750 Encyclopedia of the Solar System
FIGURE 10 Typical 13-cm echo spectra for the terrestrial
planets are compared to echo spectra for Jupiter’s icy moon
Europa. The abscissa has units of half the echo bandwidth.
Echoes from the Moon, Mercury, Venus, and Mars are
characterized by sharply peaked OC echo spectra (Fig. 10).
Although these objects are collectively referred to as “quasi-
specular” radar targets, their echoes also contain a diffusely
scattered component and have full-disk circular polariza-
tion ratios averaging about 0.07 for the Moon, Mercury, and
Venus, but ranging from 0.1 to 0.4 for Mars, as discussed
next.
Typical rms slopes obtained at decimeter wavelengths
for these four quasi-specular targets are around 7◦and con-
sequently these objects’ surfaces have been described as
“gently undulating.” As might be expected, values estimated
forS 0 increase as the observing wavelength decreases. For
instance, estimates ofS 0 for the Moon increase from∼ 4 ◦at
FIGURE 11 Structure on the lunar
surface near theApollo 17landing
site. Most of the surface is smooth and
gently undulating at scales much
larger than a centimeter. This smooth
component of the surface is
responsible for the predominantly
quasi-specular character of the
Moon’s radar echo atλ>>1 cm.
Wavelength-scale structure produces
a diffuse contribution to the echo.
Wavelength-sized rocks are much
more abundant atλ∼4 cm than at
λ∼10 m (the scale of the boulder
being inspected by astronaut H.
Schmitt), and hence diffuse echo is
more substantial at shorter
wavelengths.20mto∼ 8 ◦at 10 cm, to∼ 33 ◦at 1 cm. At visual wavelengths,
the Moon shows no trace of a central glint, that is, the scat-
tering is entirely diffuse. This phenomenon arises because
the lunar surface (Fig. 11) consists of a regolith (an uncon-
solidated layer of fine-grained particles) with much intricate
structure at the scale of visible wavelengths. At decimeter
wavelengths, the ratio of diffusely scattered power to quasi-
specularly scattered power is about one-third for the Moon,
Mercury, and Venus, but two to three times higher for Mars.
This ratio can be determined by assuming that all the SC
echo is diffuse and then calculating the diffusely scattered
fraction (x) of OC echo by fitting to the OC spectrum a
model based on a “composite” scattering law, for example,
S 0 (θ)=xσDIF(θ)+(1−x)σQS(θ). HereσQS(θ) might be
the Hagfors law and usuallyσDIF(θ)=cosmθ; when this is
done, estimated values ofmusually fall between 1 (geomet-
ric scattering, which describes the visual appearance of the
full Moon) and 2 (Lambert scattering).
For the large, spheroidal asteroids 1 Ceres and 2 Pallas
(see Section 3.12), the closeness ofμCto zero indicates
quasi-specular scattering, but the OC spectra, rather than
being sharply peaked, are fit quite well using a Cosine law
withCbetween 2 and 3, or a Gaussian law withCbetween
3 and 5, and here we can interpret the diffuse echo as due to
the distribution of surface slopes, withS 0 > 20 ◦. OC echo
spectra obtained from asteroid 4 Vesta and Jupiter’s satellite
Io have similar shapes, but these objects’ substantial polar-
ization ratios (μC∼0.3 and 0.5, respectively) suggest that
small-scale roughness is at least partially responsible for the
diffuse echoes. Circular polarization ratios between 0.5 and