Collinear equilibrium points in the elliptic R3BP with oblateness and radiation

We have studied the positions and stability of the collinear equilibrium points, L_1,2,3 of an infinitesimal body in the elliptic restricted three-body problem (ER3BP) when both primaries of the system are luminous and oblate spheroids moving in elliptic orbits around their common center of mass. We observe that their positions are affected by the radiation pressure forces, oblateness and the eccentricity of the orbits, but the stability character remains unchanged and are unstable. The effects of the parameters involved on the collinear points, in particular for the binary systems Achird, Luyten 726-8, Kruger 60, Alpha Centauri AB and Xi Bootis, and their stability in general have been investigated numerically using the analytical results obtained.     

Mapping orbits around the asteroid 2001SN263

The present paper has the goal of mapping orbits, with respect to the perturbations, for a spacecraft traveling around the asteroid 2001SN₂₆₃. This asteroid is a triple system, which center of mass is in an elliptic orbit around the Sun. The perturbations considered in the present model are the ones due to the oblateness of the central body, the gravity field of the two satellite bodies (Beta and Gamma), the Sun, the Moon, the asteroids Vesta, Pallas and Ceres and all the planets of the Solar System. This mapping is important, because it shows the relative importance of each force for a given orbit for the spacecraft, helping to make a decision about which forces need to be included in the model for a given accuracy and nominal orbit. Another important application of this type of mapping is to find orbits that are less perturbed, since it is expected that those orbits have good potential to require a smaller number of station-keeping maneuvers. Simulations under different conditions are made to find those orbits. The main reason to study those trajectories is that, currently, there are several institutions in Brazil studying the possibility to make a mission to send a spacecraft to this asteroid (the so-called ASTER mission), because there are many important scientific studies that can be performed in that system. The results showed that Gamma is the main perturbing body, followed by Beta (10 times smaller) and the group Sun–Mars-oblateness of Alpha, with perturbations 1000 times weaker than the effects of Gamma. The other bodies have perturbations 10⁷ times smaller. The results also showed that circular and polar orbits are less perturbed, when compared to elliptical and equatorial orbits. Regarding the semi-major axis, an internal orbit is the best choice, followed by a larger external orbit. The inclination of the orbit plays an important role, and there are values for the inclination where the perturbations show minimum and maximum values, so it is important to make a good decision on those values.     

A deformation model of flexible,HAMR objects for accurate propagation under perturbations and the self-shadowing effects

A new type of space debris in near geosynchronous orbit (GEO) was recently discovered and later identified as exhibiting unique characteristics associated with high area-to-mass ratio (HAMR) objects, such as high rotation rates and high reflection properties. Observations have shown that this debris type is very sensitive to environmental disturbances, particularly solar radiation pressure, due to the fact that its motion depends on the actual effective area, orientation of that effective area, reflection properties and the area-to-mass ratio of the object is not stable over time. Previous investigations have modelled this type of debris as rigid bodies (constant area-to-mass ratios) or discrete deformed body; however, these simplifications will lead to inaccurate long term orbital predictions. This paper proposes a simple yet reliable model of a thin, deformable membrane based on multibody dynamics. The membrane is modelled as a series of flat plates, connected through joints, representing the flexibility of the membrane itself. The mass of the membrane, albeit low, is taken into account through lump masses at the joints. The attitude and orbital motion of this flexible membrane model is then propagated near GEO to predict its orbital evolution under the perturbations of solar radiation pressure, Earth’s gravity field (J₂), third body gravitational fields (the Sun and Moon) and self-shadowing. These results are then compared to those obtained for two rigid body models (cannonball and flat rigid plate). In addition, Monte Carlo simulations of the flexible model by varying initial attitude and deformation angle (different shape) are investigated and compared with the two rigid models (cannonball and flat rigid plate) over a period of 100?days. The numerical results demonstrate that cannonball and rigid flat plate are not appropriate to capture the true dynamical evolution of these objects, at the cost of increased computational time.     

Experimental study of impact-cratering damage on brittle cylindrical column model as a fundamental component of space architecture

The cylindrical column of brittle material processed from soil and rock is a fundamental component of architectures on the surface of solid bodies in the solar system. One of the most hazardous events for the structure is damaging by hypervelocity impacts by meteoroids and debris. In such a background, cylindrical columns made of plaster of Paris and glass-bead-sintered ceramic were impacted by spherical projectiles of nylon, glass, and steel at velocity of about 1–4.5 km/s. Measured crater radii, depth, and excavated mass expressed by a function of the cylinder radius are similar irrespective of the target material, if those parameters are normalized by appropriate parameters of the crater produced on the flat-surface target. The empirical scaling relations of the normalized crater radii and depth are provided. Using them, crater dimensions and excavated mass of crater on cylindrical surface of any radius can be predicted from the existing knowledge of those for flat surface. Recommendation for the minimum diameter of a cylinder so as to resist against a given impact is provided.     

Stability and mass flow in Saturn's rings

Besides gravitational effects, interesting electrodynamical processes could also take place in the vicinity of the rings of Saturn. In part, this is because of the electrostatic charging of the ring particles by the magnetospheric and ionospheric plasma, and in part, the generation of impact plasma by meteoroid bombardment at the ring plane could lead to strong coupling between the rings and the ionosphere via a variety of current systems. The mass transport and angular momentum transfer in association with the ring-ionosphere coupling may cause quite large changes in the ring configuration over the age of the solar system. The presence of the sharp boundary between the B and the C rings perhaps is a good example. To highlight these new developments, we describe several of the electrodynamical mechanisms (with emphasis on their corresponding electric fields and current systems) which have been postulated to be of importance in determining the mass transport of the ring system. Further points are made that, besides mass exchange between the rings and the planetary atmosphere, the mass injection from the rings could also have significant effect on the mass and energy budget of the magnetosphere, maintenance of the E ring, the Titan hydrogen torus as well as aeronomic process in the upper atmosphere of Titan.     

Symmetry,reduction and relative equilibria of a rigid body in the J2 problem

The J₂ problem is an important problem in celestial mechanics, orbital dynamics and orbital design of spacecraft, as non-spherical mass distribution of the celestial body is taken into account. In this paper, the J₂ problem is generalized to the motion of a rigid body in a J₂ gravitational field. The relative equilibria are studied by using geometric mechanics. A Poisson reduction process is carried out by means of the symmetry. Non-canonical Hamiltonian structure and equations of motion of the reduced system are obtained. The basic geometrical properties of the relative equilibria are given through some analyses on the equilibrium conditions. Then we restrict to the zeroth and second-order approximations of the gravitational potential. Under these approximations, the existence and detailed properties of the relative equilibria are investigated. The orbit–rotation coupling of the rigid body is discussed. It is found that under the second-order approximation, there exists a classical type of relative equilibria except when the rigid body is near the surface of the central body and the central body is very elongated. Another non-classical type of relative equilibria can exist when the central body is elongated enough and has a low average density. The non-classical type of relative equilibria in our paper is distinct from the non-Lagrangian relative equilibria in the spherically-simplified Full Two Body Problem, which cannot exist under the second-order approximation. Our results also extend the previous results on the classical type of relative equilibria in the spherically-simplified Full Two Body Problem by taking into account the oblateness of the primary body. The results on relative equilibria are useful for studies on the motion of many natural satellites, whose motion are close to the relative equilibria.     

Electrostatic discharges in Saturn's B-ring

The Voyager observations of electrical discharges in Saturn's rings strongly support earlier speculations on the role played by electrostatics, magnetic fields, and lightning phenomena in the primitive solar system. They also suggest conditions then by direct analogy rather than by extrapolating backwards through time from conditions now. The observed discharges show a pronounced 10^h periodicity, which suggests a source in Keplerian orbit at 1.80 ± 0.01 Saturn radii (1 R_S = 60,330 km). In that region, the B ring is thicker than optical depth 1.8 for about 5,000 km. At 1.805 ± 0.001 Saturn radii, however, the ring is virtually transparent for a gap of width 200 m. We conclude that a small satellite orbits Saturn at that radius and clears the gap. The gap edges must prevent diffusive filling of the gap by fine material which is especially abundant at this position in the rings and would otherwise destroy the gap in minutes. The discharges represent the satellite's interaction with the outer edge of the gap. Spoke formation may involve the interaction of ring material in the vicinity of the gap.     

Dynamics of a spacecraft and normalization around Lagrangian points in the Neptune–Triton system

The problem of a spacecraft orbiting the Neptune–Triton system is presented. The new ingredients in this restricted three body problem are the Neptune oblateness and the high inclined and retrograde motion of Triton. First we present some interesting simulations showing the role played by the oblateness on a Neptune’s satellite, disturbed by Triton. We also give an extensive numerical exploration in the case when the spacecraft orbits Triton, considering Sun, Neptune and its planetary oblateness as disturbers. In the plane a × I (a = semi-major axis, I = inclination), we give a plot of the stable regions where the massless body can survive for thousand of years. Retrograde and direct orbits were considered and as usual, the region of stability is much more significant for the case of direct orbit of the spacecraft (Triton’s orbit is retrograde). Next we explore the dynamics in a vicinity of the Lagrangian points. The Birkhoff normalization is constructed around L₂, followed by its reduction to the center manifold. In this reduced dynamics, a convenient Poincaré section shows the interplay of the Lyapunov and halo periodic orbits, Lissajous and quasi-halo tori as well as the stable and unstable manifolds of the planar Lyapunov orbit. To show the effect of the oblateness, the planar Lyapunov family emanating from the Lagrangian points and three-dimensional halo orbits are obtained by the numerical continuation method.     

Particle erosion mechanisms and mass redistribution in Saturn's rings

A variety of physical processes can erode the surfaces of planetary ring particles. According to current estimates, the most efficient of these over the bulk of Saturn's rings is hypervelocity impact by 100 micron to one centimeter radius meteoroids. The atoms, molecules, and fragments ejected from ring particles by erosion arc across the rings along elliptical orbits to produce a tenuous halo of solid ejecta and an extensive gaseous atmosphere. Continuous exchange of ejecta between different ring regions can lead to net radial transport of mass and angular momentum. The equations governing this ballistic transport process are presented and discussed. Both numerical and analytic studies of idealized ring systems illustrate that ballistic transport can cause significant mass redistribution in the rings, especially near regions of high density contrast, such as the inner edges of the A and B rings. Ejecta exchanges can also alter local particle sizes and compositions and may produce pulverized regoliths at least several centimeters deep. The meteoroid erosion rate is so high that significant global torques and mass loss are possible on times shorter than a solar system life time.     

On the Lagrange and Hill stability of motion in the three-body problem

In the three-body problem, we consider the Lagrange and Hill stability including the Lagrange stability for the manifold of symmetric motions that exists in the case where two of three bodies have equal masses. To analyze the stability, in addition to integrals of energy and angular momentum we use the Lagrange–Jacobi equality. We prove theorems on the Lagrange and Hill stability. The theorem on the Hill stability has effective application in the case where the mass of a body is much less than masses of two other bodies. In this case, as it is known, the model of the restricted three-body problem is usually applied.     

Analytic and numerical treatment of motion of dust grain particle around triangular equilibrium points with post-AGB binary star and disc

This paper investigates the motion around the triangular equilibrium points, of a passively gravitating dust particle in the gravitational field of a low-mass post-AGB binary system, surrounded by circumbinary disc. The two bodies of the binary are modeled as a triaxial star and a radiating-oblate star. Due to small deviation of disc stars on circular orbits, we have assumed that the Coriolis and centrifugal forces of the stars are slightly perturbed. The triangular equilibrium points of the particle are found. These points are defined by, triaxiality of the primary star, oblateness and radiation of the secondary one and the gravitational potential from the disc mass. Further, when the disc mass increases, the particle moves nearer to the stars and farther away from the disc. In general, these equilibrium points are linearly stable when μ < μ_C; where μ is the mass ratio and μ_C is the critical mass function, defined by the parameters of the system. The effects of each of these parameters on the size of the stability region are stated, and the periodic motion around the stable points is examined. It is seen that the orbits are ellipses, and the orientation, eccentricities, lengths of the semi-major and semi-minor axes are influenced by the parameters of the problem. In particular, for our numerical linear stability analysis, we have taken an extremely depleted pulsating star, IRAS 11472-0800 as the post-AGB triaxial star, with a weakly-radiating young white dwarf star; G29-38 as the secondary. For this system, the stability result of the triangular points comes out different. Here, μ_C < μ throughout the entire range of the mass ratio and the critical mass function. Hence, the triangular equilibrium points are unstable. The stability of the orbits is tested using the Poincaré surfaces of section (Pss). The region of stability is controlled by the introduced parameters and the Jacobi constant.     

Planetary rings

The individual ring systems are described with dust/magnetosphere interactions high-lighted somewhat. Jupiter's main ring is tenuous and enveloped by the magnetosphere; it principally contains micron-sized silicate grains. A vertically-extended, radially-localized “halo” of submicron particles lies inward of the main ring while a newly-discovered very faint ring lies outside it. The classical Saturnian system is composed of water ice chunks with sizes principally between cm and meters. Satellite resonances determine some ring structure but most is not understood. The faint exterior rings (E, G, F and one just identified between the A and F rings) are intimately associated with magnetospheric particles and contain mainly small grains, which are also prominent in the “spokes” located in the dense, middle portion of the B ring. Most of the nine narrow Uranian rings are slightly inclined and eccentric, and presumably lie within the putative Uranian magnetosphere. Particles are likely carbonaceous; sizes are thought to be larger than microns.     

Gravimorphogenesis and ultrastructure of the fungus Flammulina velutipes grown in space, on clinostats and under hyper-g conditions.

The D-2-mission provided the facilities to cultivate the higher basidomycete Flammulina velutipes (Agaricales) in space for about 8 days. Gravimorphogenesis of developing fruiting body primordia in weightlessness was documented in comparison to cultures incubated on a 1xg reference centrifuge in space. Chemical fixation of fruiting bodies took place for later ultrastructural analysis. The microgravity grown fruiting bodies exhibited random orientation compared to the 1xg-cultures where fruiting bodies showed exactly negative gravitropic orientation. Weightlessness did not impair fruiting body morphogenesis and growth although flat and helically twisted stipes were observed. Ultrastructural analyses of microgravity-, 1xg- and 20xg-samples did not reveal sedimentable cell components. Gravitropic bending involves growth inhibition at the upper side of a horizontally oriented transition zone, the graviperceptive region of the stipe. The fastest ultrastructural response to the altered direction of the accelerational force is the accumulation of cytosolic vesicles at the lower part of this region. They contribute to the expansion of the central vacuole and therefore to the differential enlargement of the lower side of the stipe.     

Spin deployment of Hub-Spoke tethered satellite formation with sliding mode tether tension control

This work develops a tension control strategy for deploying an underactuated spin-stable tethered satellite formation in the hub-spoke configuration. First, the Lagrange equation is used to model the spin-deployment dynamics of the tethered satellite formation. The central spacecraft is modeled as a rigid body, and the tethered subsatellites are simplified as lumped masses. Second, a pure tension controller has been proposed to suppress the tether libration motion in the deployment without thrusting at the subsatellites. A nonlinear sliding mode control is introduced in the tension controller for the underactuated system to suppress the periodic gravitational perturbations caused by the spinning hub-spoke tethered satellite formation. The unknown upper bounds of the perturbations are estimated by adaptive control law. The bounded stability of the closed-loop tension controller has been proved by the Lyapunov theory. Finally, numerical simulations validate the effectiveness and robustness of the proposed controller, i.e., tethers are fully deployed stably to the desired hub-spoke configuration.     

The problems of simulation of planetary systems accumulation processes

Evolution of a system consisting of a great number of bodies that are gravitationally interacting and aggregating in contacts is considered. Body motions take place in the gravitational field of a central massive body (Sun or planet) in the same plane and at the initial time of system evolution orbits of all bodies are circular. It is shown that during evolution of the protoplanetary cloud, ring zones of matter rarefaction and condensation develop. Development of the condensation zones leads to the formation of planets, the most part of which acquire a direct rotation about their axes. In the case under consideration, approximate agreement between the law of planetary distances and that of geometric progression takes place as it is observed in planetary and satellite systems. The formation of the terrestrial planets and Jovian planets has been simulated. The principal numerical results have been obtained through digital simulation of planetary accumulation.     

Dust ring/torus around Mars,waiting for detection by NOZOMI

Two small satellites of Mars, Phobos and Deimos, can be dust sources around Mars. Orbits of circummartian dust particles are controlled by solar radiation pressure as well as Martian oblateness. Their orbital eccentricity and inclination can be enhanced greatly by the orbital resonance. Particles from Phobos would form a thin dust ring where dust radius is dominant in 20–200μm. On the other hand, particles from Deimos would form an extended dust torus. Collisions of ring particles on Phobos and Deimos may be the most important dust source. The upper limit of dust production from this self-sustaining mechanism can be estimated from the erosion rate of Phobos. Japanese Mars mission NOZOMI (PLANET-B) could discover dust ring/torus through direct detection by MDC (Mars Dust Counter).     

Heliotropic dust rings for Earth climate engineering

This paper examines the concept of a Sun-pointing elliptical Earth ring comprised of dust grains to offset global warming. A new family of non-Keplerian periodic orbits, under the effects of solar radiation pressure and the Earth’s J₂ oblateness perturbation, is used to increase the lifetime of the passive cloud of particles and, thus, increase the efficiency of this geoengineering strategy. An analytical model is used to predict the orbit evolution of the dust ring due to solar-radiation pressure and the J₂ effect. The attenuation of the solar radiation can then be calculated from the ring model. In comparison to circular orbits, eccentric orbits yield a more stable environment for small grain sizes and therefore achieve higher efficiencies when the orbit decay of the material is considered. Moreover, the novel orbital dynamics experienced by high area-to-mass ratio objects, influenced by solar radiation pressure and the J₂ effect, ensure the ring will maintain a permanent heliotropic shape, with dust spending the largest portion of time on the Sun facing side of the orbit. It is envisaged that small dust grains can be released from a circular generator orbit with an initial impulse to enter an eccentric orbit with Sun-facing apogee. Finally, a lowest estimate of 1 × 10¹² kg of material is computed as the total mass required to offset the effects of global warming.     

Numerical simulation of three-dimensional reconnection due to the instability of collisionless current sheets

Based on analytical calculations we have currently argued that spontaneous reconnection through thin collisionless current sheets is an essentially three-dimensional (3 D) process (Büchner, 1996 a, b). Since 3 D kinetic PIC codes have become available, the three dimensional nature of the collisionless current sheet decay are now illustrated by numerical simulations (Büchner and Kuska, 1996; Pritchett and Coroniti, 1996; Zhu and Winglee, 1996). While the latter two claim a coupling to a longer wavelength kink mode as a main factor, destabilizing thin current sheets in 3 D, our simulations have revealed that even shorter scale perturbations in the current direction suffice to destabilize thin sheets very quickly. Since past simulation runs, however, were limited to mass ratios near unity, the influence of the electrons was not treated adequately. We have now investigated the stability of thin collisionless current sheets including 64 times lighter negatively charged particles. We can now show that while the two-dimensional tearing instability slows down for M = M_p/m_e = 64, the three-dimensional current sheet decay is a much faster process — practically as fast as the mass ratio M = 1 3 D sheet decay, even without kinking the sheet. We further conclude that, unlike the two-dimensional tearing instability, the three-dimensional decay of thin current sheets is not controlled by the electrons. For a sheet width comparable with the ion inertial length, we also recovered signatures of the Hall effect as predicted by Vasyliunas (1975) in the mass ratio M = 64 case. The ion inertial length seems to be the critical scale at which the sheet starts to decay.     

红外地球敏感器测量值修正算法及其应用研究

 圆锥扫描式红外地球敏感器常用于测算地心矢量,而地球扁率影响地心矢量精度。研究了基于地球扁率的地心矢量的修正算法,并将该方法应用于双圆锥红外地球敏感器,给出了考虑扁率的地心矢量计算方法。仿真结果表明,该方法能有效地提高地心矢量的计算精度。     

半浮区液桥自由面振荡特征

使用一套双路同步显微放大录像及图像处理系统,研究了夹角为90°的两个竖直剖面沿轴向不同高度液桥自由表面的位移振荡,得到轴向不同高度上的环向相位差,观测到在振荡周期内液桥表面轮廓线在不同时刻均不相交的特点。实验结果表明,液桥自由面振荡除具有径向扰动及轴向振荡变化外,还存在环向波动变化。根据实验结果,讨论了环向波动基本变化规律以及本实验在测量精度和测量误差方面存在的问题。