( 10 ) recently reported that main belt comet P/2013 R3 experienced a breakup , probably due to rotational disruption , with its components separating on mutually hyperbolic orbits .
We propose a technique for constraining physical properties of the proto-body , especially the initial spin period and cohesive strength , as a function of the body ’ s estimated size and density .
The breakup conditions are developed by combining mutual orbit dynamics of the smaller components and the failure condition of the proto-body .
Given a proto-body with a bulk density ranging from 1000 kg/m ^ { 3 } to 1500 kg/m ^ { 3 } ( a typical range of the bulk density of C-type asteroids ) , we obtain possible values of the cohesive strength ( 40 - 210 Pa ) and the initial spin state ( 0.48 - 1.9 hr ) .
From this result , we conclude that although the proto-body could have been a rubble pile , it was likely spinning beyond its gravitational binding limit and would have needed cohesive strength to hold itself together .
Additional observations of P/2013 R3 will enable stronger constraints on this event , and the present technique will be able to give more precise estimates of its internal structure .