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Radar observations can resolve Earth-crossing asteroids (ECAs) by measuring the distribution of echo power in time delay (range) and Doppler frequency: Planes normal to the line of sight cut the target into range cells, and for a rigid target, planes parallel to both the line of sight and the target's apparent spin vector (1) cut the target into Doppler-frequency cells (2). Hence, a delay-Doppler image can be visualized as the projection of the target's radar brightness onto a plane that contains the radar and is normal to the constant-delay, constant-Doppler lines. Each of those lines can intersect two or more noncontiguous points on the target; therefore, parts of the image can represent a many-to-one mapping, that is, can be "north/south ambiguous." Moreover, the length equivalent of frequency in radar images is a function of the target's apparent spin vector, which may be poorly known. The accurate interpretation of ECA radar images is consequently nontrivial and usually requires multiple images that sample diverse orientations of the target.
Radar observations (3) of 4769 Castalia (formerly 1989 PB) yielded useful resolution and definition of this ECA's shape: A 2.5-hour sequence of 64 images resolved the echo into a few dozen cells and revealed a bimodal distribution of echo power. Visual inspection and analysis of the echoes' frame-to-frame bandwidth variation indicated that Castalia is bifurcated into two kilometer-sized lobes apparently in contact with each other (3). In this report, we describe an estimation of Castalia's three-dimensional shape from the delay-Doppler images.
Each of the 64 images in our data set (3) is the result of a 29-s integration and consists of an estimate of radar cross section sigma as a function of time delay tau and Doppler frequency nu. The length equivalent of the 2-mu-s interval between time samples is 300 m. The length equivalent of the frequency-sampling interval, where Delta-nu=0.95 Hz, is
(Equation 1)
Delta-chi=Delta-nu-Rho-lambda/4-pi cos delta
where Rho is the apparent rotation period, lambda is the wavelength (0.126 m), and delta is the subradar latitude (measured from the asteroid's equatorial plane to the radar line of sight). For the estimated period, 4.07 +/-0.02 hours (3), the 64-frame sequence covers 220 degs of rotation phase psi; each image spans Delta-psi=0.7 degrees. Because the asteroid's position on the sky...