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At least 379 records · Page 21

A note on an attempt at more efficient Poisson series evaluation

A substantial reduction has been achieved in the time necessary to compute lunar libration series. The method involves eliminating many of the trigonometric function calls by a suitable transformation and applying a short SNOBOL processor to the FORTRAN coding of the transformed series, which obviates many of the multiplication operations during the course of series evaluation. It is possible to accomplish similar results quite easily with other Poisson series.

Shelus, P. J.↗

The rotation of the moon

The present review attempts to give a comprehensible demonstration that the Cassini determination of the geometric laws describing the gross rotation of the moon relative to the precessing lunar orbit in terms of the mean orientation elements of the orbit (the Cassini motion) is an approximation to a dynamically consistent system. Traditional approaches to the derivation of the physical librations of the moon are presented, in addition to recent studies on flaws in the traditional theories. For future research, the advantages of an analytic theory will be required.

Mulholland, J. D.↗

Adiabatic invariants and phase equilibria for first-order orbital resonances

In the planar circular restricted three-body problem, the evolution of near-commensurable orbits is studied under change in the mass ratio, mu. The evolution involves preservation of two adiabatic invariants. Transition from circulation to libration may occur; such transitions are of two types. Type I transition occurs when the evolutionary track in phase space passes through near-zero eccentricity; as in the ordinary case (no transition), pre- and post-evolutionary states are linked by solution of a two-point boundary-value problem. Type II transition occurs when the evolutionary track encounters an unstable phase equilibrium or periodic orbit. There is then a discontinuous change in one adiabatic invariant, and pre- and post-evolutionary states are linked by solution of a three-point boundary-value problem. No evolutionary track can encounter a stable phase equilibrium, but the class of all stable phase equilibria is mapped into itself under mu change.

Heppenheimer, T. A.↗

Space exploration and the history of solar-system volatiles

The thermochemical history of volatile substances in all solar-system planets, satellites, and planetoids is discussed extensively. The volatiles are viewed as an interface between the abiotic and biotic worlds and as a key to the history of bodies of the solar system. A flowsheet of processes and states is exhibited. Differences in bulk volatiles distribution between the planetary bodies and between the interior, surface, and atmosphere of each body are considered, as well as sinks for volatiles in degassing. The volatiles-rich Jovian and Saturnian satellites, the effect of large-planet magnetosphere sweeps on nearby satellites, volatiles of asteroids and comets, and the crucial importance of seismic, gravity, and libration data are treated. A research program encompassing analysis of the elemental and isotopic composition of rare gas in atmospheres, assay of volatiles-containing phases in regoliths, and examination of present or past atmospheric escape/accretion processes is recommended.

Fanale, F. P.↗

Surface roughness estimation at three points on the lunar surface using 23-CM monostatic radar

Differences in quasi-specular scattering by the lunar surface have been observed at 23-cm wavelength by using earth-based radar. By taking advantage of libration, three subradar points were isolated, and distinct scattering laws were identified for terrain near Hipparchus, Sinus Medii, and the crater Schroeter F. Interpretations of lunar radar data should henceforth incorporate a recognition that these variations take place. Unidirectional rms surface slope estimates of 6-8 deg in the Central Highlands and 4-5 deg in old mare are appropriate to horizontal scales of 100 m.

Simpson, R. A.↗

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.↗

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.↗

VLBI Observations of ALSEP Transmitters

The technique of differential very-long-baseline inteferometry (VLBI) Apollo Lunar Surface Experiments Package was used to measure the relative positions of the (ALSEP) transmitters at the Apollo 12, 14, 15, 16, and 17 lunar landing sites with uncertainties less than 0.005 sec of the geocentric arc. These measurements yielded improved determinations of the selenodetic coordinates of the Apollo landing sites, and of the physical libration of the moon.

Counselman, C. C.↗

Dynamical study of the Hilda asteroids. I - Resonant orbital motion of the PLS objects from the Palomar-Leiden Survey

Schubart's (1968) model of a planar elliptic restricted three-body problem is used to study the orbital motion of the Hilda asteroids from the Palomar-Leiden Survey. The 3:2 resonant coupling to Jupiter of some of these small asteroids is found to be stable. However, some of the small asteroids with absolute magnitude greater than 15 have large amplitude of variation in their orbital elements in one libration period. Since the lifetime scales against catastrophic collision of the Hilda asteroids are estimated to be several times larger than those of the main-belt objects, a significant portion of these resonant asteroids could be the original members of the Hilda group. From this point of view, it is suggested that such 'size dependence' of resonant orbital motions might be the result of cosmogonic effects of jet-stream accretion.

Ip, W.-H.↗

Lunar dynamics and selenodesy - Results from analysis of VLBI and laser data

Very long base line interferometry (VLBI) observations of lunar radio transmitters have been combined with data from laser ranging to lunar retroreflectors to estimate simultaneously (1) parameters in models of the lunar orbit and libration and (2) the selenodetic coordinates of the radio transmitters and retroreflectors. For the ratio of the mass of the sun to that of the earth plus moon, a value of approximately 328,900.5 is obtained. The lunar moment-of-inertia ratios beta and gamma are also determined. The values and most of the uncertainties obtained for the third-degree harmonics of the moon's gravity field are comparable to those which have been obtained by others from observations of lunar-orbiting spacecraft. However, the results for the two third-degree gravity coefficients have much less uncertainty than determinations based on laser data alone. For the relative position vectors of the lunar radio transmitters and the retroreflectors, the estimates have uncertainties of about 30 m along the earth-moon direction and about 10 m in each of the two transverse coordinates.

King, R. W.↗

An improved value of the lunar moment of inertia

The lunar gravitational research reported on by Gapcynski et al., (1975) has been extended to include an additional 600 days of the time variation of ascending node for the Explorer 49 spacecraft. Analysis of these additional data resulted in an improved value of the second-degree zonal harmonic coefficient C(20) = (-2.0219 equal to 0.0091) times 10 to the minus 4. This value of C(20) used in conjunction with the parameters beta equal to libration (631.27 + or - 0.03) times 10 to the minus 6 and gamma to (227.7 + or - 0.7) times 10 to the minus 6 yields a more accurate definition of the lunar moment of inertia ratio equal to 0.391 + or - 0.002.

Blackshear, W. T.↗

Theory of motion of Jupiter's Galilean satellites

Final results are presented for a theory enabling one to calculate the positions of the Galilean satellites and their partial derivatives. Extensive use of algebraic manipulation software on a digital computer is made to generate the final expressions. The theory is, in effect, a revitalization of Sampson's (1921) theory. Algebraic and mathematical errors existing in Sampson's work are removed, some neglected effects due to solar interactions and the 3-7 commensurability are introduced, allowance is made for nonzero amplitude and phase of the free libration, and the final results are expressed as analytic functions of variations in 49 arbitrary constants of integration and physical parameters. The theory is constructed in a manner which readily allows for future revision, and analytic expressions are provided for the partial derivatives with respect to the 49 parameters.

Lieske, J. H.↗

Space manufacturing facilities: Space colonies; Proceedings of the Princeton Conference, Princeton University, Princeton, N.J., May 7-9, 1975

Reports submitted to the conference encompass: administration and law relating to inhabited space facilities and colonies; space manufacturing and processing; organization and construction of space habitats and management of space colony farms; winning and acquisition of lunar and asteroidal materials for sustaining autonomous space colonies. Attention is given to trajectories between earth, low earth orbit, earth-moon libration points (specifically L5), circumlunar parking orbits, and trajectories in translunar space; effects of low gravity and zero gravity on human physiology and on materials processing; architecture and landscaping for space colonies; closed ecosystems of space colonies. Varieties of human cultures and value hierarchies around the earth are examined for broader perspectives on the social organization of space colonies.

Grey, 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.↗

Phobos and Deimos - Geodesy

Results of geodesy studies of Phobos and Deimos based on Mariner 9 imaging data are presented. This analysis includes a review of the surface coverage and high resolution pictures obtained and the determined sizes, shapes, topographies, and librations of the two Martian satellites. Also, exploration of Phobos and Deimos by missions such as Viking is discussed.

Duxbury, T. C.↗

Orbit of 1976 AA

The orbit of Asteroid 1976 AA is described, with attention given to calculations of its period and its distance from earth, both of which could be accurately and quickly determined by measuring the minor planet's position over wide ranges of hour angle on one to three nights. The geometry of the asteroid's orbit is compared to that of earth's orbit, and the periodicity of the minor planet's approaches to earth is projected. The motion of 1976 AA over an interval of seven centuries into both past and future is also studied; the possibility of its libration with respect to earth or to Venus is examined. Some data on closest approaches of the asteroid to Mars and Venus, as well as to earth, are given.

Marsden, B. G.↗

Research studies using OSO-6 zodiacal light experiment data

The results of research studies on the OSO-6 zodiacal light experiment, conducted during the period from May 1976 to October 1977 are described. A discussion is included of the instrument performance and the empirical calibrations developed. Main areas of the research performed, i.e., (1) zodiacal light variation analysis; (2) integrated starlight and diffuse galactic light; and (3) earth/moon libration region counterglow, are covered. Considerable data processing was performed during these studies and it is summarized. Recommendations for future research to complete the interim results are given.

Source record↗

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.↗