Engineering topics

Lissauer, Jack J.

Publications and source records attributed to Lissauer, Jack J..

At least 73 records · Page 4

NASA NTRS1997

The Birth of Planetary Systems

Models of planet formation and of the orbital stability of planetary systems are described and used to discuss possible characteristics of undiscovered planetary systems. Modern theories of star and planet formation, which are based upon observations of the Solar System and of young stars and their environments, predict that rocky planets should form in orbit about most single stars. It is uncertain whether or not gas giant planet formation is common, because most protoplanetary disks may dissipate before solid planetary cores can grow large- enough to gravitationally trap substantial quantities of gas. Another potential hazard to planetary systems is radial decay of planetary orbits resulting from interactions with material within the disk. Planets more massive than Earth have the potential to decay the fastest, and may be able to sweep up smaller planets in their path. The implications of the giant planets found in recent radial velocity searches for the abundances of habitable planets are discussed.

Lissauer, Jack J.↗

NASA NTRS1995

Formation Of the Giant Planets By Concurrent Accretion Of Solids And Gas

New numerical simulations of the formation of the giant planets are presented, in which for the first time both the gas and planetesimal accretion rates are calculated in a self-consistent, interactive fashion. The simulations combine three elements: 1) three-body accretion cross-sections of solids onto an isolated planetary embryo, 2) a stellar evolution code for the planet's gaseous envelope, and 3) a planetesimal dissolution code within the envelope, used to evaluate the planet's effective capture radius and the energy deposition profile of accreted material. Major assumptions include: The planet is embedded in a disk of gas and small planetesimals with locally uniform initial surface mass density, and planetesimals are not allowed to migrate into or out of the planet's feeding zone. All simulations are characterized by three major phases. During the first phase, the planet's mass consists primarily of solid material. The planetesimal accretion rate, which dominates that of gas, rapidly increases owing to runaway accretion, then decreases as the planet's feeding zone is depleted. During the second phase, both solid and gas accretion rates are small and nearly independent of time. The third phase, marked by runaway gas accretion, starts when the solid and gas masses are about equal. It is engendered by a strong positive feedback on the gas accretion rates, driven by the rapid contraction of the gaseous envelope and the rapid expansion of the outer boundary, which depends on the planet's total mass. The overall evolutionary time scale is generally determined by the length of the second phase. The actual rates at which the giant planets accreted small planetesimals is probably intermediate between the constant rates assumed in most previous studies and the highly variable rates that we have used. Within the context, of the adopted model of planetesimal accretion, the joint constraints of the time scale for dissipation of the solar nebula and the current high-Z masses of the giant planets lead to estimates of the initial surface density (sigma(sub init)) of planetesimals in the outer region of the solar nebula. The results show sigma(sub init) approx. = 10 g/sq cm near Jupiter's orbit and that sigma(sub init) proportional to alpha(sup -2), where alpha is the distance from the Sun. These values are a factor of 3 - 4 times as high as that of the "minimum mass" solar nebula at Jupiter's distance and a factor of 2 - 3 times as high it Saturn's distance. Our estimates for the formation time of Jupiter and Saturn are 1 - 10 million years while those for Uranus fall in the range of 2 - 16 million years. These estimates follow from the properties of our Solar System and do not necessarily apply to giant planets in other planetary systems.

Pollack, James B.↗

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 NTRS1993

Planet formation

Models of planetary formation are developed using the present single example of a planetary system, supplemented by limited astrophysical observations of star-forming regions and circumstellar disks. The solar nebula theory and the planetesimal hypothesis are discussed. The latter is found to provide a viable theory of the growth of the terrestrial planets, the cores of the giant planets, and the smaller bodies present in the solar system. The formation of solid bodies of planetary size should be a common event, at least around young stars which do not have binary companions orbiting at planetary distances. Stochastic impacts of large bodies provide sufficient angular momentum to produce the obliquities of the planets. The masses and bulk compositions of the planets can be understood in a gross sense as resulting from planetary growth within a disk whose temperature and surface density decreased with distance from the growing sun.

Lissauer, Jack J.↗

NASA NTRS1992

Accretion rates of protoplanets. II - Gaussian distributions of planetesimal velocities

In the present growth-rate calculations for a protoplanet that is embedded in a disk of planetesimals with triaxial Gaussian velocity dispersion and uniform surface density, the protoplanet is on a circular orbit. The accretion rate in the two-body approximation is found to be enhanced by a factor of about 3 relative to the case where all planetesimals' eccentricities and inclinations are equal to the rms values of those disk variables having locally Gaussian velocity dispersion. This accretion-rate enhancement should be incorporated by all models that assume a single random velocity for all planetesimals in lieu of a Gaussian distribution.

Greenzweig, Yuval↗

NASA NTRS1991

The origin of the systematic component of planetary rotation. I - Planet on a circular orbit

A computation is undertaken of the rotation rate of a planet that has accreted from small solid planetesimals, as a function of the eccentricities of the planetesimals' orbits at or near the plane of the planet's orbit. The spin angular momentum generated by a given collision can be either positive or negative; due to the tendency to approximately cancel out, this perturbation process must be pursued to the second order in the ratio of the planetary radius to the planetesimal radial excursions' amplitude. It is found that material accreted from the area of the planet feeding zone's outer edges furnishes the planet positive spin angular momentum.

Lissauer, Jack J.↗

NASA NTRS1991

The random component of planetary rotation

In the present computation of the rms rotational angular momentum accumulated by a planet as a result of the stochastic off-center impacts of large planetesimals over the course of the accretionary epoch, planets' observed spin periods and obliquities were used to estimate the masses of the largest bodies which impacted each planet during its history. Several planets have likely undergone at least one collisional event with a body having over 5 percent of the planet's ultimate mass, thereby supporting giant-impact theories of the origins of the moon and Charon as well as the explanation of Mercury's excess Fe in terms of the partial collisional stripping of its mantle.

Lissauer, Jack J.↗

NASA NTRS1991

Long-term evolution of a planetesimal swarm in the vicinity of a protoplanet

Many models of planet formation involve scenarios in which one or a few large protoplanets interact with a swarm of much smaller planetesimals. In such scenarios, three-body perturbations by the protoplanet as well as mutual collisions and gravitational interactions between the swarm bodies are important in determining the velocity distribution of the swarm. We are developing a model to examine the effects of these processes on the evolution of a planetesimal swarm. The model consists of a combination of numerical integrations of the gravitational influence of one (or a few) massive protoplanets on swarm bodies together with a statistical treatment of the interactions between the planetesimals. Integrating the planetesimal orbits allows us to take into account effects that are difficult to model analytically or statistically, such as three-body collision cross-sections and resonant perturbations by the protoplanet, while using a statistical treatment for the particle-particle interactions allows us to use a large enough sample to obtain meaningful results.

Kary, David M.↗

NASA NTRS1991

Collision probabilities in the presence of nebular gas drag

We are developing a model to determine what fraction of the planetesimals would have hit a protoplanet on their sunward journey as opposed to having a close approach and passing into an inferior orbit. The model involves direct numerical integration of restricted-three-body orbits using a predictor-corrector integrator. A simple gas drag law with a v(exp 2) dependence was also included in the equations of motion. Runs of 100 to 500 particles were already performed, while some future runs may require several times this number in order to get good impact statistics. All planetesimals start in superior orbits with semi-major axes 5 to 10 R(sub H) from the protoplanets, where R(sub H) is the protoplanet's Hill Sphere radius. The orbit is followed until the planetesimal passed into an inferior orbit at least 10 R(sub H) from the protoplanet. This process typically requires 10(exp 4) to 10(exp 5) orbits.

Kary, David M.↗

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

A geometrical model for shepherding

Shepherding is the process by which a satellite secularly exchanges angular momentum with a nearby particle or gaseous disk. The sense of the torque is such that the separation between the orbits of the particles and the shepherd increases secularly with time. I devised a new technique to analyze the physical nature of shepherding through study of evolution of the vector eccentricity of the particles. This method appears to analyze the physical nature of shepherding in sparse particle disks. Thus, it may be very useful in calculating the torque on Neptune's rings and on protoplanets in the solar nebula. Moreover, the techniques are useful in estimating how long numerical simulations of resonant processes must be run in order to reach a quasi-steady state.

Lissauer, Jack J.↗

NASA NTRS1991

Accretion rates of protoplanets

The rate at which planetesimals in a uniform surface density disk collide with, and are (assumed to be) accreted by, a massive protoplanet is calculated. The collision cross-section of a protoplanet is enhanced relative to its geometric cross-section due to its gravitational focusing of planetesimal trajectories. The gravitation enhancement (eccentricities and inclinations) decrease. For large random velocity planetesimals, encounters are sufficiently rapid (less than or approximately = 5 percent of and orbital period) that F(sub g) is well approximated by the two-body particle in a box formula, which neglects the gravitational effect of the Sun. As planetesimal velocities decrease, F(sub g) increases to approximately twice the two-body value, and then rises less rapidly than the two-body value, eventually dropping below it and asymptotically approaching a constant for sufficiently small random velocities. A scaling argument is presented that generalizes the results to protoplanets of arbitrary mass, radius, and orbital semimajor axis. Gravitational scatterings by a protoplanet prevent random velocities of the planetesimals within its accretion zone from becoming to small. When gravitational stirring is included, the maximum plausible value of the gravitation enhancement factor for rock protoplanets 1 Au from the Sun is F(sub g) of approximately 1000. If one protoplanet dominates gravitational scatterings in a given region of a protoplanetary disk, then it was found that the planetesimal inclinations are excited much less rapidly than eccentricities, in contrast to the two-body approximation, in which energy is roughly equipartitioned between eccentric and inclined random motions. The resulting skewed velocity dispersion allows for a more rapid rate of protoplanet growth.

Greenzweig, Yuval↗

NASA NTRS1991

Accretion rates of protoplanets 2: Gaussian distribution of planestesimal velocities

The growth rate of a protoplanet embedded in a uniform surface density disk of planetesimals having a triaxial Gaussian velocity distribution was calculated. The longitudes of the aspses and nodes of the planetesimals are uniformly distributed, and the protoplanet is on a circular orbit. The accretion rate in the two body approximation is enhanced by a factor of approximately 3, compared to the case where all planetesimals have eccentricity and inclination equal to the root mean square (RMS) values of those variables in the Gaussian distribution disk. Numerical three body integrations show comparable enhancements, except when the RMS initial planetesimal eccentricities are extremely small. This enhancement in accretion rate should be incorporated by all models, analytical or numerical, which assume a single random velocity for all planetesimals, in lieu of a Gaussian distribution.

Greenzweig, Yuval↗

NASA NTRS1990

Accretion rates of protoplanets

Projections are made of the collision/accretion rates of planetesimals in a uniform surface-density disk with a massive protoplanet, whose collision cross-section is enhanced, relative to its geometric cross-section, by a gravitational focusing of the planetesimals' trajectories. A scaling method is presented which generalizes the results obtained to protoplanets of arbitrary mass, radius, and orbital semimajor axis. It is established that, in the case where one protoplanet dominates gravitational scattering in a given protoplanetary disk region, planetesimal inclinations are substantially less rapidly excited than eccentrocities; the skewed velocity dispersion thus generated allows for a more rapid rate of protoplanet growth.

Greenzweig, Yuval↗

NASA NTRS1990

Models of Neptune's arc rings

Models proposed to explain the dynamical confinement of such structures as incomplete arc rings in orbit about the planet Neptune are reviewed and tested against the currently available observational data. It is shown that satellites can confine arc rings to very limited radial and azimuthal extents via a combination of corotation and Lindblad resonances. The resonances can be produced by the same moon or by different moons.

Lissauer, Jack J.↗

NASA NTRS1989

Rotation of Halley's comet

Numerical simulations supported by analytical calculations are used to model the suspected condition of Comet Halley's nucleus, which has been suggested to not be in a state of principal-axis rotation. It is found easy to numerically generate lightcurves from modulated jets of material which exhibit both of the observed periodicities of 2.2 and 7.4 days, after choosing initial conditions for a representative nucleus such that the shorter period is the rotation period, and the longer period is that of precession of the spin vector in the body frame-of-reference. The improbability of exciting a spin precession about the axis of minimum moment-of-inertia, the relative instability of this state to the jet-induced torques, and the smaller probability of observing significant seasonal changes in the lightcurve in this state, all favor the model in which Halley's nucleus precesses about the axis of maximum moment-of-inertia.

Peale, S. J.↗

NASA NTRS1989

Erosion of circumstellar particle disks by interstellar dust

Circumstellar particle disks appear to be a common phenomenon; however, their properties vary greatly. Models of the evolution of such systems focus on internal mechanisms such as interparticle collisions and Poynting-Robertson drag. Herein it is shown that 'sandblasting' by interstellar dust can be an important and even dominant contributor to the evolution of circumstellar particle disks. Stars spend up to about 3 percent of their main-sequence lifetimes within atomic clouds. Among an IRAS sample of 21 nearby main-sequence A stars, beta Pictoris has the brightest disk; it also possesses the smallest random velocity and therefore the slowest predicted erosion rate.

Lissauer, Jack J.↗