Engineering topics

Ward, William R.

Publications and source records attributed to Ward, William R..

15 records

NASA NTRS2003

Type II Migration and Giant Planet Survival

Type II migration, in which a newly formed large planet opens a gap in its precursor circumstellar nebula and subsequently evolves with it, has been implicated as a delivery mechanism responsible for close stellar companions. Large scale migration is possible in a viscously spreading disk of surface density sigma (r,t) when most of it is sacrificed to the primary in order to promote a small portion of the disk to much higher angular momentum orbits. Embedded planets generally follow its evolution unless their own angular momentum is comparable to that of the disk. The fraction of the starting disk mass, M (sub d) = 2pi integral rsigma(r,0)dr, that is consumed by the star depends on the distance at which material escapes the disk's outer boundary. If the disk is allowed to expand indefinitely, virtually all of the disk will fall into the primary in order to send a vanishingly small portion to infinity. For such a case, it is difficult to explain the survival of any giant planets, including Jupiter and Saturn. Realistically, however, there are processes that could truncate a disk at a finite distance, r(sub d). Recent numerical modeling has illustrated that planets can survive in this case. We show here that much of these results can be understood by simple conservation arguments.

Ward, William R.↗

NASA NTRS2000

Satellite Recoil from a Circumplanetary Disk

The eccentricity and inclination acquired by a satellite during its recoil from a disk interior to the Roche limit are estimated. Possible implications for the early history of the Earth-Moon system are discussed.

Ward, William R.↗

NASA NTRS1998

Dynamics of the Trans-Neptune Region: Apsidal Waves in the Kuiper Belt

The role of apsidal density waves propagating in a primordial trans-Neptune disk (i.e., Kuiper belt) is investigated. It is shown that Neptune launches apsidal waves at its secular resonance near 40 AU that propagate radially outward, deeper into the particle disk. The wavelength of apsidal waves is considerably longer than waves that might be launched at Lindblad resonances, because the pattern speed, g(sub s), resulting from the apsis precession of Neptune is much slower than its mean motion, Omega(sub s). If the early Kuiper belt had a sufficient surface density, sigma, the disk's wave response to Neptune's secular perturbation would have spread the disturbing torque radially over a collective scale lambda(sub *) approx. = r(2(mu)(sub d)Omega/ absolute value of r dg/dr)(sup 1/2), where mu(sub d)equivalent pi(sigma)r(exp 2)/(1 solar mass) and Omega(r) and g(r) are respectively the mean motion and precession frequency of the disk particles. This results in considerably smaller eccentricities at resonance than had the disk particles been treated as noninteracting test particles. Consequently, particles are less apt to be excited into planet-crossing orbits, implying that the erosion timescales reported by earlier test-particle simulations of the Kuiper belt may be underestimated. It is also shown that the torque the disk exerts upon the planet (due to its gravitational attraction for the disk's spiral wave pattern) damps the planet's eccentricity and further inhibits the planet's ability to erode the disk. Key words: celestial mechanics, stellar dynamics - comets: general minor planets, asteroids

Ward, William R.↗

NASA NTRS1998

Neptune's Eccentricity and the Nature of the Kuiper Belt

The small eccentricity of Neptune may be a direct consequence of apsidal wave interaction with the trans-Neptune population of debris called the Kuiper belt. The Kuiper belt is subject to resonant perturbations from Neptune, so that the transport of angular momentum by density waves can result in orbital evolution of Neptune as well as changes in the structure of the Kuiper belt. In particular, for a belt eroded out to the vicinity of Neptune's 2:1 resonance at about 48 astronomical units, Neptune's eccentricity can damp to its current value over the age of the solar system if the belt contains slightly more than an earth mass of material out to about 75 astronomical units.

Ward, William R.↗

NASA NTRS1997

Dynamics of the Trans-Neptune Region: Apsidal Waves in the Kuiper Belt

Trans-Neptune↗

NASA NTRS1997

On Planet Formation and Migration

Some consequences of protoplanet migration for the planetary formatin process are discussed. Migration of planet-sized objects can be caused by disk tidal torques.

Protoplanet Migration Planetary Formation↗

NASA NTRS1995

Disk tides and accretion runaway

It is suggested that tidal interaction of an accreting planetary embryo with the gaseous preplanetary disk may provide a mechanism to breach the so-called runaway limit during the formation of the giant planet cores. The disk tidal torque converts a would-be shepherding object into a 'predator,' which can continue to cannibalize the planetesimal disk. This is more likely to occur in the giant planet region than in the terrestrial zone, providing a natural cause for Jupiter to predate the inner planets and form within the O(10(exp 7) yr) lifetime of the nebula.

Ward, William R.↗

NASA NTRS1994

Damping of orbital inclinations by bending waves

An inclined secondary orbiting in a disk will launch bending waves from resonance sites where the Doppler shifted forcing frequency matches the disk's natural frequency for vertical oscillations. These vertical resonances are of two types: external resonances falling interior and exterior to the perturber's semimajor axis that excite its inclination and coorbiting resonances that fall at the perturber's orbit and damp its inclination. We show that torques from coorbiting resonances dominate the bending wave interaction for a constant density disk. In this case the inclination ultimately decay and an estimate of the characteristic time scale for this process is made.

Ward, William R.↗

NASA NTRS1992

Long-term orbital and spin dynamics of Mars

This review of the long-term dynamical behavior of Mars covers secular variations of the orbit, oscillations of the obliquity, and polar wandering. Calculations of the large-scale obliquity oscillations of Mars are updated using the most recent orbit theory and contrasted with the earth. The motion for Mars is characterized by about 100,000-yr oscillations driven by differential spin axis and orbit plane precession rates during which the obliquity may change by as much as about 20 deg. The possible role of spin-orbit secular resonances to the spin axis histories of the earth and Mars is also considered. Numerical integrations of the equations of motion indicate that Mars may have passed through resonance as little as 5 Myr ago and that obliquities approaching about 45 deg could have been achieved during such an event.

Ward, William R.↗

NASA NTRS1991

Resonant obliquity of Mars?

The large-scale oscillations generated by the obliquity of Mars through spin-axis and orbit-plane precessions constitute basic climate system drivers with periodicities of 100,000 yrs in differential spin axis-orbit precession rates and of over 1 million yrs in amplitude modulations due to orbital-inclination changes. Attention is presently given to a third time-scale for climate change, which involves a possible spin-spin resonance and whose mechanism operates on a 10-million-yr time-scale: this effect implies an average obliquity increase for Mars of 15 deg only 5 million yrs ago, with important climatic consequences.

Ward, William R.↗

NASA NTRS1991

Bending waves and orbital inclinations

Disk tides may play an important role in the formation of a planetary system. Modification of protoplanet semi-major axes and eccentricities through density waves was suggested and calculations of linear and non-linear protoplanet-nebula interactions were carried out by a number of researchers. The possible significance of radial drift to the accretion process was discussed, while the evolution of orbital eccentricities was studied for a perturber orbiting external to a ring and for a perturber embedded in the ring. The possible importance of bending waves to the early evolution of protoplanet inclinations is described.

Ward, William R.↗

NASA NTRS1989

Orbital migration of protoplanets - The inertial limit

The dynamical evolution of a disk and the orbital migration of an embedded protoplanet are examined. It is shown how the migration of a protoplanet due to density wave torques can suppress the tendency for tidal truncation of the disk. A critical mass is determined as a function of the disk properties that represents the limiting mass that can sustain drift without stalling. This inertial limit is derived analytically, using a quasi-steady state theory, and confirmed by numerical experiment. This result contradicts the claim of Lin and Papaloizou (1986) that such a limit does not exist. Orbital mobility of objects due to density wave torques may have played an important role in the early evolution of the solar system.

Ward, William R.↗

NASA NTRS1989

On the rapid formation of giant planet cores

The formation of the ice-rock cores of the giant planets by density wave-assisted accretion is outlined. The process could be rapid (100,000-1,000,000 yr) and completed within the probable lifetime of the solar nebula. The mechanism works for both Jupiter and Saturn and does not require a large excess of mass over that believed present in their cores.

Ward, William R.↗

NASA NTRS1989

Corotation torques in the solar nebula - The cutoff function

The behavior of high-order corotation resonances in a disk of finite thickness is examined. The torque exerted at an mth-order resonance is determined by employing a vertically averaged disturbing function, and the ratio of this torque to that exerted on a cold, two-dimensional disk is identified as the so-called torque cutoff function. This function is then used to calculate contributions from the corotation torques to eccentricity variations of a perturber's orbit assumed orbiting in the disk.

Ward, William R.↗

NASA NTRS1988

On disk-planet interactions and orbital eccentricities

While Lindblad resonances both within and without a perturber's orbit excite its eccentricity, the present study of the eccentricity evolution due to the density wave interaction between a planetesimal and a Keplerian disk notes that coronation resonances in these regions lose their eccentricity damping effectiveness if the object is embedded in a continuous disk without a gap. Attention is given to another class of Lindblad resonances which, under these conditions, operates on disk material coorbiting with the perturber; these resonances thereby become the most important source of eccentricity damping. A model problem indicates that eccentricity ultimately undergoes decay.

Ward, William R.↗