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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.

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At least 73 records · Page 4
All sourcesNASA NTRSDOE OSTI
NASA NTRS1991

Symplectic maps for the n-body problem

The present study generalizes the mapping method of Wisdom (1982) to encompass all gravitational n-body problems with a dominant central mass. The rationale for the generalized mapping method is discussed as well as details for the mapping for the n-body problem. Some refinements of the method are considered, and the relationship of the mapping method to other symplectic integration methods is shown. The method is used to compute the evolution of the outer planets for a billion years. The resulting evolution is compared to the 845 million year evolution of the outer planets performed on the Digital Orerry using standard numerical integration techniques. This calculation provides independent numerical confirmation of the result of Sussman and Wisdom (1988) that the motion of the planet Pluto is chaotic.

Wisdom, Jack↗
NASA NTRS2001

Chaos in the Solar System

The physical basis of chaos in the solar system is now better understood: In all cases investigated so far, chaotic orbits result from overlapping resonances. Perhaps the clearest examples are found in the asteroid belt. Overlapping resonances account for its kirkwood gaps and were used to predict and find evidence for very narrow gaps in the outer belt. Further afield, about one new "short-peroid" comet is discovered each year. They are believed to come from the "Kuiper Belt" (at 40 AU or more) via chaotic orbits produced by mean-motion and secular resonances with Neptune. Finally, the planetary system itself is not immune from chaos. In the inner solar system, overlapping secular resonances have been identified as the possible source of chaos. For example, Mercury in 1012 years, may suffer a close encounter with Venus or plunge into the Sun. In the outer solar system, three-body resonances have been identified as a source of chaos, but on an even longer time scale of 109 times the age of the solar system. On the human time scale, the planets do follow their orbits in a stately procession, and we can predict their trajectories for hundreds of thousands of years. That is because the mavericks, with shorter instability times, have long since been ejected. The solar system is not stable; it is just old!

Lecar, Myron↗
NASA NTRS1993

Physics of the magnetotail current sheet

The Earth's magnetotail plays an important role in the solar-wind-magnetosphere coupling. At the midplane of the magnetotail is a current sheet where the dominant magnetic field component reverses sign. The charged particle motion in and near the current sheet is collisionless and nonintegrable, exhibiting chaotic scattering. The current understanding of the dynamical properties of the charged particle motion is discussed. In particular, the relationships between particle dynamics and global attributes of the system are elucidated. Geometrical properties of the phase space determine important physical observables on both micro- and macroscales.

Chen, James↗
NASA NTRS1992

Numerical Study of Mixing of Two Fluids Under Low Gravity

The mixing characteristics of two fluids inside a cavity due to buoyancy driven flow fields for low gravity conditions is investigated via numerical experiments. The buoyancy driven flow, depending on the parametric region, stretches and deforms the material interface into a wave morphological pattern. The morphological pattern affects the resulting stratification thickness of the mixed region. Three basic mixing regimes occur: convective, diffusive, and chaotic. In the convective regime, an overturning motion occurs which gives rise to a stable wave formation. This wave oscillates and its decay leads to a stable stratification. Whereas, in the diffusive regime, the length of the interface remains constant while mixing occurs. This limiting behavior is very important to materials processing in space, and it admits a closed form solution corresponding to vanishing convective terms which agrees with computational results. Finally, in the chaotic regime, the material interface continuously stretches and folds on itself similar to a horseshoe map. The length of stretch of the interface increases exponentially. Internal wavebreaking occurs for this case. This wavebreaking generates local turbulence, and provides an effective mechanism for mixing.

Duval, Walter M. B.↗
NASA NTRS1990

Tidal evolution of the Uranian satellites. III - Evolution through the Miranda-Umbriel 3:1, Miranda-Ariel 5:3, and Ariel-Umbriel 2:1 mean-motion commensurabilities

Numerical experiments have been conducted which indicate that the orbital eccentricity of Miranda may have reached a value sufficiently large to have affected its thermal evolution. There is a large chaotic zone associated with the Miranda-Ariel 5:3 mean-motion commensurability, even in the planar approximation; the orbital eccentricities of both satellites may vary chaotically for a considerable period. Since the anomalously high orbital inclination of Miranda is a consequence of passage through the 3:1 commensurability with Umbriel, the requirement that the satellites encountered this resonance places a lower limit on the Uranian specific dissipation function of 39,000.

Tittemore, William C.↗
NASA NTRS1992

Inferences concerning the magnetospheric source region for auroral breakup

Inferences concerning the magnetospheric source region for auroral arcs obtained from particle measurements on polar orbiting satellites are presented and contrasted with other ideas. An argument that the magnetospheric source region for auroral arc breakup and substorm initiation is along Boundary Plasma Sheet (BPS) magnetic field lines is given. This source region lies beyond a distinct central plasma sheet region and sufficiently far from the Earth that energetic ion motion violates the guiding center approximation (is chaotic). The source region is not constrained to any particular range of distances from the Earth, and substorm initiation may be possible over a wide range of distances from near synchronous orbit to the distant tail. It is also argued that the layer of low energy electrons and velocity dispersed ion beams observed at low altitudes on Aureol 3 is not a different region from the region of auroral arcs. Both comprise the BPS. The two regions occasionally appear distinct at low altitudes because of the effects of arc field aligned potential drops on precipitating particles.

Lyons, L. R.↗
NASA NTRS2007

Fuel-Optimal Trajectories in a Planet-Moon Environment Using Multiple Gravity Assists

For low energy spacecraft trajectories such as multi-moon orbiters for the Jupiter system, multiple gravity assists by moons could be used in conjunction with ballistic capture to drastically decrease fuel usage. In this paper, we outline a procedure to obtain a family of zero-fuel multi-moon orbiter trajectories, using a family of Keplerian maps derived by the first author previously. The maps capture well the dynamics of the full equations of motion; the phase space contains a connected chaotic zone where intersections between unstable resonant orbit manifolds provide the template for lanes of fast migration between orbits of different semimajor axes. Patched three body approach is used and the four body problem is broken down into two three-body problems, and the search space is considerably reduced by the use of properties of the Keplerian maps. We also introduce the notion of Switching Region where the perturbations due to the two perturbing moons are of comparable strength, and which separates the domains of applicability of the corresponding two Keplerian maps.

Ross, Shane D.↗
NASA NTRS2019

MultiLayer Clustered Sampling (MLCS) technique for near-earth asteroid impact hazard assessment

Because of planetary encounters, the motion of near-Earth asteroids is chaotic and small differences in the initial conditions tend to diverge exponentially. Linear approximations for propagating orbital uncertainties can lead to inaccurate estimates of the probability of an Earth collision. We present a novel fully nonlinear strategy for estimating the probability of an asteroid impact using sequential Monte Carlo layers. The method first explores a low-resolution layer to locate potentially relevant regions. Then, we conduct localized searches on deeper layers with higher resolution. The method retains the accuracy of brute-force Monte Carlo sampling while reducing the computational cost by only sampling relevant regions.

Farnocchia, Davide↗
NASA NTRS1991

Tidal evolution of planetary satellites

Early in the history of the Solar System, Europa and Ganymede may have evolved through a 3:1 mean-motion commensurability, which would have been encountered prior to the establishment of the current Laplace resonance involving Io, Europa, and Ganymede. If Europa and Ganymede passed through the 3:1 mean-motion commensurability, the orbital eccentricities of both satellites may have increased to large values during a phase of chaotic behavior, after which the satellites would have escaped from the resonance. In spite of the relatively large J sub 2 of Jupiter, Europa, and Ganymede are sufficiently massive and distant from the planet that resonances at the 3:1 mean-motion commensurability interact strongly, leading to chaotic behavior via the same kinds of dynamical mechanisms present at resonances among the Uranian satellites. As a result of the large eccentricity increases possible during the evolution of Europa and Ganymede through the 3:1 mean-motion commensurability, tidal heating may have melted water ice in the mantles of both satellites, and stresses on the lithosphere of both satellites due to tidal deformation may have been sufficient to cause extensive fracturing, making resurfacing possible. This may account for the post-heavy bombardment geological activity on both Europa and Ganymede. In addition, the effects of resonance passage on Ganymede may provide an explanation of the Ganymede-Callisto dichotomy by providing Ganymede with an intense source of internal heat and lithospheric stress not present in Callisto. Further possibilities of this evolution are presented.

Tittemore, William C.↗
NASA NTRS1987

H-alpha Fabry-Perot interferometric observations of blue compact dwarf galaxies

H-alpha Fabry-Perot interferometric observations of the two blue compact dwarf galaxies (BCDs) 7 Zw 403 and 1 Zw 49 are presented. The velocity field of 7 Zw 403 shows no clear large-scale organized motion but the velocity field is not completely chaotic either. The gas associated with the 8 H II regions in 7 Zw 403 has neither the highest nor lowest velocities. The BCD 1 Zw 49 is dominated by a single H II region which is about 50 times brighter than any other feature in the galaxy. There is a chain of fainter H II regions extending across the galaxy. The velocity field is well ordered along the H II region chain, but it is very complex around the dominant H II region, suggesting H-alpha loops and filaments around the latter. Both BCDs show velocity gradients of about 25 km/s on scales of about 10 pc in 7 Zw 403 and of about 50 pc in 1 Zw 49. These velocity discontinuities compress the gas and are probably responsible for the star formation.

Thuan, Trinh Xuan↗
NASA NTRS1992

Inferences Concerning the Magnetospheric Source Region for Auroral Breakup

It is argued that the magnetospheric source region for auroral arc breakup and substorm initiation is along boundary plasma sheet (BPS) magnetic field lines. This source region lies beyond a distinct central plasma sheet (CPS) region and sufficiently far from the Earth that energetic ion motion violates the guiding center approximation (i.e., is chaotic). The source region is not constrained to any particular range of distances from the Earth, and substorm initiation may be possible over a wide range of distances from near synchronous orbit to the distant tail. It is also argued that the layer of low-energy electrons and velocity dispersed ion beams observed at low altitudes on Aureol 3 is not a different region from the region of auroral arcs. Both comprise the BPS. The two regions occasionally appear distinct at low altitudes because of the effects of arc field-aligned potential drops on precipitating particles.

Lyons, L. R.↗
NASA NTRS2014

F Ring Core Stability: Corotation Resonance Plus Antiresonance

The decades-or-longer stability of the narrow F Ring core in a sea of orbital chaos appears to be due to an unusual combination of traditional corotation resonance and a novel kind of "antiresonance". At a series of specific locations in the F Ring region, apse precession between synodic encounters with Prometheus allows semimajor axis perturbations to promptly cancel before significant orbital period changes can occur. This cancellation fails for particles that encounter Prometheus when it is near its apoapse, especially during periods of antialignment of its apse with that of the F Ring. At these times, the strength of the semimajor axis perturbation is large (tens of km) and highly nonsinusoidal in encounter longitude, making it impossible to cancel promptly on a subsequent encounter and leading to chaotic orbital diffusion. Only particles that consistently encounter Prometheus away from its apoapse can use antiresonance to maintain stable orbits, implying that the true mean motion nF of the stable core must be defined by a corotational resonance of the form nF = nP(-kappa)P/m, where (nP, kappaP) are Prometheus' mean motion and epicycle frequency. To test this hypothesis we used the fact that Cassini RSS occultations only sporadically detect a "massive" F Ring core, composed of several-cm-and-larger particles. We regressed the inertial longitudes of 24 Cassini RSS (and VGR) detections and 43 nondetections to a common epoch, using a comb of candidate nP, and then folded them modulo the anticipated m-number of the corotational resonance (Prometheus m = 110 outer CER), to see if clustering appears. We find the "true F Ring core" is actually arranged in a series of short longitudinal arcs separated by nearly empty longitudes, orbiting at a well determined semimajor axis of 140222.4 km (from 2005-2012 at least). Small particles seen by imaging and stellar occultations spread quickly in azimuth and obscure this clumpy structure. Small chaotic variations in the mean motion and/or apse longitude of Prometheus quickly become manifest in the F Ring core, and we suggest that the core must adapt to these changes for the F Ring to maintain stability over timescales of decades and longer

Cassini RSS occultations↗
NASA NTRS1993

The chaotic obliquity of Mars

The discovery (by Laskar, 1989, 1990) that the evolution of the solar system is chaotic, made in a numerical integration of the averaged secular approximation of the equations of motions for the planets, was confirmed by Sussman and Wisdom (1992) by direct numerical integration of the whole solar system. This paper presents results of direct integrations of the rotation of Mars in the chaotically evolved planetary system, made using the same model as that used by Sussman and Wisdom. The numerical integration shows that the obliquity of Mars undergoes large chaotic variations, which occur as the system evolves in the chaotic zone associated with a secular spin-orbit resonance.

Touma, Jihad↗
NASA NTRS1995

(abstract) Satellite Dynamics About Eros

The Near Earth Asteroid Rendezvous (NEAR) mission spacecraft will arrive at Asteroid 433 (Eros) in February 1999. Following an initial period of characterization, the science phase of the mission will commence, and unprecedented information concerning an asteroid's shape, mass, density, composition, and rotational dynamics will be sent to Earth for analysis. It will also mark the start of orbital operations about the most complex and irregular gravity field ever encountered in the history of space exploration. The severity of Eros' distortion from the usual spheroid bodies encountered in planetary exploration leads to fundamental differences in the orbital dynamics about it. Operations about Eros will also serve as an exciting test of orbital determination and prediction in an orbital environment which can be chaotic in some instances. General orbital dynamics about Eros are discussed. Some simple formulae are given for the secular motion of the node and argument of periapsis. Conditions for a satellite orbit to escape from Eros are discussed, and some simple results derived. Finally, the chaotic nature of certain orbits about Eros are discussed, and the consequences for orbit prediction are investigated.

Near↗
NASA NTRS1986

Chaotic instability in the three-body problem

The existence of global exponential instability leading to chaos in plane (nonrigid) motions of the three-body system is demonstrated. In the presence of Newtonian attracting forces the trajectories of the three-body system in the configuration space will no longer be geodesic, and their convergence will depend on the geodesic curvature in addition to the Gaussian curvature. It is noted that the global exponential instability occurs in the n-body problem for n greater than 3 if at least two angular coordinates are disturbed, and that the chaotic instability is not necessarily accompanied by an exponential increase of the distance between the mass-points, but is associated with the exponential divergence of trajectories in the configuration space.

Zak, M.↗
NASA NTRS1986

Modeling aerodynamic discontinuities and the onset of chaos in flight dynamical systems

Various representations of the aerodynamic contribution to the aircraft's equation of motion are shown to be compatible within the common assumption of their Frechet differentiability. Three forms of invalidating Frechet differentiality are identified, and the mathematical model is amended to accommodate their occurrence. Some of the ways in which chaotic behavior may emerge are discussed, first at the level of the aerodynamic contribution to the equation of motion, and then at the level of the equations of motion themselves.

Tobak, M.↗
NASA NTRS1987

Modeling aerodynamic discontinuities and onset of chaos in flight dynamical systems

Various representations of the aerodynamic contribution to the aircraft's equation of motion are shown to be compatible within the common assumption of their Frechet differentiability. Three forms of invalidating Frechet differentiability are identified, and the mathematical model is amended to accommodate their occurrence. Some of the ways in which chaotic behavior may emerge are discussed, first at the level of the aerodynamic contribution to the equations of motion, and then at the level of the equations of motion themselves.

Tobak, M.↗