The mass of the asteroid 15 Eunomia from observations of 1313 Berna and 1284 Latvia

The mass of the asteroid 15 Eunomia was determined from its perturbations of 1313 Berna and 1284 Latvia. The perturbation of Berna gives a mass for Eunomia of (4.2 +/- 1.1) x 10(-12) M.. The perturbation of Latvia gives an upper bound on the mass for Eunomia of 8 X 10(-12) M.. The mass determined using Berna gives a density of only 0.79 +/- 0.21 g cm(-3) assuming that Eunomia is a homogeneous sphere with a diameter of 272 km. However, Eunomia is not spherical; hence, its volume is very poorly known. Since a sphere has the highest volume to mean projected area ratio of any body the density of Eunomia may be much higher than indicated. Radar range observations will determine the position of the perturbed asteroid to a higher precision than the uncertainty in the current ephemerides. The estimated reduction in the uncertainty for the mass of Eunomia from a single ideal radar time delay measurement of Berna is a factor of 2. This reduction in the uncertainty makes radar ranges the best way to reduce the uncertainty in the mass of Eunomia. Both Latvia and Berna will be in position to be observed by the Arecibo radio telescope at opposition during 1998 and 2000.