Phase integral of asteroids

Abstract: The values of the phase integral q were determined for asteroids using (i) a numerical integration of the brightness phase functions over a wide phase-angle range and (ii) the relations between q and the G parameter of the HG-function and q and the G1, G2 parameters of the HG1G2-function. The phase-integral values for asteroids of different albedo range from 0.34 to 0.54 with an average value of 0.44. These values can be used for the determination of the Bond albedo of asteroids. Estimates for the phase-integral values using the G1 and G2 parameters are in very good agreement with the available observational data. We recommend using the HG1G2-function for the determination of the phase integral. Comparison of the phase integrals of asteroids and planetary satellites shows that asteroids have systematically lower values of q.