We evaluated the prospects of quantifying the parameterized post-Newtonian parameter \beta and solar quadrupole moment J _ { 2 \odot } 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 J _ { 2 \odot } can be obtained with precisions of 6 \times 10 ^ { -4 } and 3 \times 10 ^ { -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 \times 10 ^ { -4 } and 10 ^ { -8 } , respectively .
A purely dynamical determination of solar oblateness with asteroid radar astronomy may therefore rival the helioseismology determination .