Engineering topics

Ward, W. R.

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

At least 19 records

NASA NTRS1986

Density waves in the solar nebula - Differential Lindblad torque

The differential torque exerted by Lindblad resonances on a perturbing object embedded in a two-dimensional nonself-gravitating disk with density, pressure and sound speed gradients is quantified. First-order corrections are made to account for Keplerian rotation and the presence of the gradients. The total torque is calculated by summing over all resonances in the absence of local wave damping. When applied to the primordial solar nebula disk, the calculations show that disks that cool with increasing heliocentric distance will cause decay of the orbit of the perturbing object. Conditions in which the perturber will escape orbit delay are also described. The characteristic drift time will be no greater than the stochastic accretion time scales. Implications of the calculations for planetary formation are discussed.

Ward, W. R.↗

NASA NTRS1984

Radial migration of preplanetary material - Implications for the accretion time scale problem

Radial drift of planetesimals due to density wave interaction with the solar nebula is considered. The mechanism is most effective for large masses and provides mobility over a size range where aerodynamic drag is unimportant. The process could shorten accretion time scales to O(100,000-1,000,000 years) throughout the solar system. Accumulation stalls down when growing objects are massive enough to open gaps in the gas disk. Implications of this process for current cosmogonic models are discussed.

Hourigan, K.↗

NASA NTRS1984

The solar nebula and the planetesimal disk

Two popular theories of solar system formation are briefly reviewed, then used as background in an examination of several new developments related to planetary ring dynamics that promise to have great impact on future research. Most important are the incorporation of accretion disk and density wave theories into cosmogonic theory. A successful integration of these mechanisms may significantly constrain evolutionary models of the early solar system and also provide new insight into the mechanisms themselves.

Ward, W. R.↗

NASA NTRS1982

Comments on the long-term stability of the earth's obliquity

Continued tidal evolution of the earth-moon system will lengthen the day and expand the lunar orbit. Both of these changes increase the present 26,000-year equinoctial precession period. In less than two billion years, this period will become comparable to the approximately 49,000- and 69,000-year periods of important terms describing the precession of the earth's orbit plane due to planetary perturbations. These events occur when the lunar orbital semimajor axis drifts past approximately 66.5 and 68.0 earth radii, respectively, and will be accompanied by large oscillations of the obliquity and severe climatic alterations. The current rate of lunar recession implies that these resonances should have been encountered already, had present conditions been the norm throughout geologic time.

Ward, W. R.↗

NASA NTRS1982

Dynamical constraints on the formation and evolution of planetary bodies

The present investigation is concerned with a number of inferences as to the origin of planetary bodies, taking into account the present dynamical state of the solar system and some of the limitations which apply to the considered conclusions. Attention is given to the dynamical processes, specifically those processes which may have influenced the orbital or rotational properties of the planets and satellites. Collisional processes are explored, taking into consideration orbital spacing, planetary rotation, and stochastic effects. In connection with a discussion of the evolution of rotational motion, spin state evolution is investigated along with spin axis precession and resonance variation, and the Cassini states. The evolution of planetary orbits is also studied. The subjects considered are related to tides, secular resonances, disk dynamics, and disk-satellite interactions.

Harris, A. W.↗

NASA NTRS1982

On the radial structure of planetary rings

Viscous shear stress of a ring of particles in orbit about a planet due to the radial gradient of orbital velocity is discussed. This stress tends to spread the ring with time. At low optical depth (t) and at high t, the shear stress is an increasing function of t. In the intermediate range stress may decrease with increasing t, leading to a diffusive instability which tends to break an initially uniform ring into ringlets of high and low optical depths. According to the shepherd satellite model of narrow ring confinement, the viscous shear stress is opposed by tidal torques from neighboring shepherds, so that radial spreading does not occur. By requiring that the gradient of the viscous shear stress (i.e., angular momentum deposited) be equal to the shepherd satellite torque density at all radii in the rings, equilibrium radial density profiles of a confined ring were constructed. The most noteworthy feature of these profiles is a narrow, high density ringlet surrounded by a low optical density halo of greater width.

Harris, A. W.↗

NASA NTRS1982

Diffusion instability in a bimodal disc

A simplified model of radial diffusion in a planetary disk with a bimodal size distribution is presented. The large particle component excites the small particles' dispersion velocity via gravitational scattering. The resulting small particle viscous stress goes through a maximum near optical depth = sq root 3. Such a stress profile promotes the development of high and low optical depth zones. The resulting ringlet appearance is due primarily to the distribution of small particles, which produce most of the optical depth but may constitute only a minor portion of system mass.

Ward, W. R.↗

NASA NTRS1981

Solar nebula dispersal and the stability of the planetary system. I - Scanning secular resonance theory

Secular resonances in the early solar system are investigated with the aim of establishing constraints on the time scale and method of solar nebula dispersal. Simplified nebula models and dispersal routines are used to approximate changes in an assumed axisymmetric nebula potential. These changes drive an evolutionary sequence of Laplace-Lagrange solutions for the secular variations of the solar system. These sequences are characterized by a sweep of one or more giant planet resonances through the inner solar system. Their effect is rate-dependent; characteristic dispersal times of not greater than 10,000 to 100,000 years are required to avoid the generation of terrestrial eccentricities and inclinations in excess of observed values.

Ward, W. R.↗

NASA NTRS1981

On the radial structure of Saturn's rings

Voyager 1 cameras revealed that Saturn's B ring appears to be subdivided into hundreds of chaotically spaced narrow rings in a hierarchy that extends to the limit of resolution. A disk model is proposed and applied to Saturn's rings: it is shown that the radial diffusion in a particulate Keplerian disk, under the influence of a viscosity law that decreases more steeply with a certain surface density than with another, will promote the breakdown of the system into an ensemble of thin rings.

Ward, W. R.↗

NASA NTRS1981

Orbital inclination of Iapetus and the rotation of the Laplacian plane

This paper explores the possibility that the orbit of Iapetus, with its relatively large inclination but small eccentricity, was generated by a rapid dispersal of a gaseous circumplanetary disk, assumed to be the progenitor of the satellite system. The orientation of the local Laplacian plane is shown to be a sensitive function of the disk's structure. Modification of the disk on a time scale comparable to the precession of the orbit's nodal line can produce a large inclination from one that is initially zero, while leaving the eccentricity unchanged. This time scale is of the same order of magnitude as the viscous evolution time scale for a fully turbulent disk. Hence, Iapetus need not be a captured satellite to account for its curious orbital signature.

Ward, W. R.↗

NASA NTRS1979

Does Venus wobble

The free wobble damping time for Venus due to solar tides and rotational flexing is found to be approximately 700,000 times Q sub omega years, where Q sub omega is the dissipation function associated with the wobble frequency. The slow spin and expected small (nonhydrostatic) J2 predict a very long wobble period of about 100,000 years. As a result, a simple scaling of the earth's Chandler wobble excitation rate to that of Venus suggests that an appreciable wobble could exist. Detection (or lack thereof) of a free wobble may thus place constraints on the dynamic activity (e.g., mantle convection, Venusquakes, etc.) of the Venus interior.

Yoder, C. F.↗

NASA NTRS1979

Comments on the Venus rotation pole

Possible orientations of the Venus rotation pole as a function of planetary oblateness are calculated, taking into account the variation of the orbital inclination and motion of the nodal line produced by long-term planetary perturbations and assuming the obliquity to be fully damped. If the obliquity is stabilized against solar tides by core-mantle viscous coupling, a fully damped obliquity is the expected state. An analysis of earth-based radar data from 1964 to 1977 yields a pole position which lies near damped pole positions of small oblateness, no more than about 10 to the 6th. Possible implications of this result are considered.

Ward, W. R.↗

NASA NTRS1979

Present obliquity oscillations of Mars - Fourth-order accuracy in orbital e and I

A long period analysis of solar system orbital evolution, correct to fourth order in orbital eccentricities and inclinations (Bretagnon, 1974), and an improved value of the planet's moment of inertia (Reasenberg, 1977) have been incorporated in a recalculation of the obliquity oscillations of Mars. A linearized solution predicts a maximum oscillation amplitude of 13.6 deg centered on a long-term average value of 24.4 deg. A numerical integration of the obliquity for the past 10,000,000 years is also presented. Epochs of minimal oscillation like the present occur at intervals of the order of 4 m.y.

Ward, W. R.↗

NASA NTRS1979

Past obliquity oscillations of Mars - The role of the Tharsis uplift

The paper deals with possible ancient variations of the obliquity of Mars. Consideration of data on internal differentiation, Tharsis uplift and crustal phenomena, mantle convection, and eigenfrequencies and mean motion suggest that (1) differentiation with core formation decreased the primeval spin precession constant (alpha) by 4-5%, driving it through resonance with the j = 2 orbital term; (2) a combination of geophysical processes caused alpha to drift back and forth through resonance with the j = 2 orbital term during part of Mars' history; (3) this situation was turned off by the Tharsis uplift, which drove alpha away from j = 2 resonance and possibly through the j = 26 resonance. The consequences of such events for the planet's obliquity are analyzed. Various types of motions are calculated, demonstrating the sensitivity of the obliquity to passage through resonance with such minor orbital terms.

Ward, W. R.↗

NASA NTRS1976

Secular resonance, solar spin down, and the orbit of Mercury

A mechanism is investigated which may provide an evolutionary explanation for the large mean eccentricity and inclination of Mercury. It is proposed that if the gravitational field of the rapidly rotating early sun had a larger second-degree harmonic, the decreasing value of this harmonic during the subsequent solar spindown would drive Mercury through two secular resonances with Venus, one involving a commensurability in the apsidal motion of the two planets and the other involving their nodal rates. An analysis is performed, showing that these resonances could increase both the inclination and eccentricity of Mercury at nearly the same time, that an initial solar rotational period of 5.5 hr or less would guarantee passage through the resonances, and that a spindown time of about 1 million years could have produced the observed inclination and eccentricity.

Ward, W. R.↗

NASA NTRS1975

Past orientation of the lunar spin axis

The orientation of the lunar spin axis is traced from the early history of the earth-moon system to the present day. Tides raised on the earth by the moon have caused an expansion of the lunar orbit. Tides raised on the moon by the earth have de-spun the moon to synchronous rotation and driven its spin axis to a Cassini state - that is, in a coprecessing configuration, coplanar with the lunar orbit normal and the normal to the Laplacian plane (which is at present coincident with the normal to the ecliptic). This combination of events has resulted in a complex history for the lunar spin axis. For much of the period during which its orbital semimajor axis expanded between 30 and 40 earth radii, the obliquity of the moon was of order 25 to 50 deg. In fact, for a brief period the obliquity periodically attained a value as high as 77 deg; that is, the spin axis of the moon was only 13 deg from lying in its orbit plane.

Ward, W. R.↗

NASA NTRS1975

Tidal friction and generalized Cassini's laws in the solar system

The tidal drift toward a generalized Cassini state of rotation of the spin axis of a planet or satellite in a precessing orbit is described. Generalized Cassini's laws are applied to several solar system objects and the location of their spin axes estimated. Of those considered only the moon definitely occupies state 2 with the spin axis near to the normal of the invariable plane. Most objects appear to occupy state 1 with the spin axis near to the orbit normal. Iapetus could occupy either state depending on its oblateness. In addition, the resonant rotation of Mercury is found to have little effect on the tidal drift of its spin axis toward state 1.

Ward, W. R.↗

NASA NTRS1974

Climatic variations on Mars. I - Astronomical theory of insolation

Description of variations in the solar insolation on Mars that result from oscillations of the orbital eccentricity and the obliquity of the planet. Changes in the eccentricity and obliquity are produced by gravitation perturbations from the sun and the other planets, and a detailed account of the time evolution of these quantities is given. Particular attention is paid to the obliquity oscillations, which exert a strong influence on the climate of Mars. Changes in the earth's obliquity are also calculated, and its behavior is contrasted with that of Mars. Although the eccentricity produces important north-south seasonal asymmetries, a change in the obliquity causes a strong latitudinal redistribution of the solar insolation. Especially noteworthy is the fact that the yearly insolation at the poles of Mars varies by over 100% between the extremes of the obliquity range.

Ward, W. R.↗