Engineering topics
Publications and source records attributed to Lissauer, Jack J..
The Earth is teeming with life, which, occupies a diverse array of environments; other bodies in our Solar System offer fewer, if any, niches which are habitable by life as we know it. Nonetheless, astronomical studies suggest that a large number of habitable planets-are likely to be present within our Galaxy.
We have conducted a set of approximately 200 numerical experiments to test the hypothesis that a giant impact leading to the formation of Earth's Moon could have occurred tens of millions of years after most of the small debris in the inner Solar System had been incorporated into terrestrial planets or been removed from the region. More than half of these simulations ended with a giant impact between two of the five terrestrial planets that were initially present. Neglecting any rotational angular momentum prior to the collision, the merged planet typically has a rotation period of less than five hours. The mean planetary obliquity is 91.7 degrees, and the median is 87.9 degrees; thus, there is no statistically significant difference between the number of bodies with prograde rotation and the number with retrograde rotation. There is a paucity of planets with obliquity close to 90 degrees, but the total number of impacts was too small for this result to be of much significance. Several encounters leading to collisions are dominated by three-body effects, with the velocity at impact being slightly less than the free-space escape velocity of the two bodies; the obliquity distribution produced by these impacts appears to be random.
We present results of long-term numerical orbital integrations designed to test the stability of the three-planet system orbiting Upsilon Andromedae and short-term integrations to test whether mutual perturbations among the planets can be used to determine planetary masses. Our initial conditions are based on the latest fits to the radial velocity data obtained by the planet-search group at Lick Observatory. The new fits result in significantly more stable systems than did the initially announced planetary parameters. An analytic analysis of the star and the two outer planets shows that this subsystem is Hill stable up to five. Our integrations involving all three planets show that the system is stable for at least 100 Myr for up to four. In our simulations, we still see a secular resonance between the outer two planets and in some cases large oscillations in the eccentricity of the inner planet.
If a planetary-mass body were present in the asteroid belt, the orbits of the terrestrial planets and those of the giant planets would be more closely coupled. A greater exchange in angular momentum could affect the stability of the terrestrial planets. To study this effect, we have simulated several systems consisting of the Solar System planets and a 0.1 - 10 Earth mass object on the orbit of a main belt asteroid. An integration with Ceres at five Earth masses remained stable for a billion years. Ceres at ten Earth masses, however, caused the system to become unstable at 25 - 50 million years. When additional mass was given to both Ceres (bringing it up to five Earth masses) and Mars (one Earth mass), the systems self-destructed within 40 million years. Systems with Pallas at five Earth masses became unstable at 150 - 170 million years. Vesta at five Earth masses caused the system to become unstable in as little as 13 million years, but systems with Vesta at two Earth masses remained stable for 100 million years.
Theories of planet formation indicate that a diverse range of physical and chemical processes determine the characteristics of a planetary system. Extensive numerical modeling is required to understand how planetary systems form, and to make quantitative assessments of the factors which determine the masses, spacings and volatile compound inventories of planets and small bodies within a planetary system. Fluid flow problems associated with the formation and evolution of protoplanetary disks include specific local calculations to provide physical insight, which are best performed on workstations, and large multifaceted simulations which require supercomputers with large memories. Formation and early growth of planetesimals display a similar range of computational requirements. Modeling the late stages of planetary accumulation is very CPU intensive, as it requires following a simple system of approx. hundreds of bodies for millions of dynamical (orbital) times. These varied computational needs could be met in the most cost-effective manner by a diverse set of computers, including workstations for individual PI's and dedicated time on various types of supercomputers which are specialized for differing tasks.
An overview of current theories of planetary growth, emphasizing the formation of habitable planets, is presented. These models are based upon observations of the Solar System and of young stars and their environments. They predict that rocky planets should form around most single stars, although it is possible that in some cases such planets are lost - to orbital decay within the protoplanetary disk. Terrestrial planets are believed to grow via pairwise accretion until the spacing of planetary orbits becomes large enough that the configuration is stable for the age of the system. Giant planets begin their growth like terrestrial planets, but if they become massive enough before the protoplanetary disk dissipates, then they are able to accumulate substantial amounts of gas. Specific issues to be discussed include: (1) how do giant planets influence the formation and habitability of terrestrial planets? (2) could a giant impact leading to lunar formation have occurred - 100 million years after the condensation of the oldest meteorites?
An overview of current theories of star and planet formation is presented. These models are based upon observations of the Solar System and of young stars and their environments. They predict that rocky planets should form around most single stars, although it is possible that in some cases-such planets are lost to orbital decay within the protoplanetary disk. The frequency of formation of gas giant planets is more difficult to predict theoretically. Terrestrial planets are believed to grow via pairwise accretion until the spacing of planetary orbits becomes large enough that the configuration is stable for the age of the system. Giant planets begin their growth like terrestrial planets, but they become massive enough that they are able to accumulate substantial amounts of gas before the protoplanetary disk dissipates. Specific issues to be discussed include: (1) how large a solid core is needed to initiate rapid accumulation of gas? (2) can giant planets form very close to stars? (3) could a giant impact leading to lunar formation have occurred approx. 100 million years after the condensation of the oldest meteorites?
An overview of current theories of star and planet formation is presented. These models are based upon observations of the Solar System and of young stars and their environments. They predict that rocky planets should form around most single stars, although it is possible that in some cases such planets are lost to orbital decay within the protoplanetary disk. The frequency of formation of gas giant planets is more difficult to predict theoretically. Terrestrial planets are believed to grow via pairwise accretion until the spacing of planetary orbits becomes large enough that the configuration is stable for the age of the system. Giant planets begin their growth like terrestrial planets, but they become massive enough that they are able to accumulate substantial amounts of gas before the protoplanetary disk dissipates.
Modern theories of star and planet formation and of the orbital stability of planetary systems are described and used to discuss possible characteristics of undiscovered planetary systems. The most detailed models of planetary growth are based upon observations of planets and smaller bodies within our own Solar System and of young stars and their environments. Terrestrial planets are believed to grow via pairwise accretion until the spacing of planetary orbits becomes large enough that the configuration is stable for the age of the system. Giant planets begin their growth as do terrestrial planets, but they become massive enough that they are able to accumulate substantial amounts of gas before the protoplanetary disk dissipates. These models 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. A 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, and the methods that are being used and planned for detecting and characterizing extrasolar planets are reviewed.
An overview of current theories of planetary formation, with emphasis on giant planets, is presented. The most detailed models are based upon observations of our own Solar System and of young stars and their environments. While these models predict that rocky planets should form around most single stars, the frequency of formation of gas giant planets is more difficult to predict theoretically. Terrestrial planets are believed to grow via pairwise accretion until the spacing of planetary orbits becomes large enough that the configuration is stable for the age of the system. Giant planets begin their growth as do terrestrial planets, but they become massive enough that they are able to accumulate substantial amounts of gas before the protoplanetary disk dissipates. Most models for extrasolar giant planets suggest that they formed as did Jupiter and Saturn (in nearly circular orbits, far enough from the star that ice could), and subsequently migrated to their current positions, although some models suggest in situ formation.
An overview of current theories of the formation of our Solar System, with emphasis on giant planets, is presented. The most detailed models are based upon observations of planets and smaller bodies within our own Solar System and of young stars and their environments. Terrestrial planets are believed to grow via pairwise accretion until the spacing of planetary orbits becomes large enough that the configuration is stable for the age of the system. Giant planets begin their growth as do terrestrial planets, but they become massive enough that they are able to accumulate substantial amounts of gas before the protoplanetary disk dissipates. Larger disk mass allows for faster growth of solid planetary bodies. The ability of a solid planet to trap gas from the protoplanetary disk increases rapidly as its mass increases (because the depth of its gravitational potential well increases), but decreases as the planetesimal accretion rate is increased (as it becomes hotter). The net effect of increasing disk mass is that gas giant planets form more rapidly, but with larger core masses. Observations of circumstellar disks suggest an upper bound on the time available prior to dissipation of the gas, and planetary models place upper limits on core sizes. Together, these constraints suggest that Jupiter and Saturn formed in 1-10 million years, and the density of solids in the region of their formation was a few times as large as the lower bound provided by the traditional minimum mass nebula.
An overview of current theories of star and planet formation, with emphasis on terrestrial planet accretion and the formation of the Earth-Moon system is presented. These models are based upon observations of the Solar System and of young stars and their environments. They predict that rocky planets should form around most single stars, although it is possible that in some cases such planets are lost to orbital decay within the protoplanetary disk. The frequency of formation of gas giant planets is more difficult to predict theoretically. Terrestrial planets are believed to grow via pairwise accretion until the spacing of planetary orbits becomes large enough that the configuration is stable for the age of the system. Giant impacts during the final stages of growth can produce large planetary satellites, such as Earth's Moon. Giant planets begin their growth like terrestrial planets, but they become massive enough that they are able to accumulate substantial amounts of gas before the protoplanetary disk dissipates.
If Earth lies in or near the orbital plane of an extrasolar planet, that planet passes in front of the disk of its star once each orbit as viewed from Earth. Precise photometry can reveal such transits, which can be distinguished from rotationally-modulated starspots and intrinsic stellar variability by their periodicity, square-well shapes and relative spectral neutrality. Transit observations would provide the size and orbital period of the detected planet. Although geometrical considerations limit the fraction of planets detectable by this technique, many stars can be surveyed within the field of view of one telescope, so transit photometry is quite efficient. Scintillation in and variability of Earth's atmosphere limit photometric precision to roughly one-thousandth of a magnitude, allowing detection of transits by Jupiter-sized planets but not by Earth-sized planets from the ground. The COROT spacecraft will be able to detect Uranus-sized planets orbiting near stars. The Kepler Mission, which is being proposed to NASA's Discovery Program this year, will have a photometer with a larger aperture (1 meter) than will COROT, so it will be able to detect transits by planets as small as Earth. Moreover, the Kepler mission will examine the same star field for four years, allowing confirmation of planets with orbital periods of a year. If the Sun's planetary system is typical for single stars, Kepler should detect approximately 480 terrestrial planets. Assuming the statistics from radial velocity surveys are typical, Kepler should also detect transits of 150 inner giant planets and reflected light variations of 1400 giant planets with orbital periods of less than one week.
An overview of current theories of star and planet formation is presented. These models are based upon observations of the Solar System and of young stars and their environments. They predict that rocky planets should form around most single stars, although it is possible that in some cases such planets are lost to orbital decay within the protoplanetary disk. The frequency of formation of gas giant planets is more difficult to predict theoretically. Terrestrial planets are believed to grow via pairwise accretion until the spacing of planetary orbits becomes large enough that the configuration is stable for the age of the system. Giant planets begin their growth like terrestrial planets, but they become massive enough that they are able to accumulate substantial amounts of gas before the protoplanetary disk dissipates.
An overview of current theories of star and planet formation is presented. These models are based upon observations of the Solar System and of young stars and their environments. They predict that rocky planets should form around most single stars, although it is possible that in some cases such planets are lost to orbital decay within the protoplanetary disk. The frequency of formation of gas giant planets is more difficult to predict theoretically. Terrestrial planets are believed to grow via pairwise accretion until the spacing of planetary orbits becomes large enough that the configuration is stable for the age of the system. Giant planets begin their growth like terrestrial planets, but they become massive enough that they are able to accumulate substantial amounts of gas before the protoplanetary disk dissipates.
An overview of current theories of the formation of our Solar System, with emphasis on giant planets, is presented. The most detailed models are based upon observations of planets and smaller bodies within our own Solar System and of young stars and their environments. Terrestrial planets are believed to grow via pairwise accretion until the spacing of planetary orbits becomes large enough that the configuration is stable for the age of the system. Giant planets begin their growth as do terrestrial planets, but they become massive enough that they are able to accumulate substantial amounts of gas before the protoplanetary disk dissipates. Larger disk mass allows for faster growth of solid planetary bodies. The ability of a solid planet to trap gas from the protoplanetary disk increases rapidly as its mass increases (because the depth of its gravitational potential well increases), but decreases as the planetesimal accretion rate is increased (as it becomes hotter). The net effect of increasing disk mass is that gas giant planets form more rapidly, but with larger core masses. Observations of circumstellar disks suggest an upper bound on the time available prior to dissipation of the gas, and planetary models place upper limits on core sizes. Together, these constraints suggest that Jupiter and Saturn formed in 1 - 10 million years, and the density of solids in the region of their formation was a few times as large as the lower bound provided by the traditional minimum mass nebula.
The process of planetary growth is extremely complicated, involving a myriad of physical and chemical processes, many of which are poorly understood. The ultimate configuration that a planetary system attains depends upon the properties of the disk out of which it grew, of the star at the center of the disk and, at least in some cases, of the interstellar environment. In an effort to numerically survey the possible diversity of planetary systems, we have constructed synthetic systems of giant planets and integrated their orbits to determine the dynamical lifetimes and thus the viability of these systems. Our construction algorithm begins with 110 -- 180 planetesimals located between 4 and 40 AU from a one solar mass star; most initial planetesimals have masses several tenths that of Earth. We integrate the orbits of these bodies subject to mutual gravitational perturbations and -as drag for 10(exp 6) - 10(exp 7) years, merging any pair of planetesimals which pass within one-tenth of a Hill Sphere of one another and adding "gas" to embryos larger than 10 Earth masses. Use of such large planetesimal radii provided sufficient damping to prevent the system from excessive dynamical heating. Subsequently, systems were evolved without gas drag, either with the enlarged radii or with more realistic radii. Systems took from a few million years to greater than ten billion years to become stable (10(exp 9) years without mergers of ejections). Some of the systems produced with the enlarged radii closely resemble our outer Solar System. Many systems contained only Uranus-mass objects. Encounters in simulations using realistic radii resulted in ejections, typically leaving only a few planets per system, most of which were on very eccentric orbits. Some of the systems that we constructed were stable for at least a billion years despite undergoing macroscopic orbital changes on much shorter timescales.
An overview of current theories of star and planet formation is presented. These models are based upon observations of the Solar System and of young stars and their environments, and they predict that rocky planets should form around most single stars, although it is possible that in some cases such planets are lost to orbital decay within the protoplanetary disk. The frequency of formation of gas giant planets is more difficult to predict theoretically. Terrestrial planets are believed to grow via pairwise accretion until the spacing of planetary orbits becomes large enough that the configuration is stable for the age of the system. Giant planets begin their growth like terrestrial planets, but they become massive enough that they are able to accumulate substantial amounts of gas before the protoplanetary disk dissipates.