Engineering topics

Stewart, Glen R.

Publications and source records attributed to Stewart, Glen R..

13 records

NASA NTRS2002

Dynamical Models of the Solar System Formation and Evolution

Mark Lewis has extended his them is work by completing a series of N-body simulations of a narrow ring that: is in the location of Saturn's F-ring and is perturbed by a single satellite comparable to Prometheus, but on a circular orbit. We had previously shown how the satellite perturbations can cause a broadly distributed sparse population of ring particles to become concentrated into narrow rings that can be maintained outside of any resonance location. For low optical depths, the collisions between ring particles are highly localized in the peaks of the satellite wakes. The inelastic collisions therefore occur at a particular orbital phase angle so as to damp the azimuthal component of the relative velocities. Since particle positions are not changed by collisions, the semimajor axes of the particles are shifted toward the actual particle positions where the collisions occur. Thus, negative radial diffusion can occur while conserving orbital angular momentum so long as the forced eccentricity is continually re-excited by the satellite. We speculated that the separation between the final ringlets was largely determined by the magnitude of the forced eccentricities induced by the satellite at closest approach. We carried out a series of simulations with a variety of different satellite masses in order to vary the magnitude of the forced eccentricity. We found that indeed the final spacing of the ringlets does increase with the magnitude of the forced eccentricity (Lewis and Stewart 2002). This occurs because neighboring eccentric ringlets drift out of phase with one another due to Keplerian shear and eventually collide with one another, leading to a smaller number of more widely spaced ringlets, The time scale required to form narrow ringlets in these simulations is much shorter than one would expect from standard theories based upon the orbit-averaged torque produced by multiple passes by the satellite. We find that the initial ringlets form in less than two synodic periods and the final state is typically reached in 10 to 20 synodic periods. These studies move us closer to understanding the significantly more complex system of Saturn's F ring, where the perturbation magnitude varies over short temporal and spatial time scales due to the orbital eccentricities of the perturbing satellite. We are currently extending the simulation to allow for an eccentric orbit of the satellite.

Stewart, Glen R.↗

NASA NTRS2002

Late Stages of Accretion of Uranus and Neptune

A series of N-body simulations were done to try and form Uranus and Neptune from a swarm of a hundred sub-Earth-sized planetary embryos initially on low-inclination, nearly circular orbits beyond Saturn. These calculations were designed to test published Monte Carlo simulations and N-body simulations. Whereas these studies reported successful formation of Uranus and Neptune sized planets, we found very little accretion at all. This occurs because the embryos are dynamically excited by each other and the gravitational effects of Jupiter and Saturn on a time scale that is short compared to the collision time scale. This process produces large orbital eccentricities and inclinations which significantly reduce the collisional cross-section of the embryos because it reduces the effect of gravitational focusing.

Stewart, Glen R.↗

NASA NTRS1993

Planetary accretion in circumstellar disks

The formation of terrestrial planets and the cores of Jovian planets is reviewed in the framework of the planetesimal hypothesis, wherein planets are assumed to grow via the pairwise accumulation of small solid bodies. Emphasis is placed on the dynamics of solid body accretion from kilometer size planetesimals to terrestrial type planets. This stage of planetary growth is least dependent on the characteristics of the evolutionary state of the central star. It is concluded that the evolution of the planetesimal size distribution is determined by the gravitationally enhanced collision cross-section, which favors collisions between planetesimals with smaller velocities. Runaway growth of the largest planetesimal in each accretion zone appears to be a likely outcome. The subsequent accumulation of the resulting protoplanets leads to a large degree of radial mixing in the terrestrial planet region, and giant impacts are probable.

Lissauer, Jack J.↗

NASA NTRS1993

Growth of planets from planetesimals

The paper reviews the formation of terrestrial planets and the cores of Jovian planets within the framework of the planetesimal hypothesis, wherein planets are assumed to grow via the pairwise accumulation of small solid bodies. The rate of (proto)planetary growth is determined by the size and mass of the protoplanet, the surface density of planetesimals, and the distribution of planetesimal velocities relative to the protoplanet. Planetesimal velocities are modified by mutual gravitational interactions and collisions, which convert energy present in the ordered relative motions of orbiting particles into random motions and tend to reduce the velocities of the largest bodies in the swarm relative to those of smaller bodies, as well as by gas drag, which damps eccentricities and inclinations. The evolution of planetesimal size distribution is determined by the gravitationally enhanced collision cross section, which favors collisions between planetesimals with smaller velocities.

Lissauer, Jack J.↗

NASA NTRS1992

Numerical simulation of satellite-ring interactions - Resonances and satellite-ring torques

The Krook kinetic equation for planetary rings is numerically solved in two spatial dimensions and in time, with (1) interparticle collisions and (2) satellite-forcing, but (3) without self-gravity, for the case of a flattened planetary ring that undergoes gravitational perturbation by a nearby satellite. It is noted that the amplitude of wakes is limited by purely kinematic effects, even in the absence of collisions. Attention is given to the results of a simulation of an inner Lindblad-resonance location, as the distribution approaches steady state; these simulations do not show an increase in velocity dispersion in the resonance zone, obviating a net torque.

Brophy, Thomas G.↗

NASA NTRS1991

Nonlinear satellite wakes in planetary rings. I - Phase-space kinematics

The explicit expression presently derived for the phase-space density of a planetary ring subjected to perturbations by a proximate satellite recovers the usual perturbed-streamline equations by drawing first-order moments of the phase-space density. The surface density obtained is positive-definite in virtue of taking the ring particles' finite-velocity dispersion into account. The satellite-wake local mean velocity components deviate from the streamline equations' sinusoidal form; this deviation grows as the wake moves downstream from the shepherding satellite.

Stewart, Glen R.↗

NASA NTRS1991

Growth of planets from planetesimals

The formation of terrestrial planets and the cores of Jovian planets is reviewed in the framework of the planetesimal hypothesis, wherein planets are assumed to grow via the pairwise accumulation of small solid bodies. The rate of (proto)planetary growth is determined by the size and mass of the protoplanet, the surface density of planetesimals, and the distribution of planetesimal velocities relative to the protoplanet. Planetesimal velocities are modified by mutual gravitational interactions and collisions, which convert energy present in the ordered relative motions of orbiting particles (Keplerian shear) into random motions and tend to reduce the velocities of the largest bodies in the swarm relative to those of smaller bodies, as well as by gas drag, which damps eccentricities and inclinations.

Lissauer, Jack J.↗

NASA NTRS1991

Models of planetary rings

The Voyager occultations provide several uniform and high quality data sets for Saturn, Uranus, and Neptune. These data are intercompared, and theoretical models for the particle sizes and the particle transport are developed. The major topics covered include: ring size distribution, torques and resonances, and satellite wakes.

Esposito, L. W.↗

NASA NTRS1990

A phase-space fluid simulation of a two-component narrow planetary ring - Particle size segregation, edge formation, and spreading rates

The Krook kinetic equation for identical planetary ring particles is presently generalized for the case of two-component systems, and the equations are numerically solved on the basis of Brophy and Esposito's (1989) phase-space CFD method. Attention is given to the simulation results obtained for a two-component narrow ring, in which the large particles are eight times as massive as the small particles. This ring's unconstrained edge dynamics are resolved by the simulation, and are found to exhibit a sharpening that would not have been expected in single-component rings.

Brophy, Thomas G.↗

NASA NTRS1989

Accumulation of a swarm of small planetesimals

The present gasdynamic study of the planetesimal-accumulation stage in which 10-km bodies in the neighborhood of 1 AU grow to 10 to the 25th-10 to the 27th g mass, or 'planetary embryo' size, attempts to identify the circumstances under which runaway growth forms a small number of massive embryos in the terrestrial-planet region on a 0.1-1.0 million year time-scale. No runaways are found, however, unless more plausible physical processes are invoked; in that case, runaways in the terrestrial planet region are probable on a 0.1 million-year time-scale, and the final stage of planetary accumulation may involve the growth of these embryos into the present planets on a 10-100 million-year time-scale.

Wetherill, G. W.↗

NASA NTRS1988

Evolution of planetesimal velocities

The velocity evolution of a general planetesimal population is treated by means of a self-consistent set of equations whose form is tailored to those early planetary accumulation stages in which the planetesimal swarm's modeling calls for gas dynamic methods. Dynamical friction is noted to be essential to the transfer of kinetic energy from larger to smaller planetesimals, thereby furnishing an energy source comparable to those furnished by viscous stirring.

Stewart, Glen R.↗

NASA NTRS1987

Evolution of planetesimal velocities

A self-consistent set of equations for the velocity evolution of a general planetesimal population is presented. The equations are given in a form convenient for calculations of the early stages of planetary accumulation when it is necessary to model the planetesimal swarm by methods of gas dynamics, rather than follow the orbital evolution of individual bodies. Steady state velocities of a simple planetesimal population consisting of two different sizes of bodies are calculated. Dynamical friction is found to be an important mechanism for transferring kinetic energy from the larger planetesimals to the smaller ones. When the small planetesimals are relatively abundant, gas drag and inelastic collisions among the smaller bodies are of comparable importance for dissipating energy from the population.

Stewart, Glen R.↗

NASA NTRS1987

The role of orbital dynamics and cloud-cloud collisions in the formation of giant molecular clouds in global spiral structures

The role of orbit crowding and cloud-cloud collisions in the formation of GMCs and their organization in global spiral structure is investigated. Both N-body simulations of the cloud system and a detailed analysis of individual particle orbits are used to develop a conceptual understanding of how individual clouds participate in the collective density response. Detailed comparisons are made between a representative cloud-particle simulation in which the cloud particles collide inelastically with one another and give birth to and subsequently interact with young star associations and stripped down simulations in which the cloud particles are allowed to follow ballistic orbits in the absence of cloud-cloud collisions or any star formation processes. Orbit crowding is then related to the behavior of individual particle trajectories in the galactic potential field. The conceptual picture of how GMCs are formed in the clumpy ISMs of spiral galaxies is formulated, and the results are compared in detail with those published by other authors.

Roberts, William W., Jr.↗