Equations of motion for rotating finite bodies in the extended PPN formalism

The equations of motion for rotating finite bodies in the extended PPN formalism of Will and Nordtvedt are developed. These equations may be used in conjunction with precise radio and laser ranging data in solar system tests of viable metric gravitational theories.This paper presents the results of one phase of research carried out at the Jet Propulsion Laboratory, California Institute of Technology, under Contract No. NAS 7-100, sponsored by the National Aeronautics and Space Administration.     

Attitude stability of a symmetric satellite at the equilibrium points in the restricted three-body problem

A problem of attitude motion of the smallest body for the restricted three-body problem is analyzed. Axial symmetry is assumed for the body, and attention is focused on the case in which the symmetry axis is normal to the orbit plane. For libration point satellites, results are similar to those for a satellite in orbit about a single body. However, for orbit equilibrium points lying on the line joining the two larger bodies, attitude stability results depart markedly from those for the two-body problem.This paper presents the results of one phase of research carried out at the Jet Propulsion Laboratory, California Institute of Technology, under Contract No. NAS 7-100, sponsored by the National Aeronautics and Space Administration.     

Reduction,relative equilibria and potential in the two rigid bodies problem

In this paper the problem of two, and thus, after a generalization, of an arbitrary finite number, of rigid bodies is considered. We show that the Newton-Euler equations of motion are Hamiltonian with respect to a certain non-canonical structure. The system possesses natural symmetries. Using them we shown how to perform reduction of the number of degrees of freedom. We prove that on every stage of this process equations of motion are Hamiltonian and we give explicite form corresponding of non-canonical Poisson bracket. We also discuss practical consequences of the reduction. We prove the existence of 36 non-Lagrangean relative equilibria for two generic rigid bodies. Finally, we demonstrate that our approach allows to simplify the general form of the mutual potential of two rigid bodies.     

On lagrange solutions in the problem of three rigid bodies

The present paper is a direct continuation of the paper (Duboshin, 1973) in which was proved the existence of one kind of Lagrange (triangle) and Euler (rectilinear) solutions of the general problem of the motion of three finite rigid bodies assuming different laws of interaction between the elementary particles of the rigid bodies. In particular, Duboshin found that the general problem of three rigid bodies permits such solutions in which the centres of mass of the bodies always form an equilateral triangle or always remain on one straight line, and each body possesses an axial symmetry and a symmetry with respect to the plane of the centres of mass and rotates uniformly around its axis orthogonal to this plane. The conditions for the existence of such solutions have also been found. The results in Duboshin's paper have greatly interested the author of the present paper. In another paper (Kondurar and Shinkarik, 1972) considering a more special problem, when two of the three bodies are spheres, either homogeneous or possessing a spherically symmetric distribution of the densities or of the material points, and the third is an axially symmetrical body possessing equatorial symmetry, the present author obtained analogous solutions of the ‘float’ type describing the motion of the indicated dynamico-symmetrical body in assuming its passive gravitation. In the present paper new Lagrange solutions of the considered general problems of three rigid bodies of ‘level’ type are found when the axes of geometrical and mechanical symmetry of all three bodies always lie in the triangle plane, and the bodies themselves rotate inertially around the symmetry axis, independently of the parameters of the orbital motion of the centres of mass as in the ‘float’ case. The study of particular solutions of the general problem of the translatory-rotary motion of three rigid bodies, which are a generalization of Lagrange solutions, is in the author's opinion, a novelty of some interest for both theoretical and practical divisions of celestial mechanics. For example, in recent times the problem of the libration points of the Earth-Moon system has acquired new interest and value. A possible application which should be mentioned is that to the orbits of artificial satellites near the triangular libration points to serve as observation stations with the aim of specifying the physical parameters in the Earth-Moon system (e.g., the relation of the Earth's mass to the Moon's mass for investigating the orientation of the satellite, solar radiation, etc.).     

Relative Equilibrium in the Three-Body Problem with a Rigid Body

In the three-body problem, where two bodies are punctual and the third is rigid, we prove the existence of some relative equilibrium configurations where the rigid body is either an homogeneous ball, an oblate or an elongated ball. In particular, we found conditions of relative equilibrium of Euler and Lagrange type and several families of relative equilibrium configurations, where the triangle of the two punctual bodies and the mass center of the rigid body is isosceles or having unequal sides. This revised version was published online in July 2006 with corrections to the Cover Date.     

超轻量镜面系统的研制

空间望远镜的研制一直要求系统的轻量化,美国宇航局（NASA）最近研制的韦伯太空望远镜,其主镜系统面密度相对于哈勃空间望远镜已大幅减轻。在韦伯望远镜主镜系统的研制过程中,NASA开展了一系列关于超轻量镜面系统的验证计划,多家机构拿出多个方案参与竞标。本文选取几个比较典型的方案,介绍这些镜面系统的设计思想、结构、材料、加工以及相关测试结果,期望能对国内相关方面的工作提供参考。     

On the Dynamics of a Deformable Satellite in the Gravitational Field of a Spherical Rigid Body

In this paper, a model is developed for the dynamics of a system of two bodies whose material points are under the influence of a central gravitational force. One of the bodies is assumed to be rigid and spherically symmetric, while the other is assumed to be deformable. To develop a tractable model for the system, the deformable body is modeled using Cohen and Muncaster's theory of a pseudo-rigid body. The resulting model of the system has several of the features, such as angular momentum conservation, exhibited by more restrictive models. We also show how the self-gravitation of the deformable body can be accommodated using appropriate constitutive equations for a force tensor. This enables our model to subsume many existing models of ellipsoidal figures of equilibrium. After the model and its conservations have been discussed, attention is restricted to steady motions of the system. Several results, which generalize recent works on rigid satellites, are established for these motions. For a specific choice of constitutive equations for the pseudo-rigid body, we determine the steady motions with the aid of a numerical continuation method. These results can also be considered as generalizations of earlier works on Roche's ellipsoids of equilibrium.     

Space Weathering of Small Solar System Bodies

Micrometeorite bombardment and irradiation by solar wind and cosmic ions cause variations in the optical properties of the small Solar System bodies surface materials. These space weathering processes are reasonably well understood for the Moon and S-type asteroids. The research is based on laboratory experiments performed by several groups on meteorites and minor bodies surface analogues, whose results have been applied to the spectral modeling and interpretation of observations from large surveys and space missions. Recent results from young asteroidal families, and the relation between spectral slopes and dynamical properties, have stressed the role of the solar wind exposure timescale. Space weathering processes remain poorly investigated in the case of other types of asteroids, and they are still unclear in the case of outer Solar System bodies, due to a strong dependence of the weathering process on the original composition.     

A programming system for analytical series expansions on a computer

A programming system is described for the manipulation of Poisson series on a computer. The general structure is described together with the most important individual subroutines. The system exists in two versions, one with 3 angular and 3 polynomial variables and the other with twice as many variables. The programming has been done first in FORTRAN IV, but the most crucial subroutines have been rewritten in machine language for more efficiency. The storage mechanism is such that obsolete series can be erased from the main memory in order to make room for new series to be created.This paper presents the results of one phase of research carried out at the Jet Propulsion Laboratory, California Institute of Technology, under Contract No. NAS 7-100, sponsored by the National Aeronautics and Space Administration.     

Apollo 12 thermal radiation properties

The spectral and total thermal radiation properties as a function of bulk density are presented for lunar fines from the Apollo 12 mission. The total emittance is presented as a function of temperature from 90 to 400°K and the solar reflectance (albedo) for near normal incidence.This research was supported by the National Aeronautics and Space Administration under Grant NGR 18-001-060.     

Iowa catalog of solar X-ray flux (2–12 Å)

The absolute X-ray flux from the whole disc of the sun in the wave length range 2 to 12 Å has been observed for a prolonged period by University of Iowa equipment on the earth-orbiting satellite Explorer 33 and the moon-orbiting satellite Explorer 35, both of the Goddard Space Flight Center of the National Aeronautics and Space Administration. The observations are continuing at the date of writing (July 1969). A comprehensive catalog of the flux F (2–12 Å) is being produced. The observational technique and the scheme of reducing data are described herein. Sample tabulations and plots are given. A catalog of tabular and graphical data with a time resolution of either 81.8 or 163.6 sec has been completed for the following periods: From Explorer 33: 2 July 1966 to 27 July 1967 From Explorer 35: 26 July 1967 to 18 September 1968 These blocks of data have been delivered to the National Space Science Data Center National Aeronautics and Space Administration Goddard Space Flight Center Greenbelt, Maryland 20771, U.S.A. and made available through that agency to interested workers in solar and ionospheric physics. Further blocks of data will be made available as they are completed. An abridged summary of principal flares is published in the monthly Solar-Geophysical Data of the U.S. Department of Commerce, Environmental Science Services Administration.     

Attitude stability of a rigid body placed at an equilibrium point in the restricted problem of three bodies

This paper is based on the restricted problem of three bodies with the unusual feature that the lightest particle is replaced by a rigid body. The attitude stability of the body is considered when its centre of mass is located at one of the equilibrium points. The stable attitude is determined when the satellite is stationary relative to the primaries. It is found that for some bodies there are two such attitudes, and these are determined.     

The general motion of three mutually-interacting,axisymmetric spherical rigid bodies

In this paper, the translational-rotational motions of an axisymmetric rigid body and two spherical rigid bodies under the influence of their mutual gravitational attraction are considered. The equations of motion in the canonical elements of Delaunay-Andoyer are obtained. The elements of motion in the zero and first approximations can be determined.     

A more general system for Poisson Series manipulation

We describe the design of a working Poisson Series Processor that is more general than others in use today. We try to show that the price of generality is worth paying in active research areas in celestial mechanics.This work was supported in part by grant NGR 09-015-002 from the National Aeronautics and Space Administration.     

On the minimum intensity of the Na D2-5890 Å line in sunspot umbra

The line-to-continuum intensity ratio for the center of the Na D₂ absorption line in a spot of area 20 × 10^–6 in the Rome Group 5847 was found to be 0.033±0.05 on 6–7/7/70 by two methods.Goethe Link Publication No. 139. This work was supported by the National Science Foundation and the National Aeronautics and Space Administration.     

Simulation of the full two rigid body problem using polyhedral mutual potential and potential derivatives approach

Herein we investigate the coupled orbital and rotational dynamics of two rigid bodies modelled as polyhedra, under the influence of their mutual gravitational potential. The bodies may possess any arbitrary shape and mass distribution. A method of calculating the mutual potential’s derivatives with respect to relative position and attitude is derived. Relative equations of motion for the two body system are presented and an implementation of the equations of motion with the potential gradients approach is described. Results obtained with this dynamic simulation software package are presented for multiple cases to validate the approach and illustrate its utility. This simulation capability is useful both for addressing questions in dynamical astronomy and for enabling spacecraft missions to binary asteroid systems.     

Counting relative equilibrium configurations of the full two-body problem

Consider a system of two rigid, massive bodies interacting according to their mutual gravitational attraction. In a relative equilibrium motion, the bodies rotate rigidly and uniformly about a fixed axis in \({\mathbb {R}}^3\). This is possible only for special positions and orientations of the bodies. After fixing the angular momentum, these relative equilibrium configurations can be characterized as critical points of a smooth function on configuration space. The goal of this paper is to use Morse theory and Lusternik–Schnirelmann category theory to give lower bounds for the number of critical points when the angular momentum is sufficiently large. In addition, the exact number of critical points and their Morse indices are found in the limit as the angular momentum tends to infinity.     

The libration points of axisymmetric satellite in the gravitation field of two triaxial rigid bodies

In this paper we consider the restricted problem of three rigid bodies (an axisymmetric satellite in the gravitation field of two triaxial primaries). The collinear and triangular equilibrium solutions are obtained. The effect of the primaries on the location of the libration points of a spherical satellite has been studied numerically.     

Two prominence eruptions and the problem of emission

Two flare unconnected eruptions on January 15 and 29, 1968, are discussed. The first is a filament which turns bright and erupts upward, reappearing an hour later. The second is a large eruptive arch seen against the disk. The arch is bright at the top of its trajectory, turns dark, but produces chromospheric emission at the point of impact. The emission at the top of the arch is ascribed to the velocity shift of the illuminating chromospheric Ha line. It is shown that such emission will occur only if the motion is transverse to the line of sight and the prominence is optically thin.This research was supported by the National Science Foundation under Grant 1472, the Advanced Research Projects Agency under the Office of Naval Research Grant N00014-67-C-0140, and the National Aeronautics and Space Administration under Grant NGR 05 002 034.