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Goldreich, P.

Publications and source records attributed to Goldreich, P..

53 records · Page 3
All sourcesNASA NTRSDOE OSTI
NASA NTRS1978

The formation of the Cassini division in Saturn's rings

An explanation for the size and location of the Cassini division in Saturn's rings is proposed. The explanation is based on the collective response of the particles in the ring to the resonant forcing by Mimas. An upper limit is calculated for the width of the gap that could be opened at a resonance. In addition, an estimate is obtained regarding the damping of the density waves by viscous and nonlinear effects. A picture is presented of the development of a gap. The results are compared with the observed properties of the divisions in Saturn's rings. The exact position of the inner edge of the Cassini division is difficult to predict, because the 2:1 resonance lies very near several weaker resonances (4:2 and 6:3 with Mimas, 4:1 with Tethys). However, the edge should lie near 17 seconds, and this is consistent with ground based observations.

Goldreich, P.↗
NASA NTRS1977

Revenge of tiny Miranda

An investigation is conducted concerning the resonance model for the rings of Uranus proposed by Dermott and Gold (1977). Dermott and Gold had dismissed resonances involving Miranda as insignificant. The reported investigation shows, however, that the strongest resonances are all associated with Miranda. It is also found that the hypothesis that the rings are made up of librating particles is incorrect. If the ring positions are determined by resonances, the control is more subtle than previously suggested. One possibility is that the rings are the crests of nonlinear density waves in an optically thin disk of particles.

Goldreich, P.↗
NASA NTRS1977

Solar seismology. II - The stochastic excitation of the solar p-modes by turbulent convection

We test the hypothesis that the solar p-modes are stabilized by damping due to turbulent viscosity in the convective zone. Starting from the assumption that the modes are stable, we calculate expectation values for the modal energies. We find that the interaction between a p-mode and the turbulent convection is such that the modal energy tends toward equipartition with the kinetic energy of turbulent eddies whose lifetimes are comparable to the modal period. From the calculated values of the modal energies, we compute rms surface velocity amplitudes. Our predicted rms surface velocities range from 0.01 cm/sec for the fundamental radial mode to 0.6 cm/sec for the radial mode whose period is approximately 5 minutes. The predicted surface velocities for the low order p-modes are much smaller than the velocities inferred from recent observations.

Goldreich, P.↗
NASA NTRS1977

Solar seismology. I - The stability of the solar p-modes

The stability of the radial p-modes of the sun is investigated by computing nonadiabatic eigenvalues and eigenfunctions for a solar envelope model which extends from an inner radius of about 0.3 solar radius out to an optical depth of about 0.0003. The calculations take into account in a crude fashion the response of the convective flux to the oscillation. The dynamical effect of turbulence in the convection zone is parametrized in terms of a turbulent shear viscosity. The results show that if damping by turbulent viscosity is neglected, all modes with periods longer than 6 minutes are unstable. The familiar kappa-mechanism, which operates in the H ionization-H(-) opacity region, is the dominant source of driving of the oscillations. Modes with periods shorter than 6 minutes are stabilized by radiative damping in the solar atmosphere. When turbulent dissipation of pulsational energy is included, all modes are predicted to be stable. However, the margin of stability is very small. In view of the large uncertainty that must be assigned to the estimate of turbulent damping, it is concluded that theoretical calculations cannot unequivocally resolve the question of the stability of the solar p-modes.

Goldreich, P.↗
NASA NTRS1977

Turbulent viscosity and Jupiter's tidal Q

A recent estimate of tidal dissipation by turbulent viscosity in Jupiter's convective interior predicts that the current value of the planet's tidal Q is roughly 5 million. We point out a fundamental error in this calculation, and show that turbulent dissipation alone implies that at present Q is about 50 trillion. Our reduced estimate for the rate of tidal dissipation shows conclusively that tidal torques have produced only negligible modifications of the orbits of the Galilean satellites over the age of the solar system.

Goldreich, P.↗
NASA NTRS1977

Solar oscillations

The main observational results and related theoretical investigations concerning solar oscillations are reviewed. The normal modes of oscillation of the sun are classified according to their angular eigenvalues and the number of their radial nodes. Observations of excited normal modes are discussed, particularly in relation to five-minute oscillations, nonlinearly coupled unstable g-modes, oscillations of the sun's apparent diameter, and reported oscillations of the solar surface with a period of 2 hr 40 min. Linear stability calculations are briefly examined, and stochastic excitation of p-modes by turbulent convection is considered. The five-minute oscillations are described as the superposition of many excited nonradial p-modes.

Goldreich, P.↗
NASA NTRS1973

The formation of planetesimals.

Four stages in the accretion of planetesimals are described. The initial stage is the condensation of dust particles from the gaseous solar nebula as it cools. These dust particles settle into a thin disk which is gravitationally unstable. A first generation of planetesimals, whose radii range up to about 0.1 km, form from the dust disk by direct gravitational collapse to solid densities on a time scale of the order of 1 year. The resulting disk, composed of first-generation planetesimals, is still gravitationally unstable, and the planetesimals are grouped into clusters containing approximately 10,000 members. The contraction of these clusters is controlled by the rate at which gas drag damps their internal rotational and random kinetic energies. On a time scale of a few thousand years, the clusters contract to form a second generation of planetesimals having radii of the order of 5 km. Further coalescence of planetesimals proceeds by direct collisions which seem capable of producing growth at a rate of the order of 15 cm per year at 1 AU.

Goldreich, P.↗
NASA NTRS1972

The case against Planet X.

The dynamical consequences of the hypothetical trans-Plutonian planet suggested by Brady (1972) are considered. It is concluded that the combination of large mass and unusual orbital inclination would have two serious effects on the solar system. The angle between the solar axis and the normal to the ecliptic would suffer large variations with a period of a few times ten million years, and the coplanar configuration of the outer solar system would be disrupted on a time scale of 1 m.y. The large residuals in the orbit of Halley's comet which prompted the suggestion of a trans-Plutonian planet can be explained in terms of nongravitation forces and the weak orbital binding energy of this object.

Goldreich, P.↗
NASA NTRS1970

The obliquity of Venus

Venus obliquity dynamic implications, developing equations for independent parameter set to define spin vector

Goldreich, P.↗
NASA NTRS1969

Some remarks on polar wandering.

Earth polar wanderings attributed to rotation axis angular displacements generated by density redistribution on geologic time scale

Goldreich, P.↗
NASA NTRS1966

History of the lunar orbit.

Calculating past states of earth-moon system based on three time scales for dynamical change

EARTH-MOON SYSTEM↗
NASA NTRS1966

Q in the solar system.

Tidal dissipation function in solar system, examining cases having appreciable evolution since origin of planets and satellites

SOLAR SYSTEM↗