Using our photometric observations taken between April 1996 and January 2013 and other published data , we derived properties of the binary near-Earth asteroid ( 175706 ) Â 1996Â FG _ { 3 } including new measurements constraining evolution of the mutual orbit with potential consequences for the entire binary asteroid population .
We also refined previously determined values of parameters of both components , making 1996Â FG _ { 3 } one of the most well understood binary asteroid systems .
With our 17-year long dataset , we determined the orbital vector with a substantially greater accuracy than before and we also placed constraints on a stability of the orbit .
Specifically , the ecliptic longitude and latitude of the orbital pole are 266 ^ { \circ } and -83 ^ { \circ } , respectively , with the mean radius of the uncertainty area of 4 ^ { \circ } , and the orbital period is 16.1508 \pm 0.0002 Â h ( all quoted uncertainties correspond to 3 \sigma ) .
We looked for a quadratic drift of the mean anomaly of the satellite and obtained a value of 0.04 \pm 0.20 Â deg/ \mbox { yr } ^ { 2 } , i.e. , consistent with zero .
The drift is substantially lower than predicted by the pure binary YORP ( BYORP ) theory of McMahon and Scheeres ( McMahon , J. , Scheeres , D. [ 2010 ] .
Icarus 209 , 494–509 ) and it is consistent with the theory of an equilibrium between BYORP and tidal torques for synchronous binary asteroids as proposed by Jacobson and Scheeres ( Jacobson , S.A. , Scheeres , D. [ 2011 ] .
ApJ Letters , 736 , L19 ) .
Based on the assumption of equilibrium , we derived a ratio of the quality factor and tidal Love number of Q / k = 2.4 \times 10 ^ { 5 } uncertain by a factor of five .
We also derived a product of the rigidity and quality factor of \mu Q = 1.3 \times 10 ^ { 7 } Â Pa using the theory that assumes an elastic response of the asteroid material to the tidal forces .
This very low value indicates that the primary of 1996Â FG _ { 3 } is a ‘ rubble pile ’ , and it also calls for a re-thinking of the tidal energy dissipation in close asteroid binary systems .