Engineering topics
Publications and source records attributed to Wollenhaupt, W. R..
Laser altimetry data from the Apollo 15, 16, and 17 missions show that the ringed maria surfaces lie on one particular reference surface and that the center of gravity is definitely displaced from the optical center. If these extensive surfaces are assumed to be near-hydrostatic surfaces, then there must have existed a time in lunar history when lunar tides, internal processes, or both were much different than they are today.
It is demonstrated that the mascon gravity anomalies are not produced simply by the occurrence of a superisostatic fill in mare basins. The fill alone is too thin to account for the large positive anomalies observed. The mascon anomaly can be explained if it is assumed that the mass excess occurs in two bodies rather than in a single body. The structure model discussed accounts for the gravity field so far observed at several heights over the central part of Mare Serenitatis.
Data from the Apollo 15, 16, and 17 laser altimeters have been used to study slopes, elevations, and roughness in the identifiable regions on the moon which sporadically produce plasma compressions and magnetic-field enhancements in the solar wind/lunar void boundary when those regions are at a flow limb. It is found that occurrence rates for such 'limb compressions' derived from Explorer 35 satellite measurements are significantly correlated with peak, average, and RMS slopes in the source regions, whereas rates derived from Apollo 15 and 16 subsatellite data are not correlated with topography. This suggests that two or more mechanisms operate in the source regions to produce limb compressions. Together with the known correlation between limb compressions and local surface remanent magnetic fields, the results indicate that lunar magnetization is not strongly related to surface features.
Reduction of Doppler radio tracking of the orbiting spacecraft has shown consistency with Apollo 14 data results and has revealed new gravity anomalies. Large craters are negative anomalies while wrinkle ridge regions are positive. The Central highlands are mostly a positive anomaly except for the Apollo 16 landing site, which is in a negative area. A gravity high northwest of Theophilus is not easily explained.
Gravity results are displayed as a band of contours about 60 km wide spanning 140 deg of frontside longitude. The contours traverse Grimaldi, Mare Procellarum, Copernicus, Apennines, Mare Serenitatis, Littrow, and Mare Crisium. Redundant gravity areas previously mapped by Apollos 14, 15, 16, and the Apollo subsatellites are tabulated and show excellent consistency. Modeling of Grimaldi reveals a loading greater than the known mascons and thus makes Grimaldi the smallest known mascon feature. Copernicus' gravity profile is best modeled with a mass defect for the basin and a mass excess for the rim. Mare Serenitatis has an irregular mass distribution with central gravity highs shifted approximately 3 deg in latitude.
Analysis and interpretation of the lunar gravity measurements obtained from Apollo 15 Doppler radio tracking data. The extent of surface coverage was limited to the trajectory paths of the command and service module during revolutions 3 through 11, when it was at a relatively low periapsis altitude just prior to undocking with the lunar module. The trajectory was close to the most optimal for study of the details of the Serenitatis and Crisium mascons. The periapsis altitude was about 12 km at the center of Mare Serenitatis, one of the largest mascons, and the one in the most favorable viewing geometry. The results obtained strengthen Booker's (1970) contention that all mascons have approximately the same thickness.
Dense Doppler tracking coverage of the Apollo 15 and 16 subsatellites over ten and eighteen day periods when periapsis altitudes were 15-50 km has provided detailed gravity mapping of the lunar frontside. Many new gravity features are revealed, including one that does not correlate with any visible topographic structure. All unfilled craters sampled are negative anomalies. The mascons consistently produce gravity heights that load the surface with about 800 kg/sq cm excess mass. The Orientale region is represented with a solution grid of 177 point masses that clearly show the ringed structure. The eastern limb is also displayed with a solution grid of point masses. The gravity variations over the central portion of the frontface are shown as line-of-sight acceleration contours in milligals.
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.
Global tracking coverage of the Apollo 15 subsatellite has provided gravity measurements from 50 km altitudes over the entire Humorum basin. An estimate of surface mass points at 2 degree intervals, which best fit the data reveals a mass distribution having a lesser mass excess for the very central area. When two different profiles were fit using a two disk model it was again found for each profile that the smaller central disk decreased the central mass by approximately 30%. The mass distribution per unit area however for the major portion of the mascon is still consistent with the other mascons (Crisium, Nectaris and Serenitatis) of approximately 800-900 kg/sq cm. The surface mass point solution seems to correlate somewhat with the dark areas on Whitaker's IR-UV map.
The laser altimeter data obtained from the Apollo 15 and Apollo 16 missions provide two elevation cross sections of the moon separated by 35 degrees of latitude. The data consist of measurements of the distance from the orbiting Command and Service Module (CSM) to the lunar surface at intervals of about 20 seconds. In order to extract the lunar shape parameters from the data, the position of the CSM must be known. This was accomplished by reducing the data from earth-based radio tracking of the CSM. The most striking result obtained in the studies is the consistency of the center of gravity offset in both the X and Y directions.
The purpose of this experiment was to measure the variations in the lunar gravitational field near the trajectory of orbiting space vehicles (the command and service module (CSM) and the small particles and fields subsatellites ejected from the Apollo 15 and 16 spacecraft). New information has been obtained from all Apollo orbiting spacecraft; however, this report shall be limited to the results from the Apollo 17 CSM and the Apollo 16 subsatellite. The data acquired are precise speed measurements of the orbiting spacecraft from which accelerations or gravity profiles may be inferred. Feature resolution is controlled by the spacecraft altitude and is almost a direct relationship (i.e., data taken from a 50-km altitude will resolve approximately a 50-km feature). Therefore, revolutions 3 to 12, when the CSM was in the low-altitude orbits, provided the clearest information.
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.
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.
The selenographic positions of the observed lunar features are solved for, or estimated directly from, angular measurements made from the orbiting spacecraft (Apollo missions 8, 10, 11, 12, 14, and 15) to the landmark, using least-squares techniques. It appears that the radius values derived from the Apollo landmark data provide some proof of the existence of a displacement between the center of figure and center of mass of the moon along the earth-moon line. In addition, all three components of the estimated crater locations should be useful toward establishing a selenodetic reference system for interpreting or reducing earth-based observation data.
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The experiment which derives data from three lunar-orbiting objects, the command-service module (CSM), the lunar module (LM), and the subsatellite in the S-band is described. Each provides detailed information on the near-side lunar gravitational field. The primary emphasis is on the low-altitude (20 km) CSM data. The LM data cover a very short time span and are somewhat redundant with the CSM data. The resolution of the high-altitude (100 km) CSM data is not as great as that of the low altitude data. The low-altitude CSM and LM data coverage and the complementary coverage obtained during the Apollo 14 mission are presented. The experiment uses the same technique of gravity determination employed on the Lunar Orbiter, in the data of which the large anomalies called mascons were first observed. The data consist of variations in the spacecraft speed as measured by the Earth-based radio tracking system.
It is reported that this experiment measures the lunar gravitational field, which in turn provides information on the distribution of lunar mass and its correlation with surface features such as craters, mountains, and maria. The lunar gravitational field is measured by observing the dynamical motion of spacecraft in free-fall orbits. Effective detection of mass variations is greatly enhanced by low-altitude trajectories, such as the eccentric orbits during revolutions 3 to 16 of the Apollo 16 spacecraft and the 11 km periapsis of the Apollo 16 subsatellite during May 1972. The observational data are the precise earth-based radio tracking measurements initially used for real-time navigation.