  We evaluated the prospects of quantifying the parameterized post-Newtonian
parameter beta and solar quadrupole moment J2 with observations of near-Earth
asteroids with large orbital precession rates (9 to 27 arcsec century$^{-1}$).
We considered existing optical and radar astrometry, as well as radar
astrometry that can realistically be obtained with the Arecibo planetary radar
in the next five years. Our sensitivity calculations relied on a traditional
covariance analysis and Monte Carlo simulations. We found that independent
estimates of beta and J2 can be obtained with precisions of $6\times10^{-4}$
and $3\times10^{-8}$, respectively. Because we assumed rather conservative
observational uncertainties, as is the usual practice when reporting radar
astrometry, it is likely that the actual precision will be closer to
$2\times10^{-4}$ and $10^{-8}$, respectively. A purely dynamical determination
of solar oblateness with asteroid radar astronomy may therefore rival the
helioseismology determination.
