We describe a long-term program designed to obtain and interpret high-precision radar range measurements of a number of near-Earth objects (NEOs) that have trajectories reaching deep inside the gravitational well of the Sun. Objects in our sample have perihelion shift rates 1.5 to 2.5 times that of (1566) Icarus (10″/cy) and span a wide range of inclinations and semi-major axes, allowing for an unambiguous separation of general relativistic and solar oblateness effects. Four objects have been observed at Arecibo on at least two apparitions since 2000, with typical uncertainties of a few hundred meters. Within the next three years, we anticipate securing a total of 15 observations of 5 different NEOs. This program is expected to provide a purely dynamical measurement of the oblateness of the Sun (J2 at the 10−8 level) and to constrain the Eddington parameter β at the 10−4 level. Although our objects are selected to minimize Yarkovsky orbital drift, we also anticipate measuring Yarkovsky drift rates, which are orthogonal to the GR and J2 signatures.
