Search NASA⌕ Search

SEARCH · Search NASA

Results for “LIBRATION”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 343 records · Page 19
All sourcesNASA NTRSDOE OSTI
NASA NTRS1973

Accuracy analysis of the ephemerides of the Galilean satellites

Known discrepancies between Sampson's Theory and observations of the Galilean satellites produce in plane errors of about 1200 km. Since the mean longitude is responsible for most of the discrepancy a simple time correction may be used to significantly reduce these errors. An analysis of the time corrections derived for Sampson's Theory, concludes that the dominant error in the mean longitudes results from Sampson's definition of time, which was determined by the observations which he used in constructing the theory. Imposition of the libration constraint results in changes to the time corrections which are less than the standard deviation of those quantities. The individual eclipse observational errors are shown to be proportional to the square root of the period. With improved star catalogs, the attainable accuracy of the ephemerides of the Galilean satellites is about 100 km from photographic plates versus about 200 km for eclipse observations.-

Peters, C. F.↗
NASA NTRS1973

Selenographic control

Evaluation of selenographic data obtained with use of different observational means requires the formulation of rigorous algorithms connecting the systems of coordinates, which the various methods have been referred to. The lunar principal axes of inertia are suggested as most appropriate for reference in lunar mapping and selenographic coordinate catalogues. The connection between the instantaneous axis of lunar rotation (involved in laser ranging, radar studies, astronomical observations from the surface of the moon and VLBI observations of ALSEPs), the ecliptic system of coordinates (which in reductions of observations was considered as fixed in space), the 'Cassini' mean selenographic coordinates (to which physical libration measures were referred), the lunar principal axes of inertia, and the invariable plane of the solar system is discussed.

Moutsoulas, M. D.↗
NASA NTRS1973

Orientation of the moon by numerical integration

The differential equations of rotational motion of the moon are solved by numerical integration methods. Euler's dynamical equations transformed to a convenient form are treated by techniques analogous to ordinary orbit determination procedures. The proposed method is fully consistent with the ephemeris of the moon and can utilize a variety of observational material for the solution of the selected parameters. Examples are given of comparison between the proposed method and Eckhardt's 1970 model of the physical librations of the moon. The merits of the new method are discussed in the light of conventional data sources like earth-based or satellite-based photography as well as newly available data types like laser ranging to retroreflectors on the moon.

Papo, H. B.↗
NASA NTRS1974

A method of revitalizing Sampson's theory of the Galilean satellites

A method is developed by which Sampson's theory of motion of Jupiter's Galilean satellites can be revitalized by use of algebraic manipulation software on a digital computer. The technique seeks (1) to remove algebraic errors existing in the current Sampson theory, (2) to introduce some neglected effects due to solar interactions and the 3-7 commensurability between the outer two satellites, (3) to allow for nonzero amplitude and phase of the libration, (4) to allow future revision of the arbitrary constants of integration, (5) to express the final results as analytic functions of variations in the numerous arbitrary constants of integration and arbitrary parameters, and (6) to provide analytic partial derivatives by means of which the numerical values of coefficients in the expressions for the coordinates can be adjusted. The level of precision desired is one arc second (Jovicentric) for the coordinates (2, 3.3, 5.2, and 9.1 km, respectively, for satellites I through IV).

Lieske, J. H.↗
NASA NTRS1974

Bibliography

Bibliographical listing of recently published work pertaining to 15 subject areas of lunar research, with brief abstracts for each item listed. Subject areas covered include: motion of the moon in space, dynamics of the earth-moon system, and lunar astronautics; librations; shape and gravitational field; internal structure, thermal and stress history; chemical composition; lunar exosphere; lunar coordinates and mapping of the moon; physical structure of the lunar surface; photometry of the moon; thermal emission of the lunar surface; electromagnetic properties; exploration of the moon by spacecraft.

Kopal, Z.↗
NASA NTRS1974

Moonquake predetermination and tides

A pattern in moonquakes, which correlates with the monthly tidal cycle, also correlates with a phase-shifted pattern of a 7-month tidal cycle. The lead of approximately 2 months in moonquake occurrence can be explained if local tidal forces are combined with a moonquake-driving force. This force, assumed to result from the 6-yr physical libration in latitude, would cause N-S sliding of an outer layer across a solid layer within a decoupled core in a lunar model. During 1969-1971, the sliding would be southward with a progression of monthly maxima in the combined forces. Where these forces control moonquakes, the reversal in direction of the 6-year cyclic force in early 1972 should cause a minimum in moonquake activity. Decreases toward such a minimum did occur simultaneously in the similar progressions of monthly moonquakes and maxima in the combined forces at the most active hypocenter. Repetition of the 1966-1971 force pattern in 1975-1977 should produce a corresponding repetition of the moonquake pattern.

Chapman, W. B.↗
NASA NTRS1974

Evaluating the accuracy of selenodesic reference grids

Estimates were made of the accuracy of reference point grids using the technique of calculating the errors from theoretical analysis. Factors taken into consideration were: telescope accuracy, number of photographs, and libration amplitude. To solve the problem, formulas were used for the relationship between the coordinates of lunar surface points and their images on the photograph.

Koptev, A. A.↗
NASA NTRS1975

Precision Selenodesy via Differential Very-Long-Baseline Interferometry

The technique of differential very-long baseline interferometry 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 of geocentric arc. These measurements yielded improved determinations of the selenodetic coordinates of the Apollo landing sites, and of the physical libration of the moon. By means of a new device, the differential Doppler receiver (DDR), instrumental errors were reduced to less than the equivalent of 0.001. DDRs were installed in six stations of the NASA spaceflight tracking and data network and used in an extensive program of observations beginning in March 1973.

King, R. W., Jr.↗
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 NTRS1975

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.↗
NASA NTRS1974

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.↗
NASA NTRS1975

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.↗
NASA NTRS1976

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.↗
NASA NTRS1976

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.↗
NASA NTRS1976

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.↗
NASA NTRS1976

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.↗
NASA NTRS1977

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.↗
NASA NTRS1976

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.↗