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The binaries couldn't exist other than by gravitational attraction! Of course some come undone in the process and then eject the moon to become asteroid pairs (at least thats the theory). If you meant the formation process then thats still up in the air. It is believed that the primary evolutionary process for asteroids is collisional. Is that still the case today? Cratering and surface compositions of a handful of asteroids by direct observation can be explained by density and low velocity collisional processes (anything other than low velocity and asteroids do not possess the gravitation to either hold onto/capture a moon or even hold it's own ejecta in the case of collision). It is also beleived that ultimately, the collisional process will result in nothing but rubble pile asteroids. Are we close to that point now (astronomical timescale speaking of course)? Other than direct observation, is there a way to observe/prove it one way or another?
I was reading a paper last night that stated that for rubble pile (gravitational aggregates), collisional process caused craters through indentation/compression rather than ejecta. Of course they only had the 1 rubble pile asteroid (Mathilde) to work from...
As for Keplers third law, we assume so. Few binary systems have been imaged directly (optical, radar or spacecraft) so we can't say for sure. We use Newtons form of Keplers third law to model the system based on observed rotations (P1 and P_orb) and D_2/D_1. If we have Observed H and G values (Absolute Magnitude and Slope parameter) then we can reasonably accurately generate sizes but density has to be assumed. (For those we don't have an accurate H or G value we just use the MPC published values which leaves a large margin for error ~ 30% I think). We can derive a reasonable estimate of density from the discovery of the spin barrier for rubble piles. (around 2 gm/cm^2).
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