Using light curve data, one can establish the rotation rate of asteroids—all that’s needed is differential photometry of the asteroid, over one night or several nights.  Combining that data with light curves over several apparitions, over several years, and at different phase angles, one can establish the shape and orientation of that “minor planet.”  Usually, the triaxial ellipsoid model of an asteroid provides a light curve with two peaks, when the asteroid is broadside to the viewer, and two minima, when the asteroid may be pole on.  Of course, there are several variations of this theme, especially if the asteroid has “spots”—producing a similar feature once per complete cycle—or satellites—producing more abrupt decreases as the satellite occults the primary.  Variations in orientation, cratering, shadowing, and composition modify the light curve details. 

The study of asteroid rotation rates is part of a survey to monitor the spectra of primitive asteroids, C class and subtypes, to search for evidence of water of hydration—or aqueous alteration—and to search for evidence of spectral variations within the rotation cycle.  Rotation rate, orientation and aspect ratios would be needed.  Typically, C class asteroids lie within the middle to outer part of the main belt, with the more highly altered or even differentiated, asteroid classes S, M and E, occurring closer to the Sun.  This convenient and somewhat logical variation may, instead, be a part of complex migration of planets during the formation of the solar system that scatters asteroids both inward and outward from the Jupiter area.  Thus, the study of rotation rates correlated with spectra of asteroids may lead to further evidence for the complexity of solar system formation.