  We quantify the amount of data needed in order to measure the size and
position of the $^8$B neutrino production region within the solar core, for
experiments looking at elastic scattering between electrons and solar
neutrinos. The directions of the electrons immediately after scattering are
strongly correlated with the incident directions of the neutrinos, however this
is degraded significantly by the subsequent scattering of these electrons in
the detector medium. We generate distributions of such electrons for different
neutrino production profiles, and use a maximum likelihood analysis to make
projections for future experimental sensitivity. We find that with
approximately 20 years worth of data the Super Kamiokande experiment could
constrain the central radius of the shell in which $^8$B neutrinos are produced
to be less than 0.22 of the total solar radius at 95% confidence.
