An observational test for the origin of the Titan-Hyperion orbital resonance
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Peale, S. J.↗
Engineering topics
Peale, S. J.
Publications and source records attributed to Peale, S. J..
Contribution of tidal dissipation to lunar thermal history
Possible contributions of tidal heating to the thermal history of the moon are investigated, and conditions under which such heating would have been an important factor in the evolution of the moon are defined as precisely as possible within the bounds of the uncertainties. The tidal dissipation is defined as a function of position in the moon and of the earth-moon separation for a homogeneous incompressible moon. Results for the dissipation are given for eccentricities of zero and 0.055 as well as for the lunar obliquity as determined by the equilibrium Cassini states. Possible orbital resonances which interrupt the assumed simplified expansion of the lunar orbit are considered, along with radial variations in rigidity. The dissipation in a two-layer model moon with a molten inner core and an outer mantle with the moon's present rigidity is determined, and implications of the results for the role of tidal heating in the history of the moon are discussed.
Peale, S. J.↗
Reports of planetary geology program, 1977-1978
A compilation of abstracts of reports which summarizes work conducted by Planetary Geology Principal Investigators and their associates is presented. Full reports of these abstracts were presented to the annual meeting of Planetary Geology Principal Investigators and their associates at the Universtiy of Arizona, Tucson, Arizona, May 31, June 1 and 2, 1978.
Strom, R.↗
Mercury's core - The effect of obliquity on the spin-orbit constraints
Constraints were previously placed on various properties of a Mercurian liquid core for compatibility with Mercury's escape from the stable spin-orbit resonance with the spin angular velocity equal to twice the orbital mean motion (the 2n resonance), under the assumption that the planet's obliquity was nearly zero at the time of resonance passage. Capture probabilities at arbitrary nonzero obliquities for the 2n resonance are determined for the cases where the core is strongly or weakly coupled to the mantle. It is found that the capture probabilities are reduced to below unity for all core-fluid viscosities in the weak-coupling limit, but are almost unchanged in the strong-coupling limit. The reduction in capture probability is attributed to reduction of the mantle's spin angular velocity by the core-mantle interaction, which would also reduce the obliquity to negligibly small values before the 2n resonance was even reached. It is concluded that the constraints on the core may still be maintained since Mercury most likely passed through the 2n resonance with nearly zero obliquity.
Peale, S. J.↗
Consequences and inferences from tidal interactions in the solar system
A general theory of the rotation of solid bodies in the solar system leads to the following conclusions: No special initial conditions on the primordial rotation states of most tidally evolved bodies are necessary to account for their present rotation. The possible exception is the rotation of Venus, which must have been initially retrograde unless a liquid core-solid mantle interaction or an accelerating atmospheric tide could dominate the ordinary gravitational tides. Tides eventually drive all bodies in precessing orbits to 'Cassini states', where the spin vector, normal to the orbit and normal to the invariable plane remain coplanar as the first two precess about the latter. The constant obliquity in this configuration, together with the lowest order gravitational harmonics and the amplitude of the physical libration allows the determination of the central condensation and the extent of a liquid-core for Mercury. Criteria for the existence of observable amplitudes of the free wobble, free precession and libration of the moon are established which do not exclude current, non-zero values.
Peale, S. J.↗
A spin-orbit constraint on the viscosity of a Mercurian liquid core
The escape of Mercury from the stable spin-orbit resonance in which the spin angular velocity is twice the orbital mean motion (2n) requires that the kinematic viscosity of a molten core with a laminar boundary layer be comparable to that of water (0.01 sq cm/s) and the tidal Q be less than about 100. If the boundary layer is turbulent, escape from the resonance is only consistent with a liquid core of low viscosity if the critical Reynolds number for the onset of turbulence is above about 500, the moment difference (B - A)/C is below about 0.00001, and the tidal dissipation factor Q is less than about 40. These conclusions depend on the assumptions that Mercury's obliquity was near 0 deg at the time of resonance passage, that the liquid core was not stably stratified at the time at which Mercury passed through the resonance, that a turbulent boundary layer can be characterized by a turbulent or eddy viscosity coefficient, and that the most important coupling between core and mantle is a viscous coupling at a smooth spherical boundary.
Peale, S. J.↗
Rotation histories of the natural satellites
Recent advances in the theory of rotation are combined with traditional approaches to study the rotational evolution of the 33 known natural satellites. A calculation similar to that reported by Burns and Safronov (1973) is applied to each satellite to obtain the characteristic time of decay of any wobble motion to smooth rotation about the principal axis of maximum moment of inertia. Stability criteria and capture probabilities are calculated for the 3/2 spin resonance. Results show that only the regular satellites and Iapetus, Hyperion, Triton, and the moon are tidally evolved. Of these, 13 have confirmed synchronous rotation periods; capture probabilities into the 3/2 resonance indicate that none of the remaining 10 should be captured in nonsynchronous, commensurate spin states. For the most part, the irregular satellites retain their original spins except for a relaxation to principal axis rotation. Tidal evolution of the obliquities of the satellites is evaluated in the framework of the generalization of Cassini's laws for the moon. Nearly resonant, forced librations in longitude of 4.8 and 0.5 deg are calculated on the basis of the observed shapes of Phobos and Deimos, respectively.
Peale, S. J.↗
Does Mercury have a molten core
A feasible nonseismic observational experiment is proposed for determining the existence and extent of a conducting molten core within Mercury. This experiment would utilize the effects of a liquid core on the dynamics of Mercury's rotation; two necessary conditions for performing it are that the core must not follow the mantle's forced librations in longitude but must follow the mantle on the timescale of the 250,000-yr precession. A method is developed by assuming these conditions to be satisfied, and bounds are established on the core viscosity for which they are satisfied. It is shown that the value of the ratio of the moment of inertia of the mantle to the largest principal moment of inertia of the entire planet would indicate whether the core is most probably solid, partially fluid, or entirely fluid. Techniques are suggested for determining the unknowns required to compute the necessary ratio.
Peale, S. J.↗
Inferences from the dynamical history of Mercury's rotation
The history of Mercury's spin angular momentum is reviewed. It is shown that the current nonsynchronous but resonant spin and the nearly zero obliquity place almost no restrictions on the primordial spin state. The only exception comes about from a liquid core-solid mantle interaction which excludes a slow primordial spin concurrent with a large obliquity. The current occupancy of a final evolutionary spin state leads to the description of a scheme by which we can determine the extent of a currently liquid Mercurian core.
Peale, S. J.↗
Excitation and relaxation of the wobble, precession, and libration of the moon
The rate of meteorite-impact excitation of the free wobble, free precession, and free libration of the moon above a given amplitude is estimated for two crater-size scaling laws and is compared with the rate of damping by tidal and rotational distortion as well as by a possible core-mantle interaction. Criteria for the probable existence and the probable nonexistence of observable amplitudes of the free motions are developed in terms of upper bounds on the damping factor for the various motions and in terms of ranges for the kinematic viscosity of a possible core. It is shown that although observable amplitudes are compatible with reasonable values of the damping factor and kinematic viscosity, other reasonable values could keep the amplitudes below the observable level most of the time. It is found that the free libration is the least likely motion to be observed and that a lunar core with earthlike properties might keep some of the free motions damped, but not all of them. Uncertainties in some of the assumptions used in the analysis are discussed.
Peale, S. J.↗
On the detection of a cometary mass distribution
The problem of detecting a possible cometary distribution on the fringes of the solar system is examined. The acceleration of a space probe due to a hypothetical cometary mass distribution with the surface density rising to a maximum and subsequently falling off with increasing distance from the sun is analyzed. The total minimum detectable cometary mass for the Pioneer and Mariner spacecraft is estimated on the basis of this model to be on the order of 1000 earth masses. Precision tracking of deep space probes is less sensitive by three orders of magnitude for the detection of an unseen cometary mass distribution at the fringes of the solar system than are the secular perturbations of long-period comets.
Boss, A. P.↗
Orbital resonances in the solar system
Orbital resonances are defined as any system of two or more satellites (including planets) orbiting the same primary and whose orbital mean motions are in a ratio of small whole numbers. Known orbital resonances in the solar system are identified, including those involving Jupiter's satellites Io, Europa, and Ganymede; Saturn's satellites Mimas and Tethys, Enceladus and Dione, and Titan and Hyperion; Saturn's ring gaps and Mimas; various asteroids and Jupiter; and the planets Neptune and Pluto. The stability of orbital resonances is examined, the origin of orbital commensurabilities is investigated, and a simple model of the simplest kind of eccentricity-type resonance is outlined. A method is described by which tides carry a noncommensurate pair of satellites into a stable libration, and current ideas concerning the formation of the gaps in Saturn's rings and the asteroid belt are discussed. Various approaches to the analysis of orbital resonances are laid out and illustrated. Three two-body commensurabilities in Saturn's satellite system are analyzed numerically.
Peale, S. J.↗
Dynamical consequences of meteorite impacts on the moon
The magnitudes of the excitation of free precession of the lunar spin axis about the position defined by Cassini's laws, free libration in longitude, and free wobble are determined as a function of meteorite angular momentum relative to the lunar center of mass and the position of impact on the lunar surface. Angular-momentum conservation suffices for the estimates of precession and libration excitation, but a cratering model for the ejecta distribution is necessary for the estimate of the wobble excitation. The simultaneous excitation of free wobble is always associated with the excitation of precession, and the angular amplitude is at least comparable to, but may exceed, that of the induced precession by a factor of 3 or 4. It is possible to excite a free libration in longitude with no first-order excitation of free wobble, but generally, all three free motions are excited simultaneously. The induced libration will nearly always have the largest amplitude. For crater sizes scaled as powers of impact energy, impacts leaving craters as small as a few kilometers in diameter can excite free motions which will ultimately be observable by the lunar laser-ranging experiment.
Peale, S. J.↗
Origin of Martian channels - Clathrates and water
Criticism is directed at the suggestion that Martian channels may have been eroded by liquid water produced by the depressurization of CO2 hydrate. The release of pre-existing subsurface liquid water, such as that trapped under a permafrost layer, by meteorite impact or tectonic activity could produce sufficient flow and would not require heat transfer. The presence of water in a CO2 hydrate is shown to be detrimental to its release from an underground reservoir.
Peale, S. J.↗
Possible histories of the obliquity of Mercury
Possible evolutionary paths of the spin axis of Mercury are studied theoretically in terms of generalized Cassini's laws using the Hamiltonian approach. Three stable positions (Cassini states) of the spin axis are discerned. The Cassini states in which the spin axis remains fixed in the frame rotating with the orbit precession are extremes in the tide-free Hamiltonian under the condition of constant angular momentum. The stability of the 3/2 spin resonance for Mercury as a function of obliquity is discussed, and it is shown how control of the resonance is passed from one to another term in the averaged potential as the obliquity is increased with a corresponding loss of stability at each transfer. A sampling technique is used to infer the evolution due to tidal interaction. Two tidal models are used - one with a constant value of the specific dissipation function Q and the other with Q inversely proportional to frequency. An approximate analytic solution for precession trajectories very close to a Cassini state is developed.
Peale, S. J.↗
Rotation of solid bodies in the solar system
The effects of elastic distortion, nonprincipal axis rotation, precessing orbits, and internal dissipation on the rotation of a solid solar system body, which is in the gravitational field of an exterior body, are relatively easily analyzed by a Hamiltonian theory developed here. Examples of applications include the Chandler wobble, wobble of the moon, spin-orbit coupling, generalized Cassini laws, and tidal evolution.
Peale, S. J.↗
Some effects of elasticity on lunar rotation
A general Hamiltonian for a rotating moon in the field of the earth is expanded in terms of parameters orienting the spin angular momentum relative to the principal axes of the moon and relative to coordinate axes fixed in the orbital plane. The effects of elastic distortion are included as modifications of the moment of inertia tensor, where the magnitude of the distortion is parameterized by the Love number k2. The amplitudes of the principal periodic terms in the longitude of a point on the moon due to variations of the tide caused by the earth are discussed. A detailed derivation of the free wobble of the lunar spin axis about the axis of maximum moment of inertia is given. If the moon's rigidity is close to that of the earth there is no effect of elasticity on the rotation which can be measured with the laser ranging and, therefore, no elastic properties of the moon can be determined from variations in the rotation.
Peale, S. J.↗
The gravitational fields of the major planets.
Review of the constraints imposed on models of the interiors of the major planets by the nonspherical components of their gravitational fields. Several methods for determining these nonspherical components are described and evaluated. The nature of the constraints and their effect on the models are discussed.
Peale, S. J.↗