The Bogoliubov approximation and the Gross-Pitaevskii equation characterize
the effect of repulsive interactions on a dilute ideal Bose-Einstein gas i
n a spherical harmonic trap. For large N, the interactions expand the conde
nsate relative to an ideal Bose gas; both the speed of sound and critical a
ngular velocity Omega(c1) for creation of a quantized vortex depend crucial
ly on the interparticle repulsion through the coherence length xi.