Shape and mutual orbit of near-Earth asteroid triple 3122 Florence

3122 Florence, a potentially hazardous asteroid, made a very close approach in 2017. It passed just 18 lunar distances from Earth on September 1. It was observed with radar from the Goldstone Deep Space Communications Complex (8560 MHz, 3.5 cm) on 14 days between August 29 and September 13, with range resolution as fine as 75 m. It also was observed from Arecibo Observatory (2380 MHz, 13 cm) on 4 consecutive days, September 2 through 5, with range resolution as fine as 15 m. The radar observations revealed that Florence is a triple system, with two satellites orbiting a much larger primary body. Florence is the largest of the five known near-Earth asteroid triples.
With the radar data from 2017, and with lightcurves from several apparitions, we use the SHAPE software (Magri et al. 2007, Icarus 186) to investigate the shape, rotation state, and mutual orbit of each of the three components of the Florence system. The primary is about 4 km in diameter, with a rotation period of 2.36 hours. It is round with an equatorial ridge, resembling 101955 Bennu and 162173 Ryugu. The outer satellite is about 0.3 km in diameter, with an orbital period of about 22 hours. The inner satellite is about 0.2 km in diameter, with an orbital period of about 7 hours, which is the shortest known satellite orbital period in any near-Earth asteroid system.
Given Florence's size and closest-approach distance, it was one of the best asteroid radar targets of the past decade. In particular, the Arecibo observations on the day of closest approach yielded a continuous-wave spectrum with a signal-to-noise ratio about 270 in just eight minutes of observations, and dozens of delay-Doppler images in which the primary is well resolved, with a clear signal in regions spanning hundreds of delay rows and hundreds of frequency channels. The radar observations covered a wide range of viewing geometries - about 90 degrees of sky motion. Given the bright images and wide sky coverage, Florence is a nearly perfect target for detailed shape modeling.

The image above shows a delay-Doppler image of Florence from Arecibo Observatory on 2017 September 2. The primary body is clearly visible, and one of the satellites is near the bottom of the frame. Doppler frequency is along the horizontal axis, increasing to the right. Delay (range) is along the vertical axis, increasing downward.