Engineering topics

Greenberg, R.

Publications and source records attributed to Greenberg, R..

67 records · Page 4

NASA NTRS1978

The accretion of planets from planetesimals

Collisional accretion appears to be a viable, and seemingly unavoidable, mechanism for intermediate-stage from a swarm of planetesimals into a system containing a few discrete seed planets. Some other mechanism must be invoked to explain growth of condensate grains up to at least tens of meters. Gravitational instability in the particulate disk seems a plausible means of achieving that early-stage growth up to kilometer-scale bodies. The last stage of growth in which the seed planets accrete the remaining material now presents difficulties due to the isolated, circular orbits generated from the intermediate collisional stage.

Greenberg, R.↗

NASA NTRS1977

Size distribution of particles in planetary rings

Harris (1975) has suggested that the maximum size of particles in a planetary ring is controlled by collisional fragmentation rather than tidal stress. While this conclusion is probably true, estimated radius limits must be revised upward from Harris' values of a few kilometers by at least an order of magnitude. Accretion of particles within the Roche limit is also possible. These considerations affect theories concerning the evolution of Saturn's rings, of the moon, and of possible former satellites of Mercury and Venus. In the case of Saturn's rings, comparison of various theoretical scenarios with available observational evidence suggests that the rings formed from the breakup of larger particles rather than from original condensation as small particles. This process implies a distribution of particle sizes in Saturn's rings possibly ranging up to about 100 km but with most of the cross section in centimeter-scale particles.

Greenberg, R.↗

NASA NTRS1977

Orbit-orbit resonances among natural satellites

A qualitative physical description of the orbital resonance mechanism based on a previously published (Greenberg et al. 1972; Greenberg, 1973) mathematical analysis is presented. The fundamental principles of the resonance mechanism are illustrated by an examination of the Titan-Hyperion case. More complex resonances, including Enceladus-Dione, Mimas-Tethys are considered. Resonance phenomena involving the rings of Saturn, the inner three satellites of Uranus, and the inner three Galilean satellites of Jupiter are also discussed. The role of analyses of resonance phenomena in developing theories of satellite formation and evolution is examined.

Greenberg, R.↗

NASA NTRS1977

Orbit-orbit resonances in the solar system - Varieties and similarities

Descriptions of various orbit-orbit resonance mechanisms in the solar system are brought together in such a manner that the physical processes underlying the traditional mathematical presentations are apparent. A simple qualitative model based on the resonance between Saturn's satellites Titan and Hyperion is presented, the same resonance is analyzed quantitatively, and the small-eccentricity mechanism is examined. The following resonances are investigated in detail: Enceladus-Dione, Mimas-Tethys, Neptune-Pluto, and Rhea-Titan (secular resonance). Coupled librations of several asteroids near mean motions commensurable with Jupiter's are modeled, the Laplace relation involving Io, Europa, and Ganymede is studied, and the 1:1 resonance between the Trojan asteroids and Jupiter is discussed. Some higher-order commensurabilities involving asteroids are considered, including the 3:1 resonance between Alinda and Jupiter, the 13:5 resonance of Toro with Venus, the 8:5 resonance of Toro with earth, and the 11:28 resonance of Ivar with earth.

Greenberg, R.↗

NASA NTRS1976

The Laplace relation and the masses of Uranus' satellites

It is noted that the mean motions of Uranus' satellites Miranda, Ariel, and Umbriel exhibit nearly the same commensurability as that observed among the three inner Galilean satellites of Jupiter, which is referred to as the Laplace relation. The theory of the Laplace relation among the Uranian satellites is completed by generating terms due to the first-order portions of the disturbing functions, using a generalization of Souillart's approach for the Galilean satellites. The theory is compared with past observations of Miranda's mean motion to obtain an upper limit on the product of the masses of Ariel and Umbriel. This mass limit is examined in terms of implied density and albedo constraints for comparison with the bulk properties of other solar-system bodies. The results suggest that if Ariel and Umbriel both have the same geometric albedo and density, then Ariel's radius would have to be less than about 1200 km and Umbriel's, less than about 800 km.

Greenberg, R.↗

NASA NTRS1975

On the Laplace relation among the satellites of Uranus

Three of Uranus' satellites are involved in an interaction similar to the Laplace relation among the Galilean satellites of Jupiter. However, there are no pair-wise commensurabilities in the Uranus system as there are among the Galilean satellites. Thus analysis by Fourier expansion of disturbing functions becomes too unwieldy for practical calculation. Instead, the unexpanded perturbations are numerically averaged over a time scale short compared to the important variations in the Laplace relation. Perturbations of Miranda's orbit are estimated to be of observable magnitude for reasonable masses of Ariel and Umbriel.

Greenberg, R.↗

NASA NTRS1975

Mars - Satellite origin and angular momentum

The origin of Phobos and Deimos is considered with a view to accounting for the existence of very small satellites with circular orbits in the Martian equatorial plane, and simultaneously for the suspected angular momentum deficiency of the Mars system. All models considered failed to satisfy at least one requirement, and the problem is considered more puzzling than is at first apparent. The Martian angular momentum deficiency, if physically significant, may be unrelated to the present satellites' origin, but might relate to a large ancient satellite, long ago destroyed. Accretion onto Mars of large amounts of asteroidal dust brought in by Poynting-Robertson drag may have some bearing on the angular momentum problem.

Hartmann, W. K.↗

NASA NTRS1975

The dynamics of Uranus' satellites

Current knowledge of the dynamics of Uranus' satellites is reviewed in support of preliminary planning for a mission to that planet. The determination of past and present orbital and rotational behavior is discussed. Improved understanding in this area is important not only for its own sake, but also for the implications with regard to the structure of the planet and to the general dynamical history of the solar system. A program of earth-based observations over the next few years would permit most effective use of a Uranus probe.

Greenberg, R.↗

NASA NTRS1975

Commensurabilities of satellites' apsidal precession periods

The orientation of the major axis of Saturn's satellite Rhea librates about alignment with Titan's major axis. This behavior is a result of Titan's gravitational influence on Rhea. Similar effects may be important in the Uranian satellite system if they are enhanced by commensurabilities of apsidal precession periods. Extensive observations will be required if this possibility is to be confirmed. The effects of possible stable alignments have not been included in past analyses of the motions of Uranus' satellites, so the results of those studies should be accepted only tentatively.

Greenberg, R.↗

NASA NTRS1973

Evolution of satellite resonances by tidal dissipation.

Analysis of a realistic model shows how satellites' gravitational interaction can halt their differential tidal evolution when resonant commensurabilities of their orbital periods are reached. The success of this study lends support to the hypothesis that orbit-orbit resonances among satellites in the solar system, including the Titan-Hyperion case, did evolve as a result of tidal energy dissipation. Consideration of the time scale for this evolution process, possible now that the capture mechanism has been revealed, can offer more sophisticated constraints on the tidal dissipation function, Q, and on past orbital conditions.

Greenberg, R.↗

NASA NTRS1973

Eccentricity and inclination of Miranda's orbit

Careful re-measurement of all available plates showing Uranus V (Miranda), supplemented by some recently obtained images, shows that this satellite has both a pronounced orbital eccentricity and inclination (to the plane of the other satellites). Observations are sufficient in number and distribution to allow determinations of the precession rates of both pericenter and node, with implications for the dynamical oblateness of Uranus and the gravitational interaction of the satellites. An improved value for the revolution period is a byproduct of the investigation. The success of the study is due to the improved precision of the measures resulting from the adoption of a very simple, direct method of measurement.

Whitaker, E.↗

NASA NTRS1973

Eccentricity and inclination of Miranda's orbit

Careful re-measurement of all available plates showing Uranus V (Miranda), supplemented by some recently obtained images, shows that this satellite has both a pronounced orbital eccentricity and inclination (to the plane of the other satellites). Observations are sufficient in number and distribution to allow determinations of the precession rates of both pericenter and node, with implications for the dynamical oblateness of Uranus and the gravitational interaction of the satellites. An improved value for the revolution period is a by-product of the investigation. The success of this study is due to the improved precision of the measures resulting from the adoption of a very simple, direct method of measurement.

Whitaker, E.↗

NASA NTRS1971

Multiple-mission telemetry

Progress report, block diagrams, and processing of multiple-mission telemetry of Deep Space Instrumentation Facility

Frey, W.↗