Mutual Eclipse Events in Asteroidal Binary System 1996 FG 3: Observations and a Numerical Model

We report the CCD observations of the Apollo-type asteroid 1996 FG ₃ obtained in April 1996 and December 1998. The lightcurves show a double periodicity which, following Pravec et al. ( IAU Circ. 7074, 1998), is interpreted as the signature of mutual eclipses and occultations between a non-synchronous, slightly elongated central body and its satellite. We derive a period of rotation of 3.595±0.002 h for the central body, while the orbital period of the satellite is determined to be 16.15±0.02 h. A numerical model has been developed which describes the binary system as consisting of two co-orbiting ellipsoids. The model incorporates the effects of shadowing and makes use of the Hapke photometric function. A fit of the model to the observations produces synthetic lightcurves which accurately reproduce the amplitudes, the timing, and subtler features of the eclipse events. Two possible orientations of the orbital plane normal vector (J2000) are found which can account for the observed events, one retrograde and one prograde—λ ₁=282°±10°; β ₁=-87°±3 and λ ₂=262°±10°; β ₂=+75°±3°—where the retrograde one provides a slightly better fit to the observations. We find a circular orbit normalized radius R=2.9±0.1 and primary body normalized semiaxes A=1.05±0.02, B=0.95±0.02, C=0.70±0.10. For the secondary body we find normalized semiaxes a=0.32±0.03 and b=0.23±0.03. The satellite shortest semiaxis c is not well constrained by the observations and therefore we assumed c= b throughout the modeling procedure. We also find indications that the primary body might have albedo variations across its surface. The estimated parameters allow us to determine an average bulk density of 1.4±0.3 g cm ^-3 which is highly suggestive of a rubble pile structure. The primary body shape, together with its spin rate, are not compatible with a hydrostatic equilibrium figure.