Engineering topics
Publications and source records attributed to Wetherill, George W..
The purpose of this project is to increase understanding of planet forming processes that are likely to have occurred in the Solar System during its early evolution. This was accomplished by development of computer models that are compatible with the present state of the Solar System as well as with observational and theoretical data attained from astrophysical observations and theory.
During the past decade, progress has been made by relating the 'standard model' for the formation of planetary systems to computational and observational advances. A significant contribution to this has been provided by this grant. The consequence of this is that the rigor of the physical modeling has improved considerably. This has identified discrepancies between the predictions of the standard model and recent observations of extrasolar planets. In some cases, the discrepancies can be resolved by recognition of the stochastic nature of the planetary formation process, leading to variations in the final state of a planetary system. In other cases, it seems more likely that there are major deficiencies in the standard model, requiring our identifying variations to the model that are not so strongly constrained to our Solar System.
The formation of the gas giant planets Jupiter and Saturn probably required the growth of massive approximately 15 Earth-mass cores on a time scale shorter than the approximately 10(exp 7) time scale for removal of nebular gas. Relatively minor variations in nebular parameters could preclude the growth of full-size gas giants even in systems in which the terrestrial planet region is similar to our own. Systems containing 'failed Jupiters,' resembling Uranus and Neptune in their failure to capture much nebular gas, would be expected to contain more densely populated cometary source regions. They will also eject a smaller number of comets into interstellar space. If systems of this kind were the norm, observation of hyperbolic comets would be unexpected. Monte Carlo calculations of the orbital evolution of region of such systems (the Kuiper belt) indicate that throughout Earth history the cometary impact flux in their terrestrial planet regions would be approximately 1000 times greater than in our Solar System. It may be speculated that this could frustrate the evolution of organisms that observe and seek to understand their planetary system. For this reason our observation of these planets in our Solar System may tell us nothing about the probability of similar gas giants occurring in other planetary systems. This situation can be corrected by observation of an unbiased sample of planetary systems.
Observation of circumstellar disks, regular satellite systems of outer planets, and planet-size objects orbiting pulsars support the supposition that formation of planetary systems is a robust, rather than a fragile, byproduct of the formation and evolution of stars. The extent to which these systems may be expected to resemble one another and our Solar System, either in overall structure or in detail remains uncertain. When the full range of possible stellar masses, disk masses, and initial specific angular momenta are considered, the possible variety of planetary configurations is very large. Numerical modeling indicates a difference between the formation of small, inner, terrestrial planets and the outer planets.
Present theories of terrestrial planet formation predict the rapid 'runaway formation' of planetary embryos. The sizes of the embryos increase with heliocentric distance. These embryos then emerge to form planets. In earlier Monte Carlo simulations of the merger of these embryos it was assumed that embryos did not form in the asteroid belt, but this assumption may not be valid. Simulations in which runaways were allowed to form in the asteroid belt show that, although the initial distributions of mass, energy, and angular momentum are different from those observed today, during the growth of the planets these distributions spontaneously evolve toward those observed, simply as a result of known solar system processes. Even when a large planet analogous to 'Jupiter' does not form, an earth-sized planet is almost always found near earth's heliocentric distance. These results suggest that occurrence of earthlike planets may be a common feature of planetary systems.
Formation of the terrestrial planets from planetesimals is discussed. The following subject areas are covered: (1) formation of the original planetesimals; (2) growth of planetesimals into planetary embryos; and (3) growth of runaway planetary embryos into terrestrial planets.
Three cases for which the analytic solutions to the planetary embryo coagulation equation are known, namely those of constant coagulation rate, of rate proportional to the sum of the masses of the two colliding bodies, and of rate proportional to the product of their masses, are presently used to test the mathematical validity of the Wetherill and Stewart (1989) physical model for the evolution of planetary embryos' mass distribution. In all cases, excellent agreement is found between numerical physical modeling results and those of the analytic solutions. The treatment of the runaway case can proceed via extension of the efforts of Trubnikov (1971).
The origin of the earth is discussed in the context of the formation of the sun and the planets, and a standard model for such a formation assuming gravitational instability in a dense interstellar molecular cloud is outlined, along with the most significant variant of the model in which the loss of the nebular gas occurred after the formation of the earth. The formation of the sun and solar nebulae is addressed, and the coagulation of grains and the formation of small planetesimals are covered, along with the gravitational accumulation of planetesimals into planetary embryos and final stages of accumulation - embryos of planets. It is pointed out that the final stage of accumulation consists of the collision of these embryos; because of their large size, particularly after their further growth, these collisions represent giant impacts. It is concluded that the earth was initially an extremely hot and melted planet, surrounded by a fragile atmosphere and subject to violent impacts by bodies of the size of Ceres and even the moon.
Earlier and current concepts relevant to the origin of the asteroid belt are discussed and are considered in the framework of the solar system origin. Numerical and analytical solutions of the dynamical theory of planetesimal accumulation are characterized by bifurcations into runaway and nonrunaway solutions, and it is emphasized that the differences in time scales resulting from runaway and nonrunaway growth can be more important than conventional time scale differences determined by heliocentric distances. It is concluded that, in principle, it is possible to combine new calculations with previous work to formulate a theory of the asteroidal accumulation consistent with the meteoritic record and with work on the formation of terrestrial planets. Problems remaining to be addressed before a mature theory can be formulated are discussed.
The current status on the theories of the solar-system formation is overviewed with emphasis placed on the principal concepts and processes involved. These processes include the formation of about 1 to 10 km diam planetesimals from the dust of the solar nebula; the physical processes that govern the interaction of these planetesimals with one another, which control their size and their velocity distribution; the circumstances that determine the way in which the planetesimals grow into planetary embryos; the processes that are likely to be important during the final stages of accumulation; and the possible origin of differences between the accumulation of the terrestrial planets, the giant planets, and the asteroids.
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.
The hypothesis that most meteorites are asteroid fragments generated by comparatively recent collisions in the asteroid belt runs up against spectrophotometric data indicating that asteroids with the composition of the most abundant meteorite class are either rare or absent in the asteroid belt. An understanding of the origin and evolution of the asteroid belt is essential to an adequate interpretation of meteoritic data; conversely, the detailed early asteroidal history preserved in the meteorites provides evidence otherwise unavailable for the earliest history of any other planetary bodies.
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.