We restrict ourselves to the equatorial plane, and use an acoustic approximation of the basic equations under the assumption that the self-gravity effect of the environmental gas is negligible in comparison to the main gravity of the ellipsoid. The results are applied to the pre- and post-Main Sequence phases of a rotating star, and relating astrophysical problems are discussed. 相似文献
9.
We have classified orbits in a stationary triaxial stellar system created from a cold dissipationless collapse of 100,000 particles. In order to integrate the orbits, two potential approximations with different fitting functions were used in turn. We found that the relative amount of chaotic versus regular orbits does depend on the chosen approximation of potential, even though both models resulted in very good fits of the underlying exact potential. On the other hand, the content of regular orbits, i.e., its distribution among main families, does not strongly depend of the potential approximation, being therefore a more robust signature of the gravitational system under study. 相似文献
10.
Philip J. Stooke 《Earth, Moon, and Planets》1993,62(3):199-221
Topographic models of Saturn's F-Ring shepherd satellites Prometheus and Pandora were derived from the shapes of limbs and terminators in Voyager images, modified locally to accommodate large craters and ridges. The models are presented here in tabular and graphic form, including the first published maps of the satellites. The shape of Prometheus is approximated by a triaxial ellipsoid with axes of 145, 85 and 60 km. The volume is estimated to be 3.9 ± 1.0 × 105 km3, significantly smaller than previous estimates. A system of prominent ridges and valleys cross the north polar region. Prometheus appears to be less heavily cratered than the other small satellites near the edge of the rings, though this may be an artifact of the low resolution of available images. Pandora is approximated by a triaxial ellipsoid with axes of 114, 84 and 62 km. The volume is estimated to be 3.1 ± 1.0 × 105 km3. Its surface appears to be very heavily cratered. 相似文献
11.
This paper analyzes Robe??s circular restricted three-body problem when the hydrostatic equilibrium figure of the first primary is assumed to be an oblate spheroid, the shape of the second primary is considered as a triaxial rigid body, and the full buoyancy force of the fluid is taken into account. It is found that there is an equilibrium point near the center of the first primary, another equilibrium point exists on the line joining the centers of the primaries and there exist infinite number of equilibrium points on an ellipse in the orbital plane of the second primary. It is also observed that under certain conditions, all these equilibrium points can be stable. The most interesting and distinguishable results of this study are the existence of elliptical points and their stability. 相似文献
12.
J. C. Muzzio H. D. Navone A. F. Zorzi 《Celestial Mechanics and Dynamical Astronomy》2009,105(4):379-395
We used a multipolar code to create, through dissipationless collapses of systems of 106 particles, two cuspy self-consistent triaxial stellar systems with γ ≈ 1. One of the systems has an axial ratio similar to that of an E4 galaxy and it is only mildly triaxial (T = 0.914), while the other one is strongly triaxial (T = 0.593) and its axial ratio lies in between those of Hubble types E5 and E6. Both models rotate although their total angular
momenta are zero, i.e., they exhibit figure rotation. The angular velocity is very small for the less triaxial model and,
while it is larger for the more triaxial one, it is still comparable to that found by Muzzio (Celest Mech Dynam Astron 96(2):85–97,
2006) to affect only slightly the dynamics of a similar model. Except for minor evolution, probably caused by unavoidable
relaxation effects of the N-body code, the systems are highly stable. The potential of each system was subsequently approximated
with interpolating formulae yielding smooth potentials, stationary in frames that rotate with the models. The Lyapunov exponents
could then be computed for randomly selected samples of the bodies that make up the two systems, allowing the recognition
of regular and of partially and fully chaotic orbits. Finally, the regular orbits were Fourier analyzed and classified using
their locations on the frequency map. Most of the orbits are chaotic, and by a wide margin: less than 30% of the orbits are
regular in our most triaxial model. Regular orbits are dominated by tubes, long axis ones in the less triaxial model and short
axis tubes in the more triaxial one. Most of the boxes are resonant (i.e., they are boxlets), as could be expected from cuspy
systems. 相似文献
13.
P. C. Kammeyer 《Celestial Mechanics and Dynamical Astronomy》1978,17(1):37-48
This paper studies families of symmetric periodic satellite orbits around a rotating triaxial ellipsoid. Existence of the families of orbits is established, and Morse's lemma is used to analyze their bifurcations. Several consequences of the many symmetries of the ellipsoid are discussed. 相似文献
14.
In this paper, the restricted problem of three bodies is generalized to include a case when the passively gravitating test particle is an oblate spheroid under effect of small perturbations in the Coriolis and centrifugal forces when the first primary is a source of radiation and the second one an oblate spheroid, coupled with the influence of the gravitational potential from the belt. The equilibrium points are found and it is seen that, in addition to the usual three collinear equilibrium points, there appear two new ones due to the potential from the belt and the mass ratio. Two triangular equilibrium points exist. These equilibria are affected by radiation of the first primary, small perturbation in the centrifugal force, oblateness of both the test particle and second primary and the effect arising from the mass of the belt. The linear stability of the equilibrium points is explored and the stability outcome of the collinear equilibrium points remains unstable. In the case of the triangular points, motion is stable with respect to some conditions which depend on the critical mass parameter; influenced by the small perturbations, radiating effect of the first primary, oblateness of the test body and second primary and the gravitational potential from the belt. The effects of each of the imposed free parameters are analyzed. The potential from the belt and small perturbation in the Coriolis force are stabilizing parameters while radiation, small perturbation in the centrifugal force and oblateness reduce the stable regions. The overall effect is that the region of stable motion increases under the combine action of these parameters. We have also found the frequencies of the long and short periodic motion around stable triangular points. Illustrative numerical exploration is rendered in the Sun–Jupiter and Sun–Earth systems where we show that in reality, for some values of the system parameters, the additional equilibrium points do not in general exist even when there is a belt to interact with. 相似文献
15.
《New Astronomy》2022
We numerically investigate the effect of oblateness parameter on the topology of basins of convergence connected with the equilibrium points in the restricted three-body problem when the test particle is an oblate spheroid, and the influence of the gravitational potential from the belt is taken into consideration. Additionally, the primaries are also not spherical in shape, on the contrary, it is oblate or prolate spheroid. The parametric variation of the equilibrium points, their stability, and the regions of possible motion are illustrated as the function of the parameters involved. The domain of convergence, on the several two dimensional planes, are unveiled by applying the bi-variate version of the Newton–Raphson iterative method. In addition, we perform a systematic investigation in an order to show how the used parameters affect the topology as well as the degree of fractality of basins of convergence. Moreover, it is also unveiled that how the region of the convergence is related with the number of the required iterations to achieve the desired accuracy with the corresponding probability distribution. 相似文献
16.
The collisionless Boltzmann equation governing self-gravitating systems such as galaxies has recently been shown to admit
exact oscillating solutions with planar and spherical symmetry. The relation of the spherically symmetric solutions to the
Virial theorem, as well as generalizations to non-uniform spheres, uniform spheroids and discs form the subject of this paper.
These models generalize known families of static solutions. The case of the spheroid is worked out in some detail. Quasiperiodic
as well as chaotic time variation of the two axes is demonstrated by studying the surface of section for the associated Hamiltonian
system with two degrees of freedom. The relation to earlier work and possible implications for the general problem of collisionless
relaxation in self gravitating systems are also discussed 相似文献
17.
R. Caimmi 《Astronomische Nachrichten》2006,327(9):925-935
In this paper a unified theory of systematically rotating and peculiar motions is developed for homeoidally striated Jacobi ellipsoids, where both real and imaginary rotations are considered. The effect of positive or negative residual motion excess along the equatorial plane is considered to be equivalent either to an additional real or an imaginary rotation, respectively. The principle results consist of (i) the discovery that homeoidally striated Jacobi ellipsoids always admit an adjoint configuration i.e. a classical Jacobi ellipsoid of equal mass and axes; (ii) the establishment of further constraints on the amount of residual velocity anisotropy along the principal axes for triaxial configurations; (iii) the finding that bifurcation points from axisymmetric to triaxial configurations occur as in classical Jacobi ellipsoids, contrary to earlier findings. An interpretation of recent results from numerical simulations on stability is provided in the light of the model. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
18.
The potential‐energy tensors for subsystems are evaluated in the special case of two homogeneous and coaxial ellipsoids, one lying completely within the other, bounded by a heterogeneous homeoid, where the isodensity surfaces are similar and similarly placed with respect to the outer ellipsoid. Two particular density profiles, related to the perfect ellipsoid and the isothermal sphere, respectively, are examined with more detail. 相似文献
19.
This paper examines the existence and linear stability of equilibrium points in the perturbed Robe’s circular restricted three-body problem under the assumption that the hydrostatic equilibrium figure of the first primary is an oblate spheroid, and the shape of the second primary is also an oblate spheroid. The problem is perturbed in the sense that small perturbations given to the Coriolis and centrifugal forces are being considered. Results of the analysis found two axial equilibrium points on the line joining the centre of both primaries. It is further observed that under certain conditions, points on the circle within the first primary are also equilibrium points. The linear stability of this configuration is examined; it is observed that the first axial point is unstable while the second one is conditionally stable and the circular points are unstable. 相似文献
20.
John T. Conway 《Monthly notices of the Royal Astronomical Society》2000,316(3):555-558
An infinite family of heterogeneous spheroids has been found for which exact or closed-form solutions for the Newtonian gravitational potential can be given. The family includes both axisymmetric spheroids and spheroids where the matter density varies harmonically with the azimuthal angle. For the axisymmetric family of spheroids, which have no azimuthal dependence of the density, the potential external to the spheroid is of the same form as the potential exterior to a spheroidal homoeoid. It is therefore constant on the surface of the spheroid and on all external spheroidal surfaces confocal with it. The potential is also constant on all internal confocal spheroidal surfaces, with the value on each confocal surface dependent on the density distribution chosen. However, the density is not constant on either concentric or confocal spheroids. These solutions can be considered to be generalizations of analogous spherical solutions given in a companion paper by Conway. For the classical solutions for homogeneous spheroids, the surface is not equipotential, and these are not included within the new family of solutions, except in the special case of a homogeneous sphere. 相似文献