Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Periodic orbit theory”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 181 records · Page 10

Empirical data from Oort's cloud

Empirical evidence on the size and origin of the Oort cloud of comets is compared with theories on the origin of the Oort cloud. Data on the binding energy of the very long period comets indicate that the Oort cloud is five times smaller than previously thought and that the mean velocity perturbation introduced by stellar passages is smaller than Oort believed. The bimodal brightness distribution of 'new' comets indicates that their formation mechanism is straightforward accretion without later fragmentation. Data on retrograde versus prograde orbits and their relevance to the rotation of the Oort cloud are examined. Models of the solar nebula are discussed in the light of the foregoing evidence.

Desemme, A. H.↗

Cometary dynamics

Modern theories of cometary dynamics are described. Attention is given to Oort's hypothesis that the Solar System is surrounded by a spherically symmetrical cloud of about 10 to the 11th to 10 to the 12th comets extending out to interstellar distances. Dynamical modelling and statistical analyses of cometary motion have confirmed the ability of the Oort hypothesis to explain the observed distribution of energies for the long-period cometary orbits. Some of the sources cometary motion perturbations are discussed, including: random passing stars; interstellar clouds; and the galactic gravitational field. Perturbations in cometary motion in the planetary region are attributed to the gravitational fields of the major planets and nongravitational forces resulting from jetting of volatiles on the surfaces of cometary nuclei. Observational evidence for the existence of a massive inner Oort cloud extending from just beyond the orbit of Neptune to 10,000 AU is presented.

Weissman, P. R.↗

Accurate parameterization of the kinetic energy functional

The absence of a reliable formulation of kinetic energy density functional has hindered the development of orbital free density functional theory. Using the data-aided learning paradigm, we propose a simple prescription to accurately model the kinetic energy density of any system. Our method relies on a dictionary of functional forms for local and nonlocal contributions which have been proposed in the literature and the appropriate coefficients are calculated via a linear regression framework. To model the nonlocal contributions, we explore two new nonlocal functionals - a functional that captures fluctuations in electronic density and a functional that incorporates gradient information. Since, the analytical functional forms of the kernels present in these nonlocal terms are not known from theory, we propose a basis function expansion to model these seemingly difficult nonlocal quantities. This allows us to easily reconstruct kernels for any system using only a few structures. The proposed method is able to learn kinetic energy densities and total kinetic energies of molecular and periodic systems, such as H 2 , LiH, LiF and a one-dimensional chain of 8 hydrogens using data from Kohn-Sham density functional theory calculations for only a few structures. For the ease of reproduction, codes used to generate the models are provided in the supporting materials.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

On the Orbital Elements of the Two-body Problem with Slowly Decreasing Mass: The Gyldén–Mestchersky Cases

We study the dynamics of two-body problems with gravitational parameters μ = μ(t) decreasing with the time. In particular we focus our attention on the behavior of the orbital elements in the first two Gyldén–Mestchersky cases: in the first case (GM-I) μ(t)=μ{sub 0}(1+αt){sup −1}, where μ{sub 0} is the constant initial value of the parameter and α a small positive constant. In the second case (GM-II) μ(t)=μ{sub 0}(1+2αt){sup −1/2}. In the GM-I problem, using a suitable transformation of the radius vector and the physical time, which reduces the original problem to a pure Kepler problem, we are able to obtain explicit analytical expressions of the orbital elements that hold true for all t⩾0 and therefore derive their asymptotic behavior. Moreover using the alternative scaled time these expressions show clearly their periodic and secular terms. For the GM-II problem a similar transformation to the GM-I problem leads to a perturbed Kepler problem with a radial direction perturbation. Although exact solutions in terms of elliptic functions may be obtained, the use of some integrals leads to analytical expressions of orbital elements that allow us to study their behavior. Finally, some comparisons between the time evolution of elements in both problems are also included.

79 ASTRONOMY AND ASTROPHYSICS↗

Stability of a rigid rotor supported on oil-film journal bearings under dynamic load

Most published work relating to dynamically loaded journal bearings are directed to determining the minimum film thickness from the predicted journal trajectories. These do not give any information about the subsynchronous whirl stability of journal bearing systems since they do not consider the equations of motion. It is, however, necessary to know whether the bearing system operation is stable or not under such an operating condition. The stability characteristics of the system are analyzed. A linearized perturbation theory about the equilibrium point can predict the threshold of stability; however it does not indicate postwhirl orbit detail. The linearized method may indicate that a bearing is unstable for a given operating condition whereas the nonlinear analysis may indicate that it forms a stable limit cycle. For this reason, a nonlinear transient analysis of a rigid rotor supported on oil journal bearings under: (1) a unidirectional constant load, (2) a unidirectional periodic load, and (3) variable rotating load are performed. The hydrodynamic forces are calculated after solving the time-dependent Reynolds equation by a finite difference method with a successive overrelaxation scheme. Using these forces, equations of motion are solved by the fourth-order Runge-Kutta method to predict the transient behavior of the rotor. With the aid of a high-speed digital computer and graphics, the journal trajectories are obtained for several different operating conditions.

Majumdar, B. C.↗

Hidden slow pulsars in binaries

The recent discovery of the binary containing the slow pulsar PSR 1718-19 orbiting around a low-mass companion star adds new light on the characteristics of binary pulsars. The properties of the radio eclipses of PSR 1718-19 are the most striking observational characteristics of this system. The surface of the companion star produces a mass outflow which leaves only a small 'window' in orbital phase for the detection of PSR 1718-19 around 400 MHz. At this observing frequency, PSR 1718-19 is clearly observable only for about 1 hr out of the total 6.2 hr orbital period. The aim of this Letter is twofold: (1) to model the hydrodynamical behavior of the eclipsing material from the companion star of PSR 1718-19 and (2) to argue that a population of binary slow pulsars might have escaped detection in pulsar surveys carried out at 400 MHz. The possible existence of a population of partially or totally hidden slow pulsars in binaries will have a strong impact on current theories of binary evolution of neutron stars.

Tavani, Marco↗

Martian cratering. II - Asteroid impact history.

This paper considers the extent to which Martian craters can be explained by considering asteroidal impact. Sections I, II, and III of this paper derive the diameter distribution of hypothetical asteroidal craters on Mars from recent Palomar-Leiden asteroid statistics and show that the observed Martian craters correspond to a bombardment by roughly 100 times the present number of Mars-crossing asteroids. Section IV discusses the early bombardment history of Mars, based on the capture theory of Opik and probable orbital parameters of early planetesimals. These results show that the visible craters and surface of Mars should not be identified with the initial, accreted surface. A backward extrapolation of the impact rates based on surviving Mars-crossing asteroids can account for the majority of Mars craters over an interval of several aeons, indicating that we see back in time no further than part-way into a period of intense bombardment. An early period of erosion and deposition is thus suggested. Section V presents a comparison with results and terminology of other authors.

Hartmann, W. K.↗

Ocean tides for satellite geodesy

Spherical harmonic tidal solutions have been obtained at the frequencies of the 32 largest luni-solar tides using prior theory of the author. That theory was developed for turbulent, nonglobal, self-gravitating, and loading oceans possessing realistic bathymetry and linearized bottom friction; the oceans satisfy no-flow boundary conditions at coastlines. In this theory the eddy viscosity and bottom drag coefficients are treated as spatially uniform. Comparison of the predicted degree-2 components of the Mf, P1, and M2 tides with those from numerical and satellite-based tide models allows the ocean friction parameters to be estimated at long and short periods. Using the 32 tide solutions, the frequency dependence of tidal admittance is investigated, and the validity of sideband tide models used in satellite orbit analysis is examined. The implications of admittance variability for oceanic resonances are also explored.

Dickman, S. R.↗

Long period perturbations of earth satellite orbits

All the equations involved in extending the PS phi solution to include the long periodic and second order secular effects of the zonal harmonics are presented. Topics covered include DSphi elements and relations for their conconical transformation into the PS phi elements; the solution algorithm based on the Von Zeipel method; and the elimination of long periodic terms and analytical integration of primed variables. The equations were entered into the ASOP program, checked out, and verified. Comparisons with numerical integrations show the long period theory to be accurate within several meters after 800 revolutions.

Wang, K. C.↗

Types of Information Expected from a Photometric Search for Extra-Solar Planets

The current theory postulates that planets are a consequence of the formation of stars from viscous accretion disks. Condensation from the hotter, inner portion of the accretion disk favors the formation of small rocky planets in the inner portion and the formation of gas giants in the cuter, cooler part. Consequently, terrestrial-type planets in inner orbits must be commonplace (Wetheril 1991). From the geometry of the situation (Borucki and Summers 1984), it can be shown that 1% of those planetary systems that resemble our solar system should show transits for Earth-sized (or larger) planets. Thus a photometric satellite that uses a wide field of view telescope and a large CCD array to simultaneously monitor 5000 target stars should detect 50 planetary systems. To verify that regularly recurring transits are occurring rather than statistical fluctuations of the stellar flux, demands observations that extend over several orbital periods so that the constancy of the orbital period, signal amplitude, and duration can be measured. Therefore, to examine the region from Mercury's orbit to that of the Earth requires a duration of three years whereas a search out to the orbit of mars requires about six years. The results of the observations should provide estimates of the distributions of planetary size and orbital radius, and the frequency of planetary systems that have Earth-sized planets in inner orbits. Because approximately one half of the star systems observed will be binary systems, the frequency of planetary systems orbit ' ing either one or both of the stars can also be determined. Furthermore, the complexity of the photometric signature of a planet transiting a pair of stars provides enough information to estimate the eccentricities of the planetary orbits. In summary, the statistical evidence from a photometric search of solar-like stars should be able to either confirm or deny the applicability of the current theory of planet formation and provide new information about the stability of planetary orbits in binary star systems.

Borucki, William↗

Fast and robust all-electron density functional theory calculations in solids using orthogonalized enriched finite elements

Here, we present a computationally efficient approach to perform systematically convergent real-space all-electron Kohn-Sham density functional theory calculations for solids using an enriched finite element (FE) basis. The enriched FE basis is constructed by augmenting the classical FE basis with atom-centered numerical basis functions, comprising of atomic solutions to the Kohn-Sham problem. Notably, to improve the conditioning, we orthogonalize the enrichment functions with respect to the classical FE basis, without sacrificing the locality of the resultant basis. In addition to improved conditioning, this orthogonalization procedure also renders the overlap matrix block diagonal, greatly simplifying its inversion. Subsequently, we use a Chebyshev polynomial based filtering technique to efficiently compute the occupied eigenspace in each self-consistent field iteration. We demonstrate the accuracy and efficiency of the proposed approach on periodic unit cells and supercells. The benchmark studies show a staggering 130× speedup of the orthogonalized enriched FE basis over the classical FE basis. We also present a comparison of the orthogonalized enriched FE basis with the linearized augmented plane-wave + local orbitals basis, both in terms of accuracy and efficiency. Notably, we demonstrate that the orthogonalized enriched FE basis can handle large system sizes of ~10 000 electrons. Finally, we observe good parallel scalability of our implementation with 92% efficiency at 22× speedup for a system with 620 electrons

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

A first-order global model of Late Cenozoic climatic change: Orbital forcing as a pacemaker of the ice ages

The development of a theory of the evolution of the climate of the earth over millions of years can be subdivided into three fundamental, nested, problems: (1) to establish by equilibrium climate models (e.g., general circulation models) the diagnostic relations, valid at any time, between the fast-response climate variables (i.e., the 'weather statistics') and both the prescribed external radiative forcing and the prescribed distribution of the slow response variables (e.g., the ice sheets and shelves, the deep ocean state, and the atmospheric CO2 concentration); (2) to construct, by an essentially inductive process, a model of the time-dependent evolution of the slow-response climatic variables over time scales longer than the damping times of these variables but shorter than the time scale of tectonic changes in the boundary conditions (e.g., altered geography and elevation of the continents, slow outgassing, and weathering) and ultra-slow astronomical changes such as in the solar radiative output; and (3) to determine the nature of these ultra-slow processes and their effects on the evolution of the equilibrium state of the climatic system about which the above time-dependent variations occur. All three problems are discussed in the context of the theory of the Quaternary climate, which will be incomplete unless it is embedded in a more general theory for the fuller Cenozoic that can accommodate the onset of the ice-age fluctuations. We construct a simple mathematical model for the Late Cenozoic climatic changes based on the hypothesis that forced and free variations of the concentration of atmospheric greenhouse gases (notably CO2), coupled with changes in the deep ocean state and ice mass, under the additional 'pacemaking' influence of earth-orbital forcing, are primary determinants of the climate state over this period. Our goal is to illustrate how a single model governing both very long term variations and higher frequency oscillatory variations in the Pleistocene can be formulated with relatively few adjustable parameters.

Saltzman, Barry↗

Differential Drag Demonstration: A Post-Mission Experiment with the EO-1 Spacecraft

Differential drag is a technique for altering the semi-major axis, velocity, and along-track position of a spacecraft in low Earth orbit. It involves varying the spacecrafts cross-sectional area relative to its velocity direction by temporarily changing attitude and solar array angles, thus varying the amount of atmospheric drag on the spacecraft. The technique has recently been proposed and used by at least three satellite systems for initial separation of constellation spacecraft after launch, stationkeeping during the mission, and potentially for conjunction avoidance. Similarly, differential drag has been proposed as a control strategy for rendezvous, removing the need for active propulsion. In theory, some operational missions that lack propulsion capability could use this approach for conjunction avoidance, though options are typically constrained for spacecraft that are already in orbit. Shortly before the spacecraft was decommissioned, an experiment was performed using NASAs EO-1 spacecraft in order to demonstrate differential drag on an operational spacecraft in orbit, and discover some of the effects differential drag might manifest. EO-1 was not designed to maintain off-nominal orientations for long periods, and as a result the team experienced unanticipated challenges during the experiment. This paper will discuss operations limitations identified before the experiment, as well as those discovered during the experiment. The effective displacement that resulted from increasing the drag area for 39 hours will be compared to predictions as well as the expected position if the spacecraft maintained nominal operations. A hypothetical scenario will also be examined, studying the relative risks of maintaining an operational spacecraft bus in order to maintain the near-maximum drag area orientation and hasten reentry.

differential drag↗

Differential Drag Demonstration: A Post-Mission Experiment with the EO-1 Spacecraft

Differential drag is a technique for altering the semimajor axis, velocity, and along-track position of a spacecraft in low Earth orbit. It involves varying the spacecraft's cross-sectional area relative to its velocity direction by temporarily changing attitude and solar array angles, thus varying the amount of atmospheric drag on the spacecraft. The technique has recently been proposed and used by at least three satellite systems for initial separation of constellation spacecraft after launch, stationkeeping during the mission, and potentially for conjunction avoidance. Similarly, differential drag has been proposed as a control strategy for rendezvous, removing the need for active propulsion. In theory, some operational missions that lack propulsion capability could use this approach for conjunction avoidance, though options are typically constrained for spacecraft that are already in orbit. Shortly before the spacecraft was decommissioned, an experiment was performed using NASA's EO-1 spacecraft in order to demonstrate differential drag on an operational spacecraft in orbit, and discover some of the effects differential drag might manifest. EO-1 was not designed to maintain off-nominal orientations for long periods, and as a result the team experienced unanticipated challenges during the experiment. This paper will discuss operations limitations identified before the experiment, as well as those discovered during the experiment. The effective displacement that resulted from increasing the drag area for 39 hours will be compared to predictions as well as the expected position if the spacecraft maintained nominal operations. A hypothetical scenario will also be examined, studying the relative risks of maintaining an operational spacecraft bus in order to maintain the near-maximum drag area orientation and hasten reentry.

orbital lifetim↗

Generating Bright Emissive States by Modulating the Bandgap of Monolayer Tungsten Diselenide

Transition metal dichalcogenides (TMDs) are essential due to their fascinating electronic and optical properties, strong exciton binding energy, and layer-dependent bandgap. They can be tuned to function as a single-photon emitter, but the quantum yield of photoluminescence of single-layer WSe 2 is low. There is some evidence that a bright emissive state can be produced by introducing local defects through functionalization. In this paper we use spin-polarized periodic density functional theory (DFT) to study the effect of functionalization for the specific case of cyclic carbenes. We find that the simplest of these molecules, cyclopentadiene carbene (Cyc), binds to the surface by a covalent bond leading to a substantial change in the bandgap (1.24 eV compared to 1.64 eV for the pristine surface). Moreover, there are semiflat bands below the Fermi level that originate from σ bonding and the interaction between the lone-pair p orbitals on the carbon of Cyc that bonds with Se on the TMD. Cyc is found to form a Type IIa heterojunction before and after contact with the surface, where the “a” refers to ordering of the energy levels where the TMD levels have the larger splitting and “b” to the reverse. The effect of various electron-withdrawing and electron-donating groups on Cyc is investigated, and it is found that the direct bandgap and heterointerfaces can be chemically tuned with covalently bound functional groups. With an electron-withdrawing group (EWG) such as –CHO, –COCl, and –CN attached to Cyc, a Type III//Type IIa interface is formed, whereas all other EWGs used in this study form a Type IIa junction, before and after contact to the surface. The electron-donating groups (EDG) form Type Ib//Type Ia junctions, and in particular, we find that the system WSe 2 + Cyc-Me band structure consists of semiflat bands at valence band maxima localized on Cyc-Me and the conduction band minimum is coupled between the surface and functional group with a direct bandgap of 0.88 eV. Hence, we predict that the Cyc-Me-functionalized monolayer WSe 2 will produce a red-shifted bright emissive state. Furthermore, we also find that carbenes with the Cyc all-carbon ring have (1) a triplet ground state and (2) form covalent bonds to WSe 2 , while heterocyclic carbenes (1) have a singlet ground state and (2) do not form covalent bonds to WSe 2 .

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Observational constraints on the masses of neutron stars

The present state of empirical knowledge about neutron-star masses is reviewed. It is shown how the mass function of a pulsar-containing binary system can be inferred from measurements of the pulsation period and the projected semimajor axis of the pulsar orbit plus independent information concerning the inclination of the orbital plane, the mass of the companion star, or both. Relevant observational properties, the type of information used to constrain the pulsar mass, and the range of allowable pulsar masses are summarized for the binary systems 3U 0900-40, Cen X-3, SMC X-1, Her X-1, and PSR 1913+16. It is found that as long as the general theory of relativity is correct, neutron-star masses should range from about 1.4 to 1.9 solar masses if the companion is a normal white dwarf or should be less than about 1.9 solar masses if the companion is some other object. It is concluded that these mass estimates are entirely consistent with the predictions of nuclear physics theory.

Joss, P. C.↗

Theory of plasma contactors in ground-based experiments and low earth orbit

An examination of several models of electron collection by plasma contactors leads to a definition of the range of validity and applicability for each model. It is noted that most present ground-based experiments are of limited relevance to space applications of plasma contactors, since they operate in a regime where the magnetic field and effective collisions are at most only marginally important. An exception is the experiment of Stenzel and Urrutia (1986), which examined a plasma whose electron Larmor radius was small by comparison to the scale of the potential, and in which the anomalous transport of electrons across the magnetic field was important. The enhanced electron current was not continuous in time, but occurred in periodic bursts as the instabilities periodically emerged, saturated, and decayed.

Gerver, M. J.↗

Lunar perturbations of artificial satellites of the earth

The disturbing function for the lunar perturbations of an artificial satellite are derived, using ecliptic elements for the moon and equatorial elements for the satellite. Secular, long-period, and short-period perturbations are then computed, with the expressions kept in closed form in both inclination and eccentricity of the satellite. Alternative expressions for short-period perturbations of high satellites are also given, assuming small values of the eccentricity. The moon's position is specified by the inclination, node, argument of perigee, true (or mean) longitude, and its radius vector from the center of the earth. The results can then be applied to numerical integration by using coordinates of the moon from ephemeris tapes or to analytical representation by using results from lunar theory, with the moon's motion represented by a precessing and rotating elliptical orbit.

Giacaglia, G. E. O.↗