  We empirically constrain how galaxy size relates to halo virial radius using
new measurements of the size- and stellar mass-dependent clustering of galaxies
in the Sloan Digital Sky Survey. We find that small galaxies cluster much more
strongly than large galaxies of the same stellar mass. The magnitude of this
clustering difference increases on small scales, and decreases with increasing
stellar mass. Using Halotools to forward model the observations, we test an
empirical model in which present-day galaxy size is proportional to the size of
the virial radius at the time the halo reached its maximum mass. This simple
model reproduces the observed size-dependence of galaxy clustering in striking
detail. The success of this model provides strong support for the conclusion
that satellite galaxies have smaller sizes relative to central galaxies of the
same halo mass. Our findings indicate that satellite size is set prior to the
time of infall, and that a remarkably simple, linear size--virial radius
relation emerges from the complex physics regulating galaxy size. We make
quantitative predictions for future measurements of galaxy-galaxy lensing,
including dependence upon size, scale, and stellar mass, and provide a scaling
relation of the ratio of mean sizes of satellites and central galaxies as a
function of their halo mass that can be used to calibrate hydrodynamical
simulations and semi-analytic models.
