The proposing team will obtain high-precision radar distance and velocity measurements for twelve near-Earth asteroids (NEAs) that have trajectories strongly affected by the light of the Sun, the shape of the Sun, and the effects of General Relativity. These measurements, combined with similar measurements that this team has been obtaining since 2006 under a previous NSF award, will provide unique observational constraints on current models of asteroid physics, solar physics, and fundamental physics. Asteroid orbits are altered by the absorption and reemission of solar energy, known as the Yarkovsky effect. These changes will be quantified with the radar measurements in order to constrain the densities, compositions, and thermal properties of NEAs. Other perturbations to NEA orbits arise from the gravitational effects of Solar oblateness. The radar data will provide a direct probe of the mass distribution in the Sun's interior by measuring these changes to the asteroid trajectories. Radar tests of general relativity (GR) will also be improved by quantifying the perihelion advance (apsidal precession) of NEAs that reach deep into the gravitational well of the Sun. The effects of GR, solar oblateness, and the Yarkovsky mechanism can be separated from each other because of their different dependences on orbital semi-major axis, eccentricity, inclination, and time. Most of the measurements will be performed with the planetary radar on the Arecibo telescope at the National Astronomy and Ionospheric Center (NAIC). A computer presentation describing the project will be prepared for dissemination at the Arecibo visitor center, teacher workshops, and other venues. One or more graduate students will be supported and trained in the project, and results will be incorporated in undergraduate courses. Finally, the careful calibration required for this work may prompt improvements to the research infrastructure at Arecibo.