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1620 Geographos's pole-on shape determined from delay-Doppler observations taken in the asteroid's equatorial plane (Ostro et al., 1996). This image has been constructed from multi-run sums of twelve co-registered images, each $30^\circ$ wide in rotation phase space. The central white pixel indicates the body's center-of-mass. Rotation direction is indicated by the central circular arrow. Brightness indicates the strength of radar return, arbitrarily scaled. Despite substantial smearing of the periphery features, some distinguishing characteristics can be observed: (i) The long axis is tapered on both ends, with one tip narrow and the other more pinched and squat. (ii) One side is smooth and convex; the opposite side has a ``hump''. (iii) Cusps at each end are swept back against the rotation direction, giving the body the appearance of a pinwheel when viewed from various aspect angles. The insets show close-ups from three of the twelve summed co-registered $30^\circ$ images used to make the composite image; they have resolution of 500 ns x 1.64 Hz (75 x 87 m). The cusps are more prominent here, though considerable smearing remains.

The ellipticity values of our model asteroids plotted against the fraction of mass shed in each tidal disruption outcome. 79 S-class, 40 B-class, and 76 M-class disruptions are shown. The starting ellipticity for our model rubble pile is $\varepsilon _{{\rm rem}} = 0.43$. Geographos's ellipticity $\varepsilon _{\rm rem} = 0.64$. Note that most M-class disruptions produce high ellipticities.

The final spin periods of our model asteroids plotted against the fraction of mass shed in each of the 195 S-, B-, and M-class outcomes. Starting spin periods are P = 4-12 h and $P= \infty$ (i.e., no spin). Note that three S-class and one M-class events have final spin periods between 10-20 hours (i.e., beyond our P = 10 h plotting limit). Regardless of the starting spin period, most disruptions spin-up the model asteroid to P < 6 h.

Four snapshots of the tidal breakup by the Earth of a P = 6 h prograde rotating rubble pile having $q = 2.1 R_\oplus$ and $v_\infty = 8$ km s^-1. (a) shows the asteroid before encounter. (b) shows the body shortly after perigee passage. (c) shows the latter stages of tidal disruption as the body recedes from the Earth. Particles shed near the tips do not return to the rubble pile. (d) shows the final shape of the object. Its spin (P=5.03 h) and elongation ($\sim 2.9$ times the mean diameter of the minor axes, or $\varepsilon _{{\rm rem}} \sim 0.65$) are virtually identical to Geographos (Fig. 1). Spiral distortion associated with tides produces a smooth convex surface along the long axis, cusps on either end, and a ``hump''-like mound of material on the opposing side.

[Eros.eps]Pole-on silhouette of Eros, based on a model where radar data were fit to a reference ellipsoid using 508 triangular facets defined by 256 vertices (Mitchell et al., 1998). The silhouette is viewed from the asteroid's south pole. Definitions for center of figure, center of rotation, and rotation direction are given in Fig. 1. The body is tapered along its length, with a smooth convex side on the right and one or more concavities on the left, making it look something like a kidney bean. Resolution does not permit interpretation of the concavities on the left side (i.e., whether they are craters, troughs, or bends in Eros's shape).

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