Engineering topics

Wetherill, G. W.

Publications and source records attributed to Wetherill, G. W..

At least 19 records

NASA NTRS2000

Terrestrial planet and asteroid formation in the presence of giant planets. I. Relative velocities of planetesimals subject to Jupiter and Saturn perturbations

We investigate the orbital evolution of 10(13)- to 10(25) -g planetesimals near 1 AU and in the asteroid belt (near 2.6 AU) prior to the stage of evolution when the mutual perturbations between the planetesimals become important. We include nebular gas drag and the effects of Jupiter and Saturn at their present masses and in their present orbits. Gas drag introduces a size-dependent phasing of the secular perturbations, which leads to a pronounced dip in encounter velocities (Venc) between bodies of similar mass. Plantesimals of identical mass have Venc approximately 1 and approximately 10 m s-1 (near 1 and 2.6 AU, respectively) while bodies differing by approximately 10 in mass have Venc approximately 10 and approximately 100 m s-1 (near 1 and 2.6 AU, respectively). Under these conditions, growth, rather than erosion, will occur only by collisions of bodies of nearly the same mass. There will be essentially no gravitational focusing between bodies less than 10(22) to 10(25) g, allowing growth of planetary embryos in the terrestrial planet region to proceed in a slower nonrunaway fashion. The environment in the asteroid belt will be even more forbidding and it is uncertain whether even the severely depleted present asteroid belt could form under these conditions. The perturbations of Jupiter and Saturn are quite sensitive to their semi-major axes and decrease when the planets' heliocentric distances are increased to allow for protoplanet migration. It is possible, though not clearly demonstrated, that this could produce a depleted asteroid belt but permit formation of a system of terrestrial planet embryos on a approximately 10(6)-year timescale, initially by nonrunaway growth and transitioning to runaway growth after approximately 10(5) years. The calculations reported here are valid under the condition that the relative velocities of the bodies are determined only by Jupiter and Saturn perturbations and by gas drag, with no mutual perturbations between planetesimals. If, while subject to these conditions, the bodies become large enough for their mutual perturbations to influence their velocity and size evolution significantly, the problem becomes much more complex. This problem is under investigation.

NASA Discipline Exobiology↗

NASA NTRS1996

Ways that our Solar System helps us understand the formation of other planetary systems and ways that it doesn't

Models of planetary formation can be tested by comparison of their ability to predict features of our Solar System in a consistent way, and then extrapolated to other hypothetical planetary systems by different choice of parameters. When this is done, it is found that the resulting systems are insensitive to direct effects of the mass of the star, but do strongly depend on the properties of the disk, principally its surface density. Major uncertainty results from lack of an adequate theoretical model that predicts the existence, size, and distribution of analogs of our Solar System, particularly the gas giants Jupiter and Saturn. Nevertheless, reasons can be found for expecting that planetary systems, including those containing biologically habitable planets similar to Earth, may be abundant in the Galaxy and Universe.

NASA Discipline Exobiology↗

NASA NTRS1992

Giant and large impacts in the context of planetary formation theory

Of particular relevance to the subject of this workshop is the expected size and velocity distribution of the interplanetary projectiles during the late stages of planet formation. This will in turn be determined by the evolution of these distributions throughout the planet forming process. Even at this early stage of understanding, it seems clear that assumption of simple power-law mass distributions are certain to lead to incorrect conclusions. Furthermore, the lunar cratering evidence, valuable as it is for relatively late (i.e., less than 4.2 b.y.) events, cannot provide information regarding stochastic events of potentially moon-destroying energy expected to be experienced by the early Earth. The early stages of terrestrial planet formation are discussed in more detail.

Wetherill, G. W.↗

NASA NTRS1991

End products of cometary evolution - Cometary origin of earth-crossing bodies of asteroidal appearance

The present state of the understanding of the dynamic mechanisms under which the orbits of some comets evolve into those observed for Apollo-Amor objects is reviewed. Observed Jupiter-family objects of asteroidal appearance, e.g., 1983SA, are much more likely to be of cometary rather than asteroidal origin. 'Decoupling' is facilitated by several mechanisms: perturbations by terrestrial planets, perturbations by Jupiter and the other giant planets, and nongravitational orbital changes caused by the loss of gas and dust from the comet. The dynamical time scale for decoupling is argued to be 100,000-1,000,000 yr, and almost all decoupled comets are likely to be of asteroidal appearance. Estimates can be made of the number of cometary Apollo-Amor 'asteroids', the observed number of earth-crossing active and inactive short-period comets, and the production rate of short-period comets. These estimates are compatible with other theoretical and observational inferences that suggest the presence of a significant population of Apollo objects that formerly were active comets.

Wetherill, G. W.↗

NASA NTRS1989

Cratering of the terrestrial planets by Apollo objects

An asteroidal collision model and Monte Carlo program used for studies of the terrestrial meteorite flux, the steady-state number of Apollo-Amor objects, and the orbital distribution of both meteorites and Apollo-Amor objects is used to calculate absolute and relative cratering rates on the terrestrial planets. It is found that the 'best' estimates of the predicted asteroidal cratering rate are three times lower than estimates of the observed terrestrial cratering rate. If this is due to errors in the asteroidal production rate of Apollo-Amor objects, the predicted present-day cratering rate per unit area on Mars is four times that on earth, whereas that on Mercury is twice that on earth.

Wetherill, G. W.↗

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

Where do the Apollo objects come from?

The orbital evolutions of 1-45 km-diameter Apollo and Amor bodies generated by asteroid belt collisions interior to 2.6 AU are presently traced by Monte Carlo calculations. About 3 percent of the asteroidal fragments of this type and size that are ejected with velocities of 100 m/sec are perturbed into earth-crossing orbits by the 3:1 Jovian commensurability resonance at 2.5 AU, as well as a secular resonance in the innermost asteroid belt. While the initial earth-crossing orbits of these bodies are concentrated near 1 AU, their steady-state orbital distribution is widely dispersed. Additional objects that may be characterized as inactive comets are inferred from strongly suggestive data.

Wetherill, G. W.↗

NASA NTRS1988

Accumulation of Mercury from planetesimals

Calculations of 19 new Monte Carlo simulations of terrestrial planet growth were used in a study of the accumulation history of Mercury-size bodies. Three cases are presented, involving different assumptions regarding the initial state of the final stage of planetary accumulation and the degree and the ease with which planets can be collisionally disrupted. It is found that the same conditions that lead to Mars-size giant impacts on earth and Venus imply a more catastrophic fragmentation history for a Mercury-size bodies and the fragments from which it accumulated. It is also found that the terrestrial planets, including Mercury, will accumulate material originating over the entire terrestrial planet range of heliocentric distances.

Wetherill, G. W.↗

NASA NTRS1987

Accumulation of the planets

In modeling the accumulation of planetesimals into planets, it is appropriate to distinguish between two stages: an early stage, during which approximately 10 km diameter planetesimals accumulate locally to form bodies approximate 10 to the 25th g in mass; and a later stage in which the approximately 10 to the 25th g planetesimals accumulate into the final planets. In the terrestrial planet region, an initial planetesimal swarm corresponding to the critical mass of dust layer gravitational instabilities is considered. In order to better understand the accumulation history of Mercury-sized bodies, 19 Monte-Carlo simulations of terrestrial planet growth were calculated. A Monte Carlo technique was used to investigate the orbital evolution of asteroidal collision debris produced interior to 2.6 AU. It was found that there are two regions primarily responsible for production of Earth-crossing meteoritic material and Apollo objects. The same techniques were extended to include the origin of Earth-approaching asteroidal bodies. It is found that these same two resonant mechanisms predict a steady-state number of Apollo-Amor about 1/2 that estimated based on astronomical observations.

Wetherill, G. W.↗

NASA NTRS1986

Accumulation of the terrestrial planets and implications concerning lunar origin

In order to provide a context for understanding lunar formation, 28 new three-dimensional simulations of terrestrial planet formation from a gas-free planetesimal swarm have been carried out. The natural orbital and collisional evolution of 500 initial planetesimals ranging in mass from 5.7 x 10 to the 24th g to 1.1 x 10 to the 26th g is followed until only final planets in noncrossing orbits remain. The results are in general agreement with the number, size, and orbits of the observed terrestrial planets, but also show considerable variation of stochastic origin. These results are combined with 11 simulations using 500 bodies of equal initial mass presented earlier, as well as with some other numerical studies, to conclude that for a wide range of initial conditions, terrestrial planet accumulation was characterized by giant impacts, ranging in mass up to 3 times the mass of Mars, at typical impact velocities of about 9 km/sec. These large planetesimals and the impacts they produce are sufficient to explain the unexpectedly large angular momentum of the earth-moon system.

Wetherill, G. W.↗

NASA NTRS1985

The range of validity of the two-body approximation in models of terrestrial planet accumulation. II - Gravitational cross sections and runaway accretion

The validity of the two-body approximation in calculating encounters between planetesimals has been evaluated as a function of the ratio of unperturbed planetesimal velocity (with respect to a circular orbit) to mutual escape velocity when their surfaces are in contact (V/V-sub-e). Impact rates as a function of this ratio are calculated to within about 20 percent by numerical integration of the equations of motion. It is found that when the ratio is greater than 0.4 the two-body approximation is a good one. Consequences of reducing the ratio to less than 0.02 are examined. Factors leading to an optimal size for growth of planetesimals from a swarm of given eccentricity and placing a limit on the extent of runaway accretion are derived.

Wetherill, G. W.↗

NASA NTRS1985

Occurrence of giant impacts during the growth of the terrestrial planets

Three dimensional Monte Carlo simulations of the accumulation of the terrestrial planets in the absence of gas drag produced results that are in general agreement with the number and distribution of the present planets. The accumulation process appears to be characterized by impact of bodies as large as three times the mass of Mars at velocities of about 9 kilometers per second. These giant impacts on earth may have supplied the material and angular momentum that formed the moon, should have heated earth to the melting point, and may have been responsible for the differences in the content of inert gases of the atmospheres of earth and Venus.

Wetherill, G. W.↗

NASA NTRS1985

Accumulation of the Terrestrial Planets

The validity of the two body approximation in calculations of planetary growth is examined. Use of this approximation is essential to practical 3 dimensional simulations of planetary growth. With regard to gravitational perturbations, the changes in semimajor axis, eccentricity, and inclination resulting from close planetesimal encounters (near 1 A.U.) out to 10 Tisserand sphere of influence radii were calculated by two and three dimensional numerical integration. These were compared with the results of treating the encounter as a two body problem, as is customary in Monte Carlo calculations of orbital evolution and in numerical and analytical studies of planetary accumulation. It is found that for values of (V/V sub e) approx. 0.35 (V = relative velocity, V = escape velocity of largest body), the two body approximation fails to describe the outcome of individual encounters. In this low velocity region, the two body gravitational focusing cross section is no longer valid.

Wetherill, G. W.↗

NASA NTRS1985

Asteroidal source of ordinary chondrites (Meteoritical Society Presidential Address 1984)

The orbital evolution of asteroidal fragments injected into the 3-1 Kirkwood gap resonance at 2.5 AU is investigated on the basis of a Monte Carlo simulation. The diameters of the fragments in the simulation were between 10 cm and 20 km, and it was assumed that the fragments cross the orbital path of the earth every one million years. The effects of close encounter planetary perturbations, the nu dot 6 secular resonance, and the ablative effects of the earth atmosphere were also taken into account. It is found that: (1) the predicted meteorite orbits closely matched the known orbits of ordinary chondrites; and (2) the total flux was in approximate agreement with the observed fall rate of ordinary chondrites. About 90 percent of the predicted impacting bodies were created by fragmentation of larger earth crossing asteroidal fragments, the largest of which were observed in the vicinity of the Apollo-Amor objects. The numerical results are presented in a series of graphs.

Wetherill, G. W.↗

NASA NTRS1984

Grain abundance in the primordial atmosphere of the earth

For models of planetary accumulation in the presence of solar nebular gas, the initial surface temperature of the earth is controlled by the grain opacity of the atmosphere. The surface temperature in turn controls the quantity of neon dissolved and trapped within the interior of the earth. To compare accumulation theory with observation, calculations have been made of the grain opacity expected to be associated with accumulation in a gaseous nebula. There are two parameters that are in principle determined by the theory, but actually are at present uncertain: the mean eccentricity(e) of the planetesimal swarm, and the fraction (xi) of the accretional energy that is expended in the release of grains into the atmosphere by ablation of the incoming planetesimal. It is found that if e is low (0.001), rather low values of xi (0.00001) are required to match the observed neon data. In contrast higher values of xi (0.1) are required for the most probable case with e = 0.01. For the high-eccentricity case (e = 0.1), xi must be greater than 0.01. The results show that avoidance of excess trapped neon of solar composition places restrictive, but not necessarily impossible, conditions on the parameters of the accumulation theory.

Mizuno, H.↗

NASA NTRS1984

The asteroidal source region of ordinary chondrites

The final, Earth-impacting orbits of ordinary chondritic meteorites have a very special distribution. By use of visual radiant and time of fall data, as well as photographic fireball orbits (1) it is inferred that chondrite perihelia are concentrated near 1 A.U., eccentricities are usually rather high (approximately 0.5), and inclinations are low (approximately 10 deg). Velocity selection resulting from atmospheric ablation plays a significant role in determining this orbital distribution, but by no means suffices to explain it. The observed distribution is a fragile one, and can easily be destroyed by Earth and Venus perturbations. This places severe constraints on the location of the original source bodies, of which these meteorites are fragments. New calculations were made of the expected distribution of final orbits from a range of initial sources, taking into consideration close encounter planetary perturbations, secular resonance, destruction by collision in space, and atmospheric ablation.

Wetherill, G. W.↗

NASA NTRS1981

Solar wind origin of Ar-36 on Venus

An examination is conducted concerning the circumstances under which the difference between earth and Venus (and Mars) fits naturally into theories in which the terrestrial planets formed by the gradual sweeping up of planetesimals in an essentially gas-free protoplanetary swarm. The primary purpose of the reported investigation is to use observational data to define restrictions on planetary formation theories that would be imposed if most of Venus' inert gases come from the solar wind. The observational data support the suggestion that the abundances of Ar, Kr, and Xe on Venus have been augmented by a component of solar composition. Solar wind implantation at an early stage of accumulation provides a natural way of producing the observed extreme heliocentric distribution of this component, provided that accumulation occurred after dissipation of solar gas from the solar nebula

Wetherill, G. W.↗

NASA NTRS1981

Nature and origin of basin-forming projectiles

The formation of the observed lunar multi-ring basins is discussed in the context of current theories of terrestrial planet formation, particularly those in which these planets formed by the accumulation of large planetesimals. The observed number, size, and timing of lunar basin-forming impacts is in the range expected for such theories. Tidal disruption during close encounters to earth and Venus can provide a single mechanism that explains a number of details concerning the number, size distribution, and stochastic nature of the timing of these impacts. A basin time scale is suggested in which Nectaris is associated with the 4.1 b.y. age of the Apollo 16 light matrix breccias. In accordance with the present consensus, Serenitatis is 3.86 b.y., Imbrium and Orientale 3.80-3.82 b.y. in age. Other nearside circular basins (e.g., Humorum and Crisium) are intermediate in age between 3.86 and 4.12 b.y. The large number of 3.8-3.9 b.y. ages is attributed primarily to the magnitude of the Imbrium and Serenitatis impacts, and sampling bias resulting from concentration of collection sites in proximity to these basins.

Wetherill, G. W.↗