On the wavelength dependence of radar echoes from the Moon

140

The results of the remote probing of the moon by means of infrared and microwave emissions and by radar are reviewed. Also, we discuss how the various observational results can help to explain physical parameters of the lunar surface, such as thermal and electrical conductivities, dielectric constant, density, particle sizes in the lunar regolith, depth of the surface layer, roughness of the surface, variation of these parameters from point to point on the surface, and amount of heat generated in the lunar interior. 190 T. HAGFORS ' at several different phase angles in order to obtain maps of isotherms on the moon. The resolution used was 25 seconds of arc as compared with the diameter of the moon which is about 30 minutes of arc. The data in the figure were obtained from the thermal contours at a few different phase angles. The data ascribed to Saari and Shorthill [1967] were obtained in a wavelength interval from 10 to 12t• with an instrument having an angular resolution of 8 seconds of arc. The post-sunset data were obtained by Murray and Wildey [1964] at 8-13t• with a resolution of 26 seconds of arc and by Shorthill and Saari [1965] at 10-12tz with their higher resolution instrument. The pre-sunrise observations are particularly difficult to make because of the high sensitivity required. Having special instrumentation Low [ 1965] was able to determine the pre-sunrise temperature by scanning over the cold limb of the moon at a wavelength of 20t•. He found an average pre-dawn temperature of 90øK and also observed colder localized areas with temperatures down to 70øK.

Section: Such a Complete Set Of Observations Has Only Beensupporting

confidence: 53%

Remote Probing of the Moon by Infrared and Microwave Emissions and by Radar

Hagfors¹

1970

140

“…We believe that the present observations are free of these effects, except perhaps in the region of the Flamsteed ring where enhanced reflectivities have been reported [Tyler, 1968c]. Burns [1969] has suggested that reflectivity may also be a function of slope, particularly in terra where the surface has undergone widespread modification owing to downslope creep and slumping of the regolith [Sho.emaker et al, 1968]. In particular, reflectivities at angles greater than the natural angle of repose for the regolith (• 30 ø, Quaide and Oberbeck, [1968]) are probably the reflectivities of the underlying rock.…”

Section: Evans For Originally Pointing Out This Discrepancy)mentioning

confidence: 51%

“…Assuming Gaussian slope distributions, the corresponding unidirectional value is 2.3 ø . We obtain the same value using the intrinsic one-half power bandwidth (1.12 kHz) in Table III There is radar evidence, summarized by Burns [1969], that the Gaussian assumptions regarding slope distribution and surface autocorrelation are valid for the range of wavelengths considered here. Direct photoclinometric measures of slope distribution from orbiter photography [Rowan and Mc-Cauley, 1966] yield Gaussian functional dependencies for the probability density functions of the slopes and magnitudes very similar to those inferred from the observations reported here.…”

Section: Evans For Originally Pointing Out This Discrepancy)mentioning

confidence: 78%

Bistatic Radar Measurements of Topographic Variations in Lunar Surface Slopes With Explorer 35

Tyler¹,

Simpson²

1970

Bistatic radar observations of the lunar surface conducted with Explorer 35 at 2.2 meters have been used to measure the average large-scale (tens to hundreds of meters) lunar slopes. Data obtained for the equatorial band between 70 ø east and west longitude show significant (3'1) regional variations. Unidirectional rms slopes of 2 ø, 3 ø, and 6 ø were obtained for Mare Fecunditatis and Oceanus Procellarum, the central highlands and terra surrounding the crater Alfraganus, and the Censorinus highlands, respectively. A comparison of the slope variations and visible surface structure suggests that the meter wavelength radar slopes are those of the visible surface measured on the set of scales given above. TOPOGRAPHIC VARIATIONS IN LUNAR SURFACE SLOPES 265 IN LUNAR SURFACE SLOPES 269

“…Strong wavelength dependence between h = 13 cm and h = 116 cm has been observed in quasispecular scattering from lunar mare, but is absent in scattering from lunar highlands [Simpson, 1973;Tyler and Howard, 1973;Burns, 1970]. In terms of •t, "within the highlands, the rms slopes obtained at the two wavelengths are very nearly equal...," while within the mare, "... the slopes obtained at the 116 cm wavelength are typically one-half as large as those obtained at 13 cm.…”

Section: Discussionmentioning

confidence: 99%

Wavelength dependence in radio‐wave scattering and specular‐point theory

Tyler¹

1976

Radio‐wave scattering from natural surfaces contains a strong quasispecular component that at fixed wavelengths is consistent with specular‐point theory, but often has a strong wavelength dependence that is not predicted by physical optics calculations under the usual limitations of specular‐point models. Wavelength dependence can be introduced by a physical approximation that preserves the specular‐point assumptions with respect to the radii of curvature of a fictitious, effective scattering surface obtained by smoothing the actual surface. Wavelength dependence of the scattering, as expressed in terms of the mean‐square tilt of the smoothed surface, then depends on an integral of the two‐dimensional surface power spectral density. A uniform low‐pass filter model of the scattering process yields explicit results for the effective surface roughness versus wavelength. Interpretation of experimental results from planetary surfaces indicates that the asymptotic surface height spectral densities fall at least as fast as an inverse cube of spatial frequency. Asymptotic spectral densities for Mars and portions of the lunar surface evidently decrease more rapidly, at least as fast as an inverse fourth or fifth law of the spatial frequency.