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Explicit expressions in equinoxial elements are derived for the n-th term in the disturbing potential for three-body and zonal harmonics. A method for recursive computation of the disturbing potential and the partial derivatives is proposed. Preliminary results for an arbitrary geopotential term are obtained.
Two articles discuss the recent experimental work of Hong et al. on the production of amino acids and gas-phase organic compounds from the ultraviolet irradiation of simple gases, with hot hydrogen atoms used as the principal energy conversion agent. The reaction possibilities involving frozen ices are mentioned in both articles, as well as the significance of three-body collisions in this situation.
An investigation regarding the occurrence of Si ions is conducted, taking into account an unusual metal ion structure observed during a meteor shower event. Loss processes involving silicon oxides are considered in connection with a study of the reasons for the unique Si(+) distribution found. It is suggested that below 100 km Si(+) is rapidly depleted by two- and three-body reactions with molecular oxygen, forming SiO2(+) which then recombines.
The origin of comets and the evolution of their orbits are discussed. Factors considered include: the law of survival of comets against ejection on hyperbolic orbits; short-period comets are not created by single close encounters of near-parabolic comets with Jupiter; observable long-period comets do not evolve into observable short-period comets; unobservable long-period comets with perihelia near Jupiter can evolve into observable short-period comets; long-period comets cannot have been formed or created within the planetary region of the solar system (excluding the effects of stellar perturbations); it is possible that some of the short-period comets could have been formed inside the orbit of Neptune; circularly-restricted three-body problem, and its associated Jacobi integral, are not valid approximations to use in studying origin and evolution of comets.
The kinetics of the CN violet band emission produced by the reaction of nitrogen with cynogen is investigated as a function of the densities of atomic carbon and atomic nitrogen and of total pressure. It is shown that CN is formed in a three-body recombination reaction from C and N atoms. The reactions studied have relevance to investigations of the chemistry of interstellar molecules.
Schubart's (1968) model of a planar elliptic restricted three-body problem is used to study the orbital motion of the Hilda asteroids from the Palomar-Leiden Survey. The 3:2 resonant coupling to Jupiter of some of these small asteroids is found to be stable. However, some of the small asteroids with absolute magnitude greater than 15 have large amplitude of variation in their orbital elements in one libration period. Since the lifetime scales against catastrophic collision of the Hilda asteroids are estimated to be several times larger than those of the main-belt objects, a significant portion of these resonant asteroids could be the original members of the Hilda group. From this point of view, it is suggested that such 'size dependence' of resonant orbital motions might be the result of cosmogonic effects of jet-stream accretion.
Variational functionals of Braunn and Rebane (1972) for the imagery-frequency polarizability (IFP) have been generalized by the method of Gramian inequalities to give rigorous upper and lower bounds, valid even when the true (but unknown) unperturbed wavefunction must be represented by a variational approximation. Using these formulas in conjunction with flexible variational trial functions, tight error bounds are computed for the IFP and the associated two- and three-body van der Waals interaction constants of the ground 1(1S) and metastable 2(1,3S) states of He and Li(+). These bounds generally establish the ground-state properties to within a fraction of a per cent and metastable properties to within a few per cent, permitting a comparative assessment of competing theoretical methods at this level of accuracy. Unlike previous 'error bounds' for these properties, the present results have a completely a priori theoretical character, with no empirical input data.
The manner of mass flow in close binary systems is examined with a special view to the role of the so-called critical Roche (or Jacobian) lobe, taking into consideration relevant physical conditions such as radiation pressure that may affect the restricted three-body problem treatment. The mass does not necessarily flow from component one to component two through the L1 point to form a gaseous ring surrounding the latter. These considerations are applied to X-ray binaries with early-type optical components, such as Cyg X-1 (HDE 226868) and 3U 1700 - 37 (HD 153919). In the two bright close binary systems Beta Lyr and UW CMa, which are believed to be undergoing dynamic mass transfer, recent Copernicus observations show that the gas giving rise to the prominent ultraviolet emission lines surrounds the entire binary system rather than merely component two. Implications of these observations are also discussed.
Libration-point capture is analyzed in the framework of the restricted three-body problem in order to obtain general results capable of predicting the major features of an arbitrary postcapture orbit, with specific reference to capture as the presumed mode of origin of Jupiter's outer satellites. Some examples of libration-point capture are computed, the time a body remains captured is estimated, and a long-term numerical integration of orbits is carried out which shows that the equation used to estimate capture lifetimes is quite conservative. An extended capture criterion is proposed and used to demonstrate that direct postcapture orbits lie outside retrograde ones. Mass change involving one or both primaries is evaluated as a means of producing permanent capture, it is found that mass-change effects can produce 'pull-down capture', and consideration is given to the orbital evolution of Jupiter's outer satellites. The effect of drag in the solar nebula or in a nebula around proto-Jupiter on the capture process is briefly investigated. It is concluded that a capture origin for the outer satellites is improbable within the last 4.6 billion years but that either mass change or nebula drag could have been effective in producing capture.
Flight-mechanics problems associated with large-scale transport of lunar mass to a space colony or manufacturing facility are discussed. The proposed transport method involves launch of payloads from a mass-driver on the lunar surface, onto ballistic trajectories to a passive mass-catcher located near the L2 libration point, with the caught mass subsequently being transported to the colony. Arrival velocities at L2, sensitivities in arrival dispersion due to launch errors, and effects of launch site location are treated, via numerically integrated orbits in the restricted three-body problem. From any launch site it is possible to define a target point reached with zero dispersion due to errors in a selected component of launch velocity. Effects of lunar geometrical librations and of obliquity, as well as the conditions for biasing a trajectory away from L2 so as to reduce stationkeeping costs, are dealt with along with transfer orbits from L2 to the colony. The theory of capture and the theory of resonance lead to a colony orbit, with period approximately two weeks, reached from L2 with velocity increment as low as 9.02 m/sec.
A 3-axis active attitude control system with only one rotating part was developed using a momentum wheel with magnetic gimballing capability as a torque actuator for all three body axes. A brief description of magnetic bearing technology is given. It is concluded that based on this technology an integrated energy storage/attitude control system with one air of counterrotating rings could reduce the complexity and weight of conventional systems.
A summary is presented of an investigation which supplements the largely qualitative analysis conducted by Dermott and Gold (1977). Dermott and Gold have attempted to explain the locations of Uranus's rings in terms of resonances between ring particles and pairs of satellites. An equation of motion, analogous to that of a pendulum, is derived, taking into account a study by Wilkens (1933) of possible three-body resonances involving one minor and two major planets. Dermott and Gold had concluded that the observed pattern is probably due primarily to the effect of Ariel-Titania and Ariel-Oberon pairs. However, on the basis of the values derived in the reported investigation it is seen that Miranda plays the key role rather than Ariel, in spite of the small mass of the former. It is concluded that a decisive test of the Dermott-Gold theory has to await further observational details concerning the Uranus's rings.
The role of Miranda-Ariel orbital resonances in determining the structure of the rings of Uranus is discussed. In particular, it is argued that the three-body orbital resonances of Miranda and Ariel may function as a mechanism for the formation of narrow rings, rather than as a mechanism for trapping freely orbiting particles; the formation of narrow rings, in this hypothesis, would involve an inelastic collision process. The narrowness of the resonances may account for the sharply defined ring boundaries.
A model is proposed for single close encounters between two small masses, m1 and m2, which orbit a much larger mass, M. The main new feature of the model is the assumption of conic motion of the center of mass of m1 and m2 in the gravitational field of M. Comparisons of the model with the three-body equations of motion indicate that the model is a useful approximation for m1, m2 not exceeding 0.00001 M. The model is therefore applicable for encounters between bodies of the order of an earth mass or smaller in the presence of the sun. Comparisons are also made of outcomes obtained by the model with outcomes of numerical integration for a large variety of close encounters. The above comparisons reveal that for many purposes the model is an adequate approximation for encounters with an eccentricity of the hyperbolic orbit of m1 about m2 not less than 4.
The reported investigation is concerned with the solution of systems of differential equations which are derived from a Hamiltonian function in the extended phase space. The problem selected involves a one-dimensional perturbed harmonic oscillator. The van der Pol equation considered has an exact asymptotic value for its amplitude. Comparisons are made between a numerical solution and a known analytical solution. In addition to the van der Pol problem, known solutions regarding the restricted problem of three bodies are used as examples for perturbed Keplerian motion. The extended phase space Hamiltonian discussed by Stiefel and Scheifele (1971) is considered. A description is presented of two canonical formulations of the perturbed harmonic oscillator.
A quantitative measure of stability based on Hill's definition is evaluated for direct and retrograde satellite orbits. These orbits are known as Poincare's first kind in the restricted problem of three bodies. Onsets of possible instabilities and captures are established. A critical (maximum) value of the satellites orbital radius is found for stability as a remarkably simple function of the mass-parameter. The results are applied to the natural satellites of the solar system.
Three methods of obtaining stability information on satellite motion are compared by means of numerical and analytical computations. The model of the restricted problem of three bodies is used to describe the motion. Kuiper's (1961) approximate results, Szebehely's (1978) approximate results, and computer solutions obtained by successive iterations show close agreement regarding the maximum values of the orbital radii for stability. The lowest value, i.e., the most conservative estimate, is provided by the simplified form of Szebehely's formula.
The ortho/para molecular hydrogen ratio in the interstellar medium is considered. It is shown that the ortho/para ratio will be 3:1 in practically all chemical reactions, even at relatively low temperatures. Two examples of exothermic processes that will result in the formation of a 3:1 ortho:para ratio, corresponding to a high-temperature equilibrium, are examined: H2 formation via three-body or surface recombination and catalytic recombination involving electrons and H(-) ions. Gas-phase scrambling ion reactions are also discussed, and it is suggested that virtually all the H2 equilibrated via scrambling reactions involving H(+) and H3(+) ions should exist as parahydrogen in the J ? 0 quantum state. Arguments are given that deuterium cannot interfere with the long scrambling chain that results in parahydrogen formation.