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ASTEROID CHARACTERISTICS BY RADAR

R. M. GOLDSTE/W
Jet Propulsion Laboratory

The techniques of radar offer a potentially powerful tool for the study of planetoids. It is a new approach, having been applied to extraterrestrial targets only recently in the history of astronomical study. Although the Moon was first, Venus has been observed by radar only since 1961. Since that time the techniques and capability of radar have evolved rapidly and many important new facts about Venus have been gathered. Further, the more distant and difficult targets, Mercury and Mars, have also yielded up secrets to radar probing. Finally, during the close approach of June 1968 Icarus itself was observed by radar from two different observatories (Goldstein, 1969; Pettengill et al., 1969). Review articles on radar studies of the planets are given in Shapiro (1968) and Goldstein (1970).

It is to be hoped that radar study of the asteroids will prove as fruitful as the study of the inner planets. However, asteroids present extra difficulties to radar as compared to the familiar planets. A diagram of the radar situation is given in figure 1. A tight beam of microwaves (0.1° is the current state of the

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Figure 1.-Illustration of geometric difficulties of radar asteroid astronomy. The received power is extremely weak, and the antenna beam cannot resolve individual parts of the target.

art) is directed toward the target. However, only a minute fraction of the power is actually intercepted. Of that amount, most is dissipated by the surface as heat. The balance, which contains the desired information, is scattered more or less uniformly throughout the solar system. The echo power received by the antenna is incredibly small. For the Icarus measurements of 1968, the transmitted power was 450 kW; the echo power was 6 x 10723 W. Thus the overriding problem of radar asteroid astronomy is one of signal-to-noise ratio (SNR). The second important difficulty, related to the first, is angular resolution. It is necessary to be able to relate the echo to specific areas of the surface—to isolate different parts of the surface for separate study. It can be seen from the figure that angular resolution of the antenna is quite inadequate. However, radar commonly allows two dimensions to effect this separation: time delay and Doppler shift. Both of these dimensions consist of two parts: an orbital part, measured to the closest (or sub-Earth) point, and a part that relates other points on the surface to the sub-Earth point. Generally, the orbital part is accounted for by tuning, automatically, the radar receiver to track the sub-Earth point. This is analogous to sidereal drive on a telescope to hold the image still during a long time exposure. The contours of constant time delay and constant Doppler shift for the balance of the effect (for a spherical surface) are given in figure 2. For time delay the contours are circles, concentric about the sub-Earth point. The Doppler shift is caused by any rotation the target might have relative to the radar. The constant Doppler contours are also concentric circles, but seen edgewise from the radar. Radar echoes from the inner planets have been analyzed into time-delay rings and into Doppler-shift rings and, in fact, both simultaneously. However, for asteroid study, only Doppler analysis has been used. The reason for this is the much weaker received power and the fact that narrowband signals are inherently easier to detect in the presence of noise. The narrowest band signals, of course, are those originating along a constant Doppler contour.

ROTATION
AXIS

TO EARTH

Figure 2.-Contours of constant time delay and of constant Doppler shift for a spherical target.

The most likely asteroid radar experiment, then, consists of transmitting a spectrally pure, monochromatic wave toward the target. The received signals are analyzed by a process such as the fast Fourier transform to yield the power spectrum of the echoes. This is equivalent to a scan across the disk with a narrow slit, parallel to Doppler contours. As usual, there is an essential compromise between high resolution (narrowness of the slit) and SNR.

A result of applying this technique to the planet Mercury is given in figure 3. These data were taken when Mercury was 0.6 AU distant, spinning such that the limb-to-limb bandwidth was 100 Hz. It required 1 hr of integration time (time exposure).

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Figure 3.-Spectrogram of echoes from Mercury. Power density is plotted against Doppler frequency shift.

The center frequency of this spectrum is a direct measure of the relative velocity between Mercury and the radar, accurate to about 15 cm/s. Such data can be used to refine the orbit of an asteroid as it has been used for Venus. This is a bootstrap procedure, however, because knowledge of the orbit is needed to take the data. During the long time exposure, the receiver must be tuned continuously to keep the spectrum from moving, and hence blurring the data. For the weakest signals, appreciable blurring would render the signals undetectable. The bootstrapping converges very quickly if a fairly good orbit can be obtained in advance. For the Icarus radar experiment, a good orbit was obtained with the help of last-minute optical observations and reduction by Elizabeth Roemer. The width of the spectrum at the base gives directly the line-of-sight velocity of the limbs, which equals the relative angular velocity, projected across the line of sight, times the target radius. When the SNR is good enough to detect the edges of the spectrum over an applicable arc as the asteroid passes Earth, the bandwidth data are sufficient to recover all three components of the spin vector and the radius. This is true because the Doppler broadening has two components: one due to spin and the other due to orbit-induced relative angular motion. The presumably known orbital part can be used to calibrate the effect of the spin. The shape of the spectrum contains important information about surface slopes. For example, the Mercury spectrum of figure 3 is highly peaked at the center (although not so much as for Venus). This shows that most of the received power is reflected from regions near the sub-Earth point, where the Doppler shift is small. Hence the surface is relatively smooth, to a scale somewhat larger than the wavelength used (12.5 cm for the Goldstone radar). Under the assumption of a uniform surface, the spectrum can be converted uniquely to a backscattering function (Goldstein, 1964), which shows how the radar cross section of an average surface element varies with the angle of incidence. This backscattering function can be considered directly as the distribution of surface slopes. That is, the backscattering function of a surface element at a given angle represents that portion of the element which is perpendicular to the incident rays. Of course, the slope distribution, per se, gives no knowledge of the linear extent of any given slope. Surface roughness can be tested to a scale smaller than the wavelength by a polarization technique. Right-handed circular polarized waves are transmitted. Because reflection from a smooth dielectric sphere reverses the sense, the receiver is usually set for left-handed polarization. A rough surface, however, will reflect signals equally into both polarizations. To measure this effect, right circular polarization is both sent and received. Figure 4 presents spectrograms from Venus and Mercury taken in this so-called depolarized mode at similar SNR's. The high central peaks of these spectra have been suppressed by the polarization in much the same way as optical glare can be removed by polarized sunglasses. Furthermore, for Venus, the signal power has dropped by

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