Engineering topics

Greenberg, Richard

Publications and source records attributed to Greenberg, Richard.

15 records

NASA NTRS2010

The Roles of Tidal Evolution and Evaporative Mass Loss in the Origin of CoRoT-7 b

CoRoT-7 b is the first confirmed rocky exoplanet, but, with an orbital semimajor axis of 0.0172 au, its origins may be unlike any rocky planet in our Solar System. In this study, we consider the roles of tidal evolution and evaporative mass loss in CoRoT-7 b's history, which together have modified the planet's mass and orbit. If CoRoT-7 b has always been a rocky body, evaporation may have driven off almost half its original mass, but the mass loss may depend sensitively on the extent of tidal decay of its orbit. As tides caused CoRoT-7 b's orbit to decay, they brought the planet closer to its host star, thereby enhancing the mass loss rate. Such a large mass loss also suggests the possibility that CoRoT-7 b began as a gas giant planet and had its original atmosphere completely evaporated. In this case, we find that CoRoT-7 b's original mass probably did not exceed 200 Earth masses (about two-third of a Jupiter mass). Tides raised on the host star by the planet may have significantly reduced the orbital semimajor axis, perhaps causing the planet to migrate through mean-motion resonances with the other planet in the system, CoRoT-7 c. The coupling between tidal evolution and mass loss may be important not only for CoRoT-7 b but also for other close-in exoplanets, and future studies of mass loss and orbital evolution may provide insight into the origin and fate of close-in planets, both rocky and gaseous.

Jackson, Brian↗

NASA NTRS1994

Velocity distributions among colliding asteroids

The probability distribution for impact velocities between two given asteroids is wide, non-Gaussian, and often contains spikes according to our new method of analysis in which each possible orbital geometry for collision is weighted according to its probability. An average value would give a good representation only if the distribution were smooth and narrow. Therefore, the complete velocity distribution we obtain for various asteroid populations differs significantly from published histograms of average velocities. For all pairs among the 682 asteroids in the main-belt with D greater than 50 km, we find that our computed velocity distribution is much wider than previously computed histograms of average velocities. In this case, the most probable impact velocity is approximately 4.4 km/sec, compared with the mean impact velocity of 5.3 km/sec. For cases of a single asteroid (e.g., Gaspra or Ida) relative to an impacting population, the distribution we find yields lower velocities than previously reported by others. The width of these velocity distributions implies that mean impact velocities must be used with caution when calculating asteroid collisional lifetimes or crater-size distributions. Since the most probable impact velocities are lower than the mean, disruption events may occur less frequently than previously estimated. However, this disruption rate may be balanced somewhat by an apparent increase in the frequency of high-velocity impacts between asteroids. These results have implications for issues such as asteroidal disruption rates, the amount/type of impact ejecta available for meteoritical delivery to the Earth, and the geology and evolution of specific asteroids like Gaspra.

Bottke, William F., Jr.↗

NASA NTRS1993

Asteroidal collision probabilities

Several past calculations of collision probabilities between pairs of bodies on independent orbits have yielded inconsistent results. We review the methodologies and identify their various problems. Greenberg's (1982) collision probability formalism (now with a corrected symmetry assumption) is equivalent to Wetherill's (1967) approach, except that it includes a way to avoid singularities near apsides. That method shows that the procedure by Namiki and Binzel (1991) was accurate for those cases where singularities did not arise.

Bottke, William F., Jr.↗

NASA NTRS1991

Planetary accretion rates - Analytical derivation

New analytical formulae that are valid even in cases where Keplerian shear determines the approach velocity in planetary accretion rates are presently shown to accurately reproduce Monte Carlo study results. The formulae yield accretion rates over a great variety of planet formation-conducive conditions. Since the absolute values of impact rates yielded by the formulae were expected to have factor-of-2-to-3 uncertainties, the good agreement with Monte Carlo experiments obtained suggests the reasonableness of many of the estimates adopted, or the mutual cancelling-out of various uncertainties.

Greenberg, Richard↗

NASA NTRS1990

Viscosity and mass transport in nonuniform Keplerian disks

A quantitative formalism for Keplerian particulate disk dynamics having its basis in a heuristic description of viscous transport is presently applied to the case of a ring with optical thickness radial gradient. A steady-state velocity distribution solution directly yields both the radial mass transport and the viscosity. The analytical method employed involves the solution of a novel form of the Krook equation through the separation of the phase-space collisional-products distribution into a symmetrical component and a delta function-approachable remainder. While this model is simplified for the case treated, its general approach may be extended to less artificially restricted cases.

Ojakangas, G. W.↗

NASA NTRS1989

Dust bands in the asteroid belt

This paper describes the original IRAS observations leading to the discovery of the three dust bands in the asteroid belt and the analysis of data. Special attention is given to an analytical model of the dust band torus and to theories concerning the origin of the dust bands, with special attention given to the collisional equilibrium (asteroid family), the nonequilibrium (random collision), and the comet hypotheses of dust-band origin. It is noted that neither the equilibrium nor nonequilibrium models, as currently formulated, present a complete picture of the IRAS dust-band observations.

Sykes, Mark V.↗

NASA NTRS1989

Delivery of asteroids and meteorites to the inner solar system

Two major models of asteroid/meteorite demographics are described and reviewed critically: the collisional model of Greenberg and Chapman (1983), and the orbital evolution model of Wetherill (1985). It is shown that each of the two models tends to gloss over the central processes in the other and tends to ignore (and to some degree violate) the key observables that constrain the other model. The uncertainties that prevent definite acceptance of any particular model for the delivery of asteroidal material to the earth are described.

Greenberg, Richard↗

NASA NTRS1988

Infrared lightcurves of asteroids 532 Herculina and 45 Eugenia - Proof of the absence of significant albedo markings

Time-resolved thermal maxima and minima from near- and mid-IR photometry for the asteroids 532 Herculina and 45 Eugenia are noted to occur at nearly the same time as the maxima and minima in reflected light, while model lightcurves for Herculina, based on Taylor et al.'s (1987) albedo distribution, had predicted a 90-deg out-of-phase relationship. It is presently found through a comparison of model and observed lightcurves that the light variations of both Herculina and Eugenia are primarily the result of variations in shape rather than in albedo.

Lebofsky, Larry A.↗

NASA NTRS1988

Particle properties and the large-scale structure of planetary rings - Rebound characteristics and viscosity

The present treatment of the apparently paradoxical reversal of momentum transport, or 'negative viscosity', in such swarms of particles on Keplerian orbits as planetary rings, illuminates the importance of particles' physical properties. Even the slightest deviation from the idealized (uniform, highly elastic, perfectly slippery, spherical) particles will affect viscosity, yielding predictions that are inconsistent with the observed ring structure. It is presently suggested that the size of the larger bodies in the rings determines random velocities, viscosity, and a substantial portion of ring structural characteristics.

Greenberg, Richard↗

NASA NTRS1988

Planetary astronomy: Rings, satellites, and asteroids

Studies of planetary rings focus on the dynamical processes that govern astronomically observable ring properties and structure. These investigations thus help reveal properties of the rings as well as probe the gravity fields of the planets. Satellite studies involve interpretation of orbital motion to extract information regarding the gravity fields of the outer planets and the physical properties of the satellites themselves. Asteroid lightcurve work is designed to investigate the large-scale shapes of the asteroids, as well as to reveal anomalous features such as major topography, possible satellites, or albedo variations. Work on the nature of viscous transport in planetary rings, emphasizing the role of individual particles' physical properties, has yielded a method for estimating both angular momentum and mass transport given an optical-thickness gradient. This result offers the prospect of ringlet instability, which may explain the square-profile ringlets in Saturn's C Ring. Thermal and reflected lightcurves of 532 Herculina have been interpreted to show that albedo variations cannot be the primary cause of variations. A lightcurve simulation has been developed to model complex asteroidal figures. Bamberga was observed during the December occultation as part of the joint LPL-Lowell program.

Greenberg, Richard↗

NASA NTRS1988

Outcomes of planetary close encounters - A systematic comparison of methodologies

Several methods for estimating the outcomes of close planetary encounters are compared on the basis of the numerical integration of a range of encounter types. An attempt is made to lay the foundation for the development of predictive rules concerning the encounter outcomes applicable to the refinement of the statistical mechanics that apply to planet-formation and similar problems concerning planetary swarms. Attention is given to Oepik's (1976) formulation of the two-body approximation, whose predicted motion differs from the correct three-body behavior.

Greenberg, Richard↗

NASA NTRS1987

The chronology of Mercury's geological and geophysical evolution - The Vulcanoid hypothesis

The possibility that constraints on Mercury's chronology can be relaxed through reference to a Mercury-specific bombarding population of planetesimals interior to its orbit, and therefore only occasionally encountering the planet at times of secular perturbations, is investigated. While such vulcanoids may have been a significant source of early cratering, those in the pertinent orbits are depleted by mutual collisions and can therefore only furnish a modest extension of the heavy bombardment period. A search is conducted for vulcanoids further within Mercury's orbit; evidence that Mercury's intercrater plains are of volcanic origin is discussed.

Leake, Martha A.↗

NASA NTRS1987

Collision mechanics and the structure of planetary ring edges

The present numerical simulation of collisional evolution, in the case of a hypothetical ring whose parameters are modeled after those of Saturn's rings, gives attention to changes in radial structure near the ring edges and notes that when random motion is in equilibrium, the rings tend to spread in order to conserve angular momentum while energy is dissipated in collisions. As long as random motion is damped, ring edges may contract rather than spread, producing a concentration of material at the ring edges. For isotropic scattering, damping dominates for a coefficient of restitution of velocity value of up to 0.83.

Spaute, Dominique↗

NASA NTRS1987

Galilean satellites - Evolutionary paths in deep resonance

While the Laplace resonance among the three inner Galilean satellites possesses stable configurations where the mean motions taken by pairs are in nearly 2:1 ratios, or 'deep resonance', the current satellite configuration is unstable near this exact commensurability. There is presently noted, however, a continuous path of stable conditions branching toward deep resonance which furnishes a track for the tidal evolution of the system and renders scenarios involving (probably episodic) evolution from deep resonance viable; this eliminates the requirement for rapid tidal dissipation of Jupiter by the alternative equilibrium hypothesis.

Greenberg, Richard↗

NASA NTRS1986

Orbital acceleration and the energy budget in the galilean satellite system

Theories concerning the resonance which gives rise to the tidal heating of Io are discussed. Yoder's (1979) suggestion that the resonance is maintained by tides raised on Jupiter by Io is examined along with the proposal of Greenberg (1982) that with smaller Jovian torque the system could be evolving away from resonance. The significance of Lieske's (1986) finding of a much smaller than expected negative value for Io's orbital acceleration is addressed.

Greenberg, Richard↗