It’s a lot easier to determine an orbit than size, and the error in the orbit is many, many times the dimension of the asteroid, but not many times the size of earth. Even in the most powerful telescopes this object’s image will not subtend more than a few pixels at closest approach.
Radar has much poorer angular resolution than optics, but it’s range resolution is independent of range, if the signal to noise ratio is high enough. Determining an orbit requires solving for six parameters equivalent to three position variables (x, y, z) and three velocity variables (dx/dt, dy/dt, dz/dt), or equivalently, six Keplerian elements. Given six [linearly independent] measurements of the subject’s range, one can solve for orbital parameters within the limitations of the observational accuracy. More measurements provide increased accuracy by averaging effects of measurement “noise”. In principle, three optical measurements provide the same information, but the accuracy of optical measurements at these ranges is on the order of several kilometers, radar as small as a meter.
Taking measurements over a long temporal baseline improves velocity estimates. Errors in position are the same, but the denominator, “delta time” is much larger.
One very slick technique for measuring the dimensions of an asteroid is optical occlusion timing. If an asteroid happens to throw past in front of star and cast a tiny shadow on earth, the moving shadow reveals the exact dimensions of the asteroid, whether it is a binary (a surprising fraction are) and gives highly precise position information for orbital refinement. If a number of observers on earth can reliably time the onset and end of occlusion, their observations can be processed to make high resolution silhouettes. When the shadow falls across North America during good weather there are a number of amateurs who have the required instrumentation, talent, time and enthusiasm to make these measurements.
As always, your post is hugely informative.
Regarding the binary nature, probably most asteroids are made up of a pile of smaller rocks that finally embraced one another, but were once in mutual orbit around a central point.
Hold On Loosely — 38 Special
https://www.youtube.com/watch?v=vJtf7R_oVaw