Echo Power in Delay and Doppler

In principle, echo bandwidth measurements obtained for a sufficiently wide variety of directions can yield aU three scalar coordinates of the target s intrinsic (i.e., sidereal) spin vector W. This capability follows from the fact that the apparent spin vector Wapp is the vector sum of W and the contribution (Wsky = e x e, where the unit vector e points from the target to the radar) from the target s plane-of-sky motion. Variations in e, e, and hence Wsky, all of 

For Mercury, long imagined on the basis of optical observations to rotate once per 88-day revolution around the Sun, radar bandwidth measurements (see Fig. 6) demonstrated direct rotation with a period (59 days) equal to two-thirds of the orbital period. This spin-orbit coupling is such that during 2 Mercury years, the planet rotates three times with respect to the stars but only once with respect to the Sun, so a Mercury-bound observer would experience alternating years of daylight and darkness. 

FIGURE 6 Measurements of echo bandwidth (i.e., the dispersion of echo power in Doppier frequency) used to determine the rotations of (a) Venus and (b) Mercury. [From Dyce, R. B., Pettengiii, G. H and Shapiro, i. i. (1967). Astron. J. 72, 351-359.] 

FIGURE 7 Geometric relations between an irregular, noncon-vex rotating asteroid and its echo power spectrum. The plane fo contains the asteroid s spin vector and the asteroid-radar line. The cross-hatched strip of power in the spectrum corresponds to echoes from the cross-hatched strip on the asteroid. 

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