A determination of the internal structure and composition of the asteroids will give us important information concerning the origin of the solar system and the formation of the planets. We can obtain this information by measuring the total mass and the internal mass distribution through the use of spacecraft missions to flyby or to rendezvous, orbit, and land on the asteroids. The Doppler tracking technique used for mass measurement on planetary probes is suitable only for a flyby mission of the larger asteroids (> 20 km) because the gravity force field of the smaller asteroids is not strong enough to appreciably affect the trajectory of the probe during a flyby. If a rendezvous mission is used and the spacecraft is placed in orbit about an asteroid, the mass can be determined from the orbital period, but the effect on the spacecraft orbit due to the mass anomalies under the surface will not be easily seen unless the anomaly is very large because again the gravity force field decreases rapidly with decrease in anomaly size.