Power-law indices of asteroidal grooves and strength

strength of an asteroid is a valuable parameter, but it is difficult to measure directly. Although impact experiments have made a large contribution, the problem of the relationship between an asteroid's size and its strength has not been solved. This paper introduces a valuable parameter for natural bodies, the power-law index phi of the size distribution of fracture planes [N-S = k(S)S(-phi /2)]. This index can be regarded as parameterizing the strength, because strength is controlled by the size of the largest fracture. The power-law indices phi of the Martian satellite Phobos and the asteroid Gaspra were found to be 5.9 and 6.5, respectively. These values are close to 6, which is the theoretical value expected for the "fully cracked" condition of Housen and Holsapple (1999). The implications of this result for the size-strength relationship of asteroids are discussed.