Engineering topics

Kaula, W. M.

Publications and source records attributed to Kaula, W. M..

At least 73 records · Page 4

NASA NTRS1975

Absolute plate motions by boundary velocity minimizations

The main interaction of the earth's interior with the lithosphere is as a material source and sink. An absolute reference frame defined by minimizing the translational motion of tectonic plate boundaries differs by 0.6 cm/year from a frame defined by hot spot traces and by 0.4 cm/year from the frame defined by the most plausible model of drag forces on the plates. The rms absolute translational velocities are about 2 cm/year for ocean-ocean plate boundaries and 1.5 cm/year for ocean-continent plate boundaries. The close agreement between the source and sink and the drag-dependent definitions suggests that the lithosphere, as a stress guide, to some extent controls the locations of its sources and sinks.

Kaula, W. M.↗

NASA NTRS1974

Error analysis for station position from tracking of the Lageos satellite

The earth physics satellite systems error analysis program was applied to the problem of predicting the relative accuracy of station position determinations under varying orbital and observing geometries. The reference case consists of nine ground stations extending over 1500 km which lasers ranged to a LAGEOS satellite, with simultaneous Doppler tracking from a geosynchronous satellite for 16 days. Eleven variations from the reference case were tested. The results showed little sensitivity to whether the LAGEOS altitude is 3700 or 5690 km. More significant were the high inclination, and that LAGEOS was tracked by a geosynchronous satellite.

Parmenter, M. E.↗

NASA NTRS1974

Benefits to the study of oceanic tectonics expected from Seasat-A

A more detailed gravity field such as provided by the SEASAT-A altimeter would help resolve several problems of marine geology, such as the relationship of spreading rises to convective upstreams and the tectonics of subduction zones and the associated marginal basins. In addition, the gravity field should be measured in more detail over continental shelves accessible to mineral exploration. A secondary contribution of SEASAT-A would be to sedimentation processes, through its influence on models of ocean currents.

Kaula, W. M.↗

NASA NTRS1974

Apollo laser altimetry and inferences as to lunar structure

Weighted mean laser altimetry data from Apollo 15, 16, and 17 tracks were analyzed, yielding a mean lunar radius of 1737.7 km and an offset of center-of mass from center of figure of 2.55 km toward 24 deg E. Weighted mean elevations with respect to a 1738 km radius sphere for various terrain types are: (1) farside terrae +1.8 km, (2) nearside terrae -1.4 km, (3) ringed maria -4.0 km, and (4) other maria -2.3 km. Comparison of gravity and topography data indicates that there is a variation in density in the outer parts of the moon and that the moon has a crust which is equivalent to at least 60 km of material of 2.95 grams per cu cm density. This result and moment-of-inertia data are consistent with a lunar interior model with a uniform density gradient in the mantle to the bottom of the lithosphere, constant density in the asthenosphere, and no core.

Kaula, W. M.↗

NASA NTRS1973

The lunar laser ranging experiment.

The scientific objectives achievable through high-accuracy range measurements to lunar retroreflectors are considered. A specific study of design questions related to the operation of retroreflectors on the lunar surface indicated that a reflector panel containing a number of solid fused silica corner reflectors would be capable of maintaining essentially diffraction limited performance under direct solar illumination. Initial Apollo 11 observations are discussed together with the installation of additional lunar retroreflectors in connection with the Luna 17, Apollo 14, Apollo 15, and Luna 21 missions. Range measurements at the McDonald Observatory are considered along with new results from lunar range data, and prospects regarding future lunar ranging stations.

Bender, P. L.↗

NASA NTRS1973

Dynamically plausible hypotheses of lunar origin

The implausibility of the capture hypothesis of lunar origin is pointed out. The reason for this implausibility is the extreme weakness of the only known energy sink for pure capture, tidal friction. A mechanism proposed by Alfven and Arrhenius (1972) is the locking of the moon in synchronization with a longitudinal variation in the earth's gravitational field. It is shown that collision with preexisting satellite matter is the most effective means of capturing a moon.

Kaula, W. M.↗

NASA NTRS1973

Lunar physical librations and laser ranging

The analysis of lunar laser ranging data requires very accurate calculations of the lunar physical librations. Libration terms are given which arise from the additive and planetary terms in the lunar theory. The large size of the recently discovered terms due to third degree gravitational harmonics will allow some of these harmonics to be measured by laser ranging to the moon. Numerical integration promises to be an effective method of calculating librations. Comparison of numerical integrations with analytic series indicates that the calculation of the series due to third and fourth degree harmonics is not yet as accurate as the more extensively developed second degree terms.-

Williams, J. G.↗

NASA NTRS1973

The physical librations of the moon, including higher harmonic effects

The equations of the physical libration of the moon are developed using a representation of the earth-moon orbit as a Kepler ellipse referred to the lunar equator and expanding the lunar potential in terms of these Kepler elements. The Improved Lunar Ephemeris is used to calculate solar perturbations, and a linear integration of all effects arising from lunar gravitational harmonics through the fourth degree is performed. Aside from unobservable constant offsets of the principal axes, the main effects of the higher harmonics on longitude are: 10-sec six-yearly (argument omega), 1.2-sec three-yearly, 0.5-sec annual, and 0.1-sec monthly; on pole direction they are on the order of 0.5-sec six-yearly and 1.0-sec monthly. The higher harmonics must hence be taken into account in analyzing ranging data of 10 cm accuracy.

Kaula, W. M.↗

NASA NTRS1973

Potentialities of lunar laser ranging for measuring tectonic motions.

The lunar laser-ranging system at McDonald Observatory, Texas, is currently attaining accuracies of plus or minus 15 cm, and plus or minus 3 cm appears feasible. Numerical error analyses containing 97 parameters (35 of them for error sources) indicate that the plus or minus 3 cm system would measure station motions to plus or minus 1 cm/year accuracy within a year for east-west motions and within about 3 years for north-south. Furthermore, the correlations of station motions with other parameters are low, so that it is unlikely that the estimate is too optimistic because of modeling inadequacies of the error analysis.

Kaula, W. M.↗

NASA NTRS1973

Apollo 17 laser altimeter

The performance and operation of the Apollo 17 laser altimeter after several modifications are discussed. Functions of the instrument include precise altitude measurement of the CSM above the lunar surface, and measurement of broad scale topographic relief around the entire circumference of the moon.

Wollenhaupt, W. R.↗

NASA NTRS1973

Lunar topography from Apollo 15 and 16 laser altimetry

In the orbital plane of Apollo 15 the mean lunar radius is 1737.3 km, the mean altitude of terrae above maria is about 3 km, and the center-of-figure is displaced from the center-of-mass by about 2 km away from longitude 25 E. The Apollo 16 laser altimeter obtained a total of about 7.5 revolutions of partially overlapping data. The principal difference in results from Apollo 16 is the absence of any great far-side basin similar to the 1400-km wide feature found by Apollo 15, 1200 km to the south. This absence of a far-side depression in the Apollo 16 orbital plane largely accounts for a greater mean radius: 1738.1 km; a greater mean altitude of terrae above maria: about 4 km; and a greater offset of centers: about 3 km, also away from 25 E. In the Apollo 16, as well as Apollo 15, data the far-side terrae are much 'rougher' than the near-side terrae. Mare surfaces are generally smooth to within plus or minus 150 m, and have slopes of 1:500 to 1:2000 persisting over distances as great as 500 km.

Kaula, W. M.↗

NASA NTRS1972

Error analysis of earth physics satellite systems

Error analysis of distant-satellite-to-close-satellite range-rate, satellite-to-sea altimetry, and ground station to satellite range are made by simulations in which observational variances are assumed, observation equations are formed, and normal equations incremented. The final normal equation matrix is inverted to obtain standard deviations and correlation coefficients. The natural parameters solved for are the broad variations of the gravity field, represented by harmonic coefficients; local variations of gravity, represented by point masses; and the departure of the sea level from the geoid, represented by area means. A standard case of a low (263 km) polar close satellite, three equatorial geosynchronous satellites, and eight ground tracking stations is set up.

Kaula, W. M.↗

NASA NTRS1972

Laser ranging retroreflector

The lunar laser ranging retroreflector (LRRR) experiments to define the motion of the moon in its orbit are described, and the properties of the LRRR arrays and ground-station operation are discussed. It is concluded that primary benchmarks on the lunar surface are provided by the Apollo 11 and 14 arrays, and the placement of the Apollo 15 reflector.

Faller, J. E.↗

NASA NTRS1972

Apollo 15 laser altimeter, part D

The laser altimeter, consisting of a Q switched ruby laser, transmitting optics, counting timer, receiving optics, and a photomultiplier is described. Harmonic analysis of the mission data is also presented.

Robertson, F. L.↗

NASA NTRS1972

Physical structure of the moon.

The moon has a much thicker lithosphere than the earth, as predicted by thermal models and as evidenced by the support of mascons, lack of surface folding, etc. More in question is whether the moon has a core (more properly, asthenosphere) of high temperature, as suggested by the volcanism 1.0-1.3 b.y. after origin and by the large low-degree harmonics in the gravity field. The moon is like the earth in having a large offset of center-of-mass from center-of-volume, apparently the residue of an early convective overturn associated with large-scale differentiation. The moon differs significantly from the earth in its lower iron content, gross homogeneity, much slower rate-of-change, and closer approach to isostatic equilibrium in the sense of stress-difference magnitudes.

Kaula, W. M.↗

NASA NTRS1972

Geodesy results obtainable with lunar retroreflectors.

Retroreflector packages have been carried to the moon by the Apollo 11, Apollo 14, and Apollo 15 missions, as well as by Luna 17. Laser ranging from the earth onto these packages should eventually yield information on polar motions and crustal movements accurate to a few centimeters, and on UT1 to 100 microsec. Present (1971) error of the range measurements is 30 cm, but accuracy to 3 cm should be obtainable with improvements in methods and equipment.

Faller, J. E.↗

NASA NTRS1972

Analysis and interpretation of lunar laser altimetry.

About 4.5 revolutions of laser altimetry were obtained by Apollo 15. This altimetry indicates a 2-km displacement of the center of mass from the center of figure toward the earthside. The terrae are quite rough, with frequent changes of 1 km or more in successive altitudes at about 33-km intervals. The mean altitude of terrae above maria is about 3 km with respect to the center of mass, indicating a thickness of about 24 km for a high-alumina crust. The maria are extremely level, with elevations varying not more than plus or minus 150 m about the mean over some stretches of 200 to 600 km. However, different maria have considerably different mean elevations. The largest unanticipated feature found is a 1400 km wide depression centered at about 180 deg longitude, and 2 km deep with respect to a 1737-km sphere (about 6 km deep with respect to the surrounding terrae). This basin has the appearance of typical terrae, although there are indications of a ring structure of about 600-km radius in the Orbiter photography. Altitudes across circum-Orientale features suggest that Mare Orientale is also a deep basin. The data appear to corroborate a model of early large-scale differentiation of a crust, followed a considerable time later by short intense episodes of mare filling with low viscosity lavas.

Kaula, W. M.↗

NASA NTRS1971

The lunar laser ranging experiment

With data from two or more well-located observing stations, the lunar range can be corrected accurately for the effects of polar motion and fluctuations in the earth's rotation rate. Very accurate corrections can be made for the earth tides at each station. It appears that the use of lasers giving roughly 0.1-msec pulse lengths is highly desirable. With them, single-shot ranging accuracies of about 3 cm are expected. The actual lunar range results will be analyzed by fitting a numerical integration for the lunar motion to the data. A mathematical model for lunar range is given. Tests of the theory of gravitation are considered.

Bender, P. L.↗