  This paper investigates the rate-distortion function, under a squared error
distortion $D$, for an $n$-dimensional random vector uniformly distributed on
an $(n-1)$-sphere of radius $R$. First, an expression for the rate-distortion
function is derived for any values of $n$, $D$, and $R$. Second, two types of
asymptotics with respect to the rate-distortion function of a Gaussian source
are characterized. More specifically, these asymptotics concern the
low-distortion regime (that is, $D \to 0$) and the high-dimensional regime
(that is, $n \to \infty$).
